Signal Processing Requirements for WiMAX (802.16e) Base Station M SHAKEEL BAIG

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1 Signal Processing Requirements for WiMAX (802.16e) Base Station M SHAKEEL BAIG Signal Processing Group Department of Signals and Systems Chalmers University of Technology Göteborg, Sweden, 2005 EX018/2005

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3 Signal Processing Requirements for WiMAX (802.16e) Base Station (Master thesis) M Shakeel Baig Supervisors: Yusuf Jamal; Klas Brink; Rickard Fahlqvist Analog Devices Inc. Stockholm, Sweden Examiner: Prof. Mats Viberg Signal processing group Department of Signals and systems Chalmers University of Technology Gothenburg, Sweden 2005 ii

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5 Abstract e provides specifications for non line of sight, mobile wireless communications in the frequency range of 2-6 GHz. It is well implemented by using OFDMA as its physical layer scheme. The OFDM symbol time ( T s ) is to be selected depending on the channel conditions, available bandwidth and, simulations provide a means of selecting right values of T s in different channel conditions. Additionally it has been shown that certain values of T s outperform others in all conditions, thus invalidating their use. Moreover, a solution proposed by INTEL is also analyzed. One of the major requirements of OFDM is high synchronization. Detecting the timing offset of a new mobile user, entering the network, which is not time aligned using cross-correlation and auto-correlation in time domain and cross-correlation in frequency domain at the base station has been simulated. Results point that the processing load can be significantly reduced by using frequency domain correlation of the received data or by using auto-correlation followed by cross-correlation on localized data. The use of adaptive antenna system in e improves the system performance, where beamforming is implemented in the direction of desired user. Capon s method and MUSIC method have been simulated to compute the direction of arrival for OFDMA uplink. A new user, while in the ranging process, transmits data with unknown time offset and unknown direction. The thesis describes the procedure to find the two unknown one after another. iv

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7 Acknowledgements This thesis was possible because of the will and wish of ALMIGHTY and I am grateful to Him. Next, I express thanks to my Parents for their support during all these years of my education. I am grateful to Analog Devices Inc, Sweden for allowing me to work at their office for the thesis, and my thanks to its employees for providing an encouraging environment, during my stay at the office. I express my sincere thanks to my supervisors, Yusuf Jamal, Klas Brink and Rickard Fahlqvist, for their guidance and invaluable time spent on those numerous discussions we had at the office. It is in those fruitful discussions that I learned many more things apart from thesis itself and I am sure those will be helpful in future. Thanks for everything. Whenever we did not find any solution, we had one man to call to, Michel Lopez, USA. My special thanks to him for helping me during the thesis and for the careful reviewing of my thesis report. My thanks to Professor Mats Viberg, my thesis examiner, for his valuable ideas regarding beamforming, the channel model and comments on the thesis report. Lastly, I thank all my friends who helped me during my stay in Stockholm. vi

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9 Contents ABSTRACT...IV ACKNOWLEDGEMENTS...VI CONTENTS...VIII LIST OF FIGURES... X PART 0: INTRODUCTION GOAL OF THE THESIS REPORT OUTLINE INTRODUCTION TO WIMAX c a d e OFDM SYSTEM DESCRIPTION Effects of Receiver performance... 7 PART 1: CHANNEL ESTIMATION INTRODUCTION UP LINK TRANSMISSION THE BLOCK DIAGRAM Transmitter Channel Receiver PROBLEM DESCRIPTION SIMULATION RESULTS Performance in AWGN channel Performance in a Rayleigh Fading Channel Effect of mobile speed Performance in presence of Multipath Effect of multipath delay spread Effect of Channel coding DISCUSSION PART 2: RANGING INTRODUCTION PROBLEM DESCRIPTION TIMING OFFSET CALCULATION : Cross-correlation in time domain : Auto-correlation in time domain : Correlation in frequency domain FREQUENCY AND POWER OFFSET CALCULATION SIMULATION RESULTS PROCESSING LOAD CALCULATION PART 3: ANTENNA BEAMFORMING INTRODUCTION BEAMFORMING BASICS TYPES OF BEAMFORMING viii

10 3.4 PARAMETERS EFFECTING BEAMFORMING ADAPTIVE ANTENNA SYSTEM FOR OFDMA IN E DIRECTION OF ARRIVAL COMPUTATION (DOA) Capon s method MUSIC algorithm SIMULATION RESULTS CONCLUSION A. REFERENCES B. ACRONYMS ix

11 List of figures Figure 0.1: Three orthogonal subcarriers... 1 Figure 0.2: Comparison between FDMA and OFDM [5]... 6 Figure 0.3: 3 subcarriers and multipath component... 7 Figure 0.4: Perfect synchronization, no ICI... 7 Figure 1.1: Time plan from [1] Figure 1.2: Tile Structure Uplink Figure 1.3: Simulated Doppler spectrum Figure 1.4: A typical Rayleigh fading channel Figure: 1.5. The Block Diagram Figure 1.6: SNR v/s BER for AWGN channel with QPSK modulation Figure 1.7: Response of tail biting convolutional code in AWGN channel Figure 1.8: Performance of 16 QAM modulation in AWGN channel Figure 1.9: Performance in fading channel at 3GHz (without multipath) Figure 1.10: Typical channel at different Doppler frequency (350, 680, 70, 135 Hz) Figure 1.11: Performance in fading channel at 5.9GHz (without multipath) Figure 1.12: Performance of OFDM at 2 carrier frequencies Figure 1.13: Performance of 128 μs for different speed of mobile Figure 1.14: Performance of 256 μs for different speed of mobile Figure 1.15: Channel model Figure 1.16: Figure showing subcarriers and multipath Figure 1.17: Performance at 3GHz in fading channel with multi path (guard time T s /8) Figure 1.18: Performance at 5.9GHz in fading channel with multi path (guard time T s /8) Figure 1.19: Performance for different amplitudes of multipath Figure 1.20: 16QAM in fading channel Figure 1.21: Performance when multipath delay is limited with in 16 μ S (guard time T s /4).. 29 Figure 1.22: Performance when multipath delay is limited with in 100 μ S (guard time T s /4) 29 Figure 1.23: Convolutional encoder [1] Figure 1.24: Convolutional coding performance Figure 2.1: Initial ranging transmission symbol structure Figure 2.2: Process of finding peak corresponding to time offset Figure 2.3 frequency domain correlations Figure 2.4: Frequency domain correlation using IFFT Figure 2.5: Comparison of various correlation techniques Figure 2.6: Cross-correlation with double precision code and with 2 bit quantized code Figure 2.7: Effect of ranging signal amplitude on system performance Figure 2.8: cross-correlation Figure 3.1: 2 element linear array Figure 3.2: 2 element linear array far field geometry Figure 3.3: Plot of Array factor (AF) Figure 3.4: Example (non-real) of switched beamforming Figure 3.5: Switched beamforming and Adaptive beamforming Figure 3.6: Downlink part of AAS frame structure x

12 Figure 3.7: AAS diversity map zone [1] Figure 3.8: Capon s method for DOA computation (DOA of signals from two MSS is not distinguished) Figure 3.9: MUSIC method for DOA computation, DOA of signals from two MSS is seen Figure 3.10: Denominator of the MUSIC spectrum (searching for dip) Figure 3.11: Denominator of the MUSIC method. Y-axis limit set to 0 to xi

13 PART 0: Introduction Wireless communication systems have been in use for quite a long time. Many standards (to name , Bluetooth) are available based on which these devices communicate, but the present standards fail to provide sufficient data rate, when the user is moving at high speed. In view of this requirement for future mobile wireless communication systems, the present standard, e has been proposed by Institute of Electrical and Electronic Engineers (IEEE) (WiMAX) provides specifications for both fixed Line of sight (LOS) communication in the range of 10-66GHz (802.16c), and fixed, portable, Non-LOS communication in the range of 2-11GHz (802.16a, d). Also it defines wireless communication for mobiles, moving at speed of 125 KMPH, in the range of 2-6 GHz (802.16e) e is well implemented with OFDMA as its physical layer scheme, hence OFDMA is discussed here. One of the limiting factors in the performance of mobile wireless communication systems is the Inter symbol interference (ISI), caused by the multipath. In single carrier systems the symbol duration (for large system capacity) is very small and spans a wide bandwidth in frequency domain and the multipath arriving at different time instants is spread over multiple symbols leading to ISI. The complex solution is to implement an equalizer at the receiver to mitigate the effect of the channel. A much simpler solution is to opt for multicarrier systems, like OFDM, which transmit low rate data (large symbol time) on several overlapping orthogonal subcarriers. In addition a guard time is provided (Figure 0.1) at the start of each symbol. By doing so, the symbol time is made large enough so that the system becomes less sensitive to multipath. Figure 0.1: Three orthogonal subcarriers shown separately (in practice a sum of 3 is transmitted) 1

