DIT - University of Trento

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1 PhD Dissertation International Doctorate School in Information and Communication Technologies DIT - University of Trento Cognitive Radio Combined with Ultra Wideband Technology for Spectrum-Agile Wireless Communications Xiaofei Zhou Advisor: Prof. Imrich Chlamtac University of Trento DISSERTATION COMMITTEE: Prof. Imrich Chlamtac, University of Trento Prof. Maria-Gabriella Di Benedetto, University of Rome La Sapienza Prof. Marco Chiani, University of Bologna March 2007 Copyright 2007 Xiaofei Zhou

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3 DEDICATION To my wife Jing

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5 Abstract The emerging cognitive radio system can sense and adapt to the wireless environment in which it operates. Cognitive radio with intelligent capabilities of both radio link and network layers is capable of transmitting in an optimized way across the available signal dimensions allowing a potential huge increase in the prospects for spectrum efficiency, co-existence, compatibility and interoperability among the ever-proliferating wireless communication systems and devices. It s a rather new concept, and currently, there is no consensus on the practical implementation issues. Ultra Wideband (UWB) represents an outstanding example of enabling technology for the implementation of the cognitive radio concept. As we know, UWB systems are appealing for their broadband features, their low-power noise-like signalling, which basically can be exploited in the transmission over (licensed) bands producing a controlled level of interference on existing communication systems. On the other hand, UWB will face and cause severe interference from and to nearby communication systems. In this respect, coexistence and compatibility are important open issues, demanding for innovative solutions. Cognitive radio will provide the required innovative solutions, and enable coexistence, compatibility, interference avoidance, and compliance with regulation through the attribution of UWB devices with cognitive radio capabilities. Started from this point of view, this research investigates the advantages and features of integrating the cognitive radio with the UWB technology. Research contributions include: Firstly, introducing the fundamental researches on the M-ary pulse shape modulation for PSWF (Prolate Spherodial Wave Functions) based UWB systems; Secondly, developing transmit power allocation schemes for throughput and BER performance improvement, respectively, among the orthogonal pulse waveforms in cognitive UWB radio; Thirdly, proposing spectrum adaptation techniques to get the spectrum-agile waveforms in cognitive UWB

6 radio, namely, designing a number of adaptive pulse waveforms, corresponding to the expected UWB spectrum features and achieving the required spectral notches for mitigating interference to other radio systems (e.g., primary users) for effective coexistence;fourthly, developing distributed nodes cooperation scheme in cognitive UWB radio using Space-Frequency block coding, and proposing an innovative Frequency Exchange (FE) decoupling algorithm in the UWB receiver side for the signal detection. Future research could be pursed for effective transmit power control in a decentralized network consisting of multiple cognitive UWB nodes. Future research also could include the detect techniques in cognitive UWB radio capable of sensing and monitoring the spectrum usage in frequency, time and space. Keywords [Cognitive radio, Ultra Wideband (UWB), cognitive UWB radio, pulse waveform, transmit power allocation, spectrum adaptation, spectrum-agile, spectrum notch, Space-Frequency block coding, Frequency Exchange algorithm, cooperation]

7 Acknowledgements The effort and good will of many people have enabled completion of this dissertation. My sincere gratitude goes to my wife and my parents for their always love, support, and patience over the last few years. I wish to especially thank my advisor Prof. Imrich Chlamtac for inspiring and encouraging me in the Ph.D. studies, his mentorship has helped me grow professionally and personally. I am very appreciative for the support of my dissertation committee: Prof. Maria-Gabriella Di Benedetto, and Prof. Marco Chiani. They have modeled a lesson I will gladly carry forward with me in my future work. I owe a special gratitude to Dr. Honggang Zhang in Create-Net Research Consortium. Dr. Zhang has been witness to many ups and downs in my research works. He continually stimulated my analytical thinking. His character and integrity is unparalleled. I appreciate his steady wisdom and counsel, and I am honored to have worked with him and will always cherish the friendship I have developed with him. I had the pleasure of working with a number of researchers in Create-Net. I am very grateful for the support and advice I received from Dr. Gian Mario Maggio. His consistent smile made being part of Create-Net research community a pleasure. I deeply appreciate the warmly assistance and encouragement I have received these years from Sabrina Mazzi. I very much enjoyed the chatting with Iacopo Carreras, Antonio Francescon, Palo Cauzzi, Alessandro Zorer, Federico Lenzi, Antonio Matera and Tao Chen, and many thanks for all that they have helped me.

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9 Contents CHAPTER 1: INTRODUCTION HISTORY OF COGNITIVE RADIO THE EVOLUTION OF COGNITIVE UWB RADIO THE INNOVATIVE ASPECTS AND CONTRIBUTIONS DETAILS OF RESULTING PUBLICATIONS ORGANIZATION CHAPTER 2: RELATED WORKS SSA PULSE DESIGN USING PROLATE SPHEROIDAL WAVE FUNCTIONS M-ARY PULSE SHAPE MODULATION SCHEME BASED ON PSWFS PSWF-BASED UWB TRANSMISSION USING ORTHOGONAL TERNARY CODE SETS SUMMARY CHAPTER 3: TRANSMIT POWER ALLOCATION AMONG THE PSWF-BASED PULSE WAVELETS SYSTEM MODEL OPTIMAL POWER ALLOCATION FOR CHANNEL DATA THROUGHPUT IMPROVEMENT OPTIMAL POWER ALLOCATION FOR BER PERFORMANCE IMPROVEMENT Optimal Power Allocation Scheme The Case Study SIMULATION RESULTS AND DISCUSSION SUMMARY CHAPTER 4: COGNOSPECTRUM: SPECTRUM ADAPTATION IN COGNITIVE UWB RADIO ADAPTIVE PULSE WAVEFORMS GENERATION IMPLEMENTATION ISSUES i

10 4.3. UWB ANTENNA DISTORTION EFFECT AND PRE-DISTORTION SCHEME Distortion Effect of UWB Antenna on Pulse Waveform Adaptation Pre-distortion Scheme SUMMARY...63 CHAPTER 5: DISTRIBUTED NODES COOPERATION IN COGNITIVE UWB USING SPACE-FREQUENCY BLOCK CODING COOPERATIVE SCHEME WITH SPACE-FREQUENCY BLOCK CODING IN COGNITIVE UWB RADIO DS UWB SPACE-FREQUENCY SIGNALLING MODEL RECEIVER ARCHITECTURE AND PROCESSING DESCRIPTION SFBC-MIMO Decoupling: Frequency Exchange Algorithm MMSE Rake Receiving Process SIMULATION RESULTS AND ANALYSIS SUMMARY...82 CHAPTER 6: CONCLUSIONS AND FUTURE DEVELOPMENTS...83 BIBLIOGRAPHY...86 APPENDIX A: THE DECOUPLING PROCESS...92 ii

11 List of Tables Table 1.1: Related Research Publications...10 Table 2.1: A3-bit symbol generation example by the PSM scheme 21 Table 3.1: Characteristics of the IEEE a channel model for four different scenarios.. 40 Table 5.1: Simulation Parameters...78 iii

12 List of Figures Figure 1.1: FCC indoor UWB spectral mask...6 Figure 2.1: SSA for UWB systems, matching with FCC spectral mask 14 Figure 2.2: SSA-UWB pulse wavelet generation based on PSWF (lower band, GHz) Figure 2.3: Pulse Shape Modulation scheme...21 Figure 2.4: Transmitter structure of the PSM scheme Figure 2.5: Receiver structure of the PSM scheme.23 Figure 2.6: Paradigm of parallel spreading sequences for high data rate DS-UWB 25 Figure 2.7: Parallel PSWF-based pulse transmission with Ternary complementary code Figure 3.1: Transmitter structure with power allocation scheme...29 Figure 3.2: Receiver structure...29 Figure 3.3: Throughput of the proposed scheme 1 and the equal power allocation scheme (in CM1) Figure 3.4: Throughput of the proposed scheme 1 and the equal power allocation scheme (in CM3) Figure 3.5: BER performance of the proposed scheme 2 and the equal power allocation scheme (in CM1)...43 Figure 3.6: BER performance of the proposed scheme 2 and the equal power allocation scheme (in CM3) Figure 4.1: Adaptive pulse waveform and the spectrum Figure 4.2: Effects of digital quantization (bit resolution) on the adaptive pulse shape and its spectrum characteristics iv

13 Figure 4.3: Effects of sampling frequency on the adaptive pulse shape (Spectrum Analyzer, D/A converter, 4 bits/sample, 256 samples/pulse, sampling frequency: 72 GHz)...53 Figure 4.4: Effects of sampling frequency on the adaptive pulse shape (Spectrum Analyzer, D/A converter, 4 bits/sample, 128 samples/pulse, sampling frequency: 36 GHz)...53 Figure 4.5: Effects of sampling frequency on the adaptive pulse shape (Spectrum Analyzer, D/A converter, 4 bits/sample, 64 samples/pulse, sampling frequency: 18 GHz)...54 Figure 4.6: UWB antenna prototype (K-type UWB antenna)...56 Figure 4.7: Transfer function characteristics of K-type UWB antenna (S11 parameter, return loss)...56 Figure 4.8: Transfer function characteristics of K-type UWB antenna (S11 parameter, relative phase)...57 Figure 4.9: Impulse response of K-type UWB antenna (S11 parameter)...57 Figure 4.10: Time-domain characteristics of the required pulse waveform on-the-air and the returning signal waveform reflected by K-type UWB antenna (Transfer function, S11 parameter)...58 Figure 4.11: Spectrum characteristics of the required pulse waveforms on-the-air and the returning signal waveform reflected by K-type UWB antenna (Transfer function, S11 parameter)...58 Figure 4.12: Pre-distortion scheme in overcoming the pulse waveform distortion caused by antenna, filter and even wireless channel...61 Figure 4.13: Time-domain characteristics of the pre-equalized and the required on-the-air pulse waveform...62 v

14 Figure 4.14: Spectrum characteristics of the non-pre-equalized, the pre-equalized and the required pulse waveforms after being transferred through K-type UWB antenna (on-the-air spectrum)...62 Figure 5.1: The 2-hop Space-Frequency block encoded cooperation relaying scheme...68 Figure 5.2: Frequency diversity based on multiple sub-bands in cognitive UWB radio...68 Figure 5.3: Transmit signal sequence blocks at the source node...69 Figure 5.4: Encoded signal blocks to be transmitted at the relay nodes...71 Figure 5.5: Received signal sequences at the destination node...71 Figure 5.6: The decoupler structure corresponding to a SFBCbased MIMO channel...74 Figure 5.7: The Rake processing and MMSE combing structure...77 Figure 5.8: BER performance comparisons of 2-hop SFBC encoded cooperation scheme in CM Figure 5.9: BER performance comparisons of 2-hop SFBC encoded cooperation scheme in CM Figure 5.10: BER performance comparisons of 3-hop SFBC encoded cooperation scheme in CM Figure 5.11: BER performance comparisons of 3-hop SFBC encoded cooperation scheme in CM vi

15 Chapter 1: Introduction 1.1. History of cognitive radio The term cognitive radio was coined by Joseph Mitola in [1][2]. Mitola s cognitive radio (CR) definition modelled a context and location based cognition cycle mainly at an application layer. He proposed that cognitive radio is a particular extension of software defined radio (SDR) that employs model-based reasoning about users, multimedia content, and communications context. Mitola s cognitive cycle appeared as a directed graph that includes various states such as Observe, Orient, Learn, Plan, Decide, and Act. The cycle translates the resulting decision logic output to conventional radio software to initiate tasks with specific radio resources for specified amounts of time. In his dissertation [3], Mitola described how a cognitive radio could enhance the flexibility of personal wireless services through a new language called the radio knowledge representation language (RKRL). This dissertation presents a conceptual overview of cognitive radio as an exciting multidisciplinary subject. Currently, cognitive radio is of great interest to both policy makers and technologists because of the potential for order-ofmagnitude gains in spectral efficiency. As we know, spectrum availability in current wireless communication systems is fixed by the regulatory and licensing bodies. The adopted solution, based on static frequency band allocation, is the mainstream around the world. However, regulatory bodies in various countries (including the Federal Communications Commission in the United States) found that most of the radio frequency spectrum was inefficiently utilized [4] [5]. For example, cellular network bands are overloaded in most parts of the world, but amateur radio and paging frequencies are not. According to [5], temporal and geographical variations in the utilization of the assigned spectrum range from 15% to 85%. Moreover, fixed spectrum allocation prevents rarely 1

