Spectrum Efficiency Maximization in Multiband OFDM Ultra Wideband Cognitive Radio Systems

Transcription

1 Spectrum Efficiency Maximization in Multiband OFDM Ultra Wideband Cognitive Radio Systems Liaoyuan Zeng A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy. UNIVERSITY of LIMERICK 2011

2 Declaration Title: Author: Award: Supervisors: Spectrum Efficiency Maximization in Multiband OFDM Ultra Wideband Cognitive Radio Systems Liaoyuan Zeng. Doctor of Philosophy. Dr. Sean McGrath & Dr. Eduardo Cano. I hereby declare that this thesis is entirely my own work, and does not contain material previously published by any other author, except where due reference or acknowledgement has been made. Furthermore, I declare that it has not previously been submitted for any other academic award. Liaoyuan Zeng April 2011

3 Abstract Ultra Wideband is a high-speed, short-range and low-power wireless technology. UWB system is overlapped with wireless systems such as WLAN, WiMax and UMTS, which limits the use of UWB. Cognitive radio technology enables the UWB system to efficiently use the overlapped spectrum without causing interference to other wireless systems. The thesis focuses on the design of the cognitive radio resource allocation algorithms for spectrum efficiency maximization in the multiband OFDM UWB system. The spectrum efficiency of a cognitive UWB system depends on the cognitive algorithms used in spectrum sensing, spectrum sharing and spectrum management. The spectrum efficiency maximization problem is formulated to a multi-dimensional knapsack problem with constraints in the transmit power of the UWB subcarriers, the average bit error rate and the interference to the primary users. New cognitive algorithms for spectrum sensing and spectrum management are developed to solve the optimization problem. The proposed low-complexity cognitive algorithms include: primary and advanced power allocation algorithm, group power allocation algorithm and spectrum sensing time optimization algorithm. In a cognitive UWB system, the primary and advanced power allocation algorithm as well as the group power allocation algorithm are used for spectrum management, while spectrum sensing time optimization algorithm is used for spectrum sensing. The spectrum sensing time optimization algorithm computes the optimal spectrum sensing period which maximizes the cognitive UWB system s data transmission period while guaranteeing a target probability of detection/false-alarm. During the data transmission period, the primary and advanced power allocation algorithm achieves the optimal spectrum efficiency by equally allocating the transmit power and distributing the excessively allocated power to the subcarriers in a greedy manner. Also, the group power allocation algorithm can obtain the optimal spectrum efficiency by adaptively assigning the transmit power to the subcarrier groups according to the effective signal-to-noise ratio of each subcarrier group whose bandwidth is less than the coherence bandwidth of the UWB channel. For energy-limited cognitive UWB system, the proposed cognitive algorithms maximize the spectrum efficiency with lower order-of-growth than the traditional dynamic radio resource allocation algorithms.

4 Acknowledgements Sincere thanks to my supervisors Sean McGrath and Eduardo Cano for their support, encouragement, perseverance and patience over the last few years. Special thanks to the Wireless Access Research Center, working with them has made the road much more interesting and fun as well. Thanks also to all past and present visitors to the Wireless Access Research Lab in University of Limerick. I would also like to acknowledge IRCSET (Irish Research Council for Science, Engineering and Technology) under Embark Postgraduate Research Scholarship Scheme on behalf of Government of Republic of Ireland. I deeply appreciate the continued support and funding from University of Limerick Wireless Access Research Center in association with COST Finally I would like to thank my families for their constant support and to thank my life time dearest friends.

5 For family

6 Contents 1 Introduction Definition of Ultra Wideband The Ultra Wideband Signal Multiband UWB Frequency Planning OFDM Multiple Access Impulse Radio UWB Multiband UWB vs. Impulse Radio UWB Cognitive Radio Concept of Cognitive Radio Implementation of Cognitive Radio in UWB State of the Art: Cognitive Radio in UWB Systems Challenges of Integrating Cognitive Radio in UWB Systems Literature Review Contributions of the Thesis Summary of Thesis Multiband-OFDM UWB System Introduction Architecture of Multiband-OFDM UWB System i

7 CONTENTS CONTENTS 2.3 OFDM UWB Signal UWB Channel Model Saleh-Valenzuela Model MB-OFDM UWB Channel Model Bit Error Rate Probability Transmit & Received Power Signal-to-Noise Ratio Computation of BER Chapter Summary Cognitive UWB Radio Systems Introduction Cognitive Radio Functions Spectrum Sensing Matched Filter Detection Energy Detection Feature Detection Spectrum Sharing Dynamic Spectrum Access Policy Management Spectrum Management Cognitive Radio in UWB Systems Cognitive UWB Transceiver Cognitive UWB Network Network Architecture Interference to The Primary Wireless Systems Cognitive UWB Functions UWB Spectrum Sensing ii

8 CONTENTS CONTENTS UWB Spectrum Management Chapter Summary Spectrum Efficiency Analysis in Cognitive UWB Systems Introduction Research Scenarios Single User Mode Multiuser Mode Spectrum Efficiency Analysis Summary of Assumptions Single User Mode Equal Power Allocation Adaptive Power Allocation Time for Spectrum Sensing Multiuser Mode Chapter Summary The Spectrum Efficiency Maximization Algorithms Introduction Primary and Advanced Power, Bit Allocation Algorithm Primary Power and Bit Allocation Advanced Power and Bit Allocation Numerical Results Group Power Allocation Algorithm Subcarrier Grouping Group Power Allocation Numerical Results Spectrum Sensing Time Optimization The Optimal Spectrum Sensing Time iii

9 CONTENTS CONTENTS Numerical Results Chapter Summary Conclusion and Future Work Conclusions Future Work References 173 A Pseudocode of The Algorithms for Spectrum Efficiency Analysis 190 A.1 Pseudocode in Single User Mode A.1.1 Non-adaptive Power Allocation Algorithm A.1.2 Adaptive Power Allocation Algorithm A.1.3 Chow s Algorithm B Pseudocode of The Proposed Algorithms 193 B.1 Pseudocode in Single User Mode B.1.1 Primary and Advanced Power, Bit Loading Algorithm B.1.2 Group Power Allocation Algorithm C Water-filling Algorithm 196 C.1 Rate Maximization C.2 Power Minimization D Interference Power of Underlay Spectrum Sharing in Cognitive UWB 202 E Published Papers 206 E.1 Book Chapters E.2 Journal Papers E.3 Conference Papers iv

10 List of Figures 1.1 UWB s position in the field of the wireless communication technologies Definition of UWB System UWB spectral mask for indoor communication systems [FCC02] Ultra Wideband Systems Categorization Band allocation in MB-OFDM UWB system [Eur05] UWB received signal power as a function of upper frequency f u Example of TFC for the MB-OFDM UWB system Second derivative of UWB Gaussian pulses in time domain PPM pulse shapes for 1 and 0 bits in UWB system Illustration of the cognition cycle [Mit00] Software Defined Radio Layering [Bos99] Information-processing Cycle in Cognitive Radio [Hay05] Spectrum Overlapping between UWB and Incumbent Systems Interference to a WiMAX node from a UWB communication pair Flow diagram of deriving a solution to the spectrum efficiency maximization problem by mapping the problem to the classical optimization problems Structure of The Thesis Transmitter architecture for a MB-OFDM UWB system Receiver architecture for a MB-OFDM UWB system Pulse shape of p(t) v

11 LIST OF FIGURES LIST OF FIGURES 2.4 Spectrum of P (f) UWB OFDM Subcarriers Orthogonal Multiplexing MB-OFDM UWB Signal in Time-domain Power Spectral Density of an MB-OFDM UWB Signal Model of the indoor UWB multipath channel S-V Channel Model Histogram of Occurrences of the Amplitude Gain X Example of an indoor power delay profile, mean excess delay, maximum excess delay and rms delay spread [Rap01]. Excess delay denotes the time difference between an arrived multipath replica and the first arrived signal. The mean excess delay represents the expected excess delay, and the maximum excess delay is the time difference between the last arrived multipath replica which is higher than the receiving power threshold. The Root Mean Square (RMS) delay spread denotes the standard deviation of the excess delay Impulse Response for CM1. The communication distance between the UWB transmitter and UWB receiver is 2 meters. The parameters for simulate the channel impulse response is referred to CM1 in Table Impulse Response for CM3. The communication distance between the UWB transmitter and UWB receiver is 8 meters. The parameters for simulate the channel impulse response is referred to CM3 in Table Average Power Delay Profile for CM1. The communication distance between the UWB transmitter and UWB receiver is 8 meters. The parameters for simulate the channel impulse response is referred to CM1 in Table 2.1. The total energy contained in the terms α m,j is normalized to unity.. 58 vi

12 LIST OF FIGURES LIST OF FIGURES 2.15 Average Power Delay Profile for CM3. The communication distance between the UWB transmitter and UWB receiver is 8 meters. The parameters for simulate the channel impulse response is referred to CM3 in Table 2.1.The total energy contained in the terms α m,j is normalized to unity UWB Channel Frequency Response of CM1. The communication distance between the UWB transmitter and UWB receiver is 8 meters. The parameters for simulate the channel impulse response is referred to CM1 in Table 2.1. The QPSK modulation is used on all the 128 subcarriers in one OFDM symbol. The duration for one frame is set to microseconds according to [Eur05] UWB Channel Frequency Response of CM3. The communication distance between the UWB transmitter and UWB receiver is 8 meters. The parameters for simulate the channel impulse response is referred to CM3 in Table 2.1. The QPSK modulation is used on all the 128 subcarriers in one OFDM symbol. The duration for one frame is set to microseconds according to [Eur05] Overlay Spectrum Access Underlay Spectrum Access UWB emission masks considered in Europe [GK08] Integration of cognitive functions into the MB-OFDM UWB systems Transfer function energy detection at 3.3 GHz [MTBMB07] vii

13 LIST OF FIGURES LIST OF FIGURES 3.6 An example of the cognitive UWB network coexisting with the primary users network. Since the Poisson distribution is widely used to model the occupancy of the overlapped spectrum in cognitive radio networks [AT07] [YGC10], the probability that the overlapped spectrum is occupied by the primary users during a period of time follows a Poisson distribution. Chapter 4 will give a more detailed discussion of the usage probability of the spectrum. When the WiMAX technology is used in the primary users, the overlapped spectrum is from 3.40 to 3.60 GHz which covers approximately half of the subband number 1 in the MB-OFDM UWB system PSD of the n-th UWB OFDM subcarrier PSD of the a number of UWB OFDM subcarriers Relationships between the scenarios An Example of the coexisting networks in the single user mode without PU An Example of the coexisting networks in the single user mode with PUs An Example of the coexisting networks in multiuser mode without PU An Example of the coexisting networks in multiuser mode with PU Required Transmit Power for the M-ary QAM modulation on a randomly chosen UWB subcarrier M-ary QAM zone generation over CM Equal Power Allocation in CM Spectrum Efficiency of Equal Power Allocation in CM1 from uncoded BER = 10 6 to BER = Equal Power Allocation in CM Spectrum Efficiency of Equal Power Allocation in CM3 from uncoded BER = 10 6 to BER = viii

14 LIST OF FIGURES LIST OF FIGURES 4.12 Flow Diagram of Applying Equal Power Allocation in The Single User Mode without PU Adaptive Power Allocation using the HH uwb Algorithm in CM Spectrum Efficiency of Adaptive Power Allocation as a function of coded BER threshold using the HH uwb Algorithm in CM1 when P av = P tx Spectrum Efficiency of Adaptive Power Allocation as a function of coded BER threshold using the HH uwb Algorithm in CM1 when P av = 1P 4 tx Adaptive Power Allocation using the HH uwb Algorithm in CM3. The shaded areas in power allocation figure demonstrate that the allocated power on the subcarrier is equal to zero, because the corresponding subcarriers channel gains are too low to accommodate one bit with the allocated power being below the FCC s PSD mask Spectrum Efficiency of Adaptive Power Allocation as a function of coded BER threshold using the HH uwb Algorithm in CM3 when P av = P tx Spectrum Efficiency of Adaptive Power Allocation as a function of coded BER threshold using the HH uwb Algorithm in CM3 when P av = 1P 4 tx Flow Diagram of Applying the HH uwb Algorithm in The Single User Mode Without PU Adaptive Power and Bit Allocation using Chow s Algorithm in CM Spectrum Efficiency of Adaptive Power Allocation using Chow s Algorithm in CM1 from coded BER = 10 6 to BER = Flow Diagram of Applying Chow s Algorithm in The Single User Mode without PU Time for spectrum sensing for the target P f = 0.10, P d = 0.90 and P f = 0.01, P d = The fraction of time for UWB transmission under the target P f = 0.1 and P f = Spectrum Efficiency of Scenario B at γ p = 17 db in CM ix

15 LIST OF FIGURES LIST OF FIGURES 4.26 Spectrum Efficiency of Scenario B at γ p = 10 db in CM Spectrum Efficiency of Scenario B at BER threshold is 10 4 in CM Primary power and bit loading Advanced power and bit loading The value of β p in CM1 and CM Spectrum efficiency of the primary and advanced loading algorithm in CM1 with P av = P tx / Spectrum efficiency of the primary and advanced loading algorithm in CM1 with P av = P tx / Spectrum efficiency of the primary and advanced loading algorithm in CM3 with P av = P tx / Flow Diagram of the Primary and Advanced Power, Bit Allocation Algorithm in Scenario A Spectrum Efficiency of Group Power Allocation in CM Flow Diagram of Applying Group Power Allocation in Scenario A The maximum spectrum efficiency as a function of spectrum sensing time The maximum spectrum efficiency as a function of spectrum sensing time with received SNR γ p = 10 db The maximum spectrum efficiency as a function of received SNR γ p in CM The maximum spectrum efficiency as a function of received SNR γ p in CM C.1 Water-filling Power and Bit Allocation in a single user multiband OFDM UWB system under LOS channel condition x

16 List of Tables 2.1 Multipath channel target characteristics and model parameters [Foe03] Parameters in Spectrum Efficiency Maximization Problem Descriptions and Parameters Settings of Single User Mode Parameters in Spectrum Efficiency Maximization Problem Descriptions and Parameters Settings in Multiuser Mode Parameters in Spectrum Efficiency Maximization Problem Minimum Required Transmit Power for M-ary QAM Modulation on subcarriers with coded BER= Incremental Power for Modulating one bit on each Subcarrier with coded BER= Number of subcarriers in a subcarrier block in CM1 to CM4, and the number of subcarrier groups after the grouping process when N used = xi

17 Glossary 3GPP 3rd Generation Partnership Project (3GPP) AC Access Category ADC Analog to Digital Converter ADSL Asymmetric Digital Subscriber Line AGC Automatic Gain Control AWGN Additive White Gaussian Noise BER Bit Error Rate BPM Biphase Modulation CMOS Complementary Metal Oxide Semiconductor CFT Continuous-Time Fourier Transform CM Channel Model CR Cognitive Radio CSI Channel State Information DAA Detect and Avoid DAC Digital to Analog Converter DCM Dual Carrier Modulation DFT Discrete Fourier Transform DS Direct Sequence

18 LIST OF TABLES LIST OF TABLES DSSS Direct-Sequence Spread Spectrum ECC Electronic Communications Committee ECMA European Computer Manufacturers Association EIRP Equivalent Isotropically Radiated Power FCC Federal Communications Commission FFT Fast Fourier Transform GPP General Purpose Processor IDFT Inverse Discrete Fourier Transform IEC International Electrotechnical Commission IEEE Institute of Electrical and Electronics Engineers IFFT Inverse Fast Fourier Transform IR Impulse Radio ISI Inter-symbol Interference ISO International Organization for Standardization LNA Low Noise Amplifier LTE Long Term Evolution MAC Media Access Control MB-OFDM Multiband Orthogonal Frequency Division Multiplexing OFDM Orthogonal Frequency Division Multiplexing OOK On-off Keying xiii

19 LIST OF TABLES LIST OF TABLES OPM Orthogonal Pulse Modulation PAM Pulse Amplitude Modulation PAN Personal Area Network PAPR Peak-to-Average-Power Ratio PEP Pair-wise Error Probability PHY Physical Layer PLL Phase Locked Loop PPM Pulse Position Modulation PSD Power Spectral Density PSWF Prolate Spheroidal Wave Function PU Primary User QAM Quadrature Amplitude Modulation QPSK Quadrature Phase-Shift Keying SIR Signal-To-Interference Ratio SNR Signal-to-Noise Ratio SV Saleh-Valenuela TFC Time Frequency Code TH Time Hopping TH-PPM Time Hopping Pulse Position Modulation TXOP Transmission Opportunity xiv

20 LIST OF TABLES LIST OF TABLES UMTS Universal Mobile Telecommunications System UWB Ultra Wide Band WHDI Wireless Home Digital Interface WiMAX Worldwide Interoperability for Microwave Access WLAN Wireless Local Are Network WPAN Wireless Personal Area Network WWAN Wireless Wide Area Network xv

21 Chapter 1 Introduction Wireless communication technologies are widely used in daily life, such as 3G, wireless LAN, and Bluetooth. The information transmitted through wireless systems is in the order of gigabit per second (Gbps). This trend motivates the development of new radio technologies for high-speed communications. Ultra wideband (UWB) is an emerging wireless technology designed to meet the high-speed demand. UWB devices operate by employing a very large transmission bandwidth from 3.1 to 10.6 GHz. This feature enables UWB devices to provide a data rate over 1 Gbps with a low transmit power. Thus, UWB technology is suitable for many indoor high-speed wireless applications, such as wireless USB, wireless high-definition TV, and precision locating. Since UWB systems use a very large bandwidth, some parts of the UWB spectrum coexists with other wireless systems, including wireless LAN and WiMAX. To protect the existing wireless systems from being interfered by UWB transmissions, regulation parties like FCC strictly limits the maximum mean Equivalent Isotropically Radiated Power (EIRP) of the indoor UWB systems to dbm/mhz. However, UWB systems can still cause interference to other wireless systems in the overlapped spectrum 1. To handle the interference properly, a simple method is to prevent the UWB systems from using the overlapped spectrum or impose a more strict emission limits. Nevertheless, this method 1 For example, a UWB device transmits at -65 dbm/mhz will interfere with the WiMAX receiver (with a noise raise of 2 db and noise figure of 5 db) located within 1 meter range [DK09]. 1

22 will result in a low spectrum efficiency 2 since the spectrum owned by a wireless user may not be in use, then the spectrum sits idle and cannot be used by the UWB system to increase or share capacity. From the FCC Spectrum Efficiency Working Group report, many portions of the existing spectrum are not in use for significant periods of time and the spectrum efficiency can be significantly improved by temporarily using the unused spectrum [FCC03]. This critical observation motivates the use of the cognitive radio technology in the UWB systems to increase the spectrum efficiency and provide a more flexible interference control. The term cognitive radio was adopted by Mitola in 1999 [MM99]. In his work, the cognitive radio technology has the abilities to adapt a radio s use of spectrum to the realtime conditions of the wireless environment. For example, a cognitive radio system can sense its operating frequency bands and transmit in the bands that are not occupied by the primary wireless systems 3. This approach can significantly increase the spectrum efficiency since the temporarily unused spectrum could be quickly identified and used by the cognitive radio systems. Furthermore, by continuously monitoring the strength of the signals transmitted from the primary systems, a cognitive radio system can tune its transmit power in order to protect the primary systems from being interfered. Hence, there are two challenges in developing cognitive radio technologies. One is to correctly detect the idle spectrum during a specified sensing period. The other challenge is to maximize the use of the detected spectrum while guaranteeing a tolerable interference power to the primary systems. To meet those challenges, different design techniques are needed when applying cognitive radio in different wireless systems. In UWB systems, the factors that are critical to the cognitive radio design include UWB s signalling approach, transceiver structure, and channel model. Thus, the implementation of cogni- 2 Spectrum efficiency, also known as spectral efficiency is defined as the ratio of the usable information transmitted (bits-per-second) to the spectrum resource (i.e. bandwidth in megahertz) used for the information transmitting. 3 A primary wireless system is the system that has higher priority than the secondary or unlicensed wireless system (e.g., UWB systems) to access the available spectrum. In cognitive radio networks, there are many terms used to describe a primary system, such as licensed system, legacy system, and incumbent system. 2

23 tive radio in UWB systems requires an in-depth study of the UWB technology, cognitive radio techniques, and the links between them. 1.1 Definition of Ultra Wideband The first use of UWB in wireless systems was in 1901 when Marconi used a spark-gap transmitter to spread the transatlantic signal over a very large bandwidth [MNYZ03]. However, the benefit of using a large bandwidth and its relationship with the system capacity had never been understood until the Shannon-Hartley theorem was developed in the late 1940 s [Dub03]. From the late 1960 s, many contributions had been made to the design of UWB systems. In 1994, the first UWB system that could operate at very low power (lower than 50 mw) was invented, and was compact and cheap [Bar00]. Then, FCC recognized the significance of UWB technology and began the process of regulatory review [FCC02]. In February 2002, the FCC approved the use of UWB technology in commercial devices without a license [FCC02]. Since then, a surge of research activities in UWB field has took place throughout the worldwide. Figure 1.1 shows that the UWB is categorized as a high-speed and short-range wireless technology for WPAN networks. -./././!"#$%%!"#$%%& '(),+!"#$%% #$*+ Figure 1.1: UWB s position in the field of the wireless communication technologies. 3