14 Multi carrier systems have the problem of inter carrier interference (ICI), due to the loss of orthogonality between subcarriers. The use of cyclic prefix [5] in OFDM ensures orthogonality over the receiver window thus avoiding ICI. In a fading channel, an OFDM system performance is highly degraded and hence channel estimation is done to overcome the effect of fading. For this, an OFDM system has pilot symbols (on pilot subcarriers) embedded in between the data symbols (on data subcarriers), which provides the channel information at the receiver. This channel estimation values at the receiver are interpolated over the data subcarriers and data symbols are decoded. Much depends on the symbol time, subcarrier spacing and pilot location in both time and frequency domain as the channel characteristics should not change significantly between pilot subcarriers, else the interpolation would not be accurate. The first part of the present thesis investigates the performance of channel estimation for different symbol times and subcarrier spacing In any OFDM system, the performance highly depends on synchronization between the transmitter and the receiver. Loss of timing accuracy leads to ISI and ICI is the result when there is loss of frequency accuracy. During start of initial ranging (process of establishing synchronization), the timing offset between the mobile subscriber station (MSS) and the base station (BS) is more than the round trip delay (RTD), which is quite high and additionally, the system may have frequency offsets. Another challenge is that the MSS does not know what power level is to be used for transmission. It starts transmitting with the least power and waits for a response from the BS; if the BS has received the transmission from the MSS then it transmits back a ranging response to the MSS. If the transmission is lost then the MSS restarts the ranging process at a higher power level, which increases interference. In OFDMA system [7], we use code division multiple access (CDMA) codes to improve the system efficiency in detecting the new user. A new MSS will transmit this CDMA code, which the BS should detect. Part two of the thesis looks into the above situation and the amount of interference caused by the unsynchronized new user entering the network. The present demand in the field of wireless communication is not only to provide data communication when the user is mobile but also to provide high data rate by consuming less bandwidth (achieve good spectral efficiency). WiMAX, the IEEE standard provides specification for efficient forward error correction techniques and optional schemes like adaptive antenna system (AAS), space time coding (STC) and multi input multi output (MIMO) systems. Of these AAS achieves high system capacity with implementation cost mainly concentrated at the base station (BS), which can be easily tolerated. Hence is a good solution for increasing system capacity with least cost. This gives many advantages as reduced interference, increased range and SNR and Space division multiple access (SDMA) at the cost of some complexity at the transmitter (BS) which is usually acceptable. A BS, in an AAS network, faces two problems when a new MSS tries to enter the network; the timing offset is unknown and the direction of arrival is unknown. Part 3 of the thesis explains the AAS scheme in e and discusses solution to the above problems, where the two unknown are found one after another. Additionally, directional of arrival (DOA) algorithm has been simulated for e uplink. 2

15 0.1 Goal of the thesis The aim of the thesis is to get an understanding of the IEEE WirelessMAN standard and analyze the receiver signal processing requirements for e BS. The idea is to make coarse calculation for signal processing load on the DSP TigerSHARC (but this report does not include any processor specific information) when implementing certain components of the receiver signal chain. 0.2 Report outline As the thesis analyzes three different aspects of WiMAX; the report is mainly divided into 3 parts namely Channel estimation, Ranging and Antenna Beamforming. The report start with brief explanation about the IEEE standard, WiMAX, a general OFDM system and some basic problems faced when implementing the system. Next in the report, the problem of channel estimation in a mobile environment and the response of various symbol times are explained. Next is the description of the total signal chain of OFDMA for e standard, followed by simulation results. A small discussion about the symbol times conclude the session. Next, the report explains the challenges faced by the system when a new user tries to enter the network. Some methods of overcoming these in e are discussed, followed by simulations, processing load calculations and discussions. The last part deals with Antenna beamforming and the requirements to implement it in e. 0.3 Introduction to WiMAX Worldwide Interoperability for Microwave Access (WiMAX) provides specifications for both fixed Line of sight (LOS) communication in the range of 10-66GHz (802.16c), and fixed, portable, Non-LOS communication in the range of 2-11GHz (802.16a & d). In addition, it defines wireless communication for mobiles, moving at a speed of 125 KMPH, in the range of 2-6 GHz (802.16e). Support for both time division duplex (TDD) and frequency division duplex (FDD) SS is provided, both using a burst transmission format whose framing mechanism supports adaptive burst profiling in which transmission parameters, including the modulation and coding schemes, may be adjusted individually to each SS on a frame-byframe basis, thus providing high data rates c Wireless metropolitan area network- single carrier physical layer (WirelessMAN-SC PHY) specification is targeted for operation in the GHz frequency band. The BS is essentially an isotropic radiator, which transmits data (downlink) to all the users designated by their connection identifier (CID). The subscriber station (SS) shall use highly directional antennas directed towards the BS. The signal chain for this physical layer, at the transmitter is defined as, randomization, forward error correction (FEC) encoder, symbol mapping followed by 3

16 pulse shaping and transmission. Randomization is done in order to ensure the carrier recovery at the receiver. Mandatory FEC scheme comprises of Reed Solomon (RS) encoder and Block convolutional coder (BTC), optional scheme includes parity check codes and convolutional turbo codes (CTC). Moreover the encoding rate depends on channel conditions and required bit error rate (BER). Adaptive modulation schemes (Quadrature phase shift keying (QPSK), 16 Quadrature amplitude modulation (16 QAM)) are used for symbol mapping, additionally, 64 QAM is provided as an optional modulation scheme. Application of this standard includes point to point (PPP) and point to multi point (PMP) microwave communication, interconnection between remote locations and backhaul services. Implementation cost and time is saved when compared with laying of cables a This part of the WiMAX standard uses single carrier (WirelessMAN-SCa PHY) physical layer specification, similar to that of c, except that it is targeted for the frequency below 11 GHz and at NLOS. The SS can be personal computers with an external box connect to an outdoor isotropic antenna [14]. Hence this is fixed NLOS wireless communication. Support for both TDD and FDD is provided, similar to c. Since single carrier in multipath environment is used, a receiver needs to perform efficient channel estimation and equalization techniques to overcome the multipath effects. Another difference is the concatenated FEC using RS and pragmatic trellis coded modulation (TCM) (rate ½ convolutional coding (CC)) with optional interleaving. Optionally to improve the performance support is provided for BTC, CTC, Adaptive antenna systems (AAS) and space time coding (STC) are provided a devices can be used to provide with T1/E1 level services to enterprises, thus eliminating wire lines and saving the implementation cost and time. Additionally it can be used to provide backhaul for hotspots being served by Also it can be used in residential locations to provide broadband internet connections d This is targeted to provide a broadband internet connection to indoor users. The SS operating on this standard use indoor antenna and a limited mobility (portable devices) is allowed [14] d uses orthogonal frequency division multiplexing (OFDM) as its physical layer specification to enable NLOS communication below 11 GHz. Since OFDM is used, the receiver is made simple by elimination of bulky equalizer. The other features have nearly been kept similar in all the physical profiles of the standards. FEC includes concatenated RS- CC followed by interleaving. Similar to a, AAS, STC schemes are provided but are kept optional. Variable FFT size and symbol time is specified, which could be fixed depending on type of environment and allocated bandwidth e Specifications are provided such that mobility of the SS at 125 KMPH is allowed. Orthogonal frequency division multiple access (OFDMA) is used as the physical layer scheme. Channel 4

17 coding is provided by use of mandatory CC and optional BTC, CTC and low density parity check codes (LDPC). Data is randomized and interleaved to avoid loss of carrier recovery and burst errors. In addition to AAS, STC, optional multi input multi output (MIMO) scheme has been specified. Code division multiple access (CDMA) codes are used along with the random window length based contention control algorithm for initial ranging, periodic ranging, bandwidth request and handoff. The inter BS communications have been defined, which will be used as a backbone network between the BS s to aid the inter-cell mobile subscriber station (MSS) handoff. This ensures fast and accurate synchronization at the cost of slightly increased complexity. Similar to d, variable FFT size and symbol time is provided which could be set depending on the environment and allocated bandwidth. Put together, the technology would enable the SS to get broadband wireless access (BWA) at all times in all locations, either when stationary, or at pedestrian speed or when traveling at 125 KMPH. Few of the difference between d and e are presented here. In OFDM, SS uses all the available subcarriers for the allocated time, but in OFDMA, user is allocated region having definition in both time and frequency. The subcarrier mapping is different in both the standards, resulting in channel estimation done in d being complex, but done less number of times. In e the channel estimation is simple, but more frequently done (because data considered, per iteration is less Channel is flat only over limited subcarriers). Another difference is use of CDMA codes for ranging in e, the receiver performs correlation to detect the user (read part 2 of the thesis), and hence more processing is involved. 0.4 OFDM system description OFDM is a multi carrier transmission scheme where the information is transmitted on multiple subcarriers, with a lower data rate, instead of one high data rate carrier (Figure 0.1) and moreover, the subcarriers are orthogonal to each other, leading to saving of bandwidth (Figure 0.2). The major disadvantage of an OFDM system is its requirement of perfect synchronization in time and frequency. But the advantages of using OFDM are far more and provide enough reasons for the popularity of the OFDM systems. A typical channel fade will degrade only a few of the subcarriers, which in most cases can be compensated by use of efficient interleaving and channel coding [8]. OFDM systems can be implemented very efficiently by using the Inverse Fast Fourier transform (IFFT) at the transmitter and Fast Fourier transform (FFT) at the receiver. The overall complexity and its increase with data rate in OFDM systems is far less than the single carrier systems [5], hence OFDM is becoming a widely accepted technology and more prominent to be used in future mobile wireless communication standards. 5

18 Saving of bandwidth Figure 0.2: Comparison between FDMA and OFDM [5] For successful operation of OFDM system, it is required that the subcarriers should never loose orthogonality between each other at any time. The advantage of an OFDM system is lost when the subcarriers are no longer orthogonal to each other. This puts forward quite stringent requirements to be fulfilled by the transmitter and the receiver. T sin 2πft.sin 2π (2 f ) t. dt = 0 0 where T is multiple of 1 -- (eq. 0.1) f Ideally, to maintain orthogonality we need that the symbol duration be exactly inverse of the subcarrier spacing and the FFT be considered over symbol duration such that it covers integer number of cycles. Moreover, the consecutive subcarriers differ by 1 full cycle only (Figure 0.1). If the system is to operate in a multipath environment, then each subcarrier should experience a flat fading, hence the subcarrier spacing should be less than the coherence bandwidth and each symbol should experience a time-invariant channel, hence the symbol time should be less than the coherence time else the complexity of receiver increases when overcoming the fading effect. Reduction of inter symbol interference, which would require bulky equalizer to be constructed at the receiver in a single carrier system, is overcome by the use of guard time in an OFDM system. A guard time is added in time domain between two OFDM symbols and the FFT is considered over duration such that there is no component from the previous or next symbol, (Figure 0.3) which nulls the ISI and thus avoiding the bulky equalizer. ISI is completely eliminated when the multipath signal delay is within the guard time. When designing an OFDM system proper values are selected depending on the environment so as to satisfy the above condition. Multi carrier systems have the problem of inter carrier interference (ICI), which results from loss of orthogonality between the subcarriers. This happens when the FFT is considered over duration where the subcarrier is not present (non-integer number of cycles), which would be the case when multipath is present and the guard time has amplitude zero. This is reduced by use of cyclic prefix [5], where we transmit a copy the last part of the symbol followed by the symbol itself. This ensures orthogonality over the FFT period in case of delayed multipath (Figure 0.3). 6