16 CHAPTER 1: INTRODUCTION used frequencies (those assigned to specific services) from being used by unlicensed users, even when their transmissions would not interfere at all with the assigned service. However, on the other hand, the proliferation of wireless services in the recent years requires a dramatic increase in the access to the limited spectrum. Naturally, the emerging cognitive radio scenario is regarded as the most promising technical solution to the aforementioned spectrum sparse problems by allowing smart spectrum management in future wireless communication systems. Started from 2002, Defense Advanced Research Projects Agency (DAPRA) funded the next Generation (XG) program [6] in USA. The XG program is expected to develop dynamic spectrum access technologies. It aims at creating cognitive radios that sense and share the usage of spectrum, with a focus on policy-based negotiation and radio etiquettes which leverage spectrum holes that open in space, time and frequency bands. The year of 2003 proved to be a turning point for the cognitive radio researches. The FCC issued NPRM [5] on cognitive radio to discuss what CR is and what rules the FCC should impose on this fledgling technology. It aims to explore whether CR could open up competitive new wireless services through secondary or cooperative spectrum markets, i.e. reassigning underutilized spectrum in time and space. According the description of [5], by adapting its transmission or reception parameters based on cognitive interaction with the wireless environment in which it operates, cognitive radio aims at improving spectrum efficiency, capacity and fairness. This interaction may involve passive spectrum sensing or, in general, active communication and negotiation with other spectrum users based on reasoning procedures which represent the intelligence of the CR itself. As a seismic shift in information and telecommunications world, CR could potentially break the ever-serious bottleneck of limited spectrum-availability and open-up new frontiers of opportunities for wireless system designers and application developers. Moreover, CR with intelligent capabilities of both radio 2

17 link and network layers is capable of transmitting in an optimized way across the available signal dimensions allowing a huge increase in the prospects for co-existence, compatibility and interoperability among the ever-proliferating wireless communication systems and devices. In [5], four application scenarios are introduced as targets for CR technologies. First, a licensee can employ cognitive radio technologies internally within its own network to increase the efficiency of use. Second, cognitive radio technologies can facilitate secondary markets in spectrum use, implemented by voluntary agreements between licensees and third parties. For instance, a licensee and third party could sign an agreement allowing secondary spectrum uses made possible only by deployment of cognitive radio technologies. Ultimately cognitive radio devices could be developed that negotiate with a licensee s system and use spectrum only if agreement is reached between a device and the system. Third, cognitive radio technologies can facilitate automated frequency coordination among licensees of co-primary services. Such coordination could be done voluntarily by the licensees under more general coordination rules imposed by Commission rules, or the Commission could require the use of an automated coordination mechanism. Fourth, cognitive radio technologies can be used to enable non-voluntary third party access to spectrum, for instance as an unlicensed device operating at times or in locations where licensed spectrum is not in use. For the second scenario, the IEEE activity which is currently in progress is a closely relevant example. Recently, researchers noticed that the unlicensed bands (e.g., ISM and UNII) play a key role in the wireless ecosystem since the deployment of applications in these bands is unencumbered by regulatory delay sand which resulted in a plethora of new applications including last-mile broadband wireless access, health care, wireless PANs (Personal Area Networks)/LANs (Local Area Networks)/MANs (Metropolitan Area Networks), and cordless phones. This explosive success of unlicensed operations and the many advancements in technology that resulted from it, led regulatory bodies to con- 3

18 CHAPTER 1: INTRODUCTION sider opening further bands for unlicensed use. With all these facts and foundations in place, FCC released the TV band Notice of Proposed Rule Making (NPRM) [7] in May 2004, proposes to allow unlicensed radios to operate in the TV broadcast bands provided no harmful interference is caused to incumbent services (e.g., TV receivers), which can be accomplished by employing CR-based technologies. All these important events created a mindset within the IEEE that culminated in the formation of the IEEE WG for WRANs (Wireless Regional Area Networks) in November 2004 [8]. This WG has been chartered with the specific task of developing an air interface (i.e., PHY and MAC) based on CRs for unlicensed operation in the TV broadcast bands, including the requirements for incumbent service detection and protection, the techniques employed for sensing and detecting such incumbents, coexistence issues, the air interface, applications, etc. The IEEE activity is the first worldwide effort to define a standardized air interface based on CR techniques for the opportunistic use of TV bands on a non-interfering basis. It plays a key role in the evolution of CRs and its outcome will serve as foundation for many major future developments. Currently, the WG has approved its baseline document and is working on drafts. For the fourth scenario as mentioned above, especially relevant to it is the Ultra Wideband (UWB) wireless technology and devices. We will introduce it in the next section The Evolution of Cognitive UWB Radio UWB technology is regarded as a key player for broadband wireless communications in multimedia rich environment. The UWB signals by definition occupy a bandwidth in excess of 500 MHz or are such that their fractional bandwidth is greater than 20%. The UWB technology possesses several potential advantages that can be summarized as follows: (i) enhanced capability to penetrate through obstacles; (ii) high precision localization/ranging (at the centimeter level); (iii) capability to support 4

19 high data rates (>1Gbits/s) and multiple users; (iv) immunity to multipath fading and resilience to interference; and (v) supporting development of small sized and processing power-efficient devices. While UWB has generated a great deal of interest, it has also caused a number of controversies among industry, regulation and standardization bodies. As we know, The FCC has allocated the spectrum between GHz for use by ultra-wide band communication systems. Due to the unlicensed nature of this spectrum, UWB devices will coexist with both incumbent and future services that share the spectrum. Examples of incumbent services that share the same spectrum, include IEEE a devices ( GHz) and WiMax devices ( , GHz). To enable peaceful coexistence, UWB devices must be capable of detecting victim receivers and selectively controlling the emissions in the victim receiver bands, so that the coexistence and the compatibility have become critical issues. After releasing the UWB radio emission limit (i.e., spectral mask) in February 2002 [9], the FCC paved the way for the realization of coexistence with the traditional and protected wireless services by ensuring sufficient attenuation to limit adjacent channel interference. Similarly, in Europe, the European Conference of Postal and Telecommunications Administrations (CEPT) has provided recommendations for harmonizing radio spectrum usage for UWB [10]. Figure 1.1 illustrates the indoor UWB spectral mask regulated by FCC. 5

20 CHAPTER 1: INTRODUCTION Figure 1.1: FCC indoor UWB spectral mask However, it has been widely recognized that UWB signal waveform design is a quite challenging subject for complying with various spectral masks, while still achieving interference avoidance as well as efficient transmission. Researchers around the world have investigated various design methods of UWB signal optimization, aiming at achieving the expected coexistence, interference avoidance and matching with any regulatory spectral mask [11][12]. In this respect, coexistence and compatibility have become critical issues. According to FCC NPRM [5], focusing on the fourth possible application scenarios of cognitive radio, UWB communication systems represent a suitable transmission technique for implementing a cognitive radio system. Therefore, it makes senses to promote the use of the UWB technology in the context of cognitive radios. The main technical reasons can be summarized as follows: UWB radio faces/causes severe interference from/to nearby narrowband systems; therefore, it will surely benefit from utilizing CR techniques implementing col- 6

21 laborative coexistence policies. UWB is by definition an underlay technology, coexisting with the traditional narrowband non-cr devices, as an unlicensed user. It is regarded that this one is the most realistic and pragmatic scenario for introducing CR concept. Inherent capability of UWB device to observe large bandwidths, as well as intrinsic processing scalability of UWB technology makes it an ideal candidate for realizing a versatile physical layer (air-interface), adaptable to different wireless environment conditions. All these initiatives and motivations culminated in the most recent research activities focusing on the investigation of cognitive UWB radio issues [13] [14] [15] [16] [17] [18] [19] [20] [21] The Innovative Aspects and Contributions This dissertation summarizes the doctoral research we pursed that led to spectrum-agile cognitive UWB radio. The advantages and features of integrating cognitive radio with UWB technologies are investigated, in order to exploit UWB radio as an enabling technology for achieving cognitive radio through the unique attribution of UWB devices with the CR enhanced capabilities: it can easily shape the spectrum to mitigate interference into the victim receiver s band of interest. In particular, the attention is focused on the design and development of techniques for spectrumagile waveform generation devoted to impulse radio-based UWB (IR-UWB) signals, thus increasing coexistence and the efficiency in the use of spectrum resources. Then, we investigate distributed nodes cooperation in cognitive UWB radio by using Space- Frequency block coding. The first consideration of the thesis is the design of a series of core pulse wavelets. The design principle is as follows: (i) The core pulse wavelet s spectrum should be contained in a desired frequency band allocated by the FCC spectral mask or another 7

22 CHAPTER 1: INTRODUCTION spectral limitation, namely being bandwidth-limited. (ii) The core pulse wavelets should be limited to short duration with efficient energy concentration, realizing data rate as high as possible and inter-pulse-interference (IPI) as low as possible, namely being time-limited. (iii) These core pulse wavelets are preferred to be orthogonal with each other, so as to allow for linear combination of them for further designing much more complex pulse waveforms. (iv) The core pulse wavelets set is preferred be flexibly combined or extended, being capable of fitting any further wireless channel change as well as spectral mask modification by other regional regulatory committee around the world. We perform the optimized pulse wavelet design by utilizing Prolate Spheroidal Wave Functions (PSWF), and introduce the orthogonal pulse shape modulation (PSM) scheme. The second novel prospect of this thesis is to propose the optimal transmit power allocation schemes among the orthogonal UWB pulse wavelets. Considering a cognitive UWB radio environment when the transmit signal is M-ary PSWF-based pulse shape modulated, we can obtain M different eigenvalues corresponding to the M pulse waveforms after their transmission through the multipath fading channel. The mth (m=0, 1,, M-1) eigenvalue is the ratio of the combined multipath gain of the mth pulse to the noise power, representing the overall channel state for the mth pulse. Corresponding to such a cognitive UWB radio model, based on these eigenvalues, we propose two optimal transmit power allocation schemes to improve the channel data throughput and bit error rate (BER) performance, respectively. A further study is carried out to modify the pulse wavelets used in IR-UWB system. How adaptive pulse shapes can be practically generated and how the actual spectrum of the pulses can be controlled is exploited in this part. Specially, we investigate the linear combination of orthogonal PSWF based multiple UWB pulses to realize spectrum-agile waveform adaptation. Such a UWB system has cognitive radio capabilities in terms of spectral shaping and dynamically adapting to its available spectrum sources, i.e., generating several unique spectral notches to mitigate interference 8

23 into the victim receiver s band of interest, as well as satisfying any region-dependent UWB spectral emission masks. As the fourth contribution of the thesis, cooperative transmission scheme utilizing Space-Frequency block coding is introduced for distributed nodes cooperation in cognitive UWB radio communications. The proposed scheme provides efficient cooperation diversity for multiple distributed nodes in the powerlimited as well as interference-limited multi-hop environment. Although perfect timing synchronization among the multiple distributed nodes is the prerequisite in any virtual MIMO-based multi-hop communication scenario, it s a hard issue waiting for feasible resolution till now. The proposed SFBC cooperation approach makes the synchronization problem among these geographically distributed cooperation nodes unnecessary. At the receiver side, we propose a specific frequency exchange algorithm in the decoupling matrix processing unit in order to recover the MIMO channel orthogonality for the received SFBC-based UWB signals Details of Resulting Publications Table 1.1 lists papers that I have contributed to about this research, including an European patent application filed in August Table 1.1: Related Research Publications X. Zhou and H. Zhang, Cognitive Radio: Theories and Applications (in Chinese), ISBN , BUPT (Beijing University of Posts and Telecommunications) Press, Beijing, China, Feb T. Chen, H. Zhang, X. Zhou, G. M. Maggio and I. Chlamtac, CogMesh: A Cluster Based Cognitive Radio Mesh Network, 9

24 CHAPTER 1: INTRODUCTION Book chapter for Cognitive Wireless Networks: Concepts, Methodologies and Visions, ISBN: , Springer. X. Zhou, H. Zhang, and I. Chlamtac, Transmit Power Allocation among Orthogonal Pulse Wavelets for BER Performance Improvement in Cognitive UWB Radio, the 4 th Annual IEEE Consumer Communications and Networking Conference Cognitive Radio Networks Workshop (CCNC 07-CRN), Las Vegas, US. Jan X. Zhou, H. Zhang and I. Chlamtac, Transmit Power Allocation among PSWF-based Pulse Wavelets in Cognitive UWB Radio, 1st International Conference on Cognitive Radio Oriented Wireless Networks and Communications (IEEE CROWNCOM 2006), Mykonos, Greece, June, H. Zhang, X. Zhou, K.Y. Yazdandoost, and I. Chlamtac, Multiple Signal Waveforms Adaptation in Cognitive Ultra-wideband Radio Evolution, Selected Areas in Communications, IEEE Journal on, Volume 24, Issue 4, Part 1, April 2006 Page(s): F. Granelli, H. Zhang, X. Zhou, and S. Maranò, Research Advances in Cognitive Ultra Wide Band Radio and their Applications to Sensor Networks, ACM/Springer Journal on Special Topics in Mobile Networking and Applications (MONET), special issue on Ultra Wide Band for Sensor Networks, Q Page(s): X. Zhou, H. Zhang, and I. Chlamtac, Space-Frequency Coded Cooperative Scheme among Distributed Nodes in Cognitive UWB Radio, in: proc. IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC Volume 1, Sept Page(s): X. Zhou, K. Y. Yazdandoost, H. Zhang, and I. Chlamtac, Cog- 10