24 FCC defines a UWB system as any system that occupies a minimum bandwidth of 500 MHz or has a fractional bandwidth greater than 20% [FCC02]. The fractional bandwidth is the ratio of the signal bandwidth to the signal s center frequency [FCC02], B f = f H f L f c, (1.1) where B f denotes the fractional bandwidth, f H and f L are the upper and lower frequency at the 10 db emission point respectively, and f c represents the UWB signal s center frequency. +%,-% )* "#$%&'(%! Figure 1.2: Definition of UWB System The FCC allows indoor UWB devices to operate in an unlicensed spectrum from 3.1 to 10.6 GHz, as shown in Figure 1.2. Since the Shannon-Hartley theorem states that channel capacity grows linearly with increases in bandwidth, UWB systems can provide a data ratea over 1 Gbps [GK08]. However, the large UWB bandwidth creates concerns over potential interference of UWB emissions on other wireless systems. Therefore, the FCC imposes a maximum average power spectral density (PSD) limit of -41.3dBm/MHz to the UWB system. This stringent PSD limitation aims not to cause interference to other wireless systems operating under the same bandwidth, such as a wireless LAN 4

25 ( GHz) and WiMAX ( GHz) [IEE03] [IEE04]. The spectrum mask for UWB indoor communication systems is shown in Figure 1.3. Owing to the strict PSD limitation, 156 UWB communication is limited to short range. Y. Zheng et al UWB EIRP Emission Level in dbm GPS Band Indoor Limit Part 15 Limit 10 0 Frequency in GHz 10 1 Fig. 6.1 FCC-regulated spectral mask for UWB indoor communication systems (cited from [6]) Figure 1.3: UWB spectral mask for indoor communication systems [FCC02]. are the derivatives of Gaussian function. The time domain and frequency domain representations of the nth order Gaussian derivative p n (t) and P n ( f ) are given in equations (6.2) and (6.3) [14], respectively: 1.2 The Ultra Wideband Signal n/2 )t 2σ 2 2 ( p n (t) = ( 1) (3n+1)/2 n!π 1/4 e 1 ( 1) k 2 ( ) n+1/4 2k 1 n/2+1/4 k 2σ t n 2k At the early stage of UWB studies (1960 s), UWB system operates 2 (n 2k)!k! by employing short, duration pulses (< 1 nanosecond) that result in very large transmission bandwidths (6.2) [Bar00]. (2n 1)!! k=0 where σ is the standard deviation of the Gaussian function which is associated with This the formpulse of UWB duration: signaling is called impulse radio (IR), and the corresponding UWB system is called single-band UWB system 4 [WS88]. P n ( f ) = ( 1)n i n2 (2π) n+1/4 ( 2σ 2) Impulse radio does not need carrier n/2+1/4 f n e 2π 2 f 2 σ wave and is thus a baseband signaling approach. 2. (6.3) (2n 1)!! Data information can be modulated on to the UWB pulses using pulse position modulation (PPM) and pulse amplitude modulation (PAM) techniques. Transceiver Furthermore, Systemspread Architecture spectrum techniques, such as time-hopping and direct The sequence transceiver are used systemto architecture achieve multiple for a pulse-based access in single-band (IR or DS) UWB is systems. relatively simple compared to other wireless transceivers due to the absence of the intermediate frequency (IF) stage. A comparison between a basic UWB transceiver and 4 UWB systems using impulse radio can also be called pulse-based UWB system and IR-UWB system a conventional narrowband transceiver is shown in Fig. 6.2a. The transmission of 5

26 In 2003, a new UWB signaling approach multiband UWB was proposed by Anuj Batra and his colleagues [BBD03]. Rather than using the entire spectrum at the same time as impulse radio, the multiband approach divides the UWB bandwidth into band groups of GHz bandwidth, and each band group is further divided into sub-bands of 528MHz bandwidth. Each sub-band contains 128 simultaneously transmitted subcarriers. Multiband signaling approach presents high regulatory flexibility for worldwide operation because it enables independent control of portions of UWB spectrum to adapt for different environments. In multiband UWB system, orthogonal frequency-division multiplexing (OFDM) is used for data modulation, and it can capture the multipath energy more efficiently than impulse radio. An OFDM symbol is transmitted within one subband. In a multiband OFDM (MB-OFDM) UWB transmitter, the outgoing data packet is first encoded using punctured convolutional code. Then the coded data is interleaved and modulated into a series of complex M-QAM symbols. Multiple access is realized by using time-frequency codes (TFCs) to specify the time and the center frequency (i.e., sub-band number) for each UWB device to transmit. Impulse radio UWB and multiband UWB signaling approaches were the final two candidates of the physical layer standard for high-speed IEEE a WPANs [MNYZ03]. For high data-rate UWB applications, the choice is dependent on the key criteria, such as performance, complexity, and system flexibility. However, consensus could not be reached by the middle of 2003, and the IEEE had to disband the a task group. Consequently, the rival proposals are supported by their own consortia: WiMedia Alliance for multiband UWB [WiM08] and UWB Forum for impulse radio UWB 5 [UWB09]. Since OFDM technique has been successfully deployed in many wireless systems, such as a, WiMAX, and 3GPP Long Term Evolution (LTE) [IEE03, IEE04, ZM07], multiband-ofdm signaling becomes a pragmatic approach to UWB. In December 2005, the multiband-ofdm approach was accepted by the European standards organization ECMA as ECMA-368 [Eur05]. This standard is widely used by many semiconductor 5 UWB Forum has been defunct since 2006 [EE 09] 6

27 manufacturers and consumer electronics companies. In 2007, ECMA-368 was approved by ISO as ISO/IEC standards [ISO]. The work in this thesis focuses on multiband UWB. Figure 1.4 presents the categorization of the UWB systems in terms of the modulation and multiple access methods. Figure 1.4: Ultra Wideband Systems Categorization Multiband UWB In multiband UWB system, the GHz UWB bandwidth is divided into five band groups, and each band group is further divided into sub-bands. Each sub-band has a 528 MHz bandwidth. A total number of 128 orthogonal subcarriers are used for data transmission in one sub-band, and the bandwidth of a subcarrier is MHz. Figure 1.5 demonstrates this frequency planning. In a UWB transmitter, first the outgoing data packet is encoded using punctured convolutional code. Next, the coded data is interleaved and modulated into a series of complex M-ary Quadrature Amplitude Modulation (QAM) symbols. Then, the M-QAM symbols are multiplexed using OFDM, and an OFDM symbol is transmitted in one sub-band. Time-frequency code (TFC) is used to specify the time and frequency of the OFDM symbol s transmission. An in-depth discussion of the multiband UWB system is shown in Chapter 2. 7

28 groups are defined, consisting of four band groups of three bands each and one band group of two bands. The band allocation is summarized in Table 24. Band Group #1 Band Group #2 Band Group #3 Band Group #4 Band Group #5 Band #1 Band #2 Band #3 Band #4 Band #5 Band #6 Band #7 Band #8 Band #9 Band #10 Band #11 Band #12 Band #13 Band # MHz 3960 MHz 4488 MHz 5016 MHz 5544 MHz 6072 MHz 6600 MHz 7128 MHz 7656 MHz 8184 MHz 8712 MHz 9240 MHz 9768 MHz MHz f Figure 28 - Diagram of the band group allocation Figure 1.5: Band allocation in MB-OFDM UWB system [Eur05] Frequency Planning Band Group BAND_ID (n b ) Table 24 - Band Group Allocation Lower Frequency (MHz) Center Frequency (MHz) Upper Frequency (MHz) The justifications to use the frequency planning shown in Figure 1.5 are as follows. First, to find the operating bandwidth 2 for multiband UWB3 system, 960 tradeoffs need to be made between the received signal power and the complexity of the UWB circuit. The received signal power P R is a function of the transmit power P T and path loss P L. Thus, P R is expressed as P R = P T P L + G R + G T, (1.2) where G R is the antenna gain of the receiver, and G T denotes antenna gain of the transmitter. In this thesis, the value of G R and G T are set to 0 dbi Since the FCC defines the average power of UWB signal in units of decibels re ferred to 1 mw/mhz, the 14 P T (dbm) is expressed in terms of the operating bandwidth as 11.2 [BBA Channelization + 04] Unique logical channels are defined by using up to seven different time-frequency codes for each band group. The P T TFCs = 41.3 and the + 10log associated 10 (f u base f l ), sequences (and corresponding (1.3) preambles) for band group 1 are defined in Table 25 as a function of BAND_ID values. Similarly, the definitions for the TFCs and the associated base sequences (and where f corresponding preambles) for band groups 2, 3, 4, and 5 are enumerated in Table 26 through l (MHz) represents the lower frequency of the operating bandwidth which is fixed Table 29. at 3.1 GHz, and f u denotes the upper frequency which may be chosen between NOTE For band group 5, only TFC 5 and 6 shall be defined. GHz. In (1.3), the UWB transmit PSD is assumed to be flat over the entire 7.5 GHz bandwidth Since the free space path loss model was adopted by the IEEE a channel modeling committee [FL02], the path loss P L is expressed as a function the UWB operating 8

29 bandwidth and transmission distance. Thus, path loss P L (db) is computed by [FL02] [ ] 4πfg d P L = 20log 10, (1.4) c where d is the distance in meters between a UWB transmitter and receiver, c (meters/sec) is the speed of light, and f g is defined as the geometric average of f l and f u. Thus, f g (MHz) is calculated by f g = f l f u. (1.5) Figure 1.6 depicts the UWB received signal power as a function of the upper frequency f u (MHz) is plotted with d = 10 meters. Figure 1.6 shows that the power grows logarithmically with increases in upper frequency f u. The reason is that the path loss P L grows logarithmically with the increase in the center frequency f c, and the growth of the path loss leads to a slower increase in the received power P R when f u is higher. The equation (1.3) shows that the transmit power increases with the increase of the upper frequency f u. However, the increase in f u will result in the increase in the UWB receiver s noise figure, which will degrades the link margin [BBA + 04]. Furthermore, working at higher f c requires higher complexity and higher power consumption in current CMOS technology [GK08]. 9

30 70 Received power as a function of upper frequency. 71 Received Signal Power (dbm) Frequency (MHz) Figure 1.6: UWB received signal power as a function of upper frequency f u Since the FCC specifies that a system must occupy a minimum of 500 MHz bandwidth in order to be classified as an UWB system, the sub-band bandwidth of 528 MHz is used. Using a 528 MHz operating bandwidth can provide a great balance between the data rate and the complexity of the UWB circuits. Furthermore, from an implementation point-ofview, the use of 528 MHz sub-band leads to a simple and low power consumption UWB circuit [BBA + 04]. An advantage of a simple circuit is that all of the center frequencies of the sub-bands in a band group can be generated from a single phase-locked loop (PLL). Therefore, switching between the three sub-bands in a band group can be accomplished within a few nanoseconds (e.g., 2 nanoseconds). In MB-OFDM UWB system, the number of subcarriers in a sub-band depends on the performance of Fast Fourier Transform (FFT). A large FFT size (i.e., large number of subcarriers) may lead to a high sub-band capacity. However, large FFT size increases the complexity of the UWB system 6 and requires a high power back-off in UWB transmitter [Pro01]. Furthermore, the use of a small FFT size leads to a long data overhead in a sub- 6 FFT block is typically 25% of the UWB receiver s digital baseband complexity [BBA + 04] 10

31 band and degrades the range. Therefore, a number of 128 subcarriers is used in multiband UWB system, which provides an excellent balance between FFT s performance and UWB system complexity [BBA + 04] [GK08] OFDM Time dispersion due to multipath causes wireless signals to undergo frequency selective fading if the bandwidth of the signal is greater than the channel coherence bandwidth. The OFDM modulation is a widely used technique to eliminate the ISI effect, such as a, WiMAX, and 3GPP LTE [Tan03] [ZM07] [Eri09]. An OFDM-based system subdivides the available channel bandwidth into a number of orthogonal subcarriers with bandwidth of each smaller than the channel coherence bandwidth. For UWB system, using OFDM modulation has several advantages compared with using the impulse radio technique, such as lower complexity and higher energy efficiency [BBA + 04]. Therefore, OFDM modulation is used in multiband UWB system. The comparison between the OFDM UWB system and the IR-UWB system is provided in Section 1.2.3, and a detailed discussion of the OFDM scheme in the MB-OFDM UWB system is given in the next chapter. In the OFDM symbol period T, the orthogonality between N subcarriers is given by 1 T T 0 0 n m e jωnt e jωmt dt = 1 n = m, (1.6) where ω represents the center frequency of a subcarrier. A transmitted OFDM signal D(t) is denoted as D(t) = Re [ N 1 n=0 X(n) e jωnt ] = Re [ N 1 n=0 X(n) e j2πfnt/t ], t [0, T ], (1.7) where X(n), (n = [0, N 1]) is the transmitted data symbol, f n = f c + n/t denotes the 11

32 center frequency of the n-th subcarrier. At the receiver, the received OFDM data symbols X (m) are demodulated by X (m) = 1 T T 0 D(t)e jωmt dt = N 1 n=0 X(n) 1 T T 0 e jωnt e jωmt, t [0, T ]. (1.8) Since the subcarriers are orthogonal to each other (1.6), the transmitted signal successfully recovered. Furthermore, if D(t) is sampled at a sampling frequency of f s = 1/ t (where 1/ t = T/N), (1.7) is re-written as D(k) = Re [ N 1 n=0 X(n) e j2πnk/n ], k [0, N 1], (1.9) where t = k t and nt/t = nk/n. Equation (1.9) indicates that the transmitted OFDM signal can be modulated by applying inverse discrete Fourier transform (IDFT). As a result, DFT can be applied at the receiver side to demodulate the OFDM signal. The use of the IDFT/DFT in the OFDM system significantly improve the efficiency of the implementation of the OFDM system. A detailed explanation of the UWB OFDM signal is shown in Chapter Multiple Access In multiband UWB systems, multiple access is realized by using time-frequency codes (TFCs) to specify the time and the center frequency for each UWB user to transmit [Eur05]. As an example, Figure 1.7 shows the transmissions of OFDM symbols from three UWB users. In Figure 1.7, user 1 transmitted its first OFDM symbol in sub-band 1 (i.e., Band # 1) at time t = 0. Since an OFDM symbol period τ = 1/4.125 MHz = nanoseconds, user 1 transmitted its second and the third OFDM symbol in subband 2 and sub-band 3 at time t = τ and t = 2τ, respectively. Meanwhile, UWB user 2 transmitted its first OFDM symbol in sub-band 2 at t = 0 and transmitted its second and the last OFDM symbol in sub-band 1 and sub-band 3 at t = τ and t = 2τ, respectively. 12

33 Figure 1.7: Example of TFC for the MB-OFDM UWB system Furthermore, the use of TFC can provide time and frequency diversity in the multiband UWB system. Since different sub-bands in a band group have different channel conditions, such as fading and interference, time and frequency diversity can provide the multiband UWB system robustness against burst errors and narrow-band interferers. In multiband UWB systems, time and frequency diversity are achieved by transmitting the coded and interleaved data on different sub-band at different time [Eur05] Impulse Radio UWB The single-band UWB system uses very narrow pulses (< 1 nanosecond) to occupy a large bandwidth [WS88]. The commonly used pulse in single-band UWB system is derivatives of the Gaussian pulse because the Gaussian pulse is easy to generate. The Gaussian pulse is expressed as [GMK04] p(t) = 1 2πσ e ( t2 /2σ 2), (1.10) where σ is standard deviation. Hence, the n-th derivative of the Gaussian pulse is obtained by p (n) (t) = n 1 p (n 2) (t) t σ 2 σ 2 p(n 1) (t), (1.11) where p (n) (t) represents the n-th derivative of p(t). 13

34 Furthermore, the frequency response of the n-th derivative of the Gaussian pulse, P (n) (t), is computed using Fourier Transform (FT) as P (n) (f) = + 0 p n (t)e j2/pift dt (1.12) Equation (1.12) shows that the centre frequency of the signal-band UWB signal increases when the order of derivative n grows. The Gaussian pulse s second derivatives in time domain is shown in Figure 1.8. In single-band UWB system, the pulse shape determines the envelope and the shape of the PSD of the modulated pulse train. Furthermore, other UWB pulses are used, such as Hermite pulses and prolate spheroidal wave function (PSWF) pulses. An in-depth analysis of UWB pulse shaping is in [Can06]. 12 x Amplitude Time (nanoseconds) Figure 1.8: Second derivative of UWB Gaussian pulses in time domain The commonly used data modulation technique in single-band UWB systems is pulse position modulation (PPM) [SGQLN06] [Nek05]. In PPM, bit 0 is represented by a pulse originating at the time instant t = 0, while bit 1 is shifted in time by the amount of δ from t. Figure 1.9 illustrates the a PPM pattern in UWB. To transmit a message with M 14

35 bits, 2 M time shift parameters δ i, (i = 1,..., 2 M ) are needed. Therefore, fine time control is required in the UWB system to modulate pulses with nanoseconds wide. PPM is a time-based modulation technique, in single-band UWB systems, many pulse shape based modulation techniques are used as well, including pulse amplitude modulation (PAM), biphase modulation (BPM), on-off keying modulation (OOK), and orthogonal pulse modulation (OPM) [GMK04]. x Amplitude (volts) Time (seconds) x 10 9 Figure 1.9: PPM pulse shapes for 1 and 0 bits in UWB system In single-band UWB systems, multiple access is achieved by using spread-spectrum techniques, such as time hopping (TH) and direct sequence (DS) [OSB99]. The symbol time T s is divided into N s frames of duration T f. To allow multiuser access, each frame is divided into N h slots or chips of duration T c. The chip time is larger than the pulse width (T c T w ). Each UWB user transmits one pulse per frame. Therefore, N s represents the number of frames per symbol. Among the N h hopping slots of each transmit frame, one slot is allocated to one user depending on the user s hopping code consisting in the random time-hopping sequences [WS88]. Then, ISI effect can be eliminated in single-band UWB 15

36 systems, and Rake receiver is used to enhance the SNR at the UWB receiver [Gol05] Multiband UWB vs. Impulse Radio UWB Compared with the single-band UWB system, multiband-ofdm UWB system has more flexibility to sculpt the transmit spectrum, lower complexity and is more energy efficient [BBA + 04]. Additionally, OFDM technique has been successfully deployed in many wireless systems, such as a, WiMAX, and 3GPP LTE and becomes a pragmatic approach to UWB. Hence, many semiconductor manufacturers and consumer electronics companies are interested in multiband-ofdm UWB. Since RAKE receiver is used in the single-band UWB system, the complexity of the single-band UWB system increases linearly with the number of RAKE fingers and the UWB receiver s sampling rate [Pro01]. For example, in the DS-UWB system, an M-finger RAKE receiver requires a number of M complex multiplies every chip. Hence, a 16-finger RAKE receiver in a single-band DS UWB system needs 21.9 complex multiplies per nanosecond. In multiband-ofdm UWB systems, the complexity increases logarithmically with the FFT size. An N-point FFT requires (Nlog 2 N)/2 complex multiplies per OFDM symbol. Therefore, with 128 subcarriers and a sampling rate of 528 MHz, the multiband-ofdm UWB system requires only 1.48 complex multiply operations every nanosecond. Furthermore, the multiband-ofdm UWB can capture approximately 95% of the multipath channel energy, while the 16-finger RAKE receiver can only capture 56% [BBA + 04]. Thus, multiband-ofdm UWB system can capture multipath energy more efficiently. Since UWB systems use a very large bandwidth, some parts of the UWB spectrum are occupied by other wireless systems, including a and WiMAX. To protect the existing wireless systems from being interfered, a UWB system is required to adapt its transmit spectrum for interference control. Single-band UWB system needs complex pulse shaping techniques to adapt the shape of its waveform [GMK04] [Can06]. In multiband-ofdm UWB systems, since the transmit power carried by each subcarrier can be controlled, the subcarriers can be selectively turned off to avoid interference to other wireless systems. 16

37 Hence, multiband-ofdm UWB system is more flexible in spectrum management, which facilitate the use of the cognitive radio techniques in UWB systems. 1.3 Cognitive Radio Cognitive radio is a wireless technology that has self-learning ability [MM99]. A wireless system equipped with cognitive radio technology can sense the wireless environment on continuous time and adapt its behavior 7 to statistical variations in the incoming RF stimuli Concept of Cognitive Radio The term cognitive radio was adopted by Mitola in 1999 [MM99]. His work showed that transceivers with cognitive radio is capable of sensing and learning the characteristics of an existing radio channel, and adapting the transmitting and receiving parameters to accommodate the varied wireless environment. Figure 1.10 presents the cognition cycle. First, stimuli is sensed by the cognitive radio system and dispatched to the cognition cycle for response. The stimuli includes information, such as application data (e.g., images, video and temperature), and network information (e.g. location, number of users and channel gain). Next, the cognitive system analyzes the stimuli in the scheduling process. The analysis include estimating the values of the stimuli s parameters and comparing the values to the cognitive system s current states and requirements. Then, decision is made by the cognitive system according to the analysis results. Finally, the decision is executed in the act process. The learning process shown in Figure 1.10 is a function of observations, scheduling and decision [Mit00]. Different cycles of the observation, scheduling and decision can form different communication pattern. Thus, a learning process can use the accumulated knowledge of the previous experienced communication patterns to quickly react to a new stimuli by approximating the new pattern as an existing pattern. 7 The adaptation of the cognitive radio system s behavior includes adjusting its operating parameters, such as transmit power, operating frequency and packet size. 17

38 Furthermore, learning process can compare the expected results to the practical results to learn about the effectiveness of a communication pattern. Figure 1.10: Illustration of the cognition cycle [Mit00] The feasibility of designing a cognitive radio system is attributed to the significant improvement in the programmability of the integrated circuits (ICs). The digital signal processor (DSP) construction technologies, such as field-programmable gate array (FPGA) and complementary meta-oxide-semiconductor (CMOS), make the wireless signal processing highly programmable. A radio system whose signal characteristics can be completely modified by software programming is called software defined radio [Fet03] [Bos99]. A cognitive radio system is built on the software defined radio systems. Cognitive radio system can adapt the signal parameters without changing the system s hardware. Figure 1.11 illustrates that the cognitive functions can be developed in the software processing part of the wireless system. 18