19 Figure 0.3: 3 subcarriers and multipath component shown separately, in practice the signal is a sum of all subcarriers [5] Effects of Receiver performance An unstable and non synchronized local oscillator can cause frequency drift, resulting in FFT bins being placed such that it samples component from other subcarriers along with the required, leading to ICI (Figure 0.4 & Figure 0.5). Figure 0.4: Perfect synchronization, no ICI Figure 0.5: Synchronization loss, result: ICI OFDM spectrum of 5 subcarriers, vertical line representing FFT bins. The phase noise from oscillator will cause the subcarrier spectrum to change and even though FFT bins are placed at right place in frequency domain, with phase noise, we get non-zero component of other subcarriers, which also results in ICI. Hence the stability of the oscillator is very much required. In a mobile fading channel, where the channel varies fast, the performance is highly degraded and hence channel estimation is to be done to overcome the effect of fading. For this, an OFDM system has pilot symbols (on pilot subcarriers) embedded in between the data symbols (on data subcarriers), which provides the channel information at the receiver. This channel estimation values at the receiver, are interpolated over the data subcarriers and the data symbols are decoded. Much depends on the pilot spacing in both time and frequency domain as the channel characteristics should not change significantly between pilot subcarriers, else the interpolation would not be accurate. 7

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21 PART 1: Channel Estimation 1.1 Introduction A general communication system consists of two blocks, a transmitter and receiver, connected by a channel. The information transmitted by the transmitter passes through the channel and then reaches the receiver. If the channel does not distort the transmitted signal, then the receiver can retrieve the transmitted information successfully, but in practice the channel alters the transmitted information making the task difficult for the receiver. The main aim of the designer is to reduce the number of errors made at the receiver. To achieve this, information is required at the receiver, as to how the channel alters the information, so that the channel impairments can be mitigated. When the user is mobile, the channel characteristics do not remain constant for a very long time. Hence the channel parameters need to be tracked, so that the effect can be mitigated and reconstruct the transmitted data. This part of the thesis deals with the requirements of Channel estimation at the Base station (BS) for an e uplink. Symbol time has an effect on system performance depending on the channel conditions. Different symbol times are proposed in [1] and each one has been simulated and compared for various channel condition. In addition a solution proposed by Intel coop. has also been analyzed. It is concluded that the performance of the system, for few proposed symbol times, is relatively good in all conditions. 1.2 Up link Transmission Any practical standard provides details about receiver and transmitter requirements, operating details but only the transmitter construction details are provided. Receiver construction and its performance depends on the algorithms used in implementation and are often left open for vendors to compete each other. Since this thesis is analysis BS receiver requirements the uplink part of the system is being simulated a brief description about it is presented here. The Uplink transmissions (Transmission from the Mobile Subscriber station (MSS) to the BS) have definition in both frequency and time i.e. the bandwidth allocated to a MSS is defined by a number of subchannels in frequency domain and a number of slots in time domain (figure 1.1). A subchannel is a combination (non sequential) of subcarriers, and a slot in OFDMA uplink is defined as 3 OFDM symbols. Another way of representing subchannel is a combination of 6 tiles. The tile (the smallest data unit (Figure 1.2)) spans for 3 OFDM symbols in time and 4 subcarriers in the frequency domain. The data is mapped into a tile structure as shown below. Horizontal axis represents the frequency domain and the time axis is in vertical direction. 6 (or 8 in certain special case) of these tiles form a subchannel, which is the minimum allocated 9

22 transmission region for any MSS, spanning at least a total of 72 subcarriers (6*4 subcarriers * 3 (at least) OFDM symbols). The six tiles in a subchannel are mapped far apart on the total spectrum (2048 subcarriers), for example tiles use subcarriers 448 to 451; 512 to 515; 984 to 987; 1189 to1192; 1505 to 1508; 1753 to Moreover the location of the tile structure changes for every 3 OFDM symbols (due to rotation scheme). Figure 1.1: Time plan from [1] Data subcarrier Symbol 1 Symbol 2 Symbol 3 Pilot subcarrier Figure 1.2: Tile Structure Uplink (Mandatory) Since the subcarriers are far apart in both time and frequency domain except for with in a tile, the channel estimation is to be done on each tile separately and hence any knowledge or prior estimate about the channel response which could improve the system performance is not available. 1.3 The Block Diagram The Block diagram (Figure 1.5) represents the whole system model or the signal chain at base band. The block system is divided into 3 main sections namely the transmitter, receiver and the channel. The model has been tested with and without the channel coding (part in doted 10

23 box representing the channel coding and decoding). The bit error rate (BER) plots have been obtained for at least 2000 errors to get a good confidence limit Transmitter Data Generation: The data is generated from a random source, consists of a series of ones and zeros. Since the transmission is done block wise, when forward error correction (FEC) is used, the size of the data generated depends on the block size used, modulation scheme used to map the bits to symbols (QPSK, 16QAM), and whether FEC is used or not [1]. The generated data is passed on to the next stage, either to the FEC block or directly to the symbol mapping if FEC is not used. Forward error correction: In case error correcting codes are used, the data generated is randomized so as to avoid long run of zeros or ones, the result is ease in carrier recovery at the receiver. The randomized data is encoded using tail biting convolutional codes (CC) with a coding rate of ½ (puncturing of codes is provided in the standard, but not simulated here). Finally interleaving is done by two stage permutation, first to avoid mapping of adjacent coded bits on adjacent subcarriers and the second permutation insures that adjacent coded bits are mapped alternately onto less or more significant bits of the constellation, thus avoiding long runs of lowly reliable bits. Symbol mapping: The coded bits (uncoded, if FEC not used) are then mapped to form symbols. Modulation scheme used is QPSK or 16QAM (QPSK unless otherwise specified) with gray coding in the constellation map. In any case the symbol is normalized so that the average power is unity, irrespective of the modulation scheme used [1]. Subcarrier allocation: The subcarrier allocation is mentioned in the section 1.2 (Uplink transmission). This separates data into set of 4 subcarriers for 3 time symbols, named as the tile structure. Symbols are allocated indices representing the subcarriers and OFDM time symbol, and then passed onto the next stage, the IFFT, to convert into time domain. IFFT and cyclic prefix: An N point inverse discrete fourier transform (IDFT) of X(k) is defined as x 1 1 N N n= 0 ( n) = X ( k) e 2πkn j N for n =0,1,. N-1. (eq. 1.1) From the equation we can infer that this is equivalent to generation of OFDM symbol. An efficient way of implementing IDFT is by inverse fast fourier transform (IFFT). Hence IFFT is used in generation of OFDM symbol. The addition of cyclic prefix is done on the time domain symbol obtained after IFFT. The IFFT size ( N value) is considered as 2048 in 11

24 simulations. This data is fed to the channel which represents Rayleigh fading channel model and also implements multipath as shown in block diagram Channel In NLOS wireless communication, the received signal is a combination of many multipath signals, which are result of reflections from surrounding objects. These multipaths have different amplitude and phase and may add either constructively or destructively leading to a complex envelope, i.e. fading. Fading characteristics depend on the channel parameters (rms delay spread and Doppler spread) and signal parameters (symbol period and bandwidth). Multipath delay spread leads to time dispersion and frequency selective fading and Doppler spread leads to frequency dispersion and time selective fading. Any mobile channel is one of the four mentioned below [2] based on Based on multipath time delay spread Flat fading Freq selective fading BW of Signal < BW of channel [ B << B ] [ B >> ] s c s B c Delay spread < symbol period [ T s >> σ Γ ] [ T s << σ Γ ] Based on Doppler spread Fast Fading [Channel changes within symbol period] Slow fading High Doppler speed low Doppler speed Coherence time < Symbol period [ T < T ] [ T > ] c s c T s where B s = Bandwidth (BW) of signal B c = Bandwidth (BW) of channel over which the channel is flat or coherence BW T s = Symbol period (including guard unless mentioned) σ Γ = RMS delay spread (due to multipath) Γ max = maximum delay spread T = coherence time c A 3 path Rayleigh fading channel has been simulated for a given Doppler frequency (depending on vehicle speed and carrier frequency) and excess delay spread (depending on multipath). Each simulated multipath has a Rayleigh distributed amplitude and uniformly distributed phase. The fading channel has been modeled using Clarke model [2] and simulated using Smith s method [2], [15]. The power spectral density is given by 1 S( f ) = k f f m else = (eq. 1.2) 2 1 ( f f m ) where k is a constant [15]. 12

25 Two independent Gaussian random sources ( a & b ) are used to generate the complex Gaussian random variable ( G = a+jb ). A filter generated by eq. 1.2 is used to shape it in the frequency domain. By using an IFFT ( r (t) = IFFT (S (f).*g) ), we get an accurate time domain waveform of Doppler fading [2]. Figure 1.3: Simulated Doppler spectrum Using Smith s method, the system generates time samples of the fading channel. The data is multiplied in time domain with the fading channel output. 13

26 Figure 1.4: A typical Rayleigh fading channel Figure 1.5 shows simulated Rayleigh fading channel for the speed of 125 KMPH, and frequency of 5.9GHz. Output = fading * input jφ ( t) r( t) = α( t) e s( t) -- (eq. 1.3) s(t) is the transmitted signal α (t) is the amplitude of the fading channel (Rayleigh distributed) φ (t) is the phase of the fading channel (uniformly distributed) According to the standard the maximum supported speed of mobile is 125 KMPH and the operating frequency range is between 2 6 GHz. The system has been simulated for speeds 30, 80, 125 KMPH and frequency band of 3 GHz and 5.9GHz. Three multipaths were simulated with uniformly distributed phase. For multipath the amplitude and delay has been chosen as a random parameter, the first path does not have any excess delay and the amplitude is scaled by a uniformly distributed number in the range of 0 to 1. The other 2 paths have their amplitude scaled by uniformly distributed number between 0 to 0.9 and 0 to 0.7. The excess delay is selected as a uniformly distributed random parameter. Finally additive white Gaussian noise (AWGN) is added as a last component in the channel. velocy( m / s) * frequency( Hz) Doppler _ frequency( f d ) = --- (eq. 1.4) speed _ of _ light( m / s) Coherence _ time( T c ) = 0.423/ f d --- (eq. 1.5) 14