25 nospectrum: Spectrum Adaptation and Evolution in Cognitive Ultra-Wideband Radio, in: proc IEEE International Conference on Ultra-Wideband, ICU Sept Page(s): H. Zhang, X. Zhou, I. Carreras, S. Pera, I. Chlamtac, Z. Zhou and F. Zheng, Impulsive Direct-Sequence UWB Wireless Networks with Node Cooperation Relaying, IEEE a Jan H. Zhang, X. Zhou, European Patent (pending), Filing No , Multiple input-multiple output wireless communication system, Aug Organization This dissertation is organised in six chapters. Chapter 1 briefly discusses the history of cognitive radio, the state-of-art of the researches in cognitive radio and the motivation of the cognitive UWB radio evolution. Chapter 2 reviews the fundamental researches on the M-ary pulse shape modulation for PSWF-based UWB systems, the SSA (Soft-Spectrum Adaptation) realization in PSWF based UWB systems, and the design and utilization of orthogonal Ternary complementary code sets to improve the processing gain and the BER (bit-error-rate) performance of a MIMO-based UWB transmission in a multi-user environment with frequency-selective multi-path fading. In chapter 3, we present transmit power allocation schemes for throughput and BER performance improvement, respectively, among the orthogonal pulse waveforms in cognitive UWB radio. In this research process, we propose the water-filling algorithm to these PSWF-based pulse waveforms to optimally allocate the transmit power for channel data throughput improvement; then the theoretical analysis and the adaptive method-the steepest- 11

26 CHAPTER 1: INTRODUCTION descent algorithm are given to calculate the optimal set of the transmit power for BER performance improvement. Numerical results show that the proposed optimization schemes outperform the general equal power allocation scheme. Chapter 4 aims at designing a number of adaptive pulse waveforms, corresponding to the expected UWB spectrum features and achieving the required spectral notches for mitigating interference to other radio systems (e.g., primary users) for effective coexistence, namely, we investigate spectrum adaptation techniques to get the spectrum-agile waveforms in cognitive UWB radio. This kind of adaptive pulse waveforms is expressed by a limited linear combination of a series of core UWB pulse wavelets and their related auxiliary functions. Chapter 5 details the distributed nodes cooperation in cognitive UWB radio using Space-Frequency block coding. We have conducted the theoretical analyses and simulation on the cooperative transmission scheme utilizing Space-Frequency block coding (SFBC) for the MIMO-based cognitive UWB communications and networks, in the scenario where multi-hop relaying is necessary among the distributed nodes. In the case of using virtual MIMO relaying algorithms, the proposed new scheme makes the issue of the lack of required perfect synchronization on timing and propagation delay among the distributed nodes unnecessary. It has been further verified that the most promising perspective of this new scheme relies on its application to cognitive UWB networks in potentially providing full spatial and frequency diversity. In the final chapter of the thesis, conclusions on spectrum-agile cognitive UWB radio are given. Furthermore, the future developments of the thesis are discussed. 12

27 Chapter 2: Related Works Chapter 1 provided an introduction and brief history of cognitive radio research, and the motivation of the proposed cognitive UWB radio evolution. In chapter 2, we brief review current researches in cognitive UWB radio, and then introduce the previous works related to my Ph.D. research that have conducted by our team member Dr. Zhang, i.e., the Soft-Spectrum Adaptation (SSA) techniques [22] [23] [24]. As an introduction paper, [13] has noticed that UWB system would benefit more than other wireless systems from the collaborative coexistence that enabled by cognitive radio technology since UWB systems faces severe interferences from the nearby narrowband systems. In such a coexistence scenario, the UWB system will be operated in coordinated time slots, at coordinated frequencies, at known power levels and it will use smart antenna and coding to optimize performance. The literature [17] gives an example of how cognitive radio can help the UWB coexistence. It considers the performance of a TH- PPM (Time-Hopping Pulse Position Modulation) system in the presence of NB interference in a scenario characterized by Line- Of-Sight (LOS) propagation for the UWB transmitter-receiver link and Rayleigh distributed fading for the NB (Narrow Band) interferer. The analysis shows that at the interference frequency, the UWB transmitter and selects the best TH sequence that minimizes the impact of interference at the receiver. At the same time, the transmitted spectrum will have a minimum level around the interference frequency, thus the UWB system will not affect the NB system. The literature [18] investigates that in a UWB network, cognitive mechanism can improve the network life. In a UWB network which is centralized in one central node and all other nodes communicate with this central node, where the signal format is TH- PPM, and the active nodes in the network are affected by interfer- 13

28 CHAPTER 2: RELATED WORKS ers, by introducing cognitive capability to the central node, it can select the waveform that significantly minimizes transmit power for the active nodes. One approach for UWB spectrum shaping by employing Orthogonal Frequency Division Multiplexing (OFDM) is provided in [14] [20] [21]. The main technique is to zero out multiple tones that overlap with the victim bands in order to avoid interference. As we may see, cognitive UWB radio is just on its start-up stage, there are many areas that need to be explored. In the following chapters, we will introduce our research approaches and the contributions. N multiple sub-bands / MHz N Figure 2.1: SSA for UWB systems, matching with FCC spectral mask First, we introduce the Soft-Spectrum Adaptation technique. In the SSA-UWB scheme, adaptive and controllable division-andcombination of the multiple UWB frequency bands is utilized, adaptive to the actual spectrum requirements, as illustrated in Figure 2.1. The basis idea behind SSA-UWB is that it can maintain exchangeability among the existing and future UWB systems, 14

29 while keeping the pulse width in the order of nanosecond for high data rates SSA Pulse Design Using Prolate Spheroidal Wave Functions As we mentioned in chapter 1, the designed pulse wavelets should be time-limited as well as band-limited. We start from an arbitrary channel (e.g. kth sub-band) located under the FCC spectral mask ( GHz), which may be given in frequency domain and time domain as H ( f ) k 1, fkl, < f < fku, = { (2.1) 0, otherwise h ( t) = 2 f sinc(2 f t) 2 f sinc(2 f t), (2.2) k k, U k, U k, L k, L where f k, L and f k, U denote, respectively, the low and the high frequency of the kth sub-band. To design a core pulse waveform corresponding to the kth target sub-band, we may treat the subband as a target filter, send an arbitrary kernel function ψ k (t) through this target filter h k (t) and denote the filter output as λ kψ k (t), where λ k is an arbitrary constant factor. Then the output of this idealized impulse filter is given by k k k λ ψ () t = ψk ( τ) h ( t τ) dτ, (2.3) where ψ k (t) coincides with the kth target sub-band (spectral mask filter) and is required to have the following time-limited property pk(), t t< Tp 2 ψ k () t = {, (2.4) 0, elsewise 15

30 CHAPTER 2: RELATED WORKS where T p is the total pulse width, and p k (t) is the target pulse shape. Since ψ k (t) is designed to be time-limited and energyconcentrated over the pulse width [ T p 2, T p 2], equation (2.3) can be simplified as T p 2 λψ k k() t = ψ ( τ ) h ( t τ ) dτ. (2.5) k k T p 2 Then, the obtained sub-band wavelet can be further combined to form a more complex wavelet corresponding to arbitrary multiple sub-bands system including dual-, triple- and multiband architecture, as illustrated in Figure 2.1. The waveform expression for the multiband combination can be written as follows: ψ mul N () t = ψ (). t (2.6) The basic philosophy in our SSA-UWB pulse waveform design is contrary to the conventional approach, namely, not just trying to construct a pulse waveform in order to satisfy the FCC spectral mask, on the contrary, first starting from considering a required spectral mask in frequency domain (band-limited) and then inversely finding its corresponding wavelet in time-domain (timelimited). We may further observe that these core pulse waveforms ψ k (t) are the solutions of equation (2.7) T p 2 T p 2 k= 1 k sin W ( ) () ( ) k t τ λψ k k t = ψk τ dτ, (2.7) t τ where W k is the bandwidth of kth target sub-band, and λ k denotes the energy-concentration factor of ψ k (t) that lies in the time slot of [ T p 2, T p 2]. In fact, these pulse waveforms are also the solutions of a second-order differential equation eigenvalue problem 16

31 d dt dψ + = 0, dt 2 k 2 2 (1 t ) ( χk ckt ) ψ k (2.8) where ψ k (t) is usually defined as the Prolate Spheroidal Wave Functions [25], χ k is the eigenvalue of ψ k (t) and ck = Wk Tp 2 denotes the number of its freedom degrees according to (2.8). The simultaneous concentration of pulse energy in the time and frequency domain is described as following: α T p 2 W 2 k 2 ψ k () Ψk ( ) 2 T p 2 2 Wk k = βk = 2 2 ψ k () Ψk ( ) tdt f df tdt f df, (2.9) where Ψ k ( f ) is signal representation of ψ (t) in frequency domain. It can be found that the PSWFs ψ k (t) have the following k features for different orders of m and n: T p 2 ψ () t ψ () t dt= λδ (2.10) km, kn, m mn, T p 2 ψ () t ψ () t dt= δ (2.11) km, kn, mn. Since a close-form solution to (2.3), (2.5), (2.7) and (2.8) is difficult to be obtained, we can resort to the discretization algorithm, as mentioned in [26], to get a numerical solution. By sampling at a rate of N samples per pulse width, we can represent equation (2.5) or (2.7) as N 2 λψ [] n = ψ [ m] h [ n m], n =. (2.12) k k k k m= N Then, the numerical solution of (2.5) can be obtained by applying eigenvalue decomposition in the matrix expressed version of equation (2.12). By writing Equation (2.5) and (2.7) into vector form and applying eigenvalue decomposition to them, we can clearly see that the 17 N N

32 CHAPTER 2: RELATED WORKS various pulse waveforms ψ m (t) are eigenvectors of Equation (2.5), and the energy-concentrations λ m are the eigenvalues corresponding to various ψ m (t), where these eigenvalues can be arranged in decreasing order of λ 1 > λ2 > > λm. As mentioned above, each eigenvalue λ m represents the percentage of its corresponding pulse waveform s (i.e. its eigenvector) energy concentrated inside the desired spectral mask and pulse-width. Figure 2.2 illustrates an example of the PSWF-based orthogonal SSA-UWB pulse wavelets with different orders (order = 1, 2, 3, and 4, respectively), corresponding to the lower band from 3.1 GHz to 5.6 GHz. Note that all these pulse wavelets match with the FCC spectral mask requirement. 0.3 SSA-UWB optimized pulse wavelet generation based on PSWF Relative amplitude Time (second) x 10-9 (a) order = 1 18

33 0.4 SSA-UWB optimized pulse wavelet generation based on PSWF Relativr amplitude Time (second) x 10-9 (b) order = SSA-UWB optimized pulse wavelet generation based on PSWF Relative Amplitude Time (second) x 10-9 (c) order = 3 19

34 CHAPTER 2: RELATED WORKS 0.3 SSA-UWB optimized pulse wavelet generation based on PSWF Relative Amplitude Time (second) x 10-9 (d) order = 4 Figure 2.2: SSA-UWB pulse wavelet generation based on PSWF (lower band, GHz) 2.2. M-ary Pulse Shape Modulation Scheme Based on PSWFs The PSWF-based pulse wavelets can be applied to M-ary Pulse Shape Modulation (PSM), where more than one information binary bits are modulated and carried by one of the specific pulse wavelets. The basic idea here is to utilize the orthogonal combination property of PSWF pulses to increase data rates while decrease the number of needed pulses for required throughput. The inner-keying and outer-keying are used in the M-ary PSM scheme. Bi-phase (BPSK or QPSK) modulation is applied to the innerkeying to transmit 1 or bits in each pulse; while other more bits are transmitted by different pulse shapes, as illustrated in Figure 2.3. The pulse repetition interval (PRI) is variable and adaptive, according to the data rate requirement, the real channel conditions, and the interference environment. 20

35 Inner-keying: to transmit 1 bit by using BPSK in each pulse 00 or or 11 t PRI (adaptive) PRI (adaptive) Outer-keying: to transmit other more bits by different pulse shapes Figure 2.3: Pulse Shape Modulation scheme Table 2.1: A 3-bit symbol generation example by the PSM scheme Symbol 1st 2nd 3rd pulse 1 - pulse 2 - pulse pulse 1 - pulse 2 pulse pulse 1 pulse 2 - pulse pulse 1 pulse 2 pulse pulse 1 - pulse 2 - pulse pulse 1 - pulse 2 pulse pulse 1 pulse 2 - pulse pulse 1 pulse 2 pulse 3 The transmit structure for the M-ary pulse shape modulation is depicted in Figure 2.4, where one binary information bit is modulated and carried by one of the orthogonal pulses; thus the PSM scheme needs only K pulses for a symbol of K-bits, while the 21