39 OSI Layers Software Radio Layers Data link bytes Link Framing bits MAC bits Coding symbols Modulation Physical Software Hardware basband signal Multiple Access I.F.signal A D Conversion Frequency Conversion R.F. signal Figure 1-4: The Figure Software 1.11: Radio Software Layering Defined ModelRadio shiftslayering many physical [Bos99] layer functions into software. for To implementing create a cognitive data-intensive radio system signal with processing all thealgorithms abilities asand described software above radiorequires system design. comprehensive research and development in many fields of electrical and electronic engineering. During the last ten years, many prototypes of cognitive radio system were developed. Research and design of the cognitive radio devices are ongoing activities [Fet09] Signal Acquisition Research into the enabling technologies for signal acquisition include the development of Currently, tunable wideband the academic front-ends and industry and of A/D interests converters are concentrated capable of digitizing on applying wideband the cognitive signals with a signal-to-noise ratio sucient to enable digital cellular applications. radio to the spectrum management field. In 2002, FCC Spectrum Efficiency Working Ideally, the front-end could be tuned to any band of interest, and would be capable of Group capturing concluded the entire in their bandreport of interest that the (e.g. existing 26 MHz spectrum for theis900 underutilized. MHz ISM band). The report Most practical solutions involve several discrete front ends, each of which is optimized for a showed certain band. that theactive spectrum research efficiency aimedcan at producing be significantly a single improved chip tuner by temporarily that is capable usingof operating in the MHz range is being performed as part of the DARPA Glomo the program unused 1. spectrum A discussion [Spe02] of the[fcc03]. requirements In 2003, and challenges FCC authorized associated the use withofthe cognitive design of ra-dio technology for opportunistic spectrum sharing. A cognitive radio system can sense its wideband tuners can be found in: [Brannon, 1998a] [Wepman, 1995] [Akos, 1997]. The development of A/D converters capable of digitizing the entire cellular band with operating enough resolution frequency tobands implement and transmit the digital in the cellular bands standards that are not inoccupied softwareby is the a signicant primary wireless systems. Cognitive radio can adapt to real-time wireless conditions through three 1 cognitive functions: spectrum sensing, spectrum sharing and spectrum management. The 21 19

40 details of the cognitive functions are discussed in Chapter 3. In terms of manage the spectrum using cognitive radio technologies, Haykin shows the cognition cycle from the signal processing perspective, as shown in Figure Figure 1.12 shows that the cognitive radio is an example of a global closed-loop feedback control system. Transmit-power control, and spectrum management Radio environment (Outside world) Action: transmitted signal Spectrum holes Noise-floor statistics Traffic statistics Radioscene analysis Interference temperature RF stimuli Quantized channel capacity Channel-state estimation, and predictive modeling Transmitter Receiver Figure 1.12: Information-processing Cycle in Cognitive Radio [Hay05] Implementation of Cognitive Radio in UWB The GHz UWB operating spectrum overlaps with narrowband systems, such as WiMAX, UMTS, a/n and Wireless Home Digital Interface (WHDI) [MBtBM07] [Law08] [DGMV06]. Figure 1.13 shows the spectrum of the UWB system overlaps with the IEEE a ( GHz) and WiMAX devices ( GHz). To protect the incumbent wireless systems from being interfered by the UWB systems, the emission PSD of the UWB systems is strictly constrained by FCC regulations ( -70 dbm/mhz) [FCC02]. With lower than -70 dbm/mhz power emission limitations, the UWB systems cannot provide the required Quality of Service (QoS) if the interference from the primary users is high [GZ05]. Furthermore, UWB will cause intolerable in- 20

41 terference to other wireless systems if the transmit power of UWB users rises within the overlapped spectrum. Figure 1.14 illustrates that the interference from UWB transmission affects the WiMAX communication link when two networks are overlapped. Figure 1.13: Spectrum Overlapping between UWB and Incumbent Systems Figure 1.14: Interference to a WiMAX node from a UWB communication pair To deal with the problem, abandon the overlapped spectrum in UWB systems is a solution of low spectrum efficiency, since the radio spectrum is far from fully utilized 21

42 by the licensed wireless systems [Spe02]. The Electronic Communications Committee (ECC) proposed a mechanism called Detect-and-Avoid (DAA) for UWB systems to control the transmit power in the overlapped frequency band [Ele08, Int05, DGMV06]. That is, a UWB device can transmit at the power level as high as dbm/mhz in the spectrum which is not occupied by the primary wireless systems, and the UWB device will reduce its transmit power or stop transmitting if the UWB device detects the presence of the primary wireless systems in the spectrum. The use of cognitive techniques in UWB transceivers will provide UWB systems the ability to dynamically access the operating spectrum for high spectrum utilization efficiency while keep the primary wireless systems from being interfered [GZ05, BLB06, MBtBM07, GK08]. The detailed discussion of how to efficiently share the spectrum with primary users in terms of maximize the spectrum efficiency is presented in Chapter State of the Art: Cognitive Radio in UWB Systems After the concept of cognitive radio was proposed by Mitola in 1999, research works are concerned with developing cognitive radio techniques (i.e., spectrum sensing, spectrum sharing and spectrum management) to improve the UWB systems performance for objectives, such as minimizing interference, maximizing throughput, minimizing packet delay and maximizing the fairness [Lan04] [AS06] [MBtBM07] [BLB06]. The cognitive radio techniques are categorized as the radio resource allocation algorithms which can react to the stimuli from the wireless environment by tuning the internal parameters (i.e., parameters for transmitting and receiving) to achieve a certain objective. The internal parameters include PHY, MAC and higher layer parameters, such as transmit power, coding rate, packet length, packet arrival rate, routing cost and application categories. The problem of designing a cognitive radio resource allocation algorithm 8 for a certain objective can be formulated to a classical or well-known optimization problem which consists of an 8 The cognitive radio resource allocation algorithm is called cognitive algorithm for short. 22

43 objective function and a series of constraints. The solutions to the classical optimization problem can be modified to find the solutions to the cognitive algorithm design [BV04]. Research works aim to design the cognitive algorithms that can reach the optimization objectives with low complexity, i.e., the algorithms are executed quickly (i.e., in the magnitude of microseconds) with low computational resource, such as processing power and memory Challenges of Integrating Cognitive Radio in UWB Systems Challenges of designing a cognitive algorithm are to find the optimal tradeoff between the optimization objectives and the constraints. The constraint is the value range for a certain parameter when the optimal solution to the objective function is obtained. For example, a cognitive algorithm aiming to maximize the data rate needs to keep the interference to the primary users below a certain threshold. The interference threshold is a constraint of the cognitive algorithm, and the parameter corresponds to the interference is the transmit power of the cognitive radio system. The cognitive system can obtain a higher data rate by increasing the transmit power. However, the increase in transmit power will result in higher interference to the primary systems. Hence, the tradeoff in the example is to use a transmit power which can achieve a data rate as high as possible and generate the interference below the constraint. In a cognitive radio system, to sense, learn and adapt to the wireless environment presents challenges in both hardware and software level. In hardware level, cognitive radio requires the signal processing units of the system s RF and IF part to handle various signals, be fully programmable and be power efficient [GK08] [ZC08]. In terms of software challenges, the cognitive radio systems need radio resource allocation algorithms in PHY, MAC and higher layers for local and global performance optimizations with a computational complexity as low as possible [Fet09]. The work in this thesis focuses on the software level challenges and assumes that there is perfect cognitive radio hardware to accommodate the proposed software level cognitive algorithms. 23

44 The unique characteristics of the UWB system, such as the wide operating frequency (7.5 GHz), dbm/mhz mean EIRP limit and the MB-OFDM modulation scheme place particular challenges to the development of the cognitive algorithms. These are related to spectrum sensing, spectrum sharing and spectrum management. In terms of spectrum sensing, one of the objectives is to create a signal processing technique that can detect the spectrum holes accurately 9 (i.e., reach a high probability of detection, such as 90%) with low computational complexity (i.e., in a short period, such as several microseconds). Spectrum sensing techniques for cognitive radio include matched filter detection, energy detection and feature detection [CMB04]. The matched filter detection is a coherent detection technique. The energy detection performs noncoherent detection, and the feature detection analyzes the spectral correlation of the received signal to determine if a primary user is present in the overlapped spectrum. Details of the three spectrum sensing techniques are in Chapter 3. The challenge is to determine which sensing technique is suitable for the MB-OFDM UWB system in the single user and multiuser situations so as to perform an accurate signal detection with low complexity 10. Furthermore, there are other challenges, such as detecting the primary user s downlink communication (e.g., the transmission from a WiMAX base station to a WiMAX node [MTBMB07]) [BTZH10] which requires the cross-layer design [SL05]. In MB-OFDM UWB system, a goal of spectrum sharing is to determine the way of sharing the overlapped spectrum with the primary users, i.e., overlay and underlay spectrum access schemes 11. Overlay scheme requires the UWB system to use an efficient subcarrier suppression technique to attenuate the subcarriers and sidelobes which will interfere with the primary user. Underlay scheme needs the UWB system to have a dynamic power control scheme to minimize the interference to the primary users [ZS07]. Furthermore, other design requirements in spectrum sharing include to design and implement the 9 Spectrum holes come and go in a stochastic manner. 10 Other spectrum sensing techniques for the wireless environments with noise uncertainty, shadowing, and fading is another challenging problem [SHT04]. 11 In overlay spectrum access, unlicensed user can opportunistically access the spectrum holes. Underlay spectrum access scheme allows unlicensed users to simultaneously use the spectrum with the licensed users. 24

45 PHY, MAC or high layer protocols to coordinate the multiuser access to the spectrum in the cognitive network 12. The cognitive protocols need to find the optimal tradeoff between the objective of a single user and the objective of the cognitive network. For example, a cooperative spectrum sensing algorithm can increase the probability of detection and deal with the hidden terminal problem 13. However, such cooperative spectrum sensing algorithm requires more communication overhead between the UWB users [MSB06]. For UWB system s spectrum management, the design objectives involve designing a low complexity cognitive algorithm to efficiently use the detected spectrum for varied purposes. The development of the cognitive algorithm depends on the objective and constraints of the spectrum management. The work in this thesis focuses on developing a power and bit allocation algorithm to maximize the spectrum efficiency of the cognitive UWB system. The solution to the spectrum efficiency maximization problem can be derived by mapping the problem to different classical optimization problems, such as convex and nonconvex optimization problem. A challenge of the convex optimization is to find the optimal tradeoff between transforming problems into convex forms and the relaxation of the constraints 14. Another challenge is to estimate the value of certain parameters for finding the solution to the convex optimization [BV04]. To deal with a nonconvex optimization problem (e.g., combinatorial optimization problem) needs to map the spectrum maximization problem to a classical optimization problem whose solution can be used to create the cognitive algorithm. Furthermore, another challenge is to find the tradeoff between the performance of the cognitive algorithm and the algorithm s execution time in the UWB system (i.e., the complexity of the cognitive algorithm) [KV08]. 12 The architecture of a cognitive radio network includes the infrastructure with a centralized cognitive node and distributed cognitive nodes in a Ad Hoc manner [HB07]. 13 Hidden terminal problem is the problem that occurs when the cognitive radio cannot detect the presence of the primary user due to multipath fading or shadowing. Then, the cognitive radio system will access the licensed channel and cause interference to the primary users [Hay05]. 14 The relaxation of constraints will result in the use of the cognitive algorithm in UWB systems to be unpractical. 25

46 1.4.2 Literature Review The work in this thesis focuses on developing the cognitive algorithms for maximizing the spectrum efficiency in the cognitive MB-OFDM UWB systems. The proposed cognitive algorithm is a cognitive management function and can dynamically allocate the spectrum, power and bits to the UWB users subcarriers. The basic principles and methods are contributed by research works in multicarrier modulation [Gal68] [HH87] [CCB95] [Czy96] [FH96]. In [Gal68], the author Gallager derived the capacity of the multicarrier system by using the water-filling algorithm which is based on greedy algorithm [CLRS01]. In a multicarrier system whose total transmit power is limited, the water-filling algorithm allocates more power on the subcarriers which has the higher channel gains until the total transmit power is used up. The power allocation problem is formulated to a convex optimization problem. Then, the water-filling algorithm use Lagrangian method to find the closed-form solution and compute the amount of the power and bits allocated on each subcarrier 15. Water-filling algorithm assumes the number of bits allocated on a subcarrier can be a non-integer value, which cannot be implemented in practical wireless systems. Compared with water-filling algorithm, the Hughes-Hartogs algorithm developed in [HH87] requires integer number of bits to be allocated on the subcarriers, which makes the optimization problem NP-hard 16. The Hughes-Hartogs algorithm is also based on greedy algorithm and maximizes the data rate of the multicarrier systems 17. The Hughes-Hartogs algorithm formulated the radio resource allocation problem to a non-convex optimization problem and provide an greedy-based algorithm to approximate the optimal solution of the problem by allocating the source bits one by one to the subcarriers which requires the least amount of incremental power to modulate the bit. The complexity of the Hughes- Hartogs algorithm is proportional to the number of source bits and subcarriers, which is 15 The Water-filling algorithm is discussed in Annex C. 16 NP-hard mean the optimization problem cannot be solved in polynomial time, which indicates that only the solution which can approximate the solution to the optimization problem can be found [CLRS01]. 17 The maximized data rate corresponds to the maximized spectrum efficiency by normalizing the data rate with the bandwidth of the system s operating frequency bands [FCC04] 26

47 viewed as a slow algorithm [CCB95] [KRJ00]. In [CCB95], Chow et al. created a bit allocation algorithm based on the water-filling algorithm to minimize the power consumption under the constraints of a target data rate. Chow s algorithm treats the bit allocation as a convex optimization problem and use a parameter called SNR gap to calculate the number of bits that can be allocated on the subcarriers 18. Chow s algorithm averagely distribute the total transmit power to the subcarriers and compute the maximum number of bits (nonintegers) on each subcarrier by finding the optimal system margin in a limited number of iterations 19. Chow s algorithm rounds the non-integer number of bits to integer values on each subcarrier, and adds or decreases one bit at time on the subcarriers who has the largest or smallest difference between the integer and the non-integer value, so as to meet the target data rate. Then, the allocated power on each subcarrier are scaled according to the bits round procedure. Chow s algorithm has lower complexity than Hughes-Hartogs algorithm and suits the multicarrier system in high-snr regime [FU98]. Note that Chow s algorithm aims to minimize the power consumption, but the algorithm can be modified to maximize the spectrum efficiency because Chow s algorithm is based on the greedy algorithm. Thus, rate maximization and power minimization problems are dual problems and can be solved by following the same principle. Based on the review in the previous paragraph, the existing radio resource allocation algorithms for spectrum efficiency maximization in the MB-OFDM UWB systems are categorized in terms of the methods used to approximate the optimal solutions. Figure 1.15 shows the spectrum efficiency maximization problem is mapped to convex and nonconvex optimization problems. The criteria of the choosing a way to develop the optimization algorithm depends on the objective and constraints of the MB-OFDM UWB system. 18 The SNR gap corresponds to the difference between the capacity of the subcarrier and the practical number of bits that can be allocated on the subcarrier. The concept of SNR gap is discussed in Annex C. 19 Chow s algorithm is analyzed in-depth in Chapter 4. 27

48 Figure 1.15: Flow diagram of deriving a solution to the spectrum efficiency maximization problem by mapping the problem to the classical optimization problems In a single user cognitive OFDM system, the authors in [ZL09b] proposed a cognitive algorithm to maximize the bit rate under the constraints of the total transmit power and subcarrier s sidelobe interference to the primary users 20. In [ZL09b], the cognitive algorithm is formulated as a multi-dimensional knapsack problem which is a nonconvex problem. Knapsack problem is described as a problem to choose a number of items from a set of items, each having a value and weight (i.e., profit and cost), so that the total value of the chosen items is maximized while the total weight does not exceed the limit [Pis95] [KV08]. In [ZL09b], the item is the each source bit, the value of a bit is one unit (i.e., 1), and the weight of a bit is the function of the transmit power and the interference. The term multi-dimensional means that the knapsack problem has two or more constraints, which makes the problem NP-hard. The authors used the greedy algorithm to approximate the optimal solution to the knapsack problem, which follows the left 20 Overlay spectrum sharing is assumed in [ZL09b]. 28

49 side of the flow diagram in Figure Greedy algorithm is the algorithm that approximates the optimal solution to the problem by approximating the optimal solutions to the sub-problems of the whole problem [CLRS01]. The optimal solution to a sub-problem is obtained by choosing the item that has the maximum efficiency value. The efficiency value is the ratio of the item s value to the weight. In [ZL09b], there are two efficiency values defined due to the two constraints. One efficiency value is the ratio between the remaining transmit power and the incremental power to modulate one more bit on the subcarrier. Another efficiency value is defined as the ratio between the remaining interference margin of the primary user and the interference generated by allocating a bit to the subcarrier. The authors applied the greedy algorithm by allocating a bit to the subcarrier which has the maximum efficiency value in each iteration until one of the constraints is violated. Since there are multiple primary users near the signal cognitive OFDM system, there are multiple interference related efficiency values in each subcarrier. Hence, in a subcarrier, the minimum interference efficiency value is chosen to be compared with other subcarriers minimum interference efficiency values 21. The complexity of the cognitive algorithm in [ZL09b] is proportional to the number of source bits, the number of subcarriers and the number of the primary users. Figure 1.15 indicates that the rate maximization problem can also be solved by forming the problem to a convex optimization problem. Authors in [BHB08] proposed a waterfilling based cognitive algorithm to maximize the data rate of a single cognitive OFDM system. The data rate is computed by using signal-to-interference and noise ratio (SINR) instead of the SNR in the Shannon capacity formula for multicarrier systems 22 [Pro01]. The interference used to compute the cognitive user s data rate is the aggregate interference power introduced by the primary users into the cognitive user s subcarriers. The constraints of the formulated convex optimization problem in [BHB08] are the aggregate 21 Choose the minimum interference efficiency value is to guarantee the primary user with the minimum interference margin will not be interfered. 22 The Shannon capacity formula for multicarrier systems is used in water-filling algorithm and is introduced in Annex C. 29

50 interference power from the cognitive user s subcarriers sidelobes to the primary user and the maximum allowed transmit power on each cognitive user s subcarrier. A closed form solution is obtained by using two Lagrange multipliers for the constraints. The resulted data bits on each subcarrier is non-integer, and the iterations required for finding the values of the two Lagrange multipliers is significantly higher than water-filling algorithm. The authors simplified the cognitive algorithm (sub-optimal) by using the greedy algorithm to allocated more power to the subcarriers which will generate less interference to the primary user. The maximum data rate achieve in the simplified cognitive algorithm is over 50% lower than the original solution. Compared with the high complexity in finding a closed-form solution in [BHB08], Krongold et al. provided a low complexity convex power and bit allocation algorithm for rate maximization in the single user OFDM system 23 [KRJ00]. The rate maximization problem in [KRJ00] is formed as in Chow s algorithm [CC92], and the Lagrange method is used to define a Lagrange multiplier which denotes the derivative of the non-integer number of data bits as a function of the allocated power on each subcarrier. The values of the bits and power on each subcarrier are sampled, so that only integer bits are considered in approaching the optimal solution. The binary search algorithm is used to approximate the optimal value of the Lagrange multiplier [CLRS01]. Krongold s algorithm requires to estimate the upper and lower bound of the Lagrange multiplier priori to approximate the optimal value of the Lagrange multiplier every time. The search algorithm will have a high iteration number before convergence if the estimated bounds are far from the optimal value. In multiuser OFDM systems, Wong et al. proposed a radio resource allocation algorithm which dynamically allocate subcarriers to different users in the network, and each OFDM user applies the proposed radio resource allocation algorithm to dynamically distribute power and bits on the available subcarriers [WCLM99]. Wong s algorithm aims 23 Krongold s algorithm is not developed in cognitive radio system, but can be modified and applied in cognitive radio systems [BLN08]. 30

51 to minimize the power allocated on the subcarriers under the constraints of target bit rate and exclusive occupation of a subcarrier by a OFDM user. In Wong s algorithm, the subcarriers are allocated in a greedy manner, i.e., a subcarrier are allocated to the user whose channel gain in the subcarrier is the highest among other users. Wong s algorithm relaxes the constraints of integer bit values in order to form the power minimization problem to a convex optimization problem and find the lower bound solution. Two Lagrange multipliers are used in Wong s algorithm in solving the convex optimization problem. The complexity of deriving the closed form solution using Wong s method is considered as high [ZL04]. Authors in [ZL04] developed a radio resource allocation algorithm based on sequential unconstrained minimization technique to simplify the derivation of the solution for the multiuser data rate maximization problem in OFDM systems. For multiuser MB-OFDM UWB systems, the authors in [WZK07] proposed a dynamic sub-band and power allocation algorithm to minimize the power consumption of the UWB network. The optimization algorithm is developed according to the UWB PHY specification of WiMedia ECMA-368 standard [Eur05]. The power minimization problem is formed to a non-convex optimization problem under the constraints of target data rate, BER and PSD mask of the UWB systems. The numerical solution to the problem is derived in [WZK07] based on greedy algorithm. Compared with the cognitive algorithm in [ZL09b], authors in [WZK07] lower the complexity of the resource allocation algorithm by allocating the sub-band instead of subcarriers to the UWB users which will equally allocated the transmit power among the subcarriers in the sub-band 24. A UWB sub-band is assigned to the user who has the highest average sub-band SNR. The average sub-band SNR is given by computing the mean of the channel SNR on each subcarrier of the sub-band. Since the coherence bandwidth of the UWB channel is much smaller than the bandwidth of a sub-band 25, the average power allocation among 128 subcarriers in a sub-band will result in power waste and performance degradation compared with 24 In MB-OFDM UWB system, a sub-band consists of 128 subcarriers [BBA + 04]. 25 The coherence bandwidth of the UWB channel is up to 1/10 of the sub-band bandwidth, which is discussed in Chapter 4. 31