27 1.3.3 Receiver The first thing done at receiver (in simulation) is removal of cyclic prefix, thus eliminating the inter symbol interference (ISI). Data is then passed through the serial to parallel converter of size 2048 and then fed to the FFT for frequency domain transformation. The signal was distorted by the channel, to reconstruct the original signal we need information as to how the channel acted on the transmitted signal so that we can mitigate its effect. This is called equalization. In an OFDM system, this is done by channel estimation and interpolation. As we need at least one tile structure (3 OFDM symbols) to detect the data, storage of 3 OFDM symbols is provided followed by the subcarrier de mapping. The pilot subcarriers are used for channel estimation and synchronization at the receiver. In the simulation least squares (LS) estimate has been used for channel estimation at the pilot subcarriers. If D(t) is the transmitted data (known if pilot), Y (t) is the received data, and C (t) is the unknown channel response, then Y ( t) = D( t) * C( t) + N ( t) -- (eq. 1.6) where N ( t) represents the AWGN noise. The channel can be estimated for known data symbols, i.e. pilot subcarriers as, C ( t) = Y ( t) D( t) -- (eq. 1.7) The estimate is simple but is highly affected by SNR or the noise power, as the assumption made is absence of noise from the receiver power. This information about channel at pilot subcarriers is interpolated over the whole tile structure, to recover the data on each data subcarrier (Figure 1.1). Separate one dimensional linear interpolation has been done for values between two subcarriers (the result: straight line), hence the performance is not effected much for various one dimensional interpolation algorithms. Since we do linear interpolation the channel is assumed to be changing linearly with in the tile, this assumption might not be true depending on the symbol time. This generates a noise floor at the receiver (Errors are generated due to addition of AWGN noise and due to this approximation of fading channel as a linearly varying channel. Beyond a certain value of SNR, the BER is nearly constant for any further increase in SNR.). For larger symbol time, as will be seen in simulations, this noise floor is reached at lower SNR, hence results in poor performance. 15

28 Randomization Data bits Convolutional coding Modulation scheme (QPSK, 16QAM) Subcarrier allocation S/ P IFFT P/ S Cyclic prefix Interleaving AWGN fading delay fading delay fading Remove cyclic prefix Deinterleaving S/ P FFT P/ S Subcarrier demapping Channel Estimation Interpolation Symbol Demapping Convolutional decoding BER calculation Timing, Frequency and power offset detection Derandomization Figure: 1.5. The Block Diagram

29 1.4 Problem description For a mobile fading channel with the specifications given in the standard [1], the maximum Doppler frequency would be around 700Hz and the corresponding Coherence time of T c = 600 μ S. Due to scalability, the useful symbol time period is not a constant value and in some cases (FFT size = 2048; Bandwidth of total channel = 1.75 MHz) is 1024 μ S. This being far beyond the coherence time and results in fast fading (channel changes with in symbol duration), which is difficult to track leading to poor performance. An urban environment can suffer from a RMS delay spread ( σ Γ ) of μ S [2]. This would relate to a Coherence bandwidth of 8 KHz (50% frequency correlation 1/ (5* σ Γ )). The frequency spacing between subcarriers is in some cases (FFT size = 2048; BW of total channel = 28 MHz) is as large as KHz; more than the coherence Bandwidth. And the symbol will experience a frequency selective fading instead of flat fading. In [3], INTEL corp. addresses this issue by keeping a fixed subcarrier spacing of ~11.1KHz corresponding to an OFDM useful symbol time (usually ~1/ B s ) of 89.6 μ S. With these values the coherence time will span for around 6 ODFM symbols (worst case) in time domain thus making it slow fading. The exact relation between coherence BW and the rms delay spread is a function of channel impulse response and applied signal [2]. In [4] the required pilot spacing for successful interpolation in time and frequency domain is given as Ts Maximum excess delay Γ max = -- (eq. 1.8) N N f With Γmax = 20 is the pilot spacing in frequency domain f μ S and Ts = 100 μ S (symbol time including guard) we get N f = 5 For time interpolation Doppler freq should be less than 1 F D max = -- (eq. 1.8) 2N T (1 + Δ) T s t s is OFDM symbol duration including guard Δ is Guard interval factor is Pilot spacing in time domain N t With FD max = 700 Hz, T s = 100 μ S, we get min pilot spacing in time domain should be 5.7, which is well satisfied for 89.6 μs of symbol time [3] but not all the values mentioned in the standard (64 μ S,128 μ S,256 μ S,512 μ S,1024 μ S - ETSI)[1]. Even though the proposal from [3] works well theoretically, the performance is not as expected, this along with all proposals from [1] are investigated by means of simulation. 17

30 1.5 Simulation results The simulations have been made for various symbol times mentioned in the IEEE standard [1] and the Intel s recommendation [3] to see the effect of fading, multipath, operating frequency range, and mobile speed, on system performance. The hierarchal structure given below summarizes all the simulations being done. Scalable OFDMA IEEE standard INTEL recommendation Check Fading Multipath Modulation Fading Multipath Modulation Vary Speed RMS delay QPSK Speed RMS delay QPSK Frequency Amplitude 16QAM Frequency Amplitude 16QAM Simulation settings: Symbol time: 64 μ S, 128 μ S, 256 μ S, 512 μ S, 1024 μ S - ETSI Guard time: 1/4, 1/8, 1/16, 1/32 of symbol time. Frequency: 3, 5.9 GHz (2-11 GHz specified in [1]) Speed of mobile: 125 KMPH (peak) Modulation: QPSK, 16-QAM. FFT size: 2048 Assumptions Power in guard time is not considered Performance in AWGN channel The system model has been tested for QPSK and 16 QAM modulations with an AWGN channel and the simulation results are shown in the Figure 1.5 and 1.7 respectively. It is convincing to see that the theoretical and the simulation results overlap. Please note that the signal power in the cyclic prefix is not considered while simulating. If considered the performance degrades by around 0.96 db for cyclic prefix of ¼ and around 0.5 db for cyclic prefix of 1/8. The theoretical curve is given by [2] as 2E b Pe = Q where E b is the energy per bit. -- (eq. 1.9) N o 18

31 Figure 1.6: SNR v/s BER for AWGN channel with QPSK modulation Channel coding improves the performance significantly. The next simulation was done for AWGN channel with QPSK modulation scheme with rate ½ tail biting convolutional code (G1 = 171; G2 = 133). Figure 1.7: Response of tail biting convolutional code in AWGN channel Similarly the theoretical curve (symbol error rate) for 16 QAM system is given by 19

32 P e 2E min = 3 * Q where E min is the energy per bit (minimum) -- (eq. 1.10) N o Figure 1.8: Performance of 16 QAM modulation in AWGN channel Performance in a Rayleigh Fading Channel A Rayleigh fading channel has been simulated and the data is passed through it, followed by addition of AWGN noise. A carrier frequency of 3GHz is considered with an FFT size of The guard time assumed was 1/8 times the symbol period. QPSK modulation will be used in all further simulations (unless otherwise specified). Figure 1.9 shows the simulation results for a fading channel at carrier frequency of 3GHz and at a mobile speed of 125 KMPH. A single multipath channel has been considered for this simulation plot. Since there is no excess delay spread the only parameter affecting the graphs is the Doppler, and as described in the problem description the system with smallest symbol time will experience the most flat channel, as most of its symbols are well with in the coherence time. The simulation results very well corroborate it. The system performs best when the symbol time is 64 μ S, and the performance gradually reduces as the symbol time is increased. 20

33 Figure 1.9: Performance in fading channel at 3GHz (without multipath) The variations in Channel envelope are dependent on the carrier frequency and the mobile speed velocy( m / s) * frequency( Hz) Doppler _ frequency( f d ) = -- (eq. 1.11) speed _ of _ light( m / s) These variation are shown in figure 1.10, the Doppler is around 350, 680, 70, 135 Hz Figure 1.10: Typical channel at different Doppler frequency (350, 680, 70, 135 Hz) 21

34 Keeping all the parameters constant, we run the simulation for a carrier frequency of 5.9GHz. Since the carrier is much higher, the Doppler increases, fading becomes fast and we get degradation in the performance, which is shown in figure Additionally, the response of convolutional coding on the system with symbol time of 128 μ S and 256 μ S has been shown. It indicates that the response of channel coding is also dependent on the symbol time and may differ significantly. The results at two frequencies become much clear when plotted together, in figure We see that the performance degradation is more significant for symbol time 256, 512 and 1024 μ S. The reason is that for these values the tile structure is not within the coherence time of the channel. Figure 1.11: Performance in fading channel at 5.9GHz (without multipath) 22

35 Figure 1.12: Performance of OFDM at 2 carrier frequencies (dotted line for 3GHz and solid line represents 5.9 GHz) Effect of mobile speed To see the effect of mobile speed on system performance the simulations were made by keeping the system parameters same as before at frequency 5.9GHz but at different speeds 30, 80 and 125 KMPH. By changing the mobile speed, Doppler changes and the coherence time of the channel is changed according to equation (eq. 1.4) and (eq. 1.5). For low speed, the channel remain flat for much larger time (figure 1.10) hence the performance improves for certain values of symbol time. This is shown for 128 and 256 μs in figure 1.13 and 1.14 respectively. 23

36 Figure 1.13: Performance of 128 μs for different speed of mobile Figure 1.14: Performance of 256 μs for different speed of mobile Performance in presence of Multipath 24