36 CHAPTER 2: RELATED WORKS conventional PSM scheme generally needs 2 K -1 pulses. The corresponding modulation alphabets of the proposed PSM scheme is given in Table 2.1 for 3-bit symbol whereas just 3 pulse waveforms are necessary. Generally, the transmitted M-ary (M=2 K ) PSM signal for user n is given as K 1 ( n) ( n) ( n) ( n) ( n) s () t = p b ψ ( t i K T mt c T ), ik + m m f m ik c (2.13) i= m= 0 where p is the transmit signal power, b ( n) is the binary information data sequence for user n, and it is consisted of a train of i K + m i.i.d. data bits that take the values of ±1 with equal probability. ( n) ψ m with width T p and order m are the PSWF-based pulse wavelets applied to the M-ary pulse shape modulation. All these pulse shapes are normalized to have totally combined unit power. T m is the average period between two consecutive pulses (T m T p ), namely pulse repetition interval (PRI), T f is the frame repetition time of the pulse sequences for all users, and denotes the integer part. To avoid catastrophic collisions due to multiple accesses, the ith orthogonal pulse group undergoes an additional time shift ( n ) of c i K T in which c ( n ) c i K is the user-specific time-hopping (TH) code and T c is the chip width of each TH code. At a receiver as shown in Figure 2.5, the received pulse sequence signals for the nth user are generally distorted by the transmission channel and can be given as ( n) ( n) r t s t n t () = () + (), (2.14) where n(t) is the zero mean additive white Gaussian noise. Assuming that the ith orthogonal pulse sequence is transmitted, the jth decision statistics after a coherent pulse shape detection and demodulation at the receiver can be expressed as 22

37 Figure 2.4: Transmitter structure of the PSM scheme Figure 2.5: Receiver structure of the PSM scheme 23

38 CHAPTER 2: RELATED WORKS ( n ) E + n (), t j = i ( n) ( n) ( n) i i D = r () t () t dt, j ψ = j (2.15) n (), t j i j ( ) () () ψ n () j j where n t = n t t dt and E ( n ) i is the symbol energy for the PSWF pulse. In the multipath fading environment, the received pulse wavelet sequences may be overlapped and interfered with each other due to the differently delayed multipath components, accordingly, the inter-pulse-interference (IPI) and the inter-symbolinterference (ISI) would take place. In some severe multipath fading conditions, the BER performance would obviously suffer from this kind of IPI and ISI effects. In order to efficiently collect the multipath energy as much as possible and overcome the severe IPI/ISI effects, adaptive guard-time scheme is proposed in [24]. In this scheme, inter-pulse-interval (i.e. guard-time) is predetermined adjusting to the multipath channel conditions and inserted between the consecutive pulse waveforms. Then, the transmitted pulse wavelet sequence with guard-time is given as: K 1 ( n) ( n) ( n) ( n) ( n) s () t = p b ψnm, ( t i K T mt δt c T ), ik + m f m p ik c (2.16) i= m= 0 where δ is a random variable corresponding to the added guardtime with zero-padding. It is shown in [23] [24] that this PSM scheme is suitable for achieving high data throughput even in the severe multipath fading environment PSWF-based UWB Transmission Using Orthogonal Ternary Code Sets Data rate of direct sequence UWB systems is limited mainly by symbol length. Reducing symbol length while keeping the same level of system performances possibly result in the increase of 24

39 data rate. In DS-UWB, multiple chip pulses per one bit symbol period are transmitted based upon a certain spreading sequence. Therefore it is important to design a direct sequence with suitable sequence length for high data rate DS-UWB. A long length spreading sequence is not suitable for the high data rate transmission, while the parallel spreading sequences with reduced sequence length are more suitable for high data rate DS-UWB systems to achieve variable processing gain. As shown in Figure 2.6, if parallel direct sequences with length = 4 instead of direct sequence with length = 16 are used, the corresponding data rate can be 4 times greater. In [27], the mutually orthogonal ternary code is proposed as such a parallel spreading sequence. Figure 2.6: Paradigm of parallel spreading sequences for high data rate DS-UWB In a PSWF-based DS-UWB system as described in the above sections, the ternary complementary code sequences assigned to user n is further carried by the PSWF-based orthogonal pulse wavelets. As shown in the example illustrated in Figure 2.7, each user has a different 4 by 4 mutually orthogonal ternary complementary code set and each row of the ternary code set is assigned 25

40 CHAPTER 2: RELATED WORKS to a different order PSWF-based pulse wavelet, i.e. ψ 1 (), t ψ 2 (), t ψ 3 (), t and ψ 4 (), t respectively. Then, these coded pulse wavelets are transmitted by the PSM scheme. The construct method of the mutually orthogonal ternary code sets is given in [46] [27], and it is proved that the BER performance of PSWF-based orthogonal pulse transmission using the MO ternary sequence with shorter or almost the same length is superior to that using other M-, Gold and Walsh binary sequences both in the multipath fading channel and multiple user interference environment. Figure 2.7: Parallel PSWF-based pulse transmission with Ternary complementary code 26

41 2.4. Summary In this chapter, we briefly review the research works conducted in our research group that is related to my Ph.D. research. We first describe the detailed generation process of the multiple PSWF-based UWB pulse wavelets, then the M-ary pulse shape modulation scheme is introduced, finally, PSWF-based DS-UWB transmission using orthogonal Ternary code sets is presented. These foundations serve as the ingredients for the researches in chapter 3, 4 and 5. 27

42 CHAPTER 3: TRANSMIT POWER ALLOCATION AMONG THE PS WF-BASED PULSE WAVELETS Chapter 3: Transmit Power Allocation among the PSWF-based Pulse Wavelets Chapter 3 investigates two transmit power allocation schemes among the orthogonal PSWF-based pulse waveforms in a cognitive UWB radio transmission scenario, in order to improve the channel data throughput and to minimize the bit error rate, respectively. Both of the two schemes are proposed with respect to the application scenario of one specific user transmitting its UWB signals in the mode of PSM with M orthogonal pulse waveforms, under the emission limitation of FCC spectral mask System Model We consider a peer-to-peer communication system that adopts the M-ary PSWF-based pulse shape modulation scheme with optimal transmit power allocation among the M orthogonal pulse waveforms. The transmit structure is illustrated as in Figure 3.1. Taking into account the multipath fading factors, in a general way, we describe the output of the mth pulse through the multipath channel as y = p h b + n, m = 0,1,..., M 1, (3.1) m m m m m where h m denotes the multipath fading coefficient for the mth waveform, n m represents the additive noise, and these noises are assumed to be i.i.d. Gaussian random variables with zero mean and variance of σ 2. The data bit b m is carried by one orthogonal pulse ψ m of order m in the pulse shape modulation scheme, and p m represents the transmit power allocated to the mth pulse waveform, with the total power constraint given as 28

43 Power Alloc ation Transmitter Eigenvalue λ 0 p 0 p 1 Eigenvalue λ 1 M-ary Pulse Shape Modula -tion T x Binary data pm 1 Eigenvalue λm 1 Figure 3.1: Transmitter structure with power allocation scheme Figure 3.2: Receiver structure 29

44 CHAPTER 3: TRANSMIT POWER ALLOCATION AMONG THE PS WF-BASED PULSE WAVELETS M 1 p = MP, (3.2) m m= 0 where p denotes the average transmit power per pulse, when the total transmit power is equally distributed into the M pulse waveforms. At the receiver side, ψ m represents the reference template pulse. At the receiver, the SNR (signal-to-noise ratio) γ m for the mth pulse is calculated as where α m hm 2 2 γ α p m m m, = (3.3) σ is the ratio of the combined multipath gain of the mth pulse to the noise power, representing the overall channel state for the mth pulse. We further express α m by the eigenvalue λ m of the mth pulse after its transmission through the multipath channel. The channel state information α m is assumed to be known by the transmitter a priori, which is required to determine the optimal transmit powers {p m } Optimal Power Allocation for Channel Data Throughput Improvement Rooted in information theory, water-filling algorithm has been recognized as an optimal way for the transmit power allocation in either multiple bands or multiuser communication systems [28]. As we know, In mathematical terms, the essence of transmit power control for a noncooperative multiuser radio environment is stated as: Given a limited number of spectrum holes, select the transmit-power levels of n unserviced users so as to jointly maximize their data-transmission rates, subject to the constraint that the interference-temperature limit is not violated [30]. Accordingly, in our system model, we would like to state the problem as: In a M-ary pulse shape modulation transmission scheme, how to control the transmit power levels of the M pulse waveforms of a 30

45 specific user so as to jointly maximize its whole data transmission rates, subject to the constraint that the UWB emission limit is not violated. To solve this kind of optimization problem, we perform the water-filling algorithm to these PSWF-based pulse waveforms to optimally allocate the transmit power [29], as illustrated in Figure 3.1. The achievable throughput per Hertz of the mth waveform is bounded by [28] Cm = log 1+ γ = log (1 + α p ), (3.4) ( ) m m 2 m 2 where the denotations of γ m, α m, p m are the same as we described in (3.3). Hence, the throughput of the whole channel per Hertz is M 1 log2 ( 1 α p ). (3.5) m m C = + m= 0 Then, the optimization problem can be described as maximize log ( 1 + α p ) subject to M 1 2 m m m= 0 (3.6a) M 1 pm = MP (3.6b) m= 0 p 0. (3.6c) m The solutions to such objective function can be obtained by citing the ideas of optimization processing in [31]. We first transform (3.6) to a standard convex optimization problem: M 1 2 m m (3.7a) m= 0 M 1 minimize log ( 1 + α p ) subject to p = MP (3.7b) m m= 0 p m 0. (3.7c) By introducing Lagrange multipliers λ for the inequality con- 31

46 CHAPTER 3: TRANSMIT POWER ALLOCATION AMONG THE PS WF-BASED PULSE WAVELETS straint p m 0, and a multiplier ν for the equality constraint M 1 m= 0 p conditions: m = MP, we obtain the Karysh-Kuhn-Tucker (KKT) 0 (3.8a) p m M 1 pm = MP (3.8b) m= 0 λ 0 (3.8c) λ p m = 0 (3.8d) αm 1 + α p λ + ν = 0. (3.8e) m m From (3.8c) and (3.8e) we can achieve αm λ = ν (3.9) 1 + α p m m and 1 ν, (3.10) β + where β = 1 α. m m m pm From (3.8d) and (3.9) we can achieve 1 λ p = p m ν m β + p m m = 0. (3.11) Ifν < 1 β m, the condition (3.10) can only hold when p > 0, m which by the condition (3.11) implies that 1 ν = β +. (3.12) m pm 32

47 Solving this equation, we can obtain p 1 = β (3.13) ν m m. Ifν 1 β m, we assume p 0, which implies that p > 0, then m m ν 1 β > 1 ( β + p ). From (3.11), one can conclude that m m m p = 0, and it s contradiction to our assumption. So, we can get m p = 0 if ν 1 β m m. Thus we have the solution as It can be expressed more concisely as p m 1 β, ν < 1 β m m = ν, (3.14) 0, ν 1 βm 1 p = β, m m (3.15) ν where () + denotes max(0, ), and ν is determined in order to sastisfy the power constraint M 1 m= 0 p m M 1 + = MP. Substituting this expression for pm into the condition p = MP, we obtain m m= 0 M 1 1 max{ 0, β m } = MP. m= 0 ν (3.16) The left side of (3.16) is a piecewise-linear increasing function of 1 ν, with breakpoints at 1 α, so the equation has a unique solution that is readily determined. m 33

48 CHAPTER 3: TRANSMIT POWER ALLOCATION AMONG THE PS WF-BASED PULSE WAVELETS This algorithm can be implemented as follows. 1) Set a small positive termination threshold p and step sizeξ, thr initializeν and p to be zero. total 2) While p MP > p, do total thr for m = 0 : M-1 { if ν 1 β m, p = 0 ; m else 1 find pm that satisfies β + m pm = ν by following steps: a) Set a small positive termination threshold ν thr size µ ; b) Initialize p m = 0 ; 1 c) While ν β m + pm > ν thr, do 1 find derivative δ of ν β + δ = ( β p ) 2 m pm 1 1 ν. + β m + m m m p Update pm = p m µδ. } M 1 Compute ptotal = p ; m m = 0 Updateν as 1 1 = + ξ ( 1 ptotal ). ν ν 3) Output all p m. and step 2 with respect to p : m 34