52 the subcarrier-based resource allocation algorithms [SLS07] [QAA07]. In [SLS07], the authors proposed a clustered bit loading algorithm based on Chow s algorithm [CCB95]. The size of the cluster (i.e., number of subcarriers in the cluster, up to 5 in [SLS07]) is much smaller than the size of sub-band in [WZK07]. Power and bits are equally allocated on each subcarrier in the cluster. The number of the bits allocated on a cluster s subcarriers is obtained by applying the Chow s method in each subcarrier and computing the mean bit value over the subcarriers in the cluster. 1.5 Contributions of the Thesis The work in this thesis contributes to the areas of UWB and cognitive radio by presenting a new cognitive radio resource allocation algorithm in the MB-OFDM UWB system for spectrum efficiency maximization. The proposed algorithm can be applied in the single user and the multiuser UWB network. The uniqueness of the UWB systems, such as the wide operating frequency (7.5 GHz), dbm/mhz mean EIRP and the MB-OFDM modulation scheme place particular challenges to the development of the cognitive algorithm. The challenges are related to spectrum sensing, spectrum sharing and spectrum management. The work in this thesis formulate the spectrum efficiency maximization algorithm to a multiple multi-dimensional knapsack problem with constraints in total transmit power, transmit power in each UWB subcarrier, the aggregate interference to the primary users, the target BER and the exclusive use of a subcarrier by each cognitive user at a time 26. The low complexity cognitive algorithm is developed based on the greedy algorithm in order to deal with the optimization problem. The novel contributions of the thesis are listed below, as: The primary and advanced power and bits allocation algorithm: The algorithm is applied in a cognitive UWB user to allocate the transmit power on the subcarriers 26 In the single user and the multiuser UWB network, with or without primary users operating nearby, the constraints for the optimization problem are varied. 32

53 in two steps. The first step is to equally allocate the transmit power on the subcarriers. The next step is to collect the excessively allocated power in the first step and adaptively allocate the power to the subcarriers in a greedy manner. When the total transmit power is low 27, the proposed algorithm obtains the maximized spectrum efficiency with a smaller order of growth comparing with the existing cognitive algorithms. The group power allocation algorithm: The cognitive UWB system uses the algorithm to divide the 128 subcarriers in a UWB sub-band into groups. Each group consists of a number of adjacent UWB subcarriers with the total bandwidth being smaller than the coherence bandwidth of the UWB system. Different from the existing algorithms reviewed in the previous section, the effective SNR of a subcarrier group is determined by the geometric mean of the subcarriers in the group. The total transmit power of the UWB system is allocated to the subcarrier groups in a greedy manner, and the power allocated to a subcarrier group is equally distributed on each subcarrier. The complexity of the group power allocation algorithm is significantly lower than the resource allocation algorithms on subcarrrier-by-subcarrier basis. The degradation in terms of the maximized spectrum efficiency is low when the proposed algorithm is used in the UWB system with low transmit power. Optimal spectrum sensing period: The constraint of the aggregate interference to the primary users is translated into the spectrum sensing period (i.e., the time used for spectrum sensing) as a function of the primary users transmit power and the target probability of detection and false alarm. The time duration for a UWB user to transmit data is limited, the proposed cognitive algorithm determines the optimal spectrum sensing period to increase the percentage of the data transmission time. The cognitive algorithm enhances the maximized spectrum efficiency obtained in the spectrum management stage for the single user and the multiuser situations. 27 A low total transmit power means that the average PSD on each subcarrier is lower than dbm/mhz. 33

54 1.6 Summary of Thesis UWB is a high-speed, short-range wireless technology which operates over a 7.5 GHz bandwidth with low transmit power 28. UWB system s bandwidth is overlapped with wireless systems, such as WiMAX and UMTS, which limits the use of UWB in the overlapped spectrum. Cognitive radio technology enables the wireless systems to opportunistically use the overlapped spectrum without causing interference to the primary users. The UWB systems, cognitive radio technology and the implementation of the cognitive radio in the UWB systems are reviewed. The work in this thesis focuses on developing a cognitive algorithm for spectrum efficiency maximization in the cognitive MB-OFDM UWB systems. The cognitive algorithm is a radio resource management algorithm which dynamically allocate the spectrum, power and bits to the UWB user for a certain objective. The cognitive algorithms developed by previous research works were reviewed in the chapter. The literature review shows the approaches to design a cognitive algorithm under different constraints. The following chapters analyze the MB-OFDM UWB and cognitive radio in depth and proposed spectrum efficiency maximization algorithms under different UWB network architectures. Figure 1.16 presents the structure of the thesis 29. Following the review in Chapter 1, the detailed discussion of UWB and cognitive radio are in Chapter 2 and Section 3.2 in Chapter 3, respectively. In Section 3.3, using the cognitive radio techniques in the MB-OFDM UWB system is studied. The work in this thesis aims to design a cognitive algorithm in the UWB system for spectrum efficiency maximization. Chapter 4 analyzes the spectrum efficiency performance of the mutliband OFDM UWB system by using the existing cognitive algorithms which were proposed for the OFDM-based wireless systems. The analysis is carried out in four scenarios. Each scenarios represents a specific UWB network architecture. Based on the analysis in Chapter 4, new cognitive algorithm 28 In 2010, UWB system based on WiMedia standards can reach over 1 Gbps data rate in 2 meters range. The transmit PSD is limited by dbm/mhz. 29 In Figure 1.16: CR-cognitive radio; PU-primary user. 34

55 is proposed in Chapter 5 for each scenario. The results show the advantages of the proposed algorithms compared with the existing algorithms analyzed in Chapter 4. Finally, conclusions are drawn in Chapter 6, and the future works are discussed. 35

56 / 0 " 1 ) 2 1! " #!"# $% &'! $%() ()*+, )*, ) )*+, ) )*, #, () % $%&' ( - )". Figure 1.16: Structure of The Thesis

57 Chapter 2 discusses the MB-OFDM UWB system, including the architecture of the transmitter and receiver, the MB-OFDM modulation scheme and the UWB channel model. The coded BER of the UWB subcarriers as a function of transmit power and channel gain is derived 30. The BER is one of the constraints in the cognitive algorithm design. The BER expression determines the minimum transmit power which is needed in a subcarrier for the target BER value. Chapter 3 analyzes the cognitive radio functions, i.e., spectrum sensing, spectrum sharing and spectrum management. The cognitive radio functions are the algorithms for the objectives, such as maximizing the spectrum efficiency. The chapter investigates the use of the cognitive radio functions in the mutliband OFDM UWB system, including the modifications in the UWB transceiver, the cognitive UWB network architecture and the interference power to the primary users. The investigations show the constraints of using cognitive radio in UWB, and the spectrum efficiency maximization problem is formulated as a constrained optimization problem. The chapter discusses the approaches to deal with the optimization problem (i.e., to design the cognitive algorithm) in the mutliband OFDM UWB system. In Chapter 4, the existing cognitive algorithms for spectrum efficiency optimization are analyzed in four research scenarios. The classification of the scenarios is based on two parameters: the number of the UWB users and the number of the nearby primary users 31, as shown in Figure The existing algorithms are modified according to the constrained optimization function, so as to facilitate the algorithms implementation in the UWB systems. The analysis results provide insight for the new optimization algorithms design in the following chapter. Chapter 5 proposes a new cognitive algorithm in each scenario aiming to maximize spectrum efficiency with low complexity. The proposed cognitive algorithms dynamically allocate the spectrum, power and bits among the cognitive users under the constraints, 30 Convolutional coding is used in MB-OFDM UWB system. 31 The word nearby means that the distance between the cognitive UWB nodes and the primary nodes is small so that the cognitive nodes may interfere with the primary nodes [DK09]. 37

58 such as transmit power, probability of detection and BER. The proposed algorithm also determines the optimal spectrum sensing period to maximize spectrum efficiency. Furthermore, the tradeoffs between the complexity and the performance of the proposed algorithms are analyzed. In each scenario, the performances of the proposed algorithms in terms of the spectrum efficiency are compared with the results provided by Chapter 4, which will show the advantages of the proposed algorithms in the specific cognitive UWB network architectures. Finally, Chapter 6 gives the thesis a conclusion. The future work opened up for further investigation is presented in the chapter. 38

59 Chapter 2 Multiband-OFDM UWB System 2.1 Introduction OFDM is widely used by a number of standards organizations, such as asymmetric digital subscriber line (ADSL), IEEE a, IEEE g, and IEEE a. In addition, OFDM was adopted for digital audio and terrestrial broadcast in both Europe and Japan [Pra04] [CHA66]. The transceiver architecture for a multiband OFDM (MB- OFDM) system is very similar to that of a conventional wireless OFDM system. The main difference is that the MB-OFDM system uses a frequency hopping scheme to specify the center frequency for the transmission of each OFDM symbol [Eur05] [WiM08]. MB-OFDM is an ideal technical solution for the UWB systems with high-speed shortrange applications [BBA + 04]. The IEEE a task group developed a stochastic time-domain channel model to estimate the performance of UWB systems in real-world environments [Mol05]. In frequency-domain, each UWB subcarrier experiences a nonselective Rayleigh fading channel [SLS07]. UWB channel is a low-snr band-limited channel, and the fading characteristic of the UWB subcarriers has a significant impact to the design of the cognitive radio resource allocation. In this chapter, the architecture of the Multiband-OFDM UWB system is introduced, and the transmission and reception of the OFDM UWB signal is discussed. Then, the 39

60 modelling of the UWB channel is analyzed based on the analytical study and the simulation of the UWB channel s time and frequency domain response. The computation of the uncoded and coded error probability of each UWB subcarrier in a Rayleigh fading channel is given based on a discussion concerning the transmit/received power and the signal-to-noise ratio. 2.2 Architecture of Multiband-OFDM UWB System The architecture of a MB-OFDM UWB system s transmitter and receiver are shown in Figure 2.1 and Figure 2.2 [WiM09]. Transmitted Singal Input Data Scrambler Convolutional Encoder/ Puncturer Bit Interleaver Constellation Mapping IFFT Zero Padding/ Guard Interval Pulse Shaping Filter DAC Multipath Fading Channel Time-Frequency Kernel exp(j2 f c t) Figure 2.1: Transmitter architecture for a MB-OFDM UWB system. *," +* %&'( ) *" *" " ## $ # %&'( )! *," Figure 2.2: Receiver architecture for a MB-OFDM UWB system. The input data bits to the transmitter are first scrambled to combat the cross modulation and the intermodulation caused by non-linearities of the receiver. Next, the scrambled data bits are convolutionally encoded and interleaved for forward error correction (FEC). Then, the encoded bits are digitally modulated using linear memory-less modulation methods such as M-ary quadrature amplitude modulation (M-ary QAM) [Pro01]. A sequence of modulated digital symbols are produced. The number of symbols in a sequence is normally set to the power of two (e.g., 128) so as to facilitate the Fourier transform in the next step [WiM09]. Subsequently, the modulated digital symbol sequence 40

61 is passed through the inverse discrete Fourier transform (IDFT) block for multicarrier modulation. To compute the IDFT result efficiently, the inverse Fast Fourier transform (IFFT) technique is used [OSB99]. After IFFT process, an OFDM symbol is produced. The OFDM symbol contains a sequence of symbols which correspond to the time domain samples of the transmitted signal. A series of zeros are padded at the end of the OFDM symbol to create a circular convolution between the transmitted OFDM signal and the channel impulse response [WG00]. The circular convolution will lead to a simple multicarrier demodulation process at the UWB receiver. Compared with cyclic prefix in conventional OFDM systems [Pro01], UWB receiver needs to collect additional samples corresponding to the length of the zero padding and to use an overlap-and-add method to obtain the circular convolution property [OSB99]. Another advantage of using zero padding is that power backoff at the RF transmitter can be avoided 1, because the ripples in the average PSD can be reduced to zero with enough averaging [BBA + 04]. Hence, the MB-OFDM UWB system can achieve the maximum range possible. Furthermore, the zero padding process provides a mechanism to mitigate the effects of multipath, and it provides a sufficient time for the transmitter and receiver to switch between the different operating frequencies. The zero-padding process is followed by passing the OFDM symbol through a pulse shaping filter, as shown in Figure 2.1. The pulse shaping filter is used to limit the bandwidth of each M-ary QAM signal. Different pulse shaping filter can be used for various purposes [VH96] [BDH99] [BT04]. Since perfect symbol and carrier synchronization is assumed in this work, the basic rectangular pulse shape is used [Gen07]. When passing though the digital-to-analog converter (DAC), the discrete OFDM symbol is converted into a continuous time OFDM signal at baseband. The frequency domain representation of this OFDM signal contains a series of orthogonally multiplexed signals (i.e., no inter-symbol interference) which are modulated on the OFDM baseband subcarriers, and 1 OFDM UWB system with cyclic prefix requires as large as 1.5 db power backoff at the transmitter [BBA + 04]. 41

62 each of the multiplexed signals corresponds to a constellation modulated symbol in the constellation mapping block. Finally, the baseband OFDM signal is upconverted to the UWB operating frequency (i.e., RF signal) and transmitted. The center frequency (i.e., the subband) that is used to transmit an OFDM signal is determined by the time-frequency kernel. One of the goals of the time-frequency kernel is to ensure that the average number of collisions (i.e., transmit at the same center frequency) between different UWB users is low, and the other goal is to ensure that the distribution of collisions to be as uniform as possible [BBA + 04]. Since the equivalent lowpass signal of the transmitted RF OFDM signal is often represented by complex numbers, the real and the imaginary part of the OFDM signal envelope are separately modulated onto different orthonormal sinusoidal waveforms, e.g., sine and cosine wave. Figure 2.2 illustrates that the OFDM UWB receiver use coherent demodulation technique to bring the received OFDM RF signal to two lowpass signals, i.e., in-phase lowpass signal and quadrature-phase signal [Eur05]. Then, the two analog lowpass signals are converted into digital signals through analog-to-digital converter (ADC). To reconstruct the originally transmitted OFDM symbol, the linear convolution between the zero-padded OFDM signal and the UWB fading channel impulse response is converted into a circular convolution between the OFDM symbol (whose ZP is removed) and the UWB channel impulse response [WG00]. Hence, by passing the received discrete OFDM signal to the FFT block, the circular convolution is transformed into a linear multiplication between the Fourier transform of the received OFDM symbol and the UWB channel frequency response [OSB99]. Therefore, the originally transmitted M-ary QAM symbols in an OFDM symbol can be computed by using the UWB channel frequency response to divide the Fourier transform of the received OFDM symbol, provided that the channel state information (CSI) is known to the UWB receiver [Gol05]. This process will be discussed in detail in next section. Then, the original signal is decoded at later stage by the UWB receiver through a series of reverse procedures of the UWB transmitter, i.e., a de-interleaver, a Viterbi decoder and a de-scrambler, as shown in Figure

63 2.3 OFDM UWB Signal In a MB-OFDM UWB system, the transmitted signal s RF (t) in a sub-band includes a number of orthogonally multiplexed M-ary QAM signals. In ECMA-368, Quadrature Phase-Shift Keying (QPSK) and Dual Carrier Modulation (DCM) are used to modulate the bits on each OFDM subcarrier [WiM09]. The equivalent lowpass signal of s RF (t) is expressed as s(t) = N 1 n=0 D[n]p(t)e j2πfnt, t [0, T ofdm ), (2.1) where D[n] = A[n] + jb[n] (n [0, N 1]) stands for a single M-ary QAM symbol, N denotes the number of the QAM symbols in an OFDM signal, p(t) is the pulse shape for each QAM symbol, f n represents the center frequency of the n-th baseband carrier which is modulated by D[n], and T ofdm denotes the duration of the OFDM signal 2. To correctly reconstruct D[n] at the UWB receiver, p(t)e j2πfnt must constitute an orthogonal basis [BDH99]. Thus, f n is given by f n = n f = n(1/t ofdm ), n [0, N 1], (2.2) where f = 1/T ofdm is the frequency interval between baseband carriers. The measurements of the UWB channel demonstrate that the parameters of the UWB indoor channel vary slowly [DMB06]. Hence, the UWB carrier and symbol synchronization is assumed to be perfect (i.e., without synchronization error) [LSL07] [BDH99]. Thus, a rectangular pulse p(t) is sufficient for UWB signal s pulse shaping process 3, and is expressed as 1, t [0, T ofdm ) p(t) = 0, otherwise. (2.3) The spectrum of p(t) is obtained by applying the continuous-time Fourier transform 2 The actual duration T of s(t) is greater than T OF DM, since s(t) is zero-padded [WiM08] 3 Discussions of more advanced pulse shaping filters that is used in various wireless channel conditions can be referred to [Rap01] 43

64 (CFT) to p(t) [OWN02], thus P (f) = CFT (p(t)) = T o sinc (ft o ) e jπft ofdm, (2.4) where sinc(θ) = sin(πθ) πθ. Figure 2.3 and Figure 2.4 show p(t) and P (f), respectively 4. p(t) Amplitude Time (s) x 10 7 Figure 2.3: Pulse shape of p(t) 4 p(t) and P (f) are plotted by setting T ofdm = nanoseconds according to [WiM08] 44

65 0.25 P(f) 0.2 Amplitude Frequency f (MHz) Figure 2.4: Spectrum of P (f) When a number of N OFDM baseband carriers are orthogonally multiplexed, the Fourier transform of N 1 n=0 p(t)ej2πfnt is computed by [OSB99] N 1 n=0 CFT (p(t)e j2πfnt ) = N 1 n=0 P (f f n ). (2.5) The equation shows that the Fourier transform of N 1 n=0 p(t)ej2πfnt consists of P (f), replicated at the frequencies f n, where f n is the center frequency of the n-th UWB OFDM carrier. Therefore, the M-ary QAM symbols modulated on the carriers are mutually orthogonal over t [0, T ofdm ), i.e. [Pro01], Tofdm 0 s i (t)s j(t) = 0, if i j, (2.6) where s i (t) represents the i-th UWB OFDM carrier s waveform, and s (t) denotes the conjugate of s(t). Figure 2.5 illustrates an example of how a number of the carriers of s(t) are orthogonally multiplexed. 45

66 0.25 UWB OFDM Subcarriers Orthogonal Multiplexing 0.2 Spectral Amplitude Frequency f (MHz) Figure 2.5: UWB OFDM Subcarriers Orthogonal Multiplexing To efficiently generate s(t), IFFT is employed in the digital part of the UWB transmitter, as shown in Figure 2.1. With a time sampling interval T s = T ofdm /N, the quantized samples of s(t) before the DAC block are give by s[k] = s(kt s ) = N 1 n=0 D[n]e j2πnkts/t ofdm N 1 = D[n]e j2πkn/n, k [0, N]. n=0 (2.7) This equation is a synthesis equation of DFT, i.e., IDFT [OSB99]. Therefore, s[k] is calculated by passing the M-ary QAM symbol sequence D = [D[0], D[1],..., D[N 1]] through an IFFT module, as shown in Figure 2.1. To facilitate IFFT computation, the M-ary QAM symbol sequence D is converted from serial to parallel sequence to produce D T 5. When D T is passed through the IFFT 5 D T stands for the transpose of a matrix D. 46

67 block, s[k] is produced as in (2.7). The sequence s = [s[0], s[1],..., s[n 1]] is known as an OFDM symbol. Due to time dispersion in multipath fading channel, adjacent OFDM symbols will have inter-symbol interference (ISI). To eliminate the ISI, a sequence of zeros are padded at the end of each OFDM symbol. After passing through the DAC, the UWB OFDM RF signal s RF (t) corresponding to one OFDM symbol is given by s RF (t) = Re = Re [ N 1 n=0 [ N 1 D[n]p(t)e j2πn ft e j2πfct ] ] D[n]p(t)e j2π(fc+n f)t, t [0, T ofdm ], n=0 (2.8) where f c denotes the center frequency of a subband. Note that the OFDM UWB transmitted signal s RF (t) contains only the real part of the IDFT. Thus, to fully recover the baseband signal s(t) (i.e., includes both real and imaginary parts) at the UWB receiver, the sampling interval is halved at the UWB receiver [WE71]. When a series of OFDM symbols are transmitted, s RF (t) is written as s RF (t) = Re [ N 1 n=0 ] D l [n]p(t lt ofdm )e j2π(fc+n f)(t lt ofdm), t [0, T ofdm ], (2.9) l=0 where l denotes the number of the transmitted OFDM symbols, and D l [n] is the n-th M- ary QAM symbol in the l-th M-ary QAM sequence. Figure 2.6 depicts the transmitted MB-OFDM UWB signal in time-domain 6, and Figure 2.7 shows the PSD of the MB- OFDM UWB signal which is transmitted in subband 1. At the UWB receiver, the received RF signal r RF (t) corresponding to one OFDM symbol is given by 6 QPSK modulation is used on each sub-carrier. r RF (t) = s RF (t) h(t) + ϕ(t), t [0, T ), (2.10) 47

68 Signal of an OFDM Symbol in time domain Amplitude Time (s) x 10 7 Figure 2.6: MB-OFDM UWB Signal in Time-domain PSD of the signal of an OFDM symbol Power Spectral Density (V 2 /Hz) Frequency (Hz) x 10 9 Figure 2.7: Power Spectral Density of an MB-OFDM UWB Signal where h(t) denotes the UWB channel impulse response, ϕ(t) is the additive white Gaussian noise, T denotes the duration of s(t) which includes the OFDM symbol and ZP, and 48