37 Multipath delay spread leads to time dispersion and may result in frequency selective fading depending on the subcarrier spacing (figure 1.16). To maintain orthogonality between subcarriers, the subcarrier spacing is set as 1/symbol time (excluding guard time). Two multipaths, in addition to one used earlier have been considered in the simulation. The delay has been introduced as a random parameter (uniform distribution) is within the guard interval and the amplitude was scaled by a random parameter (uniform distribution) between 0 to 0.9, for the second multipath and 0 to 0.7 for the third multi path, relative to the main path (figure 1.15). Simulation was also run with the amplitude scaling of 0.1 and found that the effect of multipath becomes insignificant, as long as it is within the guard time. Figure 1.17 and 1.18 shows the simulation results for multipath Rayleigh channel at 125KMPH and two different frequency bands 3GHz and 5.9GHz respectively. In figure 1.19 we see the effect of multipath amplitude on the bit error rate. From transmitter Rayleigh fading simulator a1 U (0,1) τ 1 Rayleigh fading simulator Rayleigh fading simulator a2 U (0,0.9) τ 2 To receiver AWGN a3 U (0,0.7) Figure 1.15: Channel model One of the causes for performance degradation results from loss of orthogonality due to Inter carrier interference (ICI), but by the use of cyclic prefix this can be avoided and as long as the maximum excess delay is with in the cyclic prefix, Inter symbol interference (ISI) can be avoided. In the simulations these conditions have been satisfied. 25

38 Figure 1.16: Figure showing subcarriers and multipath separately, in practice a combination is transmitted. Figure 1.17: Performance at 3GHz in fading channel with multi path (guard time T s /8) Figure 1.18: Performance at 5.9GHz in fading channel with multi path (guard time T s /8) 26

39 The performance at T s = 64 μs is the best if we have a guard time of T s /4. Even though the multipath delay spread is within the cyclic prefix (theoretically no ISI and ICI), but still when compared with the case of no multipath, we find a degradation in performance of the system. This is due to the different phase offset on different subcarriers, resulting form multipath [5]. Figure 1.19: Performance for different amplitudes of multipath. Amplitudes are attenuated relative to the main path At the receiver we get an added version of pure sine waves (delayed) on each subcarrier. The addition does not destroy the orthogonality, because we do not consider the cyclic prefix for samples in FFT period (figure 1.16), but the addition results in different phase shifts on each subcarrier [5]. Different phase shift on pilot and data subcarriers and due to the interpolation scheme being used to equalize the symbol, the phase shift results in performance degradation. This is seen in figure 1.19 for a time period of 256 μ S. Figure 1.20 gives the performance of 16QAM in a Rayleigh fading channel with multi path. The Doppler is ~680 Hz, and multi path is within the guard time, limited to 8 μ S. It should be noted that the plot shows bit error rate versus SNR per bit. 27

40 Figure 1.20: 16QAM in fading channel Effect of multipath delay spread So far we see that the symbol time of 64 μ S has performed the best, but it should be noted that this value cannot be used in channels having maximum excess delay of more than 16 μ S, else ISI would result. Table 1 gives a summary of various symbol time durations (ETSI [1]) and their corresponding maximum guard time (¼ times symbol time). Symbol time in micro sec Maximum guard time in micro sec (1/4*symbol time) INTEL Table 1.1: Symbol time and maximum guard time 28

41 Figure 1.21: Performance when multipath delay is limited with in 16 μ S (guard time T s /4) Figure 1.22: Performance when multipath delay is limited with in 100 μ S (guard time T s /4) In figure 1.21 we find that, when the delay is limited to 16 μ S, the system with a symbol time of 128 μ S performs the best. Hence it should be the obvious choice in environment where the maximum excess delay profile is around 16 μ S. Similarly Figure 1.22 shown simulation results at 100 μ S and here also we find system with symbol time of 128 μ S performs best. 29

42 The value of the delay is a characteristic of the channel and varies in different environments. Hence selection of the symbol time is to be done depending on the channel, also its worth to note that longer the guard time, more is the power wasted. In [2], the rms delay spread is given to have a value of maximum in urban environment of 25 μ S, and the maximum excess delay can be 2 4 times the rms delay spread [5]. Hence by considering the worst case we get a maximum excess delay of 100 μ S (25*4). Figure 1.22 gives the system performance at this value, we see that the performance of the system with useful symbol duration of 128, 256 μ S is better compared to other symbol durations. In case of low Doppler and same excess delay spread, system with symbol duration of 256 μ S outperforms all other systems. From the results, with simulations done at a mobile speed of 125 KMPH, we can infer that the system with a useful symbol time of 512, 1024 μ S perform worse in all cases when compared with useful symbol time of 64, 89.6, 128, 256 μ S. Hence there is no point in using these values as the useful symbol durations. Moreover 64 μ S performs better in case of low excess delay spread, 128 μ S performs better in channel with high Doppler and high excess delay spread and 256 μ S is optimal in channels having low Doppler and high excess delay spread. The solution from Intel, about the use of fixed symbol time of 89.6 μ S works well only in few channel environments, hence is not a good solution Effect of Channel coding In practice we implement channel coding, to get a better performance (reduced BER at low SNR) e specifies tail biting convolutional coding scheme as mandatory, for implementation by all the devices compliant with the standard. Optionally, it provides specification for zero terminated convolutional codes, block turbo codes, block convolutional codes and low density parity check codes [1] [7]. Figure 1.23: Convolutional encoder [1] 30

43 There are three possibilities of implementing convolutional codes [20] based on boundary conditions and initial state of encoder/decoder. One possibility is that the encoding, transmission and decoding is continuous and goes on indefinitely. But, e users are not transmitting data continuously. Second possibility is that the encoder operates on a block of data, starts and ends in the same state, known to the decoder. These are the most commonly used type of convolutional codes with the known state being all zero state. The third possibility is that the encoder operates on a block of data, encoder and decoder start and end in the same state, but the state is unknown to the decoder. Tail biting convolutional codes fall under the third category and are generated by making the encoder start state and end state same, which is given by the last bits to be encoded. As the encoder starts with an initial state being its last bits, it is referred to as tail biting. The zero terminated convolutional codes start and end in all zero state, and to end in an all zero state we require to flush the memory of the encoder by feeding extra zeros into to encoder (we transmit extra bits). For e this will be 6 bits (constraint length 7) per block (figure 1.23). By using tail biting convolutional coding this can be avoided and thus saving 6 bits per block of transmission. The result is that the decoder becomes complex as it does not know the initial state. In Viterbi decoding, no matter what state we start in, as we move along in the trellis, the path gets converged to the desired path. This fact is utilized at the decoder and the viterbi decoder is made to run on the input data in a cyclic manner. First we feed the decoder with the last few bits (equal to traceback length), followed by the original data and finally first few bits (equal to traceback length). By the time the decoder starts decoding original data it has converged to the desired path and initial state. Figure 1.24: Convolutional coding performance 31

44 Tail biting convolutional codes have been simulated in the thesis. The specified encoder is a rate ½ coder with constraint length 7, G1 = 171, G2 = 133 (figure 1.23). Additionally, puncturing capability is provided to achieve rates of 2/3, 3/4 and 5/6 (simulation was done for rate ½ only). Data is transmitted in blocks of variable length (6 to 36 bytes), as specified in [1]; block length depending on the modulation scheme (QPSK, 16QAM, 64QAM), encoding rate and the concatenation rule being used. Block length of 36 bytes was used in the simulations. Simulation was done at 2 different Doppler frequencies for systems operating using 128 and 256 μ S symbol times. Rayleigh fading channel with multi path limited to 16 μ S has been used and the system has a guard time of 32 μ S. As seen from figure 1.24, the system performance with symbol time of 128 μ S does not change much with Doppler changes when compared with system at symbol time of 256 μ S. Due to complexity and time restrictions, simulations were limited to system operating on the above two symbol times. 1.6 Discussion In [1] it is proposed that for a FFT size of 2048, to get different bandwidths, one should use symbols with different time durations. But, as we see, this does not result in good performance in all cases. In [3] the use of a fixed time period is proposed and to get variable bandwidth the size of FFT is to be varied i.e. scalable FFT. The solution seems to be good, but the value of symbol time used might be worth discussing. The coherence time and the coherence bandwidth of the channel, form the major parameters influencing the value of the symbol time. We need to have a flat channel over the subcarriers bandwidth in frequency domain and 3 subcarriers in time domain. Also from the calculations we find that the coherence time for the maximum speed and the highest carrier frequency is 600 μ S. Hence in time domain the OFDM symbol including guard band should have a span of not more than 200 μ S (600/3). The recommendation of 89.6 μ S in [3] well satisfies this limit. This is also satisfied for a symbol time of 128 μs in some cases. As mentioned in [2] the worst case rms delay spread ( σ τ ) in urban environment can be 25 μ S, which translates to a coherence bandwidth ( B c 50% correlation) of 8 KHz. 1 B c = -- (eq. 1.12) 5σ τ In an OFDM system to achieve orthogonality we need to have symbol time (excluding guard time) as multiple of 1/subcarrier spacing. Hence for 89.6 μs we need to have a subcarrier spacing of KHz and for 128 μ S we require 7.81 KHz. This shows that 128 μ S is theoretically a better option than 89.6 μ S. Also to remember is that 128 μs is more effected by fading than 89.6 μ S and in practice fading is more dominant and the maximum rms delay of high value is seen in very few environments (urban). By observing figure 1.18, 1.21 and 1.22, we can fix the symbol time as either 64 or 89.6 or 128 μ S depending on the rms delay profile of the environment [2]. 32

45 33

46 PART 2: Ranging 2.1 Introduction Total synchronization of an OFDM system is a very important criterion which should be fulfilled to avoid any interference (ISI and ICI) leading to performance degradation. In OFDMA it is required that all transmissions from various mobile subscriber station (MSS) should arrive at the base station (BS) at the same time. Imagine a cell size of 20 Km. we, then have a maximum round trip delay (RTD) of around μ S. This means that, instead of arriving at expected time at BS, data may arrive anytime within 0 to μ S of delay. If the symbol duration is 64 μ S, the amount of error in detection of data at BS is very high! The whole network should be synchronized to one reference and in WiMAX this reference is the BS clock. All data is expected to arrive at the same time at the BS receiver and all data addressed to the MSS is transmitted at same time. The MSS s, which are distributed all over the cell, receive data at different instant of time and similarly transmit data at different instant of time depending on their distance from the BS. A MSS at the cell boundary receives data quite late and transmits data very early when compared with MSS close to the BS. When a new MSS is seeking entry into the network, its distance, with reference to the BS, is not known hence the RTD is not known. The MSS does not have any idea as to what time or power should be used for transmitting the initial signal. This is the BS s job to detect this new MSS, find the misalignment between the new MSS and the network, and then send response, to correct it. Reducing system complexity without compromising with performance has been the major focus of the testing various methods in this part of the thesis. It has been shown that a better approach is to use frequency domain correlation by using IFFT, which is very simple and efficient in implementation. The below section starts with a brief description of this problem and how e system handles this situation. Next the report explains the calculation of timing, frequency and power offset. Major focus is to reduce the complexity of the system, and still maintain the system performance at an acceptable level. Methods to estimate the timing offset, using both time and frequency domain correlation have been explained and later corroborated with simulation results. It is shown that, in time domain, the complexity of implementing a full crosscorrelation is very high and can be significantly reduced if the CDMA code at the receiver is quantized and represented using just 2 bits. 34