49 3.3. Optimal Power Allocation for BER Performance Improvement In this section, we first discuss the proposed optimal power allocation scheme [32] in section Then, the case study of improving the BER performance in M-ary pulse shape modulation is performed in section Optimal Power Allocation Scheme To derive the optimal power allocation scheme, we first express the overall BER as a function of the transmit power for M waveforms, {p m m=0, 1,, M-1}, and then find {p m } that minimizes the overall BER. The BER for the mth waveform is generally a function of the SNR γ m, and thus, the BER P b (e α m ) for a given channel state α m may be expressed as ( α ) ( γ ) ( α ) p e = f = f p, m = 0,1,..., M 1, (3.17) b m m m m where f( ) is a function determined by a specific modulation scheme. In the PSM scheme, data streams are carried and transmitted by the mutual orthogonal waveforms with equal rate constraint, and since the waveforms are statistically independent with each other, the joint BER for the given channel states of {α m m=0, 1,, M-1} which were represented by the corresponding eigenvalues {λ m }, can be calculated as an arithmetic mean of p b (e α m ) M 1 M p e,,..., p e f p. (3.18) ( α α α ) = ( α ) = ( α ) b 1 2 M b m m m M m= 0 M m= 0 Note that the average BER becomes minimal when the BER in (3.18) is minimized for each orthogonal waveform. In order to find the optimal {p m } that minimizes (3.18), we use the Lagrange multiplier method with the total power constraint in (3.2). The Lagrangian function may be expressed as 35

50 CHAPTER 3: TRANSMIT POWER ALLOCATION AMONG THE PS WF-BASED PULSE WAVELETS M 1 M 1 1 J ( p, p,..., p 1 2 ) = f ( α ), M mpm λ p + m Mp (3.19) M m= 0 m= 0 where λ denotes the Lagrange multiplier. By differentiating (3.19) with respect to p m and setting it to zero, we obtain a set of equations as 1 d f ( α ) 0, 0,1,..., 1. m p + λ = m = m M (3.20) Mdp m By simultaneously solving the equations in (3.2) and (3.20), we can calculate the optimal set of the transmit power {p m }. As mentioned above, the BER function in (3.17) is a function determined by a specific modulation scheme. For a binary phaseshift keying (BPSK), for example, the BER function may be expressed as an exponential function [33], and a closed-form solution of (3.2) and (3.20) may be easily found. For M-ary orthogonal signals, however, the BER function is expressed as an integration function [33], and it is difficult to find a closed-form solution. In this case, an adaptive method, such as the steepestdescent algorithm [34], may be employed to find the solution in an iterative manner as follows. 1) Initialization: Set an iteration number i=1, a step size µ(1)=µ 1, and an arbitrary initial positive power set {p m } satisfying (5). 2) Power set update: For m=0, 1,, M-1, update the transmit power p m (i) as p ( i+ 1) = p ( i) µ ( i) J p ( i), p ( i),..., p ( i) m m 1 2 M p () i m ( ) 1 d = p () i µ () i f ( p () i ) () i, m α + λ m m Mdp() i m (3.21) where λ(i) is determined from the power constraint in (3.2) and is updated as 36

51 M 1 1 d λ() i = f ( α p () i ). (3.22) m m M dp () i 2 m= 0 3) Step-size adjustment: If all components of the updated power set {p m (i+1)} in 2) are positive, then go to 4) with µ(i+1)=µ 1. Otherwise, compute µ ( i) p ( i) ((1 M )( df ( α p ( i))) ( dp ( i)) + λ( i) ) for m, m m m m m which is associated with p m (i+1) 0, set the step size µ(i) to ρ min µ ( i), where ρ is a positive scaling factor smaller mp : m ( i+ 1) 0 m than one, and return to 2). 4) Repetition or termination: If more iterations are required for convergence, increase by one and go to 2). Otherwise, terminate the adaptive procedure. The adaptive algorithm described above converges to the global optimum solution for the convex BER function. Note that the BER function of M-ary orthogonal signals may be approximated by a Q-function upper-bound, which is a convex function [33]. m The Case Study In order to discuss the BER performance of the M-ary PSM by executing the above mentioned optimization algorithm, we first develop the Lagrangian function for the M-ary orthogonal PSM signals, and then the steepest-descent algorithm as mentioned above is carried out to calculate the optimal set of the transmit power {p m }, since we can not get a closed-form solution. According to the theoretical calculations for the M-ary orthogonal modulation from [33], the BER function is expressed as 1 M p ( e) = p ( e), (3.23) b M 2 M 1 where p M (e) is the symbol error probability (SEP) and 37

52 CHAPTER 3: TRANSMIT POWER ALLOCATION AMONG THE PS WF-BASED PULSE WAVELETS 2 M 1 2 y x M 1 2 αm m 0 π 2 m= 0 p () e M = 1 exp 2. 2π 2 e dx y p N dy (3.24) In our case study, we set M = 8. Accordingly, (,,..., p ) = J p p m= λ pm m= 0 π e dx y p N dy y x exp 2 αm m 0 2π 2 m= 0 8 p. (3.25) By differentiating (3.25) with respect to p m and setting it to zero, we can obtain x 7 1 d 1 y e dx exp y 2 αmpm N 0 dy λ π dp + = m 2π 2 m= 0 (3.26) To simplify the mathematical deduction process in solving the 2 1 above equation, we transform y x e 2 dx into Q- 2π 2 t function 1 e 2 dt Q( y) =. As we have Q( y) e y2 2 <, 2π y thus (3.26) can be further simplified by the lower bound Q( y), as 38

53 y d e exp y 2 αmpm N 0 dy λ π dp + m 2 + = m= 0 (3.27) More accurate exponential bounds for the Gaussian function and its inverse, and for M-ary phase-shift-keying (MPSK), M-ary differential phase-shift-keying (MDPSK) error probabilities over additive white Gaussian noise fading channels have been proposed in [48], readers can refer to it. Here, we just adopt Q( y) e y2 2 <. Then, by differentiating the later part of the above equation (3.27), we can further get π y e exp y 2 αmpm N 0 2 m= 0 dy + λ = αmpm N0 y 1 2N0 αmpm αm m= 0 m= 0 (3.28) 3.4. Simulation Results and Discussion In this section, the performance of the proposed two optimization schemes are evaluated in a direct-sequence UWB (DS-UWB) system, where the information bit is modulated and transmitted over the parallel sequences of orthogonal pulses. In order to express the two schemes clearly in the following figures, we hereby denote the scheme for data throughput improvement as scheme 1, and the scheme for BER performance improvement as scheme 2. 39

54 CHAPTER 3: TRANSMIT POWER ALLOCATION AMONG THE PS WF-BASED PULSE WAVELETS In the simulation, we generate eight PSWF-based orthogonal pulse waveforms and investigate the data throughput and the BER performance of the 8-ary PSM case in an indoor UWB multipath fading environment. Here, the standard IEEE a UWB channel model is considered [35]. There are four different environmental scenarios defined in this model, namely, CM1, CM2, CM3, and CM4, corresponding to different propagation conditions as described in Table 1. Table 3.1: Characteristics of the IEEE a channel model for four different scenarios. Target Channel Characteristics CM1 CM2 CM3 CM4 Distance (m) >10 (Non-) Line-of- NLO NLO LOS Sight S S NLOS Mean excess delay (ns) RMS delay spread (ns) The simulation procedures are conducted in CM1 and CM3 as the representative cases. At the transmission side, we adopt an eight by eight orthogonal Ternary complementary code set as the DS codes assigned to the eight different PSWF-based orthogonal pulses. Bit energy is allocated among these 8 pulses according to the proposed scheme. At the receiver side, we employ the selective-rake receiver to collect the multipath signals, and the Rake fingers are set to 5 and 3 in the scheme 1 and scheme 2, respectively. Figure 3.3 and Figure 3.4 show us the attainable throughput of the scheme 1 and the equal power allocation scheme. The chip pulse duration is set to 1ns, which means the maximal transmission data rate of this DS-UWB system can be as high as 1Gbps. From Figure 3.3 and Figure 3.4, it can be observed that by employing the proposed power allocation scheme (scheme 1), the 40

55 channel data throughput significantly improves about 20Mbps when SNR is below 10dB, which represents 2% of the total capacity. When SNR is above 10dB, the proposed scheme somehow performs similarly with the equal power allocation scheme. The reason behind the decreased difference is that the capacity is a logarithmic function of SNR, therefore the data rate is usually insensitive to the exact power allocation, except when the SNR is in the low range [36]. As we know, the water-filling algorithm generally allots more power to the channels with lower noise. In our DS-UWB system model, with respect to the PSWF-based pulse waveforms, the eigenvalue is the ratio of the combined multipath gain of the corresponding pulse to the noise power, which represents the overall channel state for the that specific pulse. The lower eigenvalue means that pulse has a poor combined gain. Consequently, the water-filling algorithm allocates more energy to the pulse waveform with a bigger eigenvalue, aiming at maximizing the data rate. Figure 3.5 illustrates the BER performance achieved by the scheme 2 and the equal power allocation scheme in CM1. As expected, the proposed scheme outperforms the other one by 1.5~2.5dB in the high SNR (>10dB) range, and by 1~2dB in the low SNR range. Similarly as shown in Figure 3.6, where the simulation is performed in CM3, the SNR gain of the proposed scheme is about 1.0~2.0dB in the high SNR range, and 0.5~1.0dB in the low SNR range. It is worthwhile to note that the characteristics of this optimal transmit power allocation scheme (scheme 2) derived in section differ from that of the scheme 1 in section that improves the capacity rather than the BER performance. According to the simulation results, from the power set {p m }, we can observe that in the high SNR range, the optimal power allocation scheme 2 tends to allocate more transmit powers to the more attenuated waveforms, which is contrary to the behaviour of the scheme 1. 41

56 CHAPTER 3: TRANSMIT POWER ALLOCATION AMONG THE PS WF-BASED PULSE WAVELETS Throughput (Mbps) Equal Power Allocation Scheme Proposed Scheme E b /N 0 [db] Figure 3.3: Throughput of the proposed scheme 1 and the equal power allocation scheme (in CM1) Throughput (Mbps) Equal Power Allocation Scheme Proposed Scheme E b /N 0 [db] Figure 3.4: Throughput of the proposed scheme 1 and the equal power allocation scheme (in CM3) 42

57 10 0 Equal Power Allocation Scheme Proposed Scheme 2 BER E b /N 0 [db] Figure 3.5: BER performance of the proposed scheme 2 and the equal power allocation scheme (in CM1) 10 0 Equal Power Allocation Scheme Proposed Scheme 2 BER E b /N 0 [db] Figure 3.6: BER performance of the proposed scheme 2 and the equal power allocation scheme (in CM3) 43

58 CHAPTER 3: TRANSMIT POWER ALLOCATION AMONG THE PS WF-BASED PULSE WAVELETS 3.5. Summary Chapter 3 proposes two transmit power allocation schemes among the orthogonal pulse waveforms in the cognitive UWB radio environment, for the data throughput and the BER performance improvement, respectively. Chapter 3 first considers the M different eigenvalues of the M orthogonal pulse waveforms after their transmission through the multipath fading channel. The mth (m=0, 1,, M-1) eigenvalue is the ratio of the combined multipath gain of the mth orthogonal pulse to the noise power, representing the overall channel state corresponding to the mth pulse waveform. Then, based on these eigenvalues, two transmit power allocation schemes are further developed, which are optimal in improving the data throughput and the BER performance, respectively. By adopting the water-filling algorithm, we optimize the transmit power allocation to achieve the target of the total channel throughput improvement. In the scheme for BER performance improvement, we develop the Lagrangian function from the BER functions of the M-ary orthogonal signals and simplify the mathematic expression, in a typical case of 8-ary Pulse Shape Modulation. Numerical results show that the two proposed schemes improve the data throughput and the system s BER performance respectively, compared with the equal power allocation scheme. 44

59 Chapter 4: Cognospectrum: Spectrum Adaptation in Cognitive UWB Radio Chapter 4 focuses on the key issues of spectrum-agile UWB pulse waveforms generation. It is proposed to implement a variety of UWB waveforms and their associated adaptation algorithms. Such a cognitive UWB radio would be potentially capable of dynamically changing its waveform based upon need, thus reducing the UWB physical layer interface to a software abstraction. Following this kind of signal waveforms adaptation approach in the cognitive UWB radio, we have investigated a design method of pulse waveform optimization based on the linear combination of orthogonal basis functions [13] [18], as the typical example of PWSF that we have introduced in chapter 2. Then, these specifically designed pulse waveforms are tested by high-speed digital processing unit (digital-analog converter) for implementation estimation. To verify the pulse distortion effects of UWB antenna in cognitive UWB radio, the generalized pulse waveforms are further transferred through an actual UWB antenna [37]. Furthermore, a pre-distortion scheme is considered before antenna transmission, in order to compensate the pulse distortion effects Adaptive Pulse Waveforms Generation In general, an UWB radio conveys digital binary information over a serial of ultra-short pulse waveforms and is capable of implementing a spectrum-agile pulse waveform through the modification of its generation algorithm. As we mentioned above, such adaptive UWB pulse waveforms could adjust themselves to the actual interference environment and spectral mask requirements. Taking these properties into account, we aim at designing a number of adaptive pulse waveforms corresponding to the expected UWB spectrum features achieving the required spectral notches 45