69 is the operation symbol of linear convolution. The UWB channel is assumed to be static during the transmission of the one OFDM symbol. Coherent detection method is used to obtain the received baseband OFDM signal r(t) from the OFDM RF signal r RF (t). The analog-to-digital converter (ADC) converts the analog OFDM signal to the discrete received OFDM signal which is expressed as r[k] = ŝ[k] h[k] + ϕ[k], k [0, N 1], (2.11) where ŝ[k] is the zero-padded s[k], and h[k] is the discrete-time channel impulse response. Since circular convolution of two sequences is equivalent to their linear convolution followed by time-aliasing [OSB99], (2.11) is converted to [WG00] r[k] = s[k] h[k] + ϕ[k], k [0, N 1], (2.12) where denotes a circular convolution. Therefore, the N-point discrete Fourier transform (DFT) of r[k] is computed by passing r[k] through the FFT module shown in Figure 2.2, as FFT (r[k]) = R[n] = S[n] H[n] + Ψ[n], n [0, N 1], (2.13) where S[n], H[n] and Ψ[n] represent the DFT of s[k], h[k] and ϕ[k], respectively 7. Since perfect subcarrier synchronization and CSI are assumed (i.e., no inter-carrier interference), the original transmitted OFDM symbol S[n] is reconstructed by S[n] = R[n] Ψ[n], n [0, N 1], (2.14) H[n] where S[n] = D[n] according to (2.7). Thus, each M-ary QAM modulated symbol D[n] in the original QAM symbol sequence D = [D[0], D[1],..., D[N 1]] is successfully 7 H[n] = l 1 k=0 h[k]e j2πkn/n, n [0, N 1], where l is the number of the sampled fading path. 49

70 received. To finally reconstruct the input data at the UWB transmitter, D is passed trough a de-interleaver, a Viterbi decoder and a de-scrambler, as shown in Figure UWB Channel Model For proper system design and to quantify the impact of multipath propagation, the characteristics of the UWB fading channel are captured in channel models [Rap01]. Figure 2.8 shows a indoor UWB channel environment. The UWB transmitted signal takes multiple paths from the transmitter to the receiver due to the reflections, diffractions and scattering when the signal impinges on walls, furniture and people. Thus, UWB signals arrive at the receiver with different amplitudes, phases, and delays. Figure 2.8: Model of the indoor UWB multipath channel To implement an adaptive radio resource management method in wireless systems requires the instantaneous channel knowledge at the transmitter [Gol05]. In quasi-static fading environments, such as typical indoor wireless channels, the slow time variation of the channel makes it feasible to implement a reverse link that sends back the channel information to the transmitter [Bel63, Bel08, DMB06]. In this thesis, the UWB channel is 50

71 assumed to be time-invariant during the transmission of an OFDM symbol. The channel gains are known perfectly at the transmitter and the receiver Saleh-Valenzuela Model Measurement and modeling of the UWB channel demonstrate that the multipath components of UWB channel tend to arrive in clusters [GJR + 04,CWM02,Mol05,Bel07]. Based on this clustering phenomenon observed in the measurements, a UWB channel model is derived from the Saleh-Valenuela (S-V) model [SV87] as shown in Figure 2.9. The multipath gain of the S-V channel model experiences the exponential decay, and the multipath components (rays) of the channel arrive in clusters. Independent fading is assumed for each cluster as well as each ray within the cluster. In S-V model, the lognormal distribution is used for the multipath gain magnitude in UWB channel model [Foe03] [GGHT07]. Figure 2.9: S-V Channel Model The total time impulse response of the time-invariant UWB multipath channel is 51

72 [Foe03] h(t) = X J M α m,j δ(t T j τ m,j ), (2.15) j=0 m=0 where α m,j = p m,j ξ j β m,j are the multipath gain coefficients (attenuation factor) which denotes the amplitude of multipath components. The amplitude of the multipath components are subjected to log-normal distribution. The parameter p m,j is equiprobable +/ 1 to account for signal inversion due to reflections. The parameter ξ j reflects the fading associated with the jth cluster, and corresponds to the fading associated with the mth ray of the j-th cluster 8. In (2.15), ξ j β m,j is given by ξ j β m,j = 10 Normal(µ m,j,σ 2 1 +σ2 2 ) 20, (2.16) where σ 1 and σ 2 is the standard deviation of cluster and ray log-normal fading term (db), respectively 9, and µ m,j is expressed as µ m,j = 10ln(Ω 0) 10 T j 10 τ m,j Γ γ ln(10) (σ2 1 + σ2)ln(10) 2, (2.17) 20 where Γ and γ are the cluster and ray decay factor, respectively. Moreover, in (2.15), T j is the delay of the jth cluster, τ m,j is the delay of the mth multipath component relative to the jth cluster arrival time (τ 0,j = 0). The parameter X represents the log-normal shadowing, i.e., X = 10 Normal(0,σ2 x ) 20, which models the large scale shadowing effect, where σ x is the standard deviation of log-normal shadowing term for total multipath realization (db). Figure 2.10 depicts the log-normal probability density function of X. The center of X s distribution is the value of the averaged amplitude gain when the UWB transmitter and receiver are within 2-meter communication range. 8 Since the actual energy of multipath propagation will only be accounted for when calculating the link budget, the total energy contained in the terms α m,j is normalized to unity, i.e., M 1 J 1 m=0 j=0 α m,j = 1 9 or ξ j β m,j = 10 µ m,j +n 1 +n 2 20, where n 1 = Normal(0, σ1) 2 and n 2 = Normal(0, σ2) 2 are independent and correspond to the fading on each cluster and ray, respectively, E[ ξ j β m,j 2 ] = Ω 0 e T j Γ Ω 0 is the mean energy of the first path of the first cluster. e τ m,j γ, where 52

73 45 Histogram of Occurrences of the Amplitude Gain Number of Occurrences Amplitude Gain x 10 3 Figure 2.10: Histogram of Occurrences of the Amplitude Gain X The distribution of cluster arrival time and the ray arrival time are Poisson distributions, and given by, respectively p(t j T j 1 ) = Λe Λ(T j T j 1 ), j > 0 p(τ m,j τ (m 1),j ) = λe λ(τ (m 1),j τ m,j ), m > 0. In summary, there are the following key parameters that define the model: Λ = cluster arrival rate in GHz; λ = ray arrival rate in GHz, i.e., the arrival rate of path within each cluster; Γ = cluster decay factor (time constant, nsec); γ = ray decay factor (time constant, nsec); 53

74 σ 1 = standard deviation of cluster lognormal fading term (db); σ 2 = standard deviation of ray lognormal fading term (db); σ x = standard deviation of lognormal shadowing term for total multipath realization (db) The parameters described above are derived by several primary parameters which can characterize the UWB indoor channel which include the following [Foe03]: Mean excess delay, RMS delay spread, and Number of multipath components (defined as the number of multipath arrivals that are within 10 db of the peak multipath arrival). Figure 2.11 demonstrates the concept of mean excess delay, maximum excess delay and rms delay spread. Figure 2.11: Example of an indoor power delay profile, mean excess delay, maximum excess delay and rms delay spread [Rap01]. Excess delay denotes the time difference between an arrived multipath replica and the first arrived signal. The mean excess delay represents the expected excess delay, and the maximum excess delay is the time difference between the last arrived multipath replica which is higher than the receiving power threshold. The Root Mean Square (RMS) delay spread denotes the standard deviation of the excess delay. 54

75 Four different UWB channel models (CMs) are modeled based on the measurements of the primary parameters above [Foe03], they are CM1: Line-of-sight (LOS) with a distance between transmitter and receiver of 0-4 meters, CM2: Non Line-of-sight (NLOS) for a distance 0-4 meters, CM3: NLOS for a distance 4-10 meters, CM4: an extreme NLOS multipath channel. The corresponding model parameters derived from the measured channel characteristics are shown in Table 2.1. As an example, the discrete time impulse responses of the CM1 and CM3 are shown in Figure 2.12 and Figure Furthermore, the power delay profile of UWB signal is modelled by E[ ξ j β m,j 2 ] = Ω 0 e T j Γ e τ m,j γ, (2.18) where Ω 0 is the mean energy of the first path of the first cluster. The equation (2.18) reflects the exponential decay of each cluster, as well as the decay of the total cluster power with delay. For instance, the power delay profiles φ(τ) of CM1 and CM3 are represented in Figure 2.14 and Figure

76 Table 2.1: Multipath channel target characteristics and model parameters [Foe03]. Model CM1 CM2 CM3 CM4 Parameters Λ λ Γ γ σ σ σ x Model Characteristics τ mean (Mean excess delay) τ rms (rms delay spread) NP 10dB (number of paths) Measured Channel Characteristics 10 τ mean τ rms NP 10dB 35 Coherence Bandwidth (MHz)

77 2.5 x 10 3 Discrete Time Impulse Response Amplitude Gain Time (s) x 10 7 Figure 2.12: Impulse Response for CM1. The communication distance between the UWB transmitter and UWB receiver is 2 meters. The parameters for simulate the channel impulse response is referred to CM1 in Table 2.1. Amplitude Gain 2.5 x 10 5 Discrete Time Impulse Response Time (s) x 10 7 Figure 2.13: Impulse Response for CM3. The communication distance between the UWB transmitter and UWB receiver is 8 meters. The parameters for simulate the channel impulse response is referred to CM3 in Table

78 0 Average Power Decay Profile Average power (db) Delay (nsec) Figure 2.14: Average Power Delay Profile for CM1. The communication distance between the UWB transmitter and UWB receiver is 8 meters. The parameters for simulate the channel impulse response is referred to CM1 in Table 2.1. The total energy contained in the terms α m,j is normalized to unity. 0 Average Power Decay Profile 20 Average power (db) Delay (nsec) Figure 2.15: Average Power Delay Profile for CM3. The communication distance between the UWB transmitter and UWB receiver is 8 meters. The parameters for simulate the channel impulse response is referred to CM3 in Table 2.1.The total energy contained in the terms α m,j is normalized to unity. 58

79 2.4.2 MB-OFDM UWB Channel Model Given the S-V model in (2.15), the distribution of the frequency response H(n) is given by L 1 H[n] = h[k]e j2πkn/n, n [0, N 1], (2.19) k=0 where L is the number of the sampled fading path, and h[k] denotes the discrete-time UWB channel impulse response. From (2.15), h[k] is derived by h[k] = X J M α m,j δ(kt s T j τ m,j ), k [0, L 1], (2.20) j=0 m=0 where T s denotes the sampling interval as in (2.7). Authors in [SLS07] show that H[n] is in good approximation, circularly symmetric complex Gaussian distributed, which is explained by the fact that H[n] results from the superposition of many time-domain multipath components. Hence, H[n] is approximately Rayleigh distributed [Cio91], and the probability density function p( H[n] 2 ) is approximated by [ZTS07] p( H[n] 2 ) = 1 H[n] 2 E{ H[n] 2 } e E{ H[n] 2 }, (2.21) where E{ H[n] 2 } = e ϕ σx, 2 and ϕ is a constant value. This expression will is used to calculate the BER of the MB-OFDM UWB system and the interference power to the primary radio systems on the following sections. The frequency response for CM1 and CM3 are shown in Figure 2.16 and Figure The Figures demonstrate that the UWB channel is a frequency-selective fading channel. In MB-OFDM UWB system, the bandwidth of each UWB subcarrier is set to be smaller than the coherence bandwidth of the UWB channel. Hence, each UWB subcarrier experience non-selective fading. 59

80 UWB Channel Frequency Response 10 Channel Gain (db) Subcarrier Index Transmitted Frame Index Figure 2.16: UWB Channel Frequency Response of CM1. The communication distance between the UWB transmitter and UWB receiver is 8 meters. The parameters for simulate the channel impulse response is referred to CM1 in Table 2.1. The QPSK modulation is used on all the 128 subcarriers in one OFDM symbol. The duration for one frame is set to microseconds according to [Eur05]. UWB Channel Frequency Response 0 Channel Gain (db) Subcarrier Index Transmitted Frame Index Figure 2.17: UWB Channel Frequency Response of CM3. The communication distance between the UWB transmitter and UWB receiver is 8 meters. The parameters for simulate the channel impulse response is referred to CM3 in Table 2.1. The QPSK modulation is used on all the 128 subcarriers in one OFDM symbol. The duration for one frame is set to microseconds according to [Eur05]. 60

81 Furthermore, the coherence bandwidth of each UWB channel model can be computed based on the derivation of the cross correlation of H[n] [ZTS07]. The values of the coherence bandwidth are listed in Table Bit Error Rate Probability Transmit & Received Power In UWB systems, transmit power is allocated on a per MHz basis. The FCC set the peak power spectral density (PSD) for UWB must not exceed dbm/mhz. Thus, the larger the occupied bandwidth the more available transmitter power. The total transmit power can be determined by integrate the average PSD over the UWB bandwidth and the maximum value in the spectrum can not exceed regulatory limits. The use of zero padding in MB-OFDM UWB system can keep the spectral peak-to-average ratio at a very low level so as to maximize the total transmit power [BBA + 04] [Pro01]. The maximum allowable transmit power P tx (dbm) for transmitting an OFDM symbol in a sub-band is expressed as P tx = 41.3 dbm/mhz + 10log 10 (N su B sc ), (2.22) where B sc = MHz denotes the bandwidth of each OFDM subcarrier, and N su is the number of the used UWB subcarriers in the sub-band. For frequency hopping among three sub-bands, the transmit power can be increased by a factor of 3, as [Eur05] [Nek05] P txh = P tx + 10log 10 3, (2.23) The free-space path loss model is used to estimate the losses between the UWB transmitter and receiver with a direct line of sight (LOS) [DMB06]. The average path loss P L 61

82 (db) is expressed as ( ) γ fc 4πd P L = 10log 10, (2.24) c where f c = f l f h is the center frequency calculated by using the geometric mean of upper f h and lower band edge f l, and c = m/s denotes the speed of microwave propagation. The path loss exponent γ ranges from 1.7 for LOS to 4 for NLOS situations [Foe03]. Thus, the received power P rx (dbm) at the UWB antenna with a zero antenna gain is computed by P rx = P tx (dbm) P L (db) P margin (db), (2.25) where P margin is the link margin used to account for further losses anticipated in the communication link Signal-to-Noise Ratio The received instantaneous signal-to-noise power ratio (SNR) γ per subcarrier is given by [BG04] γ = α 2 E s /N 0, (2.26) E s = λ2 T 2T 0, (2.27) λ 2 = 2( M + 1) 3( M 1), (2.28) where α is the channel gain, E s is the energy of the M-ary QAM symbol on a subcarrier, N 0 = 2σ 2 denotes the power of the Gaussian distributed noise, T = T G + T 0 denotes the total OFDM symbol duration, T G is the guard interval, T 0 represents the time that is used for transmitting each symbol on the corresponding subcarrier. In addition, the PDF of γ is obtained by introducing a change of variables in the 62

83 expression for the distribution of α, p α (α), yielding [Gol05] p γ (γ) = p α( Ωγ/ γ) 2 γ γ/ω, (2.29) where γ = ΩE s /N 0 denotes the average SNR per M-ary QAM symbol on a subcarrier, and Ω = ᾱ2 is the mean-square value of α. Since the channel for each subcarrier is modelled as a Rayleigh fading channel, the distribution of the instantaneous SNR per subcarrier, γ, is computed following (2.29) by [Pro01] p γ (γ) = 1 γ ( exp γ γ ). (2.30) This distribution will be used to develop the error probability of each subcarrier in the next section. At the input of a UWB receive antenna, the receiver sensitivity SNR in (db) (i.e., the minimum input SNR required for obtaining a certain level of BER for each subcarrier) is given by SNR in = γ in = N RF (db) + SNR required (db), (2.31) where N RF represents the effective noise figure of the UWB RF part, and SNR required denotes the minimum received SNR required to achieve a desired BER in the subcarrier. Correspondingly, the minimum required received signal power P in (dbm) of an UWB subcarrier is computed by P in = N in (dbm) + N RF (db) + SNR required (db), (2.32) where N in is the noise power for an input bandwidth of B in, and is given by N in = 10log 10 ( kt B in 1mW ) = 10log kt 1Hz 10( 1mW ) + 10log 10( B in ), (2.33) 1Hz with k = J/K representing the Boltzmann constant and T = 290K denoting 63

84 the room temperature. Replacing (2.32) into (2.25), the minimum required transmitted power P txmin (dbm) for an OFDM symbol is given by P txmin = SNR required (db)+n in (dbm)+n RF (db)+p L (db)+p margin (db)+10log 10 {E[ H[n] 2 ]}, (2.34) where 10log 10 {E[ H[n] 2 ]} denotes the average fading gain of the MB-OFDM UWB channel Computation of BER In MB-OFDM UWB system, the uncoded average BER for each subcarrier is computed by 11 Pe = 0 P e (γ)p γ (γ)dγ, (2.35) where P e (γ) denotes the BER of an M-ary QAM modulated subcarrier in AWGN channel, and p γ (γ) is computed from (2.30). The BER for M-ary QAM with coherent detection is approximated as [Gol05] ( ) P b 4( M 1) 3 Mlog2 M Q γb log 2 M, (2.36) M 1 where γ b represents the average SNR per bit, and Q(x) = x ( 1 2π exp y2 2 ) dy is the one-dimensional Gaussian Q-function, defined as the complement (with respect to unity) of the cumulative distribution function (CDF) corresponding to the normalized (zero mean, unit variance) Gaussian random variable X [Rap01]. Replacing (2.36) into (2.35), the average BER for each subcarrier is shown as [SA00] 11 Each subcarrier is modulated by M-ary QAM, and the channel state information is perfectly known at the receiver. Furthermore, the transmitted symbols are independent and identically distributed (i.i.d.) with the symbol energy. 64

85 ( ) P b 2( M 1) 3 γ b log 2 M 1. (2.37) Mlog2 M 2(M 1) + 3 γ b log 2 M As illustrated in Figure 2.1, convolutional coding and interleaving are employed before M-ary QAM constellation in MB-OFDM UWB system. With convolutional code rate R c = k/n, the BER for 2-QAM and 4-QAM (i.e., BPSK and QPSK) in a subcarrier is bounded by [Pro01] P bc < 1 β d P 2 (d), (2.38) k d=d free where β b is the weighting coefficient, d denotes the Hamming distance of the convolutional code, and d free is the free distance of the convolutional code, P 2 (d) represents the pairwise-error-probability, and is given by [Pro01] P 2 (d) = Q( 2γ b R c d). (2.39) The interleaving techniques used in MB-OFDM UWB include [Eur05] Symbol interleaving: Permutes the bits across 6 consecutive OFDM symbols, enables the PHY to exploit frequency diversity within a band group. Intra-symbol tone interleaving: Permutes the bits across the data subcarriers within an OFDM symbol, exploits frequency diversity across subcarriers and provides robustness against narrow-band interferers. Intra-symbol cyclic shifts: Cyclically shift the bits in successive OFDM symbols by deterministic amounts, enables modes that employ time-domain spreading and the fixed frequency interleaving (FFI) modes to better exploit frequency diversity. With the combination of interleaving and convolutional coding, the BER performance of the UWB system would be increased comparing with that of a UWB system without bit interleaving [WiM09]. The derivation of a closed-form for the computation of the BER 65

86 is in the future work. The discussion of bit interleaved OFDM system can be referred to [CTB98]. The use of the convolutional coding and interleaving will enhance the BER performance of the MB-OFDM UWB system [Eur05]. However, Chapter 4 and 5 will demonstrate that the employment of the coding techniques will not affect the design of the spectrum efficiency maximization algorithm, because the coding gain 12 acts as a scaling factor to each of the UWB subcarriers equally [FU98]. Furthermore, in the thesis, allocation of the subcarriers, power and bit does not depends on the applied coding technique. Radio resource management approaches which are developed based on the coding techniques are studied in [SSOL06]. 2.6 Chapter Summary This chapter described the architecture of the MB-OFDM UWB systems and the UWB channel model. The MB-OFDM scheme is analyzed. In particular, the transmission and the reception of the UWB OFDM signal are demonstrated. The use of the IFFT and FFT mechanism can not only modulate and demodulate the UWB signal, but can also be used to detect the presence of the primary wireless systems in a cognitive radio network. Chapter 3 will discuss how to integrate the cognitive radio in the UWB systems. The timedomain UWB channel model is derived from the S-V channel model with log-normal distributed channel gain. The channel gains of the UWB subcarriers in frequency domain are derived based on the analysis of the time-domain impulse response. The OFDM signal on each subcarrier effectively experiences a frequency non-selective Rayleigh fading. This feature determines the computation of the MB-OFDM UWB system s BER. Section 2.5 discussed the BER computation of each subcarrrier under AWGN and Rayleigh fading channel. Furthermore, the BER for convolutional coded subcarrier is calculated based on the PEP computation. 12 The effective coding gain of a coded modulation scheme is measured by the reduction in required or SNR to achieve a certain target error probability relative to a baseline uncoded scheme [FU98]. 66

87 Chapter 3 Cognitive UWB Radio Systems 3.1 Introduction Cognitive radio systems can sense, learn and adapt to the wireless environment. Particularly, the cognitive radio system has the learning ability to analyze sensory input, recognize patterns and modify internal behavioral specifications based on comparative analysis of the new situation [BVJK07]. The implementation of a cognitive radio system with complete learning abilities requires comprehensive research and development in many fields of electrical and electronic engineering. In the last ten years, many prototypes of cognitive radio system have been developed. Research and design of the cognitive radio devices are ongoing activities [Fet09]. Hence, cognitive radio research works focus on the spectrum management [HB07]. Measurement of spectrum utilization indicates that there are portions of the spectrum that are continuously accessed, portions that are never accessed, and portions that are accessed by a fraction of time [FCC03]. Thus, there is great potential for more efficient use of the spectrum 1. From the spectrum management prospective, cognitive radio is a radio technology that is able to complete spectrum sensing, spectrum sharing and dynamic spectrum management with transmit power control [Hay05]. 1 Moreover, in the United States, the cost of spectrum is 200 million dollars per megahertz [Fed]. 67