47 2.2 Problem Description An OFDM system performance highly depends on synchronization between the transmitter and the receiver. When a new SS or MSS is trying to enter a network, it is not synchronized. Hence it tries to achieve coarse synchronization by listening to the transmissions from the BS, and then starts transmitting to achieve fine synchronization. The MSS starts transmission by the least possible power, each time increasing it by a level, if nothing is heard back from the BS. The BS is to detect the new MSS and calculate the time offset, frequency offset and power offset, then reply back to the MSS to correct its transmitting parameters before transmitting data. The process goes on (maximum 16 number of times) until the MSS has achieved synchronization. This process of obtaining synchronization and logging onto the network is known as initial ranging. The BS requires that all the signals received at the BS be time synchronized, irrespective of the source location in the cell. During start of initial ranging (process of establishing synchronization) the timing offset between MSS and BS can be more than the RTD, which is quite high. The subcarriers carrying data from the new MSS might have frequency offset and are delayed (compared with signal from other MSS) causing loss of orthogonality over the FFT period, hence resulting in ICI. Moreover if the new MSS uses more power, its probability of getting detected is more, but it leads to increased interference to the data on other subcarriers. Hence the requirement is to detect the new MSS at BS with the least possible power. In e OFDMA system [1], [7], code division multiple access (CDMA) codes are used to improve the system efficiency in detecting the new user. A new MSS will transmit one of the predefined CDMA codes, which should be detected at the BS. The BS is not only to detect the new MSS but also to calculate its timing, frequency and power offset. Power offset can be detected just by calculating the difference between the required power and the received power. Next section describes in detail the process of recovering the timing and frequency offset information and the causes for performance degradation. 2.3 Timing offset calculation 2.3.1: Cross-correlation in time domain The CDMA code (defined in frequency domain) which is used for ranging is defined such that it has very good autocorrelation properties. This fact is harnessed in detection of the timing offset. The received signal in time domain is stored and cross-correlation is performed between the received signal and different predefined CDMA codes (to know which code was transmitted) in time domain. For the same code we get a correlation peak, index of which gives the time offset. In presence of multipath, we get many peaks corresponding to each multipath signal. 35

48 Data is represented by using double precision in MATLAB, this is correlated with double precision representation of the CDMA code (in time domain) to find the correlation peak corresponding to the time offset (eq. 2.1). n R( m) = ( k) x( m + k 1) k = 1 Where R is cross-correlation output c is the code x is the received data n is the length of code t is length of x n c m = 1,2,3,...t -- (eq. 2.1) The amount of processing required to achieve is quite high for the digital signal processor (DSP) also the BS has a limited time to process this information as the MSS is expecting ranging response from the BS. Instead, another way is to quantize the CDMA code in just two levels (consider sign bits only) and correlate it with the received data. Of course the performance is degraded and to overcome it, the received signal strength of the ranging MSS, at the BS, is required to be slightly more : Auto-correlation in time domain The time offset can be very large depending on RTD, and this corresponds to a lot of samples to operate on. Instead of running cross-correlation over all the available samples, a much faster method is to locate the probable time of transmission of the signal and then cross correlate this localized data with different codes. To locate the probable time of transmission auto-correlation (process is described below) of the received data is performed, this will result in a peak or a plateau at coarse estimate of the location on time axis. But for the process to give satisfactory results, it is required that the received signal strength at BS from the ranging SS be very high, this might cause interference to other users on data subcarriers. Figure 2.1: Initial ranging transmission symbol structure (figure 240 from [1]) The process is made possible only because of the repetitive structure in which the data is transmitted. Note that the second symbol does not have a cyclic prefix but a post fix! This fact 36

49 is utilized here. It is performed by considering few samples (one OFDM symbol) at a time (window a) and multiplying it with the same size consecutive data (window b) and computing the sum over it (Figure 2.2). This represents the correlation value at that instant of time. Similar process is repeated over the entire data, by sliding the window one sample every time. Correlation output starts increasing form when the window a goes over the cyclic prefix (figure 2.1). When the window a hold data representing the code and window b hold the same, the multiplication and sum produces a high peak (peak remains for a period of 2 * cyclic prefix) representing the time offset of the user (eq. 2.2). After this peak the correlation output starts to fall. R( m) = m+ N 1 k= m x ( k) x( N + k) m = 1,2,3,... t -- (eq. 2.2) Where R is cross-correlation output x is the received data N is the length of code t is length of x 2n Window a Window b Received data Time Figure 2.2: Process of finding peak corresponding to time offset The above procedure can be simply represented as one time correlation over the total window and the next step is nothing but one subtraction (of the first value) and one addition (of the last value) to the previously obtained value. Thus the calculation is significantly reduced. After locating the time offset plateau, cross-correlation is performed between the localized data with different codes. One single code will have a good cross-correlation value and we get two correlation peaks because of repetition of the code twice as in Figure 2.1. This is the bases for calculation of frequency offset : Correlation in frequency domain The received signal is a combination of data from synchronized users and CDMA code from the ranging subscriber. Until now we considered correlation in time domain, where the correlation is performed over the entire received signal. Timing offset can also be found by performing the correlations in frequency domain. The advantage gained is less interference, as 37

50 we can separate the data subcarriers from the subcarriers used for ranging. A time offset in time domain corresponds to phase offset in frequency domain. x( n n o DFT ) e jwn o X ( e jw ) -- (eq. 2.3) Rx data Delay CDMA code CDMA code FFT window FFT window FFT window Figure 2.3 frequency domain correlations The detection of timing offset constitutes the following steps; the ranging subcarriers are separated from data subcarriers by taking the FFT over the received signal. The data on the ranging subcarriers are provided with different phase shifts (0 to 2π ) and correlated every time with the CDMA code (in frequency domain), to check for the peak. The number of steps in between 0 to 2π provides us with the resolution in detection of timing offset. For detecting integer sample delay, the number of steps should be equal to size of the FFT. As shown in the figure 2.3, the FFT is considered over the received data and since there is a delay involved, only one of the three FFT s would correspond to the circularly shifted code. It is this FFT output, that gives us the timing offset value (second FFT in figure 2.3). Then we multiply it with phase component to get the required phase shift corresponding to integer number of samples in time domain, finally we correlate it with the CDMA code. Simulation results prove that this system works very well because of reduced interference from the data subcarriers, but the complexity is very high because of the high number of multiplications required to achieve the phase shifts. Instead of providing phase shifts by multiplication of phase component, a very simple method is to take an IFFT after multiplication of code in frequency domain. IFFT is equivalent to providing phase shift (figure 2.4), hence reduces a lot of complexity. X ( k) = 1 N N 1 n= 0 x( n) e j2πkn / N x( n) = 1 N N 1 k= 0 X ( k) e j2πkn / N Signal in FFT j 2πkn0 / N x( n n ) e Xˆ ( k) ˆ 0 e 2 ˆ 0 / N X ( k) X ( k j πkn IFFT For n = n0 ) we get a peak. CDMA code X (k) 38

51 Figure 2.4: Frequency domain correlation using IFFT. Of all the methods investigated here, the frequency domain correlation method mentioned above, turns out to be the simplest in terms of complexity. Moreover the performance, as seen from the simulation results is better. Hence, the frequency domain correlation method is a better choice for detecting the time offset of the ranging MSS. 2.4 Frequency and Power offset calculation The phase of the correlation output in time domain is equal to the phase drift between samples that are Symbol _ Time FFT _ size seconds apart. Hence frequency offset can be obtained by dividing correlation phase by 2 πt [5]. e jw o n DFT x( n) X ( e j ( w wo ) ) -- (eq. 2.4) When the MSS achieves coarse synchronization, it decodes the UCD message which contains information as to the maximum power that the BS can receive and the power which was transmitted by the BS. The MSS calculates the Received signal strength and computes the losses in the channel and calculates the maximum power that it can use for transmitting the ranging request (CDMA code). After acquiring such information it will transmit at a power level below the maximum level and start the ranging process, if it does not get a response back form the BS, then it transmits the CDMA code at a higher power level. If in case the MSS has achieved the coarse synchronization and yet unable to decode the UCD message, it will start transmitting at the lowest possible power level and increasing it a level higher until it receives a response. Power offset at the BS is simply calculated as (required power at BS - received power). 2.5 Simulation results The main aim of the simulation is to compare the performance of various methods used for detection of timing offset. Two users, one transmitting data on 64 subchannels and another user transmitting ranging code on 6 subchannels, are simulated. In all the simulations the ranging code of length 144 bits [1] was transmitted using 6 subchannels (144 subcarriers). A delay (pre initialized integer sample) was inserted so that the code, from the ranging MSS, is unsynchronized (timing offset) with data on other subcarriers. Both MSS experience different Rayleigh flat fading channel (Doppler at ~680Hz) with same AWGN noise at SNR of 6 db. At the receiver, we search for the peak of the correlation output; the index of this corresponds to the timing offset of the ranging MSS. A correct detection is noted only if the peak corresponds to the exact timing offset. However in practice, a threshold is set for the correlation output and the timing offset is detected with some tolerance. The first simulation was done in order to compare various methods for their performance in detection of new user. The cross-correlation was performed over 3 different window sizes and 39