60 CHAPTER 4: COGNOSPECTRUM: SPECTRUM ADAPTATION IN COGNITIVE UWB RADIO for cognitive coexistence with interference avoidance. This kind of adaptive pulse waveforms is preferred to be expressed by a limited linear combination of a series of core pulse shapes, namely taking advantage of the orthogonal basis functions and their related auxiliary functions and factors. As introduced in chapter 2, we have generated the PSWF-based pulse wavelets ψ k (t) as a suitable core pulses set, where k denotes the kth sub-band of the frequency band plan of UWB. These core pulse wavelets can be further combined with each other to form a more complex waveform corresponding to arbitrary spectral characteristics including dual-, triple- and multiband architecture as illustrated in Figure 2.1. The linear combination expression for this kind of adaptive and flexible pulse waveform generation may be written as follows: ψ N adap aux k k k = 1 () t = f () t + a ψ () t, (4.1) where ) (t f aux is an appropriate auxiliary function, k a is the related expansion coefficients of the truncated linear combination, and N is the number of sub-bands. As mentioned before, the cognitive UWB radio requires the pulse waveform to be adaptive in satisfying arbitrary spectral requirement for spectrum sharing and interference avoidance. For instance, in the extreme case of radio emission prohibition like in the frequency band of Astronomy Radio, any kind of UWB radio emission should be avoided. Considering the kind of special spectral requirement and still complying with the FCC emission mask ( GHz), we have designed a unique adaptive pulse wave- 46

61 2 Adaptive pulse waveform generation 1.5 Relative amplitude n 0.56n 1.125n n 2.25n n 3.375n Time (128 samples=3.6 ns) Spectrum characteristics of adaptive pulse waveform - - Relative amplitude (3.12GHz (5.8GHz GH 3.47GH 6.94GH 10.41GH 13.88GH 17.35GH Frequency (1 sample=69.4mhz) Figure 4.1: Adaptive pulse waveform and the spectrum 47

62 CHAPTER 4: COGNOSPECTRUM: SPECTRUM ADAPTATION IN COGNITIVE UWB RADIO form as illustrated in Figure 4.1, in which the limited linear combination of the PSWF-based orthogonal pulse wavelets and their related auxiliary functions is used. It is shown that the 3.6ns pulse waveform is located in the lower band of GHz in which two spectral notches with notch depth more than 25dB are generated in order to avoid any possible severe interference to the existing narrowband wireless services, such as the Astronomy Radio and the Fixed Satellite Services Implementation Issues While implementing a true cognitive UWB radio would require totally new research and development works accompanied by intelligent spectrum-sensing capabilities and advanced spectrum-sharing protocols, the implementation of a preliminary cognitive UWB radio is somehow a realizable goal today thanks to the existence of programmable pulse waveform generators and the recent digital processing technique developments in the creation of dynamic waveform generation algorithms. Especially, the impulsive UWB technologies essentially are digital in nature - without the attending complexities of RF front-end designs, a variety of such technologies potentially could be implemented within the same digital processing chipset. However, the realization of a perfect cognitive UWB radio is still quite challenging today because of the limitations of current digital processing technologies. The fact is that the analog-todigital (A/D) and digital-to-analog (D/A) converters are not fast enough to be capable of implementing a really smart cognitive radio. Therefore it is essential to investigate the basic implementation issue related to generating an adaptive pulse waveform, such as the one designed in Figure 4.1, in order to verify the preliminary feasibility and the limitation of realizing a cognitive UWB radio by the programmable digital processing technologies. Digital signal processing test-bed with high sampling frequency is used here, where the bit resolution per sample and sampling fre- 48

63 quency are variable. We analyze the effects of digital quantification in order to test how many bits per sample are necessary when using the D/A converter to generate this kind of specific adaptive UWB waveforms. By utilizing Matlab digital processing simulation tool, the digital quantization of the above-designed pulse waveforms and their corresponding spectrum characteristics are investigated, as described in Figure 4.2. In Figure 4.2, the pulse waveforms are generated corresponding to the digital bit resolution of 3, 4 and 6 bits per sample, respectively. From Figure 4.2(a), 4.2(b) and 4.2(c), it can be observed that 4 bits resolution is quite sufficient to maintain the basic spectral features of the adaptive pulse waveform, such as the spectral notch width and the notch depth, while 3 bits resolution is still acceptable. However, in the three cases, the problem of out-of-band emission happens. Furthermore, we test the effects of digital sampling frequency on the designed adaptive pulse waveforms, based on the actual Spectrum Analyzer measurement results. Here, we maintain the bit resolution as 4 bits/sample while decrease the total samples per pulse waveform (correspondingly the sampling frequency) from 256, 128 to 64 respectively, as illustrated in Figure 4.3, 4.4 and 4.5. According to the digital test-bed measurement results, we may observe that the basic spectral characteristics can be maintained even until 64 samples per pulse at the sampling frequency of 18 GHz, although the notch depths become a little shallower but are still acceptable (>20 db). On the other hand, the influence of out-of-band emissions becomes obviously, which may suggest the necessity of using extra band-pass filter to get rid of the out-of-band interference. Taking into account the current status of high-speed digital processing technology, we may conclude that it is quite feasible to realize the proposed UWB signal waveforms adaptation while employing D/A converter of 18 GHz sampling frequency with 4 or even 3 bits resolution. 49

64 CHAPTER 4: COGNOSPECTRUM: SPECTRUM ADAPTATION IN COGNITIVE UWB RADIO (a) 3 bits/sample, 1024 samples/pulse 50

65 (b) 4 bits/sample, 1024 samples/pulse 51

66 CHAPTER 4: COGNOSPECTRUM: SPECTRUM ADAPTATION IN COGNITIVE UWB RADIO (c) 6 bits/sample, 1024 samples/pulse Figure 4.2: Effects of digital quantization (bit resolution) on the adaptive pulse shape and its spectrum characteristics 52

67 Measuring samples (frequency domain) Figure 4.3: Effects of sampling frequency on the adaptive pulse shape (Spectrum Analyzer, D/A converter, 4 bits/sample, 256 samples/pulse, sampling frequency: 72 GHz) Relative signal level [db] Relative signal level [db] Measuring samples (frequency domain) Figure 4.4: Effects of sampling frequency on the adaptive pulse shape (Spectrum Analyzer, D/A converter, 4 bits/sample, 128 samples/pulse, sampling frequency: 36 GHz) 53

68 CHAPTER 4: COGNOSPECTRUM: SPECTRUM ADAPTATION IN COGNITIVE UWB RADIO Relative signal level [db] Measuring samples (frequency domain) Figure 4.5: Effects of sampling frequency on the adaptive pulse shape (Spectrum Analyzer, D/A converter, 4 bits/sample, 64 samples/pulse, sampling frequency: 18 GHz) 4.3. UWB Antenna Distortion Effect and Pre-distortion Scheme Distortion Effect of UWB Antenna on Pulse Waveform Adaptation In order to analyze the distortion effect of UWB antenna on the proposed pulse waveforms adaptation, we make use of a real UWB antenna prototype designed by the UWB Technology Group, National Institute of Information and Communications Technology of Japan, named as K-type UWB antenna - a modified version of the one in [37]. The K-type UWB antenna is illustrated in Figure 4.6. The antenna is a rectangular patch with a slot Bow-Tie on it, and is printed on a Teflon substrate with relative 54

69 permittivity of r ε = 2.17 and thickness of h = 0.46 mm. A 50 Ohms feed line is printed on the other side of substrate and connected by a filling material through hole to the radiating element. The transfer function characteristics of the K-type antenna, namely the return loss, the relative phase and the impulse response of S11 parameter, are shown in Figure 4.7, 4.8 and 4.9, respectively. Affected by the transfer function of the K-type UWB antenna (S11 parameter), the time-domain characteristics of the returning signal waveform reflected by the antenna are shown in Figure 4.10, while the required on-the-air pulse waveform is also provided as comparison. In Figure 4.11, the expected spectrum characteristics of the required pulse waveform on-the-air are compared with that of the returning signal waveform from the antenna to the pulse generator. According to Figure 4.11, we can observe that the K-type UWB antenna has not destroyed the basic spectrum features of the expected pulse waveform on-the--air. That means if we radiate the designed pulse from this kind of UWB antenna then the required pulse waveform adaptation would be maintained in some extents. Even if the K-type UWB antenna is a special case, it still provides us a preliminary evaluation on the antenna distortion effect and these first-stage analytical results are quite encouraging. Additionally, it should be noted that the reason to choose the returning signal waveform rather than the radiated pulse waveform for evaluation is that it also shows us the overlapping effect of the returning signal to the next-coming pulse while still provides us the sufficient information on the UWB antenna distortion phenomenon. 55

70 CHAPTER 4: COGNOSPECTRUM: SPECTRUM ADAPTATION IN COGNITIVE UWB RADIO Figure 4.6: UWB antenna prototype (K-type UWB antenna) Figure 4.7: Transfer function characteristics of K-type UWB antenna (S11 parameter, return loss) 56

71 Figure 4.8: Transfer function characteristics of K-type UWB antenna (S11 parameter, relative phase) Figure 4.9: Impulse response of K-type UWB antenna (S11 parameter) 57

72 CHAPTER 4: COGNOSPECTRUM: SPECTRUM ADAPTATION IN COGNITIVE UWB RADIO Figure 4.10: Time-domain characteristics of the required pulse waveform on-the-air and the returning signal waveform reflected by K-type UWB antenna (Transfer function, S11 parameter) Figure 4.11: Spectrum characteristics of the required pulse waveforms on-the-air and the returning signal waveform reflected by K-type UWB antenna (Transfer function, S11 parameter). 58

73 Pre-distortion Scheme As we have seen from the previous discussions on the UWB antenna distortion effect, the radiated pulse waveforms and their corresponding spectra would be inevitably changed by the antenna s transfer function. In general, the radiated UWB signal E rad ( t, r,θ,φ) at arbitrary far-field point is given by the following transient transmission model: E t, r, θ, φ rad ( ) Z 1 ( ) 0 dvt t 0 = at ( t, θ, φ) δ ( t τ 0 2πrc Zc dt a t 0 59 delay r ) c (4.2) in which ( t, θ, φ) is the transient response of the transmitter antenna at a reference time t 0, V t ( t) is the transmitting voltage of 0 the input pulse waveform, Z 0 is the free space impedance, Z c is the reference impedance at the antenna connector, r is the distance between the antenna and the far-filed measuring point, c is the light velocity and is the convolution processing. The transient response ( t, θ, φ) may be further expressed as a t jβ ( ω) at ( t, θ, φ) = F [ A ( ω)] [ ( ω) ] 0 t = F At e by the inverse Fourier transformation of the frequency-domain antenna transfer function A t (ω) and τ delay = dβ ( ω) dω = dβ ( f ) 2π df is the group delay of the antenna s transfer function. In order to overcome the antenna distortion effect, we propose to utilize a pulse-antenna co-design approach based on the pulse waveform pre-distortion scheme, so as to realize the FCC spectral mask matching as well as the adaptive waveforms optimization. The pulse waveform pre-distortion algorithm is carried out according to the following two equations: 1 pre ( ω) = X ( ω) At ( ω) X (4.3)

74 CHAPTER 4: COGNOSPECTRUM: SPECTRUM ADAPTATION IN COGNITIVE UWB RADIO ( ω) = ( ω) ( ω) = ( ω), (4.4) X X A X rad pre t where X (ω), X pre (ω ) and X rad (ω) is the spectral expressions (frequency domain) of the expected pulse waveform, the predistorted pulse waveform and the actually radiated pulse waveform, respectively. A t (ω) is the transfer function of the targeted UWB transmitter antenna in the frequency domain as mentioned before. The algorithm is described in Figure As we may see from Figure 4.12, generally, the proposed pulse pre-distortion can compensate any kind of UWB antenna s deterioration influence, even in the case of serious pulse waveform distortion. Potentially, the pre-distorter could be adaptively redesigned by a software-embedded approach, corresponding to arbitrary inputting pulse waveforms, antenna types, angle of incidence, load impedance, polarization, and transmitter-receiver (TR) matching/shaping networks. In addition, the pre-distortion scheme may be further extended to take advantage of the multipath fading channel, including pre-combining various LOS and NLOS multipath components of variable amplitudes and possible polarity reversals. By using the above-mentioned scheme, we pre-distort the designed pulse waveform before transmission through the K-type UWB antenna. The pre-distorted and the required pulse shapes in time-domain before and after the antenna are described in Figure The spectrum characteristics of the non-pre-distorted, the pre-distorted and the expected pulse waveform on-the-air are shown in Figure 4.14, respectively. From Figure 4.14, we can observe that if we use the proposed pre-distortion scheme the designed pulse s spectrum on-the-air is further improved and quite complied with the expected spectrum, which will surely make the cognitive UWB radio applications to be much more realizable even considering any kind of UWB antennas. 60