88 Since UWB s operating bandwidth is overlapped with wireless systems, such as WiMAX and a, Electronic Communications Committee (ECC) requires UWB system devices to continuously detect the narrowband transmissions and avoid them by reducing the transmit power or stop transmitting in the overlapping band [Ele08]. Cognitive radio is an ideal technology to be used in UWB system to avoid interfering with other wireless systems and optimize the spectrum utilization [MSB06, Lan07]. This chapter focuses on the integration of cognitive radio techniques into UWB systems for spectrum management. 3.2 Cognitive Radio Functions Cognitive radio functions are the algorithms used by the cognitive radio systems to achieve certain objectives, such as minimizing the interference to the primary users or maximizing the spectrum efficiency. Cognitive radio systems are equipped with three cognitive functions. These are: spectrum sensing, spectrum sharing and spectrum management [HB07]. Spectrum sensing consists of determining the presence or absence of the primary user in the spectrum of interest, that is, to decide whether a received signal contains the primary users signal. Spectrum sharing is a function to schedule the spectrum access among the cognitive users and the primary users. Spectrum sharing also provide guidelines for the cognitive users s use of the spectrum sensing, spectrum assignment and spectrum access methods. The spectrum management function adjusts the transmission parameters 2 to achieve a specific goal of the cognitive radio system, such as rate maximization and power minimization. Detailed descriptions of each cognitive radio function are in the following sections. 2 The parameters include transmit power, coding, modulation, packet size, etc. 68

89 3.2.1 Spectrum Sensing A cognitive radio system is able to keep track of node location, waveforms, interference level, user s usage patterns, etc. The work in this thesis is concerned with cognitive radio s spectrum sensing ability, that is, the ability to determine if a particular frequency band is occupied. The spectrum that are occupied by high-power transmitters are called black spaces, whereas unoccupied spectrum are white spaces. Furthermore, the spectrum that are occupied by low-power wireless systems are grey spaces. White space and grey space are referred to as spectrum holes [Hay05]. Once the spectrum holes are detected, the cognitive radio system will use the spectrum holes for communication. The spectrum sensing problem can be modeled by the two hypotheses: H 1 : The hypothesis that the primary user is present, H 0 : The hypothesis that the primary user is absent. In a cognitive radio network, When the primary user is active, the discrete received signal at the secondary user can be represented as y(n) = x(n) + u(n), n [1, N], (3.1) where N is the number of signal samples, which is termed hypothesis H 1, the noise u(n) is a Gaussian i.i.d. random process with mean zero and variance E[ u(n) 2 ] = σ 2 u. The primary signal x(n) is an i.i.d. random process with mean zero and variance E[ u(n) 2 ] = σ 2 x. The parameter γ r = σ 2 x/σ 2 u denotes the received SNR of the primary user under hypothesis H 1. When the primary user is inactive, the received signal is given by y(n) = u(n). (3.2) This case is referred to as hypothesis H 0. 69

90 The key parameters for developing a spectrum sensing method are [Tre68] [ZL09a]: Probability of Detection, P d : The probability of detecting under the hypothesis H 1, Probability of a False Alarm, P f : The probability of detecting that the licensed user under the hypothesis H 0, Probability of a Miss, P m : The probability of detecting the licensed user is absent under the hypothesis H 1, Detection Sensitivity: The minimum received power per unit bandwidth in dbm/mhz. The values of P F, P M and P D depend on the distribution pattern of the noise, transmitted signal and spectrum sensing methods. The value of the detection sensitivity can be determined according to the target value of P F, P M and P D. An ideal spectrum sensing method has the probability of detection P D equal to 100% while having the probabilities of false alarm P F and a miss P M equal to zero. In real application, tradeoffs are made between accuracy, sensitivity, computational complexity, sensing period, etc. Some popular signal detection techniques are used for spectrum sensing, such as matched filter detection, energy detection and feature detection [CMB04, GS08, LZPH08]. The review of sensing methods are in the following sections. For detailed performance comparison between the methods in terms of the P d, P f, and P m under a certain cognitive radio scenarios, please referred to Chapter 4 of [HB07] Matched Filter Detection Matched filter is the optimum coherent detection technique in AWGN channel. Coherent detection is a signal detection technique that uses the locally generated carrier signal to recover the received signal [TS86]. Matched filter provides the maximum SNR output when the signal x(n)) is impaired by white Gaussian noise. The matched filter detector has an impulse response equal to a conjugated and time-reversed version of x(n) in order to match to x(n). The cognitive radio system needs to store the knowledge of primary 70

91 user s signal characteristics, such as modulation scheme and packet format to perform the matched filtering. Furthermore, time and carrier synchronization is required to detect the primary user s signal [CMB04]. For example, the matched filter detector can match to the pilot signal of the a signal for signal detection, where the pilot signal includes the signal s information, such as carrier phase and frequency. In a cognitive radio system with matched filter detector, the received signal y(n) is multiplied by the unit vector in the direction of the pilot signal to produce a test statistic T (y), and T (y) is given by [LZPH08] T (y) = 1 N N y(n)ˆx(n), (3.3) n=1 where ˆx(n) denotes the unit vector in the direction of the pilot signal. The result of spectrum sensing, i.e., whether the spectrum of interest is occupied by the primary user, is determined by comparing T (y) with a threshold γ(σ 2 u), H 1, T (y) > γ(σu) 2 H 0, T (y) < γ(σu). 2 (3.4) Since T (y) is a linear combination of jointly Gaussian random variables, the probability distribution of T (y) under different hypotheses are given by [SHT04] H 1, H 0, T (y) N (0, σ 2 u/n), T (y) N (σ x, σ 2 u/n). (3.5) Thus, the probability of detection P D and the probability of false alarm P F are expressed 71

92 respectively as [SHT04] P D = P (T (y) > ɛ(n) H 1 ) ( ) (T (y) σ x )/σ u = P > (γ(σ2 u) σ x )/σ u H 1 1/N σ x 1/N ( ) (γ(σ 2 Q u) σ x )/σ u, σ x 1/N (3.6) P F = P (T (y) > ɛ(n) H 0 ) ( T (y)/σ u = P 1/N Q ( ) ɛ(n)/σ u. 1/N ) > ɛ(n)/σ u H 0 1/N (3.7) For a given target P D and P F, the minimum signal sample N is a function of γ r, and is determined by manipulating (3.6) and (3.7) as [CTB06] N 1 γ r [ Q 1 (P D ) Q 1 (P F ) ] 2, (3.8) where Q 1 ( ) denotes the inverse function the Q-function. Equation (3.8) demonstrates that the complexity of the matched filter detection is proportional to O( 1 γ r ). The O((g(n)) function gives an upper bound on a function g(n), to within a constant factor. The O((g(n)) is give by [CLRS01] O((g(n)) = {f(n) : there exist positive constant c and n 0 such that 0 f(n) cg(n) for all n n 0 } In (3.8), Q 1 (P D ) and Q 1 (P F ) are expressed as (3.9) Q 1 (P D ) = (γ(σ2 u) σ x )/σ u σ x 1/N, (3.10) 72

93 Q 1 (P F ) = ɛ(n)/σ u 1/N. (3.11) The advantage of matched filter detection is low computational complexity, and very weak signals (e.g., -136 dbm) can be detected given the number of samples N is sufficient [CTB06]. However, matched filter detection requires perfect synchronization to demodulate the primary user s signal correctly. Thus, the performance of detection is sensitive to frequency offset between the primary transmitter and cognitive radio receiver Energy Detection Coherent detection techniques is not suitable for spectrum sensing if the primary users do not share information with the cognitive radio users. A Noncoherent detector does not require a coherent local carrier to perform signal detection 3 [Gol05]. Energy detection is a common noncoherent detection technique for spectrum sensing. Energy detector is implemented by averaging the squared magnitude of the K-point FFT of the received signal over the sensing period T. The sensing period T is proportional to the number of averages N. Given a fixed point FFT, the increase of the sensing period T will improve the estimate of the signal energy 4. For the energy detector, the test statistic T (y) is given by [LZPH08] T (y) = 1 N N y(n) 2. (3.12) n=1 The sensing result is determined by comparing T (y) with the threshold ɛ(n), that is, H 1, H 0, T (y) > ɛ(n) T (y) < ɛ(n). (3.13) In an energy detector, the probability of detection P D is determined by the received 3 Coherent in this context refers to knowledge of the carrier phase [JBS02]. 4 For a 256-point FFT with 64 MHz sampling frequency, the number of spectral averages N is over 200, corresponding to T = 3.2 ms [CTB06]. 73

94 γ r, the threshold ɛ(n) and the samples number N. Thus, P D is expressed as [SHT04] P D = P (T (y) > ɛ(n) H 1 ) ( ) T (y)/σu 2 N γ r = P > ɛ(n)/σ2 u N γ r H 1 2(2γr + N) 2(2γr + N) ( ) ɛ(n)/σu 2 N γ r Q. 2(2γr + N) (3.14) The probability of false alarm P F is P F = P (T (y) > ɛ(n) H 0 ) ( ) T (y)/σ 2 = P u N > ɛ(n)/σ2 u N H 0 2N 2N ( ) ɛ(n)/σ 2 Q u N. 2N (3.15) For a given target P D and P F, the minimum N is determined by manipulating (3.14) and (3.15), as N 2 γ 2 r [ Q 1 (P F ) Q 1 (P D ) ] 2. (3.16) Thus, the complexity of energy detection is proportional to O( 1 ). γr 2 In (3.16), Q 1 (P D ) and Q 1 (P F ) are expressed as Q 1 (P D ) = ɛ(n)/σ2 u N γ r, (3.17) 2(2γr + N) Q 1 (P F ) = ɛ(n)/σ2 u N 2N. (3.18) Thus, P D and P F are related to each other by P D = Q ( Q 1 (P F ) 2N γ r 2(2γr + N) ), (3.19) 74

95 ( Q 1 (P D ) ) 2(2γ r + N) + γ r P F = Q. (3.20) 2N Compared with matched filter detection, the advantage of the energy detection is that the energy detection requires less signal information. In low-snr regime (i.e., γ r 1), the complexity of energy detection is higher than that of the matched filter detection [TS05] Feature Detection Feature detection method senses the spectrum by analyzing the spectral correlation of the received signal. The spectrum correlation is derived from the power spectral density (PSD) of a cyclostationary signal [Pro01]. A cyclostationary signal is the signal whose mean and autocorrelation function are periodic. For a cyclostationary signal x(t), the average autocorrelation function ψ(τ) is given by ψ(τ) = R x (t + τ, t) = E[x(t)x(t + τ)] = x(t)x(t + τ)p(x(t), x(t + τ))dx(t)dx(t + τ), (3.21) where x(t) is the conjugate of x(t), and p(x(t), x(t + τ)) is the joint probability density function of the pair (x(t), x(t + τ)). Since ψ(τ) is periodic, ψ(τ) is expanded by Fourier series representation as ψ(τ) = n ψ n (τ)e j2πnt, (3.22) where ψ n (τ) is the Fourier coefficient. The value of ψ n (τ) is computed by [Gar88] 1 ψ n (τ) = lim T T T 0 x(t)x(t + τ)e j2πnt. (3.23) The function ψ n (τ) is called cyclic autocorrelation function [Fet09]. 75

96 The spectral correlation function 5 is computed by calculating the Fourier transform of (3.23), as S n (f) = ψ n (τ)e j2πτ dτ. (3.24) For feature detection, the system detection model is H 1 : H 0 : S n,y (f) = S n,x (f) + S n,u (f) S n,y (f) = S n,u (f), (3.25) where S n,y (f), S n,x (f) and S n,u (f) are the spectral correlation function of y(n), x(n) and u(n), respectively. To obtain the spectral correlation function is a cognitive radio system, the following steps are performed [Ram09]. First, the feature detector divides the received digital signal x(n) into N frames, with each frame consisting of T samples (T 1/N). Next, each frame is transformed by the N-point FFT engine to produce X T = FFT (x(n)). Then, X T and its conjugate X T are multiplied to give the cyclic periodogram as S n,xt (f) = 1 T X T (t, f + n/2)x T (t, f n/2), n = 1, 2, 3,... (3.26) Passing S n,xt (f) through a moving average filter, the spectral correlation function S n (f) is obtained. Feature detector explores the received signal s spectral correlation function for spectrum sensing. However, large amounts of data analysis is required [Fet09]. Hence, peak values in the spectral correlation function is used as the test statistic T (y). The value of T (y) is computed by [Ram09] T (y) = max f S n,y (f). (3.27) 5 S n (f) is also known as cyclic spectral density function by analogy with the Fourier relationship between the autocorrelation and PSD for stationary signals [Fet09]. 76

97 The decision on the whether the primary user is present is shown as H 1 : T (y) > λ H 0 : T (y) < λ, (3.28) where λ is the threshold. If the number of observation blocks in feature detection is sufficiently large, the primary user s signal can be detected at low-snr regime (e.g., γ r = -20dB for FSK [GS08]). However, feature detection demands excessive signal processing capabilities accompanying a large amount of power consumption. The complexity of the feature detection is proportional to Nlog 2 N O(1/γr 2 ), which is significantly higher than that of the energy detection method [DXHH + 09]. Furthermore, feature detection can perform spectrum sensing only if the knowledge of the cyclic frequencies of the primary users is obtained Spectrum Sharing In cognitive radio systems, spectrum sharing is the function that provides not only the spectrum access techniques for the dynamic use of the spectrum, but also the guidelines for the use of the spectrum sensing, spectrum assignment and spectrum access methods [ALVM06]. The guidelines provided by spectrum sharing function includes the spectrum usage policies made by the regulators and the spectrum usage strategies executed by the cognitive radio system for different aims, such as minimum power consumption and maximum number of users. The dynamic spectrum access techniques and spectrum policy management are introduced below Dynamic Spectrum Access The dynamic spectrum access techniques refer to the methods that are adopted in PHY, MAC and higher protocol layers for using the available spectrum efficiently, such as minimize the interference to the primary user and maximize the spectrum efficiency. Dynamic 77

98 spectrum access schemes are categorized in terms of network architecture (centralized and distributed), spectrum sharing behavior (non-cooperative and cooperative) and spectrum access method (underlay and overlay) [ALVM06]. The centralized spectrum sharing scheme requires a centralized cognitive node (e.g., a base station or a master node) to control the spectrum sensing, spectrum assignments and spectrum access procedures. The central node collects information, such as location, power, spectrum and interference from primary and secondary users. Then, the central node applies the radio resource assignment algorithm to distribute channels to the secondary users. For example, the base station of the LTE network gathers information from the mobile nodes and dynamically assigns the OFDM subcarriers to different mobile nodes depending on the channel conditions 6 [Eri09]. The computation complexity in the central node is high, and the complexity increases when the number of cognitive users grows. The distributed spectrum access is used when there is no central node which is responsible for other cognitive node s use of spectrum. Each node in the cognitive network performs the spectrum access function on its own. The decision of how to use the spectrum is made locally in the cognitive node according to an local optimization objective. Alternatively, the cognitive nodes in the network can exchange information and decide which spectrum access strategy is the optimum one to use based on the shared information 7. The local decisions made in each cognitive node are affected by the decisions of the other nodes. A dedicated frequency or time is used for the cognitive nodes to work cooperatively [MSB06]. In cooperative spectrum sharing, cognitive nodes share information to make optimal decisions in global scale, such as maximizing spectrum utilization and minimizing interference to the primary users. Centralized spectrum sharing is a cooperative spectrum sharing scheme. Also, the distributed spectrum access can perform cooperative spectrum 6 LTE is viewed as an prototype of cognitive radio [ZM07]. 7 The shared information includes PHY, MAC and higher layer s information, such as spectrum sensing results, channel gain, battery power, medium access information, position of the node and QoS. 78

99 sharing function as discussed in the previous paragraph. In terms of spectrum sensing, a cognitive nodes in a network exchange the sensing information to detect the available spectrum with a higher probability of detection and lower probability of false alarm compared to individual spectrum sensing [LS08, LML + 07, QCS08]. In terms of spectrum assignments and access, authors [PZZ06] in demonstrate that cooperative spectrum sharing outperforms non-cooperative spectrum sharing in terms of throughput improvement and interference reduction to the primary users. Furthermore, the authors in [PZZ06] show that compared with the central spectrum access scheme, the performance degradation of using distributed spectrum access is low and the complexity is significantly decreased. In respect of spectrum access method, Figure 3.1 and Figure 3.2 depict the overlay and underlay spectrum access scheme, respectively. In overlay spectrum access, unlicensed user can opportunistically access the spectrum holes. Using efficient signal shaping or sidelobe suppression algorithms, overlay spectrum access scheme can minimize the interference to the licensed users [HH09, PY07]. Underlay spectrum access scheme allows unlicensed users to simultaneously use the spectrum with the licensed users. The transmit power of the cognitive user should be lower than the threshold, such as interference temperature in order to avoid interference. However, underlay spectrum access method increases the overall noise temperature to the licensed users. Furthermore, a strong transmit power of the licensed user will lead the analog front-end of the cognitive system to be saturate, which will bring nonlinear distortion in the cognitive systems s power amplifier [MSE08, GK08]. Figure 3.1: Overlay Spectrum Access 79

100 Figure 3.2: Underlay Spectrum Access Policy Management The policy management aims to optimize system and network performance given current spectrum activity and interference properties in space and time. Spectrum policy management refers to the development of the spectrum use polices by the policy makers, such as FCC and ECC [FCC04] [Ele08]. For example, policy makers decide how to assign frequencies to licensed, unlicensed and license free users. Also, spectrum policy management refers to the creation and dynamic use of the spectrum policies by the cognitive radio system, depending on the density of spectral activity and usages [EPT07]. The spectrum policies in this context means the strategies of spectrum access (e.g. strategies based on game theory) based on different objectives, such as maximum fairness and minimum power consumption [EPT07] Spectrum Management In cognitive radio systems, spectrum management aims to efficiently use the detected white and grey spaces (i.e. spectrum holes) while protecting the primary users from being interfered. The optimum use of the spectrum holes means to implement an optimization algorithm to achieve the objectives, such as rate maximization (i.e., spectrum efficiency maximization), interference minimization and fairness maximization [HB07]. The optimization algorithms for the radio resource allocation problems forms the foundation for dynamic spectrum management algorithms [PRSADG05]. For a specific objective, the 80

101 problem of designing an optimum spectrum management algorithm is formed into a classical optimization problem for resource allocation, such that the existing solutions to the classical resource allocation problem are adopted and developed to provide a solution to the spectrum management problem [CLRS01]. 3.3 Cognitive Radio in UWB Systems The operating spectrum of the UWB systems ( GHz) overlaps with narrowband systems, such as WiMAX, UMTS, a/n and Wireless Home Digital Interface (WHDI) [MBtBM07,Law08,DGMV06]. FCC imposes strict transmitter power limitations ( -70 dbm/mhz) on the UWB systems in order to guarantee a tolerable interference level to the primary wireless systems (i.e. licensed and license free wireless systems) when the UWB system operates simultaneously with the primary users [FCC03]. With lower than -70 dbm/mhz power emission limitations, the UWB systems cannot provide the required QoS if the interference from the primary users is high [GK08]. Furthermore, intolerable interference from the UWB system to the primary users will be generated if the transmit power of UWB users rises. ECC proposed a mechanism called Detect-and-Avoid (DAA) for UWB systems to control the transmit power in the overlapped frequency band [Ele08, Int05]. That is, a UWB device can transmit at the power level as high as dbm/mhz in the spectrum which is not occupied by the primary wireless systems, and the UWB device will reduce its transmit power or stop transmitting if the UWB device detects the presence of the primary wireless systems in the spectrum. The reduction of the transmit power in the UWB system aims to keep the interference to primary system below a certain threshold. Figure 3.3 shows the emission masks considered by ECC. Discussions in Section 3.2 indicate that the cognitive radio technique can be integrated in UWB systems for spectrum sensing and adaptive power control. Furthermore, cognitive radio provides optimized spectrum management functions for the UWB systems to increase the spectrum efficiency, 81

102 54 J.R. Foerster et al. reduce the power consumption, enhance the BER performances, etc. [GZ05]. Comparison between Possible Spectral Masks Long term DAA required Possible harmonized spectrum Power Spectral Density (dbm / MHz) No DAA near-term 70 vs. 85 dbm/mhz OOB still being debated for GHz in Europe US Outdoor Mask No DAA Required Possible Japanese Mask Possible EU near-term mask Frequency (MHz) Fig Proposed UWB emission masks being considered in Europe and Japan Figure 3.3: UWB emission masks considered in Europe [GK08] are also in the process of developing rules, including Canada, Korea, China, and others. Cognitive From a UWB UWB industry Transceiver perspective, having some harmonized spectrum to allow single implementations to be used around the world with a part of the spectrum Figure which3.4could depicts be the usedarchitecture as a control ofchannel cognitivetomb-ofdm help identify UWB the transceiver. location would Compared be a useful goal. It remains to be seen if this will happen. with the UWB transceiver without cognitive radio engine 8, two hardware modifications at the UWB receiver side are made [MTBMB07]. One is referred to the low noise amplifier Interference Modeling (LNA) that is used to strengthen the received signal. The power of primary users signals are Clearly, much higher proper than interference that of the analysis UWB user, and which modeling will lead is critical to unlinear for distortion determining in LNA. viable UWB regulations both to ensure existing services are protected from harmful Thus, interference the original andlna to ensure is changed fair access to antolna that spectrum whose dynamic from UWB rangedevices is wideunder enough re-talistic operating conditions. The first question which usually arises is how to model handle the UWB the power interference range of given primary the users range signals. of UWB Another waveform modification options. The is made simplest in the automatic model isgain to just control assume (AGC). the Since, UWB interference the transmit power looks like leveladditive of UWBwhite is very Gaussian low 9, the noise (AWGN). However, this model is only valid for UWB systems with a pulse AGC repetition that israte set greater for measuring than or UWB equal to signals the bandwidth cannot detect of the the victim primary narrowband users signals. system [16]. In order to illustrate this, Fig shows the uncoded probability of error Hence, the AGC is adjusted according to the number of bits available in the analog-todigital repetition converter frequency (ADC), toso thethat victim the UWB bandwidth receiver (denoted with new as NAGC p in the can figures) detect aand wide for a victim narrowband system as a function of SIR for different ratios of the pulse bipolar modulation for the UWB pulses. In this case, the AWGN approximation to variety the interference of power levels. is fairly Figure accurate 3.5 shows until the thepulse transfer repetition function frequency of the AGC becomes for cognitive much lower than the victim bandwidth. UWB system at 3.3GHz. In Figure 3.5, the linear range of detection is limited to 25 db. As another example to illustrate the impact of a different modulation scheme, Fig shows the inference comparison with AWGN for a binary PPM system. In this 8 As shown in Figure 2.1 and 2.2. case, since the modulation is a non-zero mean modulation scheme, it will have 9 The transmit power limits of UWB systems, i.e., dbm/mhz, is close to the white Gaussian noise floor. 82