52 the results show that larger the window size (more samples), better is the performance. Window sizes used were 2048 (for one code in time domain), 4096 (for same code repeated twice, as the same is transmitted) and over 8192 (using the optional scheme mentioned in figure 2.1). The simulation was run such that 6 subchannels were used by ranging MSS and rest 64 (FFT size 2048) were used for data from other MSS. Symbol time used is 64 μ S, giving a system bandwidth of 28 MHz [1]. Data from other MSS was transmitted with QPSK modulation and at unity power. The amplitude of the code from ranging MSS (BPSK modulated) is scaled by the factor shown on x axis of the plot. These were simulated for CDMA code in time domain represented double precision and 2 bits (1 bit real + 1 bit imaginary), (received data using double precision and CDMA code using 2 bits). Simulation shows lower probability of detection when the cross-correlation is performed using the quantized values 2 bit (1 real + 1 imaginary) instead of double precision (full correlation) representation of the code. To achieve the same probability of detection the ranging MSS must transmit at higher amplitude and the significance of this performance degradation is shown in figure 2.7. Figure 2.5: Comparison of various correlation techniques when MSS and ranging MSS experience different channel (ranging MSS on 6 subchannels and data transmitting MSS on 64 subchannels) Also plotted are the results for correlation performed in frequency domain, over a window size of 2048 samples. Since there is less interference the detection probability of the new user is more, compared with correlation in time domain. As the CDMA code, in frequency domain is represented by 2 bits, there is no quantized correlation in frequency domain. Figure 2.6 shows the simulation results for cross-correlation performed with the same settings as above (64 μ S symbol time), except that the data is transmitted on 32 subchannels instead 40

53 of 64 subchannels. Since there is less interference from data subcarriers, the correlation detects the new user timing offset accurately, even when the amplitude of it is low. Frequency domain correlation would perform better due to less ICI with data subcarriers. Next Simulation results (symbol duration 256 μ S ) show the amount of performance degradation of the data users in the presence of unsynchronized ranging MSS (uniformly distributed ranging delay: 0 to 133 μ S, corresponding to cell size). Figure 2.6: Cross-correlation with double precision code and with 2 bit quantized code (ranging MSS on 6 subchannels and data transmitting MSS on 32 subchannels) 41

54 Figure 2.7: Effect of ranging signal amplitude on system performance (ranging MSS on 6 subchannels and data transmitting MSS on 64 subchannels) Interference increases as the amplitude of ranging MSS increases (which is unsynchronized with the BS). The data from the ranging MSS is delayed, BPSK modulated and multiplied by the scaling factor (figure 2.7). The degradation is seen only for the duration for which ranging data is being transmitted, as this time is less (4 OFDM symbols + ranging delay (optional ranging code was used)), to see the effect of interference the simulation was run for only 2 slots (6 OFDM symbols). 2.6 Processing load Calculation As we have seen the signal processing load depends on the method used and the accuracy dependent on the amplitude of the ranging subscriber. Worst case, in terms of complexity would be to run cross-correlation on the received data, the CDMA code can be represented by double precision or by 2 bits. In any case the data length remains same hence first step is to calculate the worst case length of data to operate on. To get that, assume a symbol time of 64 μ S, with FFT size of Consider a cell radius of 20Km, the maximum RTD can be 133 μ S, data from the ranging subscriber can arrive anyway within this delay, hence the processing should be done for = 197 μ S. This corresponds to 6304 samples of complex data which is to be correlated with 2048 samples of CDMA code (144 bit long in frequency domain and 2048 in time domain). Correlation is performed by multiplying the two vectors followed by summation; this is repeated for the total data by shifting the window (figure 2.8). Hence the total computations made are 2048 complex multiplications and 2048 complex additions repeated 4256 times. This is repeated for n possible codes out of total 255 codes. 42

55 Received data - Length 6304 CDMA code CDMA code CDMA code 4256 CDMA code Figure 2.8: cross-correlation: multiplication between parts of received data and CDMA code The previous value is obtained in case we perform full cross-correlation, if in case we quantize the code into 2 bits and then cross-correlate the computations would reduce to 6144 complex additions repeated 4256 times per code. This is because multiplication with sign bits (2 bit quantized data; 1 real+1 complex), is equivalent to sign change and additions. By using quantized code, we will require the ranging MSS to transmit at a higher power (which has less effect on data users, as the user probably gets detected when the amplitude is below 0.4, beyond 0.4 the degradation is seen) we achieve a very high improvement in speed and reduced processing load. If auto-correlation of length N is used on the received data (figure 2.2 and figure 2.8), the required calculations would be 2048 complex multiplications and 2048 complex additions for one time, followed by 2 multiplications, 1 addition and 1 subtraction repeated 2208 times. By doing so we get the plateau or the most probable location of the new user, then to get an accurate result, cross-correlation of n CDMA codes is performed over this localized data (length m ). Further improvement is obtained when one of the codes is quantized using 2 bits before auto-correlation is performed. However, this method requires the ranging user to transmit at higher amplitude to get detected, and it may cause interference to other users. Frequency domain correlation is done on the output of the FFT on 144 subcarriers. These are provided with phase shifts which require 144 complex multiplications. This phase shifted values are multiplied with the CDMA code and added, translating into 144 additions as the code is either 1 or -1. The same process is repeated for 2048 different phase shift values and over a length of 197 μ S (3 FFT s). The total load would be (144 multiplications additions) * 2048 * 3 per code. But, the same can be implemented using an IFFT and that would reduce the load to a large extent. These values have been summarized in tabular form (Table 2.1), n denotes number of codes and m denotes the localized window size. Scheme used Computations required Cross-correlation (full representation) (2048 multiplies additions) * 4256 * n Cross-correlation (2 bit representation) 6144 additions * 4256 * n Auto-correlation (full representation) + Crosscorrelation (6464 multiplies additions) additions * m * n (2 bit representation) Auto-correlation (2 bit representation) + Crosscorrelation * m * n additions (2 bit representation) Frequency domain correlation (144 multiplies additions) * 6144 * n Table 2.1: Table showing scheme used and computations required to execute it 43

56 The frequency domain correlation mentioned in the table 2.1 does not show the computations required for implementing the IFFT method as this is dependent on the method used. However, this method is simple and gives good results, when compared with other methods. 44

57 45

58 PART 3: Antenna Beamforming 3.1 Introduction The present demand in the field of wireless communication is not only to provide data communication when the user is mobile but also to provide high data rate by consuming less bandwidth (achieve good spectral efficiency). Moreover, the system complexity and its implementation are of major concern and sometimes limit the implementation of efficient techniques. Efficient channel coding schemes and diversity schemes are used to achieve high system capacity at less power. WiMAX, the IEEE standard provides specification for efficient forward error correction techniques and optional schemes like adaptive antenna system (AAS), space time coding (STC) and multi input multi output (MIMO) systems. Of these AAS achieves high system capacity with implementation cost mainly concentrated at the base station (BS), which can be easily tolerated. Hence is a good solution for increasing system capacity with least cost. Transmitting data from a single antenna to cover the entire cell (isotropic) is difficult and has many disadvantages hence sectorized antennas are widely used in wireless communications, where the cell is divided into sectors; 3 or 6 generally. This gives many advantages as reduced interference, increased range and SNR, at the cost of some complexity at the transmitter (BS) which is usually acceptable. Beamforming is the next step used to further improve the performance of the system, where the number of sectors are many more! Apart form the advantages gained by using sectorization, Space division multiple access (SDMA) can be implemented, thus increasing the system capacity. In simple terms, beamforming can be explained as Instead of using incandescent lamp throwing light all over the room, use a torch, with same power, and point it in the direction where you want to see. Certainly you will see more clearly; in terms of Antennas this is beamforming. Beamforming is achieved by making the antenna array radiation pattern, point in one particular direction; this is obtained by using an array of antenna, fed with same signal at different time instant or provided with phase shifts. A Ranging MSS trying to enter an AAS system poses two problems to the base station: one is the unknown time offset and another is the unknown direction of arrival of signals. A simple solution to this problem is to use a single antenna output to detect the time and frequency offset information and uses this information to find data on which we can run the direction of arrival (DOA) algorithm. The present thesis simulates two DOA algorithms and compares the performance for e, OFDMA system in uplink. Rayleigh fading channel has been assumed during the simulation. 46

59 3.2 Beamforming basics Beamforming is nothing but to obtain a radiation pattern in the desired way in the desired direction. This can be achieved by using a single antenna element (directive antennas), but we are required to mechanically rotate them in order to form a beam in other location, for example old radio detection and ranging (RADAR) with rotating antenna. There are many d 2 d 2 θ 1 θ θ 2 r1 r r 2 Figure 3.1: 2 element linear array. P problems due to the mechanical rotation and are not suitable for commercial communication where the requirement is data transmission. The electronic version of this is to use an array of elements and feed them (or sample) such that the direction of radiation is maximum in one direction. The type of antenna element used and its arrangement in the array, affects the radiation pattern. The concept can be better explained by considering the simplest structure, a liner array (elements arranged in a line) of antenna elements. Let the number of elements be 2, separated by a distance of d, they need to form the beam (maxima) in the direction of point P. (figure 3.1). By making an approximation that the distance between antenna elements is very small compared to the r (distance of point P ) and from [11], we get the generalized expression for electric field vector as jkr e 1 Et = w f ( θ, ϕ)cos ( kd cosθ + β ) r N --- (eq. 3.1) Where E t is the electric field vector r w = uniform weight applied over all elements θ r = distance from antenna to the point P θ = direction of arrival with reference to array r d 2 axis θ N = number of antenna elements r β = phase shift between antenna elements φ = elevation angle f ( θ, φ) = field pattern of single element d 2 θ d = distance between two antenna elements Figure 3.2: 2 element linear array far field geometry This can be written as E (total) = [E (single element at reference point)] X [(array factor)] Where the normalized array factor is 1 AF n = cos ( kd cosθ + β ) N -- (eq. 3.2) 47