75 Figure 4.12: Pre-distortion scheme in overcoming the pulse waveform distortion caused by antenna, filter and even wireless channel 61

76 CHAPTER 4: COGNOSPECTRUM: SPECTRUM ADAPTATION IN COGNITIVE UWB RADIO Figure 4.13: Time-domain characteristics of the pre-equalized and the required on-the-air pulse waveform Figure 4.14: Spectrum characteristics of the non-pre-equalized, the pre-equalized and the required pulse waveforms after being transferred through K-type UWB antenna (on-the-air spectrum) 62

77 4.4. Summary This chapter investigates spectrum-agile pulse waveforms generation, to obtain the expected spectral notches in achieving interference avoidance as well as matching with any UWB signal emission mask, especially the FCC spectral mask. Then the specifically designed pulse waveforms with adaptive spectral notches are tested by employing the high-speed digital processing test-bed for implementation validation. It has been observed that the proposed pulse waveforms adaptation is quite realizable even using low bit resolution and sampling frequency (e.g. 4 bits/sample and 64 samples/pulse). To further verify the pulse distortion effects of UWB antenna in the cognitive UWB radio applications, the generated pulse waveforms are then transferred through an actual UWB antenna. Moreover, the pre-distortion scheme is taken into account before antenna transmission, so as to compensate for the pulse distortion effects. 63

78 CHAPTER 5: DISTRIBUTED NODES COOPERATION IN COGNIT IVE UWB USING SPACE-FREQUENCY BLOCK CODING Chapter 5: Distributed Nodes Cooperation in Cognitive UWB using Space-Frequency Block Coding For some time, multiple-input multiple-output wireless channels have been known to offer better link and capacity gains, which can be exploited by employing antenna arrays at both ends of the link. An efficient way of exploiting the MIMO channel is the use of transmit diversity be means of Space-Time block coding where the idea is to obtain space diversity and coding gains at the receiver with just simple linear processing [38] [39]. As in [38], Alamouti s STBC was first proposed for transmission with two antennas. After that, Tarokh proposed advanced STBC schemes with more than two transmit antennas in [39]. The STBC schemes developed in these previous works are valid under the assumption of a flat-fading channel only. Then in [40], block extensions of these codes that exploit multipath diversity over frequency-selective fading channel are discussed, in which the transmitted signals are coded on a block-by-block basis instead of a symbol-by-symbol basis. On the other hand, cooperative diversity or cooperation diversity among a number of distributed movable nodes has received considerable attention [41]. The main feature of such schemes is to consider the geographically distributed multiple nodes as a virtual macro antenna array, realizing MIMO spatial diversity in a distributed fashion. In such a network, several intermediate nodes serve typically as relays for an active source-anddestination pair in a cooperative manner. Recently, there have been great interests to further extend STBC into the distributed wireless networks by exploiting the cooperating capability of mobile nodes [42] [43]. It has been shown that the virtual MIMO scheme using Space-Time block coding turns distributed noses collisions into a beneficial source of cooperation, and enhances 64

79 transmission energy efficiency even in a multipath fading environment. In regard of the above-mentioned cognitive UWB radio that is capable of adapting itself to the wireless environment, one of the key issues that seems to have significant impact on whole network performance is the mutual cooperation actions among the distributed nodes to peacefully share the spectrum, and hence enable the open access to limited radio resource with varying degrees of cognitive capabilities for interference detection and mitigation. Considering that UWB signals transmission should not cause serious interference to other overlapped narrowband systems, the multihop relaying with shortened-range transferring is expected to be much more reasonable compared with a longerrange one-hop link, although some transmission delay and extra equipment complexity may cause downside influence. From this point of view, cooperative scheme among the intermediate nodes with virtual MIMO-based relaying function are quite helpful in the power-limited as well as interference-limited networking environment. To the best of our knowledge, most current researches on cooperative relaying transmission assume perfect synchronization among the multiple cooperative nodes, which means the nodes timing, carrier frequency and propagation delay are treated as identical [41] [43]. However, it is difficult and in most cases impossible to achieve perfect synchronization among distributed transceivers. It is much more harsh a case when transmitters are under FCC spectral mask limitation in UWB radio cases. Timing synchronization is usually difficult to be achieved because parameters of radio components may be drifting and handshaking among different transmitters is usually made as infrequently as possible to save energy and bandwidth. More severely, multipath delay synchronization with respect to two or more relaying nodes is almost impossible. This embarrassment prevents virtual MIMO-based STBC scheme from being directly applied to the distributed cooperative UWB communications. 65

80 CHAPTER 5: DISTRIBUTED NODES COOPERATION IN COGNIT IVE UWB USING SPACE-FREQUENCY BLOCK CODING This chapter presents a cooperative relaying scheme using Space-Frequency block coding among the distributed nodes instead of Space-Time block coding, in cognitive UWB radio environment, in order to overcome the relaying synchronization problem. As we know, among the whole 7.5 GHz UWB frequency bandwidth ( GHz), there are a number of sub-frequency band sets available, which UWB devices can operate on, therefore cooperative utilization of the multiple UWB frequency sub-bands is a natural and feasible approach in cognitive UWB radio. For example, a cognitive UWB radio operating in a WLAN frequency band might begin operations in the bands around 5.8 GHz using one adaptive signal waveform, but upon determining that the spectrum in its current location is saturated with other users, it can switch to frequencies in the lower frequency band between GHz and utilize an alternative adaptive signal waveform. Thus, with this prerequisite ability of spectrum sensing and adjusting to the operating frequency band, cognitive UWB radio provides the unique application environment for the proposed cooperation scheme of Space Frequency block coding [45], which makes the synchronization problem among the cooperative terminals unnecessary. At the same time, SFBC-based MIMO with cooperation diversity provides a suitable approach for cognitive UWB radio to meet its austere radio emission mask limitation and interference avoidance requirement Cooperative Scheme with Space-Frequency Block Coding in Cognitive UWB Radio We consider a general multihop networking scenario in cognitive UWB radio, where the communication routes between a source node and a destination node are established through a series of intermediate nodes, each pair of two sequential hops is performed by cooperative relaying of some nodes that are collocated with each other to build up an intermediate cooperation nodes group [46]. At each relaying step, the data packets are in- 66

81 dependently received by the multiple relay nodes. Then these nodes can further retransmit them to the next hop in a cooperation manner with virtual MIMO structure using the Space- Frequency block coding scheme. Although networking layer protocols for forming cooperative groups of relaying terminals are necessary, we focus on physical (PHY) layer issues and do not consider these protocols here. Note that the wireless MIMO propagation channels between each pair of cooperation nodes group are generally subjected to multipath frequency-selective fading, which will be dealt with in the following proposed SFBC scheme and Frequency Exchange (FE) algorithm. Without loss of generality, we consider a two-hop relay channel model where there is no direct link between the source and the destination nodes. These two distributed relaying nodes work as two virtual transmit antennas, and they work in a cooperation manner in retransmitting the incoming information to the destination node. Generalization to higher number of transmit antennas and receive antennas is straightforward for multiple relaying nodes in multihop scenarios. As illustrated in Figure 5.1, the source broadcasts the information to the 2 relays. At the relaying step, the sequential UWB signals will be transmitted by the two nodes functioned as two virtual antennas, each of which operates on one specific UWB frequency sub-band f 1 and f 2, respectively, as an example depicted in Figure 5.2. These two distributed antennas are capable of transmitting the relaying signals either simultaneously or at different time slots, hence makes the prerequisite synchronization issue in the scenario of STBC-based virtual MIMO cooperative communications unnecessary. In regard of a typical UWB multipath fading channel, which will be discussed in more details in section 5.3, we express the discrete-time impulse responses of the wireless MIMO channels from the source node to the intermediate relaying nodes as hsr i () t (i = 1, 2), which is usually a finite discrete-time filter represented as a polynomial by unit delay operator with discrete variable t [40], and r i denotes the ith intermediate node. Similarly, 67

82 CHAPTER 5: DISTRIBUTED NODES COOPERATION IN COGNIT IVE UWB USING SPACE-FREQUENCY BLOCK CODING hrd, () i f t (i = 1, 2; k = 1, 2) represents the impulse responses from k the two relaying nodes to the destination node, they are assumed to be known at the receiver part. f k denotes the different frequency sub-bands that these two relay nodes operate on. r () t r () t s () t s () t 1 2 source h rd f t h sr () t () i 1, 1 h () t rd f r () t r () t , 2 h rd f t h rd f t 2, 2 r() t r () t 1 2 destination distributed relaying nodes Figure 5.1: The 2-hop Space-Frequency block encoded cooperation relaying scheme 2, 1 () () f 1 f 2 Figure 5.2: Frequency diversity based on multiple sub-bands in cognitive UWB radio 68

83 We compose the transmitted signal sequences <s 1 (t)s 2 (t)> from the source node on an expended block-by-block basis as shown in Figure 5.3, corresponding to various delaying versions of multipath propagation components. Therefore the inter-block interference caused by the mutipath fading channel can be efficiently overcome by inserting sufficiently long Cyclic Prefix between the two continue blocks, as being the same case in [40]. The wireless MIMO channels are assumed to stay stationary at least over one block duration, which represents a quasi-static slow fading channel occurring when transceivers are static or moving at slow speed. S2[ N] Block 2... S 2 [ 2] S2 [] 1 Cyclic Prefix S1[ N] Block 1... S [ 2 ] S 1[] 1 1 Cyclic Prefix source Figure 5.3: Transmit signal sequence blocks at the source node Thereupon, the source node transmits two complex symbol sequence blocks <s 1 (t)s 2 (t)> to the relaying node 1 and 2 through the corresponding channel hsr i () t (i = 1, 2), which is composed of a series of delayed multipath components. Then the received signals at the ith (i = 1, 2) relaying node in a finite impulse response (FIR) manner of casual discrete-time are given as ( ) ( ) ( ) ( ) i ( ) ( ) ( ) ( ) r t = h t s t + n t (5.1) 1i sr 1 1i r t = h t s t + n t (5.2), 2i sri 2 2 i where n ki (t) is the Gaussian noise at the relay nodes. The ith relaying node encodes its two received sequence blocks with the codes associated with the ith row of the Space-Frequency block coding matrix C and then transmits the corresponding encoded sequences, where C is defined as 69

84 CHAPTER 5: DISTRIBUTED NODES COOPERATION IN COGNIT IVE UWB USING SPACE-FREQUENCY BLOCK CODING * c1 c 2 C = *. (5.3) c2 c1 The SFBC-based MIMO transmission scheme at the relaying nodes can be summarized as: At frequency f 1, the sequence c 1, and the negated, complex conjugate and time-reversal version of the sequence c 2 is transmitted through the first and the second node s antenna, respectively. At frequency f 2, c 2 is transmitted through the first node s antenna, and the complex conjugate and time-reversal version of the sequence c 1 is transmitted through the second node s antenna. Note, for the discrete signal sequence as we discussed here, ( ) * denotes the complex conjugate and time-reversal operation. The transmission process of the encoded signal blocks at the relaying nodes is illustrated in Figure 5.4. The received signals at the destination is given by () () () ()( ()) () () () () ()( ()) () r t = h t r t h t r t + n t (5.4) 1 rd 1, f1 11 rd 2, f r t = h t r t + h t r t + n t (5.5), 2 rd 1, f2 21 rd 2, f where n i is the receiving AWGN noise at the destination node. We use Figure5.5 to depict the two received signal sequences r 1 (t) and r 2 (t) at the destination. By time-reversing and complex conjugating r 2 (t), we can summarize the received signals in a convenient matrix and vector form as ( ) ( ) ( ) ( ) ( ) () r t 1 s t 1 N t 1 * = + * * r N t H s N t N t, (5.6)

85 Cyclic Prefix Cyclic Prefix r 11 [] 1 [ ] 11 2 r... r 11[ N ] r * 22 [ N ]... r * 22 [] 2 r * 22 [] 1 distributed node1 (transmitted on f1) distributed node2 (transmitted on f1) Cyclic Prefix r 21[] 1 r 21[ 2 ]... r 21[ N ] distributed node1 (transmitted on f2) Cyclic Prefix r * 12 [ N ]... r * [ 2 ] 12 r * [ 1 12 ] distributed node2 (transmitted on f2 ) Figure 5.4: Encoded signal blocks to be transmitted at the relay nodes r 1[] 1 r 1[ 2]... 1r[ N ] r 2 [] 1 r 2 [ 2]... r2 [ N] Figure 5.5: Received signal sequences at the destination node where H and () () - () () () () () () h t h t h t h t,, H H 1 2 h t h t h t h t sr2 r2d, f2 sr1 r1d, f H H, (5.7) sr1 r1d f1 sr2 r2d f1 = = * () rd ( ) ( ) ( ) ( ) ( ) 1 f1 rd 2 f1 * () ( ) ( ) ( ) ( ) ( ) N t = h t n t h t n t + n t (5.8) 1, 11, 22 1 N t = h t n t + h t n t + n t. (5.9) 2 rd 1, f2 21 rd 2, f DS UWB Space-Frequency Signalling Model In this section, the transmission signalling model, including modulation and multiple access schemes, for each distributed 71