103 Received Singal Input Data cos(j2 f c t) Pre-select Filter LNA sin(j2 f c t) Time-Frequency Kernel Scrambler Convolutional Encoder/ Puncturer LPF LPF Bit Interleaver ADC ADC AGC Synchronizatio n/remove Zero Padding AGC Constellation Mapping IFFT FFT Notch Filter Constellation De-mapping Deinterleaver Adaptive Demodulator Spectrum Sensing Cognitive Algorithm Cognitive Engine Zero Padding/ Guard Interval DAC Time-Frequency Kernel exp(j2pf c t) Viterbi Decoder Transmitted Singal Multipath Fading Channel Descrambler Output Data Figure 3.4: Integration of cognitive functions into the MB-OFDM UWB systems 83

104 Measured Measured Value (dbm) uncalibrated AGC Gain Max Bin Index (b) Linear Range Power of Sinusoidal Input (dbm) AGC Gain = Max 12 db Figure 3.5: Transfer function energy (c) detection at 3.3 GHz [MTBMB07] Fig. 4. (a) Detection Engine implemented on-chip. The DAA functionality Cognitive is implemented UWB on a Network UWB RF/digital baseband chip fabricated in TSMC 0.13um process technology. The chip contains 2 RF/ADC receiver chains, operating at 1.2V and measures 18mm 2 in silicon area. The DAA relevant Network area (FFT/Notch Architecture filter) is around 1mm 2. (b) Spectrum capture of a -81dBm tone (c) Energy Detection transfer function at 3.3 GHz estimation proc can be determi we need to rep with an averag to ignoring the of WiMax sign spurious tones. 3) Detecting narro Some WiMax small as 1.25M to detect when carriers. To allo to average acro detection capab with narrowban 4) Dealing with th the effect on t and the signal compensated fo 5) Bin Size: Sinc dia standard, t 4.125MHz. Thi easier to detect 6) Automatic Gai the transfer fun presence of the frequency spec The cognitive UWB network is modeled as an Ad Hoc based Wireless Personal Access 3 The spurious tone on stage in the RF. Network (WPAN) in a indoor wireless environment. Figure 3.6 shows several cogntive UWB networks overlap in space with the primary users networks in a indoor area. The cognitive UWB user and the primary users can move in and out of their own networks. For example, primary nodes can enter the cognitive UWB network or form a primary wireless network in the neighborhood of the cognitive users network. Thus, the cognitive UWB users are constantly sensing the overlapped spectrum to check the presence of the primary user. A cooperative sensing method is applied to deal with the hidden node problem and enhance the sensing performance. Coordination between UWB users is based on the PHY, MAC and higher layer protocols. Using cooperative spectrum sharing, cognitive UWB nodes can perform functions, such as monitor the aggregate interference to the primary users 10, control the admission of the UWB users access to each cognitive network and share spectrum information to optimize the spectrum efficiency. Note that these functions 10 The aggregate interference is the sum of interference power of multiple UWB users to the primary users [HH09, PY07]. 84

105 are related to each other. For example, when a new cognitive UWB node requires to join an existing cognitive network, the cognitive nodes in the network will allow the new node to join if the estimated aggregate interference is lower than the threshold. When cognitive nodes join (i.e., associate) with a cognitive network, the scale of the cognitive network will change. Thus, more constraints are imposed to the execution of the spectrum management algorithms. "# #! Figure 3.6: An example of the cognitive UWB network coexisting with the primary users network. Since the Poisson distribution is widely used to model the occupancy of the overlapped spectrum in cognitive radio networks [AT07] [YGC10], the probability that the overlapped spectrum is occupied by the primary users during a period of time follows a Poisson distribution. Chapter 4 will give a more detailed discussion of the usage probability of the spectrum. When the WiMAX technology is used in the primary users, the overlapped spectrum is from 3.40 to 3.60 GHz which covers approximately half of the subband number 1 in the MB-OFDM UWB system. The work in this thesis focuses on the design of the spectrum management algorithms 85

106 to maximize the spectrum efficiency under different network conditions. The communication protocols for the spectrum management algorithms are assumed to be agreed by the cognitive users Interference to The Primary Wireless Systems The calculation of the interference power to the primary systems depends on the spectrum sharing approaches used by the cognitive UWB users. The two spectrum sharing approaches are: underlay and overlay. Overlay spectrum sharing scheme is focused on, because a cognitive UWB system works in underlay mode may still produce un-tolerant interference to the primary users which are operating in the same frequency band [FCC03]. Analysis of the interference power of the underlay scheme is discussed in Annex D. As discussed in section 2.2, the complex envelope of the OFDM transmitted signal corresponding to one OFDM symbol is given by (2.1) s(t) = N 1 n=0 D[n]p(t)e j2πfnt, t [0, T o ]. (3.29) The low pass equivalent signal s n (t) on the n-th UWB OFDM subcarrier can be expressed as s n (t) = D[n]p(t)e j2πfnt, t [0, T o ]. (3.30) In this work, s n (t) is assume to be a wide-sense stationarity (WSS) stochastic process. Hence, the power spectrum density (PSD) of s n (t) equals to the Fourier transform of its autocorrelation function [Pro01]. The PSD of s n (t) can be given by Φ n (f) = σ2 T D[n] P (f) 2 + µ2 T 2 N 1 n=0 ( n P T ) 2 n δ(f ), (3.31) T where D[n] represents the n-th M-ary QAM symbol s amplitude, P (f) = T sinc (ft ) e jπft is the Fourier transform of p(t) according to (2.4), T denotes the duration of s(t) (including ZP and OFDM symbol period), µ and σ denote the mean and the variance of the 86

107 transmitted M-ary QAM symbol D[n]. It is reasonable to assume µ = 0 [Pro01]. Hence, (3.31) can be re-written as Φ n (f) = σ2 T D[n] T sinc (ft ) e jπft 2 = σ 2 D[n] 2 T sinc (ft ) 2. (3.32) PSD of s n (t) Interference to PU PSD of s n (t) Power Spectral Density f l f h Frequency f (MHz) Figure 3.7: PSD of the n-th UWB OFDM subcarrier The PSD of a s n (t) is illustrated in Figure 3.7. The blue area represents the power emitted from the n-th OFDM subcarrier into the spectral range of the adjacent PU s operating band (i.e., from f L to f H ) 11. The sidelobe leakage causes interference from UWB cognitive radio user to PUs, because the signals of the PUs are not orthogonal to the signal of the cognitive UWB radio system. The interference power generated from the n-th UWB subcarrier can be given by 11 In Figure 3.7, n = 0 and σ = 1 B fcl + l 2 I n,l = g n f cl B l 2 Φ n (f)df, (3.33) 87

108 where l represents the l-th primary user, g n denotes the channel gain of the k-th cognitive UWB user s i-th subcarrier, B l = f H f L represents the frequency spectrum occupied by the l-th primary user, and f cl denotes the center frequency of B l. Thus, the interference power from a UWB user to the l-th PU can be computed by I k,l = Ṅ I n,l = n=1 Ṅ n=1 B fcl + l 2 g k,n f cl B l 2 Φ k,n (f)df, (3.34) where k denotes the k-th cognitive UWB user, Ṅ is the total number of the activated subcarriers in the k-th cognitive UWB user, g k,n denotes the channel gain of the k-th cognitive UWB user s n-th subcarrier, and Φ k,n (f) denotes the PSD of the signal on the k-th cognitive UWB user s n-th subcarrier. Figure 3.8 illustrates the interference power to the primary user s working band from a cognitive UWB user. Figure 3.8 shows the UWB subcarriers have varied PSD values because different transmit power is allocated on each subcarrier PSD of multple s n (t) Power Spectral Density PSD of s 0 (t) PSD of s 1 (t) PSD of s 2 (t) PSD of s3(t) f L f H Frequency f (MHz) Figure 3.8: PSD of the a number of UWB OFDM subcarriers Then, the total interference power to the primary user from multiple cognitive UWB 88

109 users can be calculated by I l = K I k,l. (3.35) k= Cognitive UWB Functions UWB Spectrum Sensing In a cognitive UWB system, the spectrum sensing function is implemented at the receiver side. To demodulate the incoming UWB signals, the FFT engine is used in MB-OFDM UWB receiver. Section 3.2 shows that the energy detection and feature detection methods use FFT engine to sense the primary users signals. Hence, using energy detection or feature detection method in the UWB spectrum sensor can take advantage of the MB- OFDM UWB s FFT engine. Compared with feature detection, energy detection requires much lower computational complexity 12 and less information of the primary user. Thus, energy detection method is adopted in the thesis for UWB spectrum sensing. When the primary users presence is detected, the cognitive UWB system will deactivate the subcarriers in the spectrum that is occupied by the primary users. Then, the cognitive UWB system will deploy the resource allocation scheme within the remaining available spectrum. The probability that the primary user is operating (i.e., transmitting or receiving) in the overlapped spectrum determines the probability that a subcarrier can be used by the cognitive UWB system UWB Spectrum Management For cognitive mutliband OFDM UWB system, the thesis focuses on the development of the spectrum management algorithm for the objective of maximizing the spectrum efficiency. In other words, the objective is to maximize the use of the spectrum band by single or multiple cognitive UWB users in the cognitive network. The number of the 12 The complexity of the feature detection is Nlog 2 N times of energy detection, as discussed in Section

110 users, the subcarriers, and the primary users are set to K, I, and L, respectively. The spectrum efficiency maximization problem can be formulated as 13 : arg max Pk,i I K k=1 i=1 j=1 J b k,ij x k,ij (3.36) subject to, P e,k P e,k, k [1, K] (3.37) P k P mask,k, k [1, K] (3.38) K I k,l I l, k [1, K], l [1, L] (3.39) k=1 I x k,ij 1, j [1, J], k [1, K] (3.40) i=1 K x k,ij 1, i [1, I], j [1, J] (3.41) k=1 x k,ij {0, 1}, i [1, I], j [1, J], k [1, K] (3.42) where P k,i is the power allocated to the i-th subcarrier by the k-th user, b j represents the profit of allocating the j-th bit to the i-th subcarrier in the k-th UWB user, and J is the number of the data bits that are generated in the k-th UWB user. The value of b k,ij is set to b k,ij = 1. Furthermore, x k,ij indicates whether the j-th bit of the k-th user would be allocated on the i-th subcarrier, i.e., x k,ij = 0 denotes the j-th bit will not be allocated to the i-th subcarrier, and x k,ij = 1 represents the j-th bit will be allocated to the i-th subcarrier. The constraint formula (3.37) indicates that for all the users, the average BER of of each 13 The objective function is for the transmission on the sub-band 1 of mutliband OFDM UWB system during one OFDM symbol period. 90

111 user should be kept below an average BER threshold. In (3.37), P e,k is the average BER of the k-th user, and P e,k denotes the average BER threshold of the k-th user. The constraint formula (3.38) shows that the average transmit power allocated on each subcarrier in a user should be kept below a certain threshold, P k denotes the average transmit power of the k-th user, and P mask,k represents the threshold of the average transmit power for the k-th user. In (3.39), I k,l is the interference power generated from the k-th cognitive UWB user to the l-th primary user, and the I l denotes the interference threshold of the l-th primary user. This constraint (3.39) shows that the aggregate interference from the cognitive UWB users to the each of the primary user is limited to a certain interference threshold. Furthermore, (3.40) illustrates that the j-th bit can only be allocated to one subcarrier or discarded due to the violation of the constraints, and (3.41) show that the i-th subcarrier can only be occupied by no more than one UWB user. A summary of the parameters are shown in Table 3.1. Parameter Spectrum Efficiency Maximization Problem I Number of the available subcarriers, I Z and I 0. J Number of the bits generated in each UWB user, J Z and J 0. K Number of the UWB users in the cognitive UWB network, K Z and K 2. L Number of the primary users in the cognitive UWB network, L Z and L 0. P k,i Power (in dbm) allocated to the i-th subcarrier by the k-th user, P k,i R. b k,ij Profit of allocating the j-th bit to the i-th subcarrier in the k-th UWB user, b k,ij = 1. x k,ij Parameter that indicates whether the j-th bit would be allocated on the i-th subcarrier, x k,ij {0, 1}, i, j, k. P e,k Average BER of the k-th user, P e,k (0, 1]. P e,k Average BER threshold of the k-th user, P e,k = P k Average transmit power (in dbm) of the k-th user, P k R. P mask,k Threshold of the average transmit power (in dbm) for the k-th user, P mask,k R. I k,l Interference power (in dbm) generated from the k-th cognitive UWB user to the l-th primary user, I k,l R or I k,l. I l Interference threshold (in dbm) of the l-th primary user, I l R. Table 3.1: Parameters in Spectrum Efficiency Maximization Problem 91

112 3.4 Chapter Summary Cognitive radio aims to provide the wireless systems the ability to optimize the operating parameters according to the varied wireless environment. In the near future, the cognitive radio systems with learning abilities will be developed. The implementation of the learning functions requires comprehensive studies and research in many areas. In recent years, developing adaptive algorithms for using the radio spectrum with high efficiency is viewed as an important aspect of cognitive radio technology. This chapter reviewed the cognitive radio functions for the cognitive users to opportunistically access to the spectrum holes. The cognitive radio functions include spectrum sensing, spectrum sharing and spectrum management. Since the UWB systems overlap with other wireless systems (e.g., WiMAX, UMTS, and a/n) in operating frequencies, cognitive radio can be used by the UWB system to increase the spectrum efficiency and mitigate the interference to the primary wireless systems. The implementation of cognitive radio technologies in UWB system was also discussed. Energy detection method is adopted for the UWB system to sense the wireless environment. The work in this thesis focuses on developing an spectrum management algorithm for the cognitive mutliband OFDM UWB sytem to maximize the spectrum efficiency. The spectrum maximization problem is formulated as a constrained optimization problem. The problem can be solved in either performance-oriented or complexity-oriented way. The next chapter will give a comprehensive analysis of solutions in both ways and determine which method is more suitable for implementing cognitive radio in UWB systems. 92

113 Chapter 4 Spectrum Efficiency Analysis in Cognitive UWB Systems 4.1 Introduction Spectrum efficiency is the ratio between the transmitted information (bits per second) and the used spectrum resource (i.e., bandwidth in Hertz) [FCC03]. In a cognitive MB-OFDM UWB system, radio resource allocation algorithms are designed to provide the maximum spectrum efficiency in different network architectures 1. In this chapter, research scenarios are presented to represent different UWB network architectures. The classification of the scenarios is based on two parameters: the number of the UWB users and the number of the nearby primary users 2. In each scenario, the spectrum efficiencies achieved by the existing resource allocation algorithms are analyzed. The existing algorithms are modified to facilitate the algorithms implementation in the UWB systems. The modification is made according to the formulation of the spectrum efficiency maximization problem in the previous chapter. The results of the analysis provide insight to enable guidelines for the new optimization algorithms design in the next chapter. 1 As discussed in Section The word nearby means that the distance between the cognitive UWB nodes and the primary nodes is small so that the cognitive nodes may interfere with the primary nodes [DK09]. 93

114 4.2 Research Scenarios The cognitive UWB radio network is categorized in two modes, they are the single user mode and the multiuser mode. In the both modes, the primary nodes are assumed to move around the neighborhood of the cognitive UWB nodes, which means that the cognitive UWB nodes will interfere with the primary nodes when the primary nodes are close to the cognitive UWB network. In this case, the cognitive functions, i.e., spectrum sensing, spectrum sharing and spectrum management, will be implemented to sense the overlapped spectrum and use the available spectrum as efficient as possible 3. The spectrum efficiency of the cognitive UWB nodes is significantly affected by the algorithms used by the cognitive functions. In this chapter, the spectrum efficiency is analyzed by applying the existing radio resource management algorithms in spectrum sensing and spectrum management functions. For the spectrum sharing function, the overlapped spectrum access is adopted since the work in this thesis is concerned with the high-speed application of the cognitive UWB systems. For single and multiuser modes, many existing algorithms discussed in Section (i.e., literature review) are based on greedy algorithm to maximize the spectrum efficiency. The analysis of this chapter focuses on the study of the spectrum efficiency that is achieved by using the existing algorithms in the single user mode. As a summary, the research scenarios are presented below, as 4 : Single User Mode Without PU 5 : There is one pair of UWB nodes communicating with each other. No primary node is activated nearby. All the spectrum is available to the UWB user. With PUs: There are primary nodes which are activated near the single user UWB network. The primary nodes are assumed to use the WiMAX as the 3 The available spectrum includes the non-overlapped spectrum and the overlapped spectrum which is not temporarily occupied by the primary nodes. 4 The words node, user and device are equivalent in the contexts, such as a UWB node/user/device, a cognitive node/user/device and a primary node/user/device. 5 PU: primary user 94

115 PHY technology. The sub-band 1 of the UWB system ( GHz) is overlapped with the WiMAX users from 3.40 GHz to 3.60 GHz. Multiuser Mode Without PU: Multiple pairs of UWB nodes exist in the network without the primary node nearby. With PUs: There are primary nodes operating near the multiuser UWB network. Figure 4.1 depicts the relationships between the scenarios.! Figure 4.1: Relationships between the scenarios Single User Mode Figure 4.2 and Figure 4.3 depict the single user mode without and with primary users operating nearby, respectively. The overlay spectrum access scheme is adopted in the cognitive UWB systems, i.e., the cognitive UWB users can access the overlapped spectrum when no primary users transmission or reception is detected in the spectrum. Table 95

116 4.1 shows the parameter settings in each scenario according to the objective function and constraints from (3.36) to (3.42). The definition of each parameter is in Table 3.1. Primary User Cognitive UWB Node Primary User Cognitive UWB Node Cognitive UWB Network Primary User Primary Users Network Boundary of Cognitive UWB Network Boundary of Primary Users Network Figure 4.2: An Example of the coexisting networks in the single user mode without PU Primary User Primary User Primary User Cognitive UWB Node Cognitive UWB Node Primary User Cognitive UWB Network Primary User Primary Users Network Boundary of Cognitive UWB Network Boundary of Primary Users Network Figure 4.3: An Example of the coexisting networks in the single user mode with PUs 96

117 Single User Mode Descriptions Without PU: There is one pair of UWB nodes in the UWB network with no primary node activating nearby. With PUs: There are primary nodes which are activated near the single user UWB network. Parameter Without PU With PUs I I = 128 I 128 J J Z and J 0. J Z and J 0. K K = 2. K = 2. L L = 0. L 1. P k,i P k,i R. P k,i R. b k,ij b k,ij = 1. b k,ij = 1. x k,ij x k,ij {0, 1}, i, j, k. x k,ij {0, 1}, i, j, k. P e,k P e,k (0, 1]. P e,k (0, 1]. P e,k P e,k [10 6, 10 3 ]. P e,k [10 6, 10 3 ]. P k P k R. P k R. P mask,k P mask,k = 9.51 dbm. P mask,k = 9.51 dbm. I k,l I k,l. I k,l = I i=1 B k,ilφ k (f)df. I l I l = 0. I l R. Table 4.1: Descriptions and Parameters Settings of Single User Mode Parameter Spectrum Efficiency Maximization Problem I Number of the available subcarriers, I Z and I 0. J Number of the bits generated in each UWB user, J Z and J 0. K Number of the UWB users in the cognitive UWB network, K Z and K 2. L Number of the primary users in the cognitive UWB network, L Z and L 0. P k,i Power (in dbm) allocated to the i-th subcarrier by the k-th user, P k,i R. b k,ij Profit of allocating the j-th bit to the i-th subcarrier in the k-th UWB user, b k,ij = 1. x k,ij Parameter that indicates whether the j-th bit would be allocated on the i-th subcarrier, x k,ij {0, 1}, i, j, k. P e,k Average BER of the k-th user, P e,k (0, 1]. P e,k Average BER threshold of the k-th user, P e,k = P k Average transmit power (in dbm) of the k-th user, P k R. P mask,k Threshold of the average transmit power (in dbm) for the k-th user, P mask,k R. I k,l Interference power (in dbm) generated from the k-th cognitive UWB user to the l-th primary user, I k,l R or I k,l. I l Interference threshold (in dbm) of the l-th primary user, I l R. Table 4.2: Parameters in Spectrum Efficiency Maximization Problem 97

118 4.2.2 Multiuser Mode Figure 4.4 and Figure 4.5 show the multiuser mode without and with primary users operating nearby, respectively. The spectrum sharing scheme adopted in the cognitive UWB systems is overlay spectrum access. Table 4.3 shows the parameter settings in each scenario. Primary User Cognitive UWB Node Primary User Cognitive UWB Node Cognitive UWB Node Cognitive UWB Network Cognitive UWB Node Primary User Primary Users Network Boundary of Cognitive UWB Network Boundary of Primary Users Network Figure 4.4: An Example of the coexisting networks in multiuser mode without PU Cognitive UWB Node Primary User Cognitive UWB Node Cognitive UWB Node Primary User Primary User Cognitive UWB Node Primary User Cognitive UWB Network Primary User Primary Users Network Boundary of Cognitive UWB Network Boundary of Primary Users Network Figure 4.5: An Example of the coexisting networks in multiuser mode with PU 98