60 Since the antenna element has an isotropic (same in all direction) radiation pattern, the resultant pattern totally depends on the AF. For a given element spacing d, by changing the value of β desired null or maxima can be obtained in any directionθ. For a linear array of half wave λ / 2 dipole the AF is given as [11] N AF n = e n= 1 j( n 1)( kd cos( θ ) + β ) -- (eq. 3.3) The Half power beam width (HPBW) of any antenna radiation pattern [12] is defined as In the plane containing the direction of the maximum of a beam, the angle between two directions in which the radiation intensity is half the maximum value of the beam. The HPBW varies (figure 3.3) for different angles (minimum for 90 and maximum for 0). To differentiate between users in the same cell we would require the HPBW to be small, hence in practice, sectorized antenna array is used [13], each array operating for 30 to 150 degrees. Figure 3.3: Plot of Array factor (AF) for 6 linearly arranged λ / 2 dipole antenna elements with spacing of lamda/2 3.3 Types of beamforming There are mainly two approaches to beamforming: switched beamforming and Adaptive beamforming. Switched beamforming is a simpler approach where the direction of arrival (DOA) of the signal is detected and corresponding beam is formed in that direction by multiplying pre-computed complex vector (adding phase shift and scaling) called array factor (AF). When the user moves out of the beam, the next beam takes over (switching). In practice, the data from antennas is stored and multiplied with different AF to obtain many beams and processing the data concurrently, thus increasing the capacity by SDMA. Adaptive beamforming is more complex, but more efficient, where the radiation pattern is constructed dynamically such that interferers are blocked by placing nulls and beam is formed in the direction of users. By using fully adaptive antenna array, the beam can be constantly steered in the direction of the user as it moves. Here DOA is computed more frequently, followed by computation of AF i.e. complex weight for each antenna and the beam pattern formed by its multiplication with data at antenna array. 48

61 Figure 3.4: Example (non-real) of switched beamforming The number of beams which can be formed is such that we can either allow N-1 maxima (users) or block N-1 minima (interferers) or a combination of two, where N is the number of antenna elements in the array. This flexibility of an N element array to fix the pattern at N-1 places is termed as degree of freedom [9]. It is cost effective to implement the antenna array at the BS instead at the MSS. Filter & Amplifier Signal out lifier Filter & Amp Signal out Direction of arrival computation Complex weight selection Direction of arrival computation Complex weight computation Figure 3.5: Switched beamforming and Adaptive beamforming In the uplink, the antenna array output is multiplied with a complex vector, so as to provide required phase shift to each output, thus receiving the signal form one direction. The complex vector is computed depending on the DOA of the required signal. The information about the DOA acquired during the uplink is valid in the downlink (in TDD system), hence the same complex vector is used, but the signal being fed to the array is multiplied with this vector. An assumption is made that the user location remains same or the DOA computed is valid when the BS is used as receiver followed by transmitter. In beamforming the DOA is computed (by using algorithms like MUSIC & ESPRIT [9]) to find the direction of user and interferers, this information is fed to the next stage so as to compute the corresponding complex weight. In the switched beamforming case these weights are pre-computed for each DOA, but in the adaptive beamforming these are computed by using adaptive algorithms like LMS, SMI. The computed weight is multiplied with the signal from the antenna array and the required radiation pattern is formed. In switched beamforming, two beams on either side of the serving beam are monitored at periodic 49

62 intervals so as to check the power level; the one with higher power corresponds to the present position of the user. This reduces the implementation cost significantly. Further reduction is achieved by just selection one of the pre-computed complex weights, instead of computing them. Switched beamforming is very well suited where there is less or zero interference [11] (like in OFDMA, except for adjacent cell interference, which can be reduced by using synchronized sectorized antennas), and is very simple to implement. Switched beamforming provides non-uniform coverage; when the MSS is moving from one beam to another there might be a call drop due to no coverage zone in between two beams (figure 3.1), typically, beams cross one another at 4 db point [13]. Moreover when the MSS moves from one beam to another intra-cell handoff takes place, the frequency of which directly depends on the beam width. Whereas in adaptive beamforming the beam follows the MSS where ever it moves, thus avoiding the no coverage zone and intra-cell handoff requirement. 3.4 Parameters effecting beamforming The Beam width is inversely related to spacing between the antenna elements. We obtain a narrow beam width when the antenna spacing is large, however it is required that the spacing be less than half the wavelength, else we get spurious beams apart from the required ones. Number of antennas elements also effect the beam width inversely, more the elements, less the beam width. Additionally we have a reduction in side lobes amplitudes, with more antenna elements. Another parameter, as already seen, is the direction in which beamforming is done. The beam width is much wider in the direction 0 and 180 degree when compared with 90 degree. 3.5 Adaptive antenna system for OFDMA in e In OFDMA physical profile, the number of users which transmit or receive in a given frame is very few [1]. There might be user which have stringent requirement for quality of service (QoS), which is to be met by the serving BS, in such a situation concurrent transmission of bursts to MSS which are spatially separate (intra-cell frequency reuse), increases the system capacity. Moreover BS has full control over the transmissions; they start only after getting permission from the BS. Hence interference from one MSS to another does not happen (if controlled concurrent transmission take place) unless due to errors. If more than one user needs access and they are located close by, then they can be attended by single beam but operating at different subcarriers or different time slot in that frame; concurrently, other transmissions can be run in spatially separate MSS, thus increasing system capacity. The IEEE standard provides optional specifications for adaptive antenna systems (AAS); additionally the BS providing this service to AAS MSS should maintains compatibility between AAS users and Non-AAS users, both in Time division duplexing (TDD) and frequency division duplexing (FDD) systems [1]. To achieve this, frame is allocated 50

63 dynamically between Non-AAS and AAS subscribers. Subscribers shall ignore the traffic not intended for them. One of the major difficulties is when a new MSS is entering into the network for the first time. The BS is unaware of its presence and location, hence is not pointing its beam towards the new user. Moreover, the new MSS is unsynchronized with the BS. Hence the BS has to deal with 2 unknowns at the same time. A new MSS cannot transmit on the uplink channel until it has achieved coarse synchronization, and to achieve this it needs to listen to the preamble and acquire uplink parameters from the broadcast messages (DL-MAP, DCD, UL- MAP and UCD) from the BS. Figure 3.6: Downlink part of AAS frame structure The frame in the AAS region starts with the well known preamble, followed by broadcast messages, giving information about synchronization and possible ranging contention slots in the uplink part of the frame (figure 3.6). Apart from repetitive coding on the broadcast information, robust modulation scheme (QPSK) is chosen to allow detection of it by MSS at very low power. This information is transmitted in all directions, hence may not reach the cell boundary, but the redundant coding and modulation scheme might make it possible to detect this information at the MSS. The inherent processing gain in the preamble aids in synchronization even when the beam is not precisely pointing towards the new MSS. A MSS which is able to detect and decode these messages correctly will acquire all the information required for ranging and starts the ranging process. If in case the MSS is synchronized yet unable to decode the messages, it shall use AAS contention slots (pre-defined part of the frame for initial ranging) to alert the BS about its presence. Unlike usual initial ranging, the MSS shall use all available contention slots to allow sufficient time for BS to adapt its array. After such an attempt, the MSS will wait for DL-MAP and DCD messages from BS and shall continue network entry, as in Non-AAS case. Optionally, AAS downlink preamble is transmitted so that the MSS can attain coarse synchronization followed by AAS down link frame prefix (DLFP) (figure 3.7), transmitted by 51

64 BS, containing necessary information like, compressed DL-MAP needed for obtaining downlink parameters and uplink initial ranging allocation information. The AAS-DLFPs transmitted within the AAS diversity map zone need not carry the same information. Different beams may be used within the AAS diversity map zone, however each AAS downlink preamble and associated AAS-DLFP must be transmitted on the same beam. AAS diversity map zone AAS-DLFP AAS-DLFP AAS-DLFP AAS-DLFP AAS-DLFP AAS downlink preamble Figure 3.7: AAS diversity map zone [1] The AAS subscribers might not be able to request bandwidth using the usual contention mechanism. This happens because the adaptive array may not have a beam directed at the MSS when it is requesting bandwidth, and the Bandwidth Request will be lost. In order to avoid this situation, an AAS MSS is directed by the BS as to whether or not it may use broadcast allocations for requesting bandwidth. If yes, then BS may change its direction dynamically towards the MSS and wait for bandwidth request messages else the BS needs to ensure that the MSS is regularly polled so as to learn about its bandwidth requirements. In switched beamforming, DOA computation is used to determine the location of the new MSS when it is attempting for initial ranging, once determined the adjacent two beams can be scanned, for maximum power, at periodic intervals to determine whether the MSS has moved to another location or not. The way the AAS is described in the IEEE standard [1], suggest that there is no hard need for DOA computation, if the BS points the beam in one direction and transmits the DLFP, any new MSS, in that region, shall receive these messages and acquire all needed information to perform initial ranging in the allocated contention slots. Thus by ensuring that the BS points the beam in all direction at transmits DLFP, within a period of time, a complex part, DOA computation can be avoided. But, this comes at the cost of increased number of calculations for the initial ranging detection, which is more expensive. A more efficient solution is to find the timing offset information using the output from a single antenna and then use the DOA computation algorithm on the samples taken after that time offset. By finding the time offset we get information about from which sample the ranging data is starting, then we can apply the DOA algorithm for this data. Considering one antenna output instead of the total array reduces the gain but the inherent gain in the CDMA code used for ranging aids in the new MSS detection. 52

65 3.6 Direction of arrival computation (DOA) Two methods (the Capon s method and the MUSIC method) for the DOA computation have been discussed here followed by simulation results. The received signal sample consisting of D incident signals, at the M element antenna array can be represented as a linear combination of the incident waveforms and noise [17]. u Where D 1 l= 0 () t = a( θ ) s () t + n() t () t ( θ ) () t () t l l u is the received signal a is the steering vector in direction θ s is the input signal n is AWGN noise The input covariance matrix is given by R uu H [ uu ] -- (eq. 3.4) = Ε -- (eq. 3.5) Where H denotes Hermitian transpose An estimate of input covariance over a set of K samples is given as ˆ 1 H R uu = ukuk -- (eq. 3.6) K K 1 K = Capon s method This method is also known as MVDR (Minimum variance distortionless response filter) beamformer. It is a simple method for computing the DOA. Capon s spatial spectrum formula gives the output power of the array as a function of the angle of arrival. Pˆ ( θ ) 1 = -- (eq. 3.7) ( θ ) Rˆ a( θ ) Capon H 1 a uu The input data is divided into set of blocks and the covariance matrix is estimated over each block consisting of K input samples, followed by the spectrum estimation