86 CHAPTER 5: DISTRIBUTED NODES COOPERATION IN COGNIT IVE UWB USING SPACE-FREQUENCY BLOCK CODING node (e.g. source, relaying and destination nodes) is presented. In regard to UWB wireless communications, Space-Time (ST) coded MIMO transmission has been previously analyzed in [44] [47]. In [47], the authors considered various modulation and multiple access schemes, like PPM (pulse-position-modulation), M- ary phase shift keying, time-hopping (TH) as well as directsequence (DS) multiple accessing. In the following part, we take advantage of the direct-sequence UWB approach in constructing the space-frequency MIMO signalling structure. We extend the simple 2 1 MIMO model as described in section 5.1 to a general one where the relay cooperation group consists of more than two nodes. Hence, the nodes cooperation group is equipped with N T virtual antennas, where N T (N T = I) is the number of the nodes in the cooperation group. The information symbol sequences are divided into a series of blocks of N symbols. According to the proposed SFBC scheme, each block is encoded into a Space-Frequency (SF) codeword to be transmitted over N T (e.g. N T = 2 as in Figure 5.1) transmit antennas on K (e.g. K = 2) UWB frequency sub-bands independently. In the proposed SFBC scheme, different transmitting antennas transmit symbols on different frequencies instead of in different time slots as in the general STBC scheme. The SFBC-based codeword matrix can be further expressed as a K N T matrix D whose (k;i)th element corresponds to a block of d k,i,j (n), d k,i,j {-1,1}, which represents the nth (n=1, 2,, N) information symbol during the jth frame that is transmitted at the corresponding transmit antenna i (i = 1, 2,, I) over the frequency sub-band k, and j could be any positive integer. Therein, the cooperation nodes group uses the UWB spacefrequency signal matrix S whose (k;i)th element is the transmitted UWB pulse signal s i (k;t) corresponding to the symbol block of d k,i,j (n). The UWB signal s i (k;t) depends on particular modulation schemes. We consider UWB SFBC systems by utilizing the modulation of binary phase shift keying (BPSK). In directsequence BPSK UWB systems, the information bit is spread by a sequence of multiple pulse waveforms whose polarities are de- 72

87 N c 1 termined by the spreading sequence cn ( ), c n { 1,1} n c = 0 Finally, the transmitted DS-BPSK UWB signal for each element in the K N T matrix S is generalized as si k; t = K N E ki,, j k 1 NT N = c j= 0n= 1 nc = 0 Nc 1 ( ) ( c) ( f c c cp) d n c n w t jt n T jt c c,. (5.10) where w(t) is the transmitted pulse waveform (e.g. PSWF-based pulse wavelets) of duration T w, T f is the frame interval of each extended block which is divided into a number of segments ( NN c ) of chip duration T c, T cp is the time duration of Cyclic Prefix, and j could be any positive integer. The direct-sequence chip period is chosen to satisfy T c T w. Since each frame contains N c normalized pulse waveforms, we introduce the factor 1 Nc to ensure that the sequence of N c pulse waveforms has unit energy. With the factor E N being further included, the total transmitted energy via the antenna array is then kept to be T E Receiver Architecture and Processing Description SFBC-MIMO Decoupling: Frequency Exchange Algorithm Corresponding to section 5.2, let us still return to the scenario of 2 1 SFBC-MIMO architecture with two relaying nodes in each cooperation group. A generalized receiver structure at the destination node is described in Figure 5.6, where a MIMO combiner matrix with the proposed decoupling function is the key part before the resulting two decoupled MIMO signal sequences are sent to the next MMSE Rake processing unit for detection. 73

88 CHAPTER 5: DISTRIBUTED NODES COOPERATION IN COGNIT IVE UWB USING SPACE-FREQUENCY BLOCK CODING N1 ( t) N () Decoupler 2 t r() t s 1 () t ( H1 ) ( H 3) ( H 2 ) ( H 4 ) s 2 t () Figure 5.6: The decoupler structure corresponding to a SFBCbased MIMO channel At the decoupling process, the received UWB signal sequences are first fed into the proposed SFBC-related decoupling matched filter (i.e. decoupler circuit) to form the two decoupled outputs s () t and 1 s () t. Then the signal sequences 2 s () t and 1 s () t are 2 used independently to estimate the originally transmitted sequences s 1 (t) and s 2 (t). The succedent detection step can then be performed with a minimum-mean-square-error (MMSE) Rake combiner. As we know, in the general Space-Time block coding, the reason for the simplified linear detection lies in the channel orthogonality recovery processing so that H H H is diagonal, whereas H H is the MIMO decoupling combiner matrix on the receiver side. Note that H H means matrix transpose and complex conjugate operation. We propose a specific decoupling algorithm, named Frequency Exchange (FE) Algorithm, by employing a H H F special matrix with frequency exchange operation. It is a unique orthogonality recovery scheme corresponding to the H SFBC-based MIMO wireless channel. We define the HF matrix operation as a matrix transpose, complex conjugate and frequency exchanging operation. Detailedly, corresponding to each element in the matrix H, we have H F ( h () t ) = h ()( t, f f f f )

89 ( f ) f ()( ) and h () t = h t, f f, (5.11) where () i represents the complex conjugate, time-reversal and frequency exchanging operation between different UWB frequency sub-bands, such as f 1 and f 2. Note that the specific H HF matrix operation with frequency exchanging is only valid for the receiver decoupling procedure, not anyone else. Therefore, we can get (), () (), () () () () () ( H) ( H 1 3) ( ) ( ) h t h t h t h t, sr1 rd 1 f2 sr 2 r2d f1 H = F = h t h t h t h t sr2 r2d, f2 sr1 rd 1, f H H (5.12) χ 0 H and arrive at H H = F, 0 χ (5.13) 2 2 where χ h () t h () t h () t h () t h () t h () t = + sr1 rd 1, f1 rd 1, f2 sr2 r2d, f1 r2d, f. 2 The outputs from the MIMO decoupling matched filter are then given by 2 2 st h t h th = t+ h t h th t st+ N t (5.14) ( sr rdf, rdf, sr r df, r df, ) () () 2 2 ( sr t df df df df ) r r sr t r r () N () () () () () () () () () () () () () () () s t = h h t h t + h h t h t s t + t,(5.15) 2,,,, 2 2 and H ( ) = HF ( ) H ( ) = H ( ) N t N t (5.16) 1 1 N t N t. (5.17) 2 F 2 Please refer to appendix A for the detailed deduction process MMSE Rake Receiving Process In general, the finite impulse response of an UWB multipath channel, from the relaying node to the destination node, h rd (t), is 75

90 CHAPTER 5: DISTRIBUTED NODES COOPERATION IN COGNIT IVE UWB USING SPACE-FREQUENCY BLOCK CODING characterized by a tapped-delay-line filter model in discrete-time as following L 1 ' ' () = α ( ) δ rd ( τ ( )) hrd t l t l (5.18) ' l = 0 where L is the total number of the discrete channel taps, α rd (l ) and τ(l ) are the channel tap amplitude and delay, respectively. Since Rake combining reception is capable of collecting multipath signals effectively and there exist many resolvable multipath components due to high time resolution in an UWB propagation channel, the Rake receiving scheme could potentially be very helpful for UWB multihop communication scenarios. In the following part, we resort to MMSE Rake receiving process for information detection. We assume that the reference spreading sequence and the channel state information (CSI) are known in the MMSE Rake receiver. The autocorrelation function of the transmitted pulse waveform w(t) is defined by γ ( s) = w( t s) w( t) ds, (5.19) where γ(0) = 1. As illustrated in Figure 5.7, the Rake processing unit employs a L-finger Rake receiving architecture, each finger adopts a template correlation waveform ν(t) which comprises the spreading version of w(t). The output of the lth correlator in the Rake receiving unit is given by i () l () () x = v l s t dt, (5.20) where v() l v( t τ ()) l. With respect to the direct-sequence UWB-MIMO wireless channel, the MMSE Rake receiver adopts 1 c N 1 ' ' the pulse chip v() t = c( nc) w( t jt n f ct jt c cp) as the N ' c nc = 0 template correlation waveform, where the notations of T f,t cp and j 76 i

91 are the same as those in section 5.2. Rake receiver finger 0 ()dt ( ( 0) ) vt τ x 1 ( 0) x ( 0 2 ) Rake receiver finger 1 2 () st 1( ) s t ()dt ( () 1 ) vt τ x 1() 1 x 2 () 1 MMSE Combiner sign {} ŷ ŷ 1 2 Rake receiver finger L-1 ()dt ( τ ( L 1) ) vt x ( L ) 1 1 x ( L ) 2 1 Figure 5.7: The Rake processing and MMSE combing structure Thus during one arbitrary frame (e.g. jth frame), the correlator outputs of the desired transmitting data x i (l) can be expressed by i E ' ' l1= 0 l2= 0 N K 2 2 ( ) T x () l d h () t + h () t where = ki,, j sr1 sr2 N T i= 1 k= 1 (5.21) L 1 L 1 * ' ' ' ' ( l )( α ( l 1 2) ) f l l l Nˆ 1 2 () l α (,, ) +, rd rd i ( ) N 1 N 1 ' ' 1 ' ' ' ' (,, 1 2) ( ) ( ) ( ) ( () ( 1) ( 2) ) c c ll l c n c cn n n T+ l l l c c c c f γ τ τ τ N ' c n c = 0 nc = 0 77

92 CHAPTER 5: DISTRIBUTED NODES COOPERATION IN COGNIT IVE UWB USING SPACE-FREQUENCY BLOCK CODING N l = v l N t dt i. i Furthermore, the correlator outputs can be expressed in the matrix form as and ˆ () () () E Χ = DΑF+ N ˆ (5.22) N T where F is an L ( L L ' ' ) matrix whose (l, ( l1, l2)) th element is ' ' f l, l, l, and A is of size L L ' ' in which ( l, l ) th component is ( ) ' ' * sr () 1 sr () ) α 2 rd 1)( αrd ( 2 )), ( h t + h t ( l l and D is the relayed SFBC-based codeword matrix whose (k,i)th element in the jth frame is d k,i,j (n), d k,i,j {-1,1}. Subsequently, the MMSE decision rule can be stated as 1 2 ˆ E Y = arg min X DΑF. (5.23) D N T Simulation Results and Analysis This section describes the BER performance of the proposed SFBC-MIMO cooperative relay scheme combing with the MMSE Rake receiver in the standard IEEE a S-V UWB channel model [35]. The simulation parameters are listed in Table 5.1. In order to verify the performance of the proposed SFBC scheme. Table 5.1: Simulation parameters Symbol numbers Channel model IEEE a CM3,CM4 Modulation BPSK 78

93 Max. No. of selected paths 20 Figure 5.8 shows the proposed SFBC scheme s BER performance corresponding to the IEEE a S-V channel model CM3, and Figure 5.9 depicts the BER performance in CM4. Note that the multipath fading conditions in CM4 are much more severe than in CM3. It is shown in these two figures that the BER performance of the proposed SFBC scheme is acceptable. However, we can further observe that the BER performances have been obviously improved with the increment of Rake fingers in the destination node s receiver. Next, we investigate the cooperative relaying effects of multihop communications (e.g. 3-hops). In our simulation, we choose a non-regenerative relaying scheme, in which each intermediate relaying node in any cooperation nodes group just amplifies the received faded signal sequences coming from the previous hop without any error check and correction encoding processing, and sequentially retransmit them to the next hop. Figure 5.10 and Figure 5.11 depict the BER performance in the scenario of 3-hop cooperation relaying, in CM3 and CM4 respectively. From these results, we observe that the performance decreases as expected, because of the extended hops without any error detection and correcting process in each relaying stage. However, when a 20-finger MMSE Rake receiver is used, the performance of the proposed SFBC cooperation relaying scheme can still be acceptable even in multi-hop environment. 79

94 CHAPTER 5: DISTRIBUTED NODES COOPERATION IN COGNIT IVE UWB USING SPACE-FREQUENCY BLOCK CODING Figure 5.8: BER performance comparisons of 2-hop SFBC encoded cooperation scheme in CM3 Figure 5.9: BER performance comparisons of 2-hop SFBC encoded cooperation scheme in CM4 80

95 Figure 5.10: BER performance comparisons of 3-hop SFBC encoded cooperation scheme in CM3 Figure 5.11: BER performance comparisons of 3-hop SFBC encoded cooperation scheme in CM4 81