119 Multiuser Mode Descriptions Without PU: Multiple pairs of UWB nodes exist in the network without the primary node nearby. With PUs: There are primary nodes operating near the multiuser UWB network. Parameter Without PU With PUs I I = 128 I 128 J J Z and J 0. J Z and J 0. K K 2. K 2. L L = 0. L 1. P k,i P k,i R. P k,i R. b k,ij b k,ij = 1. b k,ij = 1. x k,ij x k,ij {0, 1}, i, j, k. x k,ij {0, 1}, i, j, k. P e,k P e,k (0, 1]. P e,k (0, 1]. P e,k P e,k [10 6, 10 3 ]. P e,k [10 6, 10 3 ]. P k P k R. P k R. P mask,k P mask,k = 9.51 dbm. P mask,k = 9.51 dbm. I k,l I k,l. I k,l = I i=1 B k,ilφ k (f)df. I l I l = 0. I l R. Table 4.3: Descriptions and Parameters Settings in Multiuser Mode Parameter Spectrum Efficiency Maximization Problem I Number of the available subcarriers, I Z and I 0. J Number of the bits generated in each UWB user, J Z and J 0. K Number of the UWB users in the cognitive UWB network, K Z and K 2. L Number of the primary users in the cognitive UWB network, L Z and L 0. P k,i Power (in dbm) allocated to the i-th subcarrier by the k-th user, P k,i R. b k,ij Profit of allocating the j-th bit to the i-th subcarrier in the k-th UWB user, b k,ij = 1. x k,ij Parameter that indicates whether the j-th bit would be allocated on the i-th subcarrier, x k,ij {0, 1}, i, j, k. P e,k Average BER of the k-th user, P e,k (0, 1]. P e,k Average BER threshold of the k-th user, P e,k = P k Average transmit power (in dbm) of the k-th user, P k R. P mask,k Threshold of the average transmit power (in dbm) for the k-th user, P mask,k R. I k,l Interference power (in dbm) generated from the k-th cognitive UWB user to the l-th primary user, I k,l R or I k,l. I l Interference threshold (in dbm) of the l-th primary user, I l R. Table 4.4: Parameters in Spectrum Efficiency Maximization Problem 99

120 4.3 Spectrum Efficiency Analysis Compared with other narrowband wireless multicarrier systems such as WiMAX and a/n, the features of the MB-OFDM UWB system include the low transmit power ( dbm/mhz), the wide operating frequency (7.5 GHz), and the multiband OFDM scheme. To efficiently use the spectrum resource, many radio resource allocation algorithms were developed for the narrowband systems, such as Hughes-Hartogs algorithm and Chow s algorithm [HH87] [CCB95]. The Hughes-Hartogs algorithm is the integer bit allocation version of the water-filling algorithm which is based on greedy algorithm, and the Chow s algorithm is developed by defining a useful parameter called the SNR gap 6 [CCB95]. When the number of bits allocated to the subcarriers in a multicarrier system is limited to integer value, the spectrum efficiency achieved by the Hughes-Hartogs algorithm can serve as an upper bound for other power/rate allocation algorithms, while Chow s algorithm can achieve a slightly lower spectrum efficiency with a significantly lower algorithm complexity [HB07]. Hence, many recently (i.e., from 2005) proposed radio resource allocation algorithms for the multicarrier wireless systems are developed based on Hughes-Hartogs or Chow s algorithm [ZL09b] [BHB08] [WZK07]. However, due to the characteristics of the UWB system, the performance of these two algorithms in terms of spectrum efficiency will be different from the narrowband systems. For spectrum management in a cognitive UWB system, the spectrum efficiency achieved by the Hughes-Hartogs algorithm and the Chow s algorithm are modified and analyzed in this section. In a cognitive UWB system, another contributor to the spectrum efficiency performance is the spectrum sensing scheme. In the UWB system, different applications have different priorities to access the spectrum and have different amount of time for data transmission after having the access to the spectrum. The time for data transmission is called transmission opportunity (TXOP) [WiM09]. The spectrum sensing is assumed to be ex- 6 The SNR gap is the parameter to compute the difference between the Shannon capacity of the multicarrier system and the practical achieved data rate of the system [FU98]. 100

121 ecuted at the start of every TXOP. Thus, the time used for spectrum sensing determines the time for data transmission. Since energy detection method is adopted for the spectrum efficiency analysis, the spectrum sensing time will be a major factor that affects the spectrum efficiency which is obtained by the spectrum management algorithms. Hence, the spectrum sensing time is analyzed for the cognitive UWB radio system Summary of Assumptions To facilitate the spectrum efficiency analysis, assumptions are made in this thesis to reduce the complexity of the system level study and concentrate the analysis on the performance of the existing radio resource allocation algorithms. The assumptions are made with respect to the cognitive UWB users, the cognitive UWB network, the primary users, and the wireless channel mode. The assumptions are listed below, as Assumptions for cognitive UWB users A cognitive UWB user is equipped with one transmitter and one receiver, and the buffer capacity of each UWB user is infinite. Each cognitive UWB user has a linear data source which can produce data bits constantly. Cognitive users have lower priority than the primary users. A cognitive UWB user senses the overlapped spectrum at the start of every TXOP, and the cognitive UWB user can only transmit in the spectrum when the spectrum is not occupied by the primary users, i.e., when no primary user is transmitting within the spectrum. Cognitive UWB users use energy detection technology to sense if there are primary users transmitting in the overlapped spectrum. The energy detection method is used because it has several advantages over the match filter detection and feature detection methods, such as: Can use the FFT/IFFT engine of MB-OFDM UWB system, 101

122 Lower complexity than feature detection, Less PU signal info is needed than matched filter detection. Other spectrums sensing techniques and the proposed algorithms to enhancing the spectrum sensing performance can be referred to [HB07] The spectrum sensing, spectrum sharing and spectrum management schemes are applied to a single UWB subcarrier. Assumptions for cognitive UWB network The cognitive UWB network is a WPAN ad hoc network. There is single or multiple cognitive UWB communicating pairs and multiple primary users 7. A cognitive UWB user transmits to only another cognitive UWB user at a time. There is no single-to-multiple or multiple-to-single transmission. The transmission protocol for all cognitive users is agreed to in advance. Thus, no overhead is needed for data transmission. The network operation is organized in identical consecutive frames of some fixed duration. Assumptions for primary users The primary users use WiMAX technology, i.e., IEEE a [IEE04]. For a WiMAX system, the Interference-to-Noise Ratio (INR) requirements at a WiMAX receiver is set to -6dB, and the receiver noise figure is set to 5dB. The maximum interference limit of the primary system with WiMAX is -115dBm. The detection sensitivity of of UWB system is set to -66dBm/MHz, which means that the UWB system can detect a WiMAX signal whose PSD is as low as -66dBm/MHz [MSB06]. 7 UWB user can also be called UWB node. 102

123 The probability of the primary users activation follows a Poisson distribution. Poisson distribution is widely used to model the occupancy of the overlapped spectrum in cognitive radio networks [AT07] [YGC10]. The primary user has higher priority than the cognitive UWB users, which indicates that the primary users can transmit at anytime without notifying the cognitive UWB user. Assumptions for the wireless channel Each UWB subcarrier undergoes a flat Rayleigh fading according to the discussion in Section The subcarrier gain is slow time-variant, which means that the subcarrier gain will not change within the duration of a data frame. The duration of a UWB data frame can be referred to the WiMedia specification [WiM09]. The Channel Distribution Information (CDI) is known to the cognitive UWB transmitters and receivers. Thus, each cognitive UWB user has the perfect knowledge of the subcarrier gain and the channel gain between the cognitive UWB user and the primary users. Gaussian noise power is known to the cognitive UWB users Single User Mode In the single user mode without primary users nearby, only one pair of UWB nodes is communicating with each other in the wireless network 8, and no primary node is activated nearby (scenario A). Thus, all the UWB spectrums are available to the transmitter of the two UWB nodes. For example, in band group one, the sub-band 1 to sub-band 3 are available. Under different BER threshold conditions, the spectrum efficiency analysis is conducted by applying non-adaptive (i.e. equal power allocation) and adaptive power al- 8 The distance between the two communicating nodes is set to 2 meters. 103

124 location schemes in the UWB transmitter in LOS (CM1) and NLOS (CM3) UWB channel model Equal Power Allocation For an UWB OFDM symbol, when the total available transmit power P av (in dbm) is allocated equally on each of the subcarrier in a sub-band, the transmit power on each subcarrier is (in milliwatt) P sc = 10Pav/10 N sc, (4.1) where P av is up-bounded by P tx which is computed by (2.22), and N sc is the number of the available subcarriers. Before calculating the number of bits allocated on each of the subcarrier, a table that demonstrates the minimum require power for a M-ary QAM modulation on each of the subcarrier is generated by manipulating (2.37), as 9 P k (i) = 2N 0(M 1)(1 Pe Mlog2 M 2( ) 2 M 1) 3H i log 2 (M)[1 (1 Pe Mlog2 M 2( ) 2 ] M 1), i [1, N sc ], M = 2 k, k [0, 5], (4.2) where P k (i) denotes the minimum required transmit power on the i-th subcarrier for the k-th level of M-ary QAM modulation (i.e., k = log 2 M), H i denotes the channel gain for the i-th subcarrier during the particular OFDM symbol period, and is calculated by (2.19), and P e is the convolutional coded BER threshold ranging from 10 6 to 10 3 for each subcarrier. The BER thresholds on difference subcarriers are the same. For example, Table shows the minimum required transmit power in dbm for M-ary QAM modulation on subcarriers number 1, 64 and The value of the channel gain for each subcarrier is known to the UWB transmitter by using an appropriate channel estimation technique [Gol05] [FRL08]. 104

125 Minimum Required Power (dbm) Subcarrier #1 Subcarrier #64 Subcarrier #128 BPSK QPSK QAM QAM QAM Table 4.5: Minimum Required Transmit Power for M-ary QAM Modulation on subcarriers with coded BER=10 3. Furthermore, Figure 4.6 shows the minimum required transmit power in a randomly chosen subcarrier for reliable reception of the M-ary QAM modulation under different BER limitations. Note that P k (i) is a convex function with k [WCLM99] [BV04], which provides the foundation for the use of greedy optimization algorithms in the adaptive power allocation. Required Transmit Power per Subcarrier(dBm) M ary QAM Modulation Level BER = 1e 6 BER = 1e 5 BER = 1e 4 BER = 1e 3 Figure 4.6: Required Transmit Power for the M-ary QAM modulation on a randomly chosen UWB subcarrier. A series of M-ary QAM zones Z k (i) are generated by assigning Z k (i) = [P k (i), P k+1 (i)) k > 0, (4.3) 105

126 where [ ) represents a half-open interval, and P 0 (i) = 0 means that no transmission power is required. The k-th order M-ary QAM will be used in the i-th subcarrier when the allocated power P sc Z k (i). Fig. 4.7 shows the M-ary QAM zone generation. Five M- ary QAM zones are generated for each subcarrier. For example, the allocated power P s c lies in M-ary QAM zone 3 of subcarrier 3. Thus, 3 bits are allocated on subcarrier 3. For example, the minimum required transmit power P k (3)(k = {1, 2, 3, 4}) in the subcarrier number 3 is lower than P k (2) in the subcarrier number 2 for each k-th level M-ary QAM, because the channel gain of the subcarrier number 3 is higher. Power Requirement (dbm) ZONE 4 ZONE 3 ZONE 2 ZONE 1 ZONE 0 Pt(2) Modulation Zones ZONE 4 ZONE 3 ZONE 2 ZONE 1 ZONE 0 Power Level for 16QAM Power Level for 8QAM Power Level for 4QAM Power Level for 2QAM Pt = Pav/N Pt(3) Excessive Power ZONE 4 ZONE 3 ZONE 2 ZONE 1 Pt(4) Pt(1) = 0 ZONE Subcarrier Sequence Number Channel Gain (db) Channel Gain for CM Subcarrier Sequence Number Figure 4.7: M-ary QAM zone generation over CM3 The constellation size B(i) allocated to the i-th subcarrier is determined as B(i) = kα(i), (4.4) where α(i) = {0, 1} is the allocation coefficient, and is expressed as 1 P sc Z k (i) α(i) = 0 P sc Z 0 (i). (4.5) An shown in Figure 4.7, where zero bit is assigned to subcarrier number 1 since P sc falls 106

127 into the zone-0 of subcarrier number 1, while 2 bits are assigned to subcarrier number 2 for 4-QAM because P sc falls into the zone-2 of subcarrier number 2. The resulting spectrum efficiency is calculated by R W = Nsc i=1 B(i) T s W, (4.6) where B(i) represents the number of bits allocated on the i-th subcarrier, R is the data rate of the UWB transmitter, W is the bandwidth of the sub-band on which the OFDM symbol is transmitted, and T s denotes the OFDM symbol period. The equal power allocation and the resulting spectrum efficiency (CM1(LOS) and CM3(NLOS)) are shown in Figure 4.8, Figure 4.9, Figure 4.10 and Figure The total transmit power P av is set to the maximum value as in (2.22). Figure 4.8 and Figure 4.10 illustrate that the number of the bits allocated on each UWB subcarrier is varied according to the corresponding channel gain of each subcarrier 10, where more bits are allocated on a subcarrier whose channel gain is relatively higher. Figure 4.9 and Figure 4.11 demonstrate the spectrum efficiency that is achieved under different BER thresholds. Comparing Figure 4.9 and Figure 4.11 shows the spectrum efficiency of the MB-OFDM UWB system is much higher under the same BER threshold when the UWB nodes communicate in LOS channel (CM1) than that in the NLOS channel (CM3). The reason is that in CM3, the UWB nodes transmitted signal experiences more severe channel fading than that in CM1. The ray and cluster decay factors in each channel model can be referenced in Table with BER is set to

128 Power allocation (dbm) Bits allocation Channel Gain x 10 6 Equal Power Allocation Subcarriers Subcarriers Subcarriers Figure 4.8: Equal Power Allocation in CM1 2 Spectrum Efficiency Analysis 1.8 Spectrum Efficiency (bps/hz) BER Threshold x 10 3 Figure 4.9: Spectrum Efficiency of Equal Power Allocation in CM1 from uncoded BER = 10 6 to BER =

129 Power allocation (dbm) Bits allocation Channel Gain x 10 7 Equal Power Allocation Subcarriers Subcarriers Subcarriers Figure 4.10: Equal Power Allocation in CM3 0.7 Spectrum Efficiency Analysis Spectrum Efficiency (bps/hz) BER Threshold x 10 3 Figure 4.11: Spectrum Efficiency of Equal Power Allocation in CM3 from uncoded BER = 10 6 to BER = 10 3 In summary, the flow diagram depicting the implementation of the equal power allocation is shown in Figure The pseudocode for equal power allocation is demonstrated 109

130 in Annex A. The pseudocode shows that the order of growth for equal power allocation is proportional to O(N sc ), which means that the algorithm takes linear time. Hence, the running time of the equal power allocation algorithm increases linearly with the size of the UWB subcarriers. )"&!& * +! " $+,- #$ % (.. & ' & " Figure 4.12: Flow Diagram of Applying Equal Power Allocation in The Single User Mode without PU 110

131 Adaptive Power Allocation The spectrum efficiency of the MB-OFDM UWB system can be optimized by implementing adaptive power allocation schemes. The optimum power distribution approaches based on the heuristic greedy algorithm can be applied, such as water-filling algorithm [Gal68] [CLRS01] 11. However, the water-filling algorithm tacitly assume subcarriers with infinite small bandwidth and loaded bits with infinite granularity in constellation size. One known finite-granularity multicarrier loading algorithm is the Hughes-Hartogs algorithm [HH87]. Hughes-Hartogs algorithm is based on greedy algorithm, it distributes the total available power to the subcarriers by assigning a specific bit to the subcarrier which needs the least amount of power to apply the M-ary QAM modulation on that subcarrier. By means of this, the OFDM system s spectrum efficiency is maximized. The Hughes-Hartogs algorithm is modified according to the constraint optimization problem expressed in (3.36), so as to be analyzed in UWB system. The modified Hughes- Hartogs algorithm is named as HH uwb algorithm in this section. The HH uwb algorithm generates an incremental power table. The table holds the incremental power which is needed to modulate one more bit on each UWB subcarrier. Then, a specific data bit is allocated to the subcarrier by searching the table to identifying the subcarrier which needs the minimum incremental power to modulate that data bit. The incremental power P t = { P t (i), (i [0, N 1])} needed to modulated one more bit in each subcarrier with M-ary QAM modulation is determined as P t (i) = P k+1 (i) P k (i). (4.7) For example, by manipulating Table , the table for HH uwb algorithm is generated. Table is illustrated below. 11 Water-filling algorithm for the capacity-achieving transmit spectrum is discussed in Annex C 111

132 Incremental Power (dbm) Subcarrier #1 Subcarrier #64 Subcarrier #128 BPSK QPSK QAM QAM QAM Table 4.6: Incremental Power for Modulating one bit on each Subcarrier with coded BER=10 3 In MB-OFDM UWB system, using the incremental power table as in Table can identify the subcarrier that requires the minimum incremental power to modulate one more bit on the subcarrier. The i-th subcarrier with the minimum P t (i) = min( P t ) is chosen to be allocated one more bits (associated with power allocation) when P t (i) P m. Thus, P t (i) and the number of the bits B(i) allocated to the i-th subcarrier are increased to P t (i) = P t (i) + P t (i) (4.8) B(i) = B(i) + B(i), (4.9) where B(i) = log 2 (M k+1 ) log 2 (M k ). After each iteration, the total available power P av is decreased as P av = P av J min( P t (j)), 0 j J N bits, (4.10) j where j denotes the j-th iteration, J is the maximum number of iterations, and N bits represents the number of the generated source bits. The process will be terminated when min( P t ) > min(p m, P av ). Note that in UWB system, transmit power is allocated on a per MHz basis, and the FCC set the peak PSD for UWB must not exceed dbm/mhz 12. Hence, transmit 12 As discussed in Section

133 power that is allocated on a UWB subcarrier is up bounded by P t (i) P max (i) = log 10 ( ) (dbm), (4.11) where P max (i) is the maximum allowable transmit power on a UWB subcarrier according to FCC s power emission regulation. That is, when the total transmit power P av is maximized (i.e., P av = P tx in (2.22)), the amount of transmit power that is saved from allocating to the deep fading UWB subcarriers can not be used to increase the bits allocation in the low fading subcarriers. Otherwise, FCC s spectrum mask will be violated. Therefore, the HH uwb algorithm can not fully utilize the total transmit power when P av = P tx to maximize the spectrum efficiency unless P av < P tx. Compared with equal power allocation scheme, the HH uwb algorithm can achieve higher spectrum efficiency when P av < P tx. Otherwise, the two algorithms will have the same performance in terms of spectrum efficiency. Furthermore, when P av = P tx, the use of the HH uwb algorithm can save the unnecessary power allocation on the deep fading subcarriers, which can facilitates the interference mitigation in the following scenarios. The adaptive power allocation using the HH uwb algorithm and the resulting spectrum efficiency in CM1(LOS) and CM3(NLOS) are shown in the following figures. Figure 4.13 and Figure 4.16 show that the power is allocated on each subcarrier adaptively according to the channel gain of each subcarrier, where more power is allocated on the subcarrier whose channel gain is higher. No power is allocated no the subcarriers whose channel gain is too low, such as subcarrier and In Figure 4.14 and Figure 4.17, the spectrum efficiencies achieved by using the HH uwb algorithm and equal power allocation are the same when the total transmit power P av equals to the maximum total transmit power P tx. Figure 4.15 and Figure 4.18 demonstrate that the spectrum efficiency achieved by using the HH uwb algorithm is significantly higher than that of using equal power allocation in both LOS and NLOS channel conditions when P av is 1 of P 4 tx. As an 113

134 example in CM1, when the BER threshold is low (i.e., lower than 10 4 ) 13, the spectrum efficiency achieved by equal power allocation is zero while the spectrum efficiency is 0.9 bps/hz with the HH uwb algorithm. Since the HH uwb algorithm is known as the finite-granularity based water-filling algorithm [CCB95], the spectrum efficiency that is achieved by implementing the HH uwb algorithm is viewed as an upper bound for all the adaptive power allocation algorithms. Power allocation (dbm) Bits allocation Channel Gain Subcarriers x 10 6 Hughes Hartogs Subcarriers Subcarriers Figure 4.13: Adaptive Power Allocation using the HH uwb Algorithm in CM1 13 A low BER threshold corresponds to a low-snr regime [FU98]. 114

135 Spectrum Efficiency (bps/hz) Total Transmit Power Pav = Ptx Hughes Hartogs Equal Power Allocation BER Threshold x 10 3 Figure 4.14: Spectrum Efficiency of Adaptive Power Allocation as a function of coded BER threshold using the HH uwb Algorithm in CM1 when P av = P tx Spectrum Efficiency (bps/hz) Total Transmit Power Pav = (1/4)Ptx Hughes Hartogs Equal Power Allocation BER Threshold x 10 4 Figure 4.15: Spectrum Efficiency of Adaptive Power Allocation as a function of coded BER threshold using the HH uwb Algorithm in CM1 when P av = 1 4 P tx 115

136 Bits allocation Channel Gain Power allocation (dbm) x Hughes Hartogs Subcarriers Subcarriers Subcarriers Figure 4.16: Adaptive Power Allocation using the HH uwb Algorithm in CM3. The shaded areas in power allocation figure demonstrate that the allocated power on the subcarrier is equal to zero, because the corresponding subcarriers channel gains are too low to accommodate one bit with the allocated power being below the FCC s PSD mask. Spectrum Efficiency (bps/hz) Total Transmit Power Pav = Ptx Hughes Hartogs Equal Power Allocation BER Threshold x 10 3 Figure 4.17: Spectrum Efficiency of Adaptive Power Allocation as a function of coded BER threshold using the HH uwb Algorithm in CM3 when P av = P tx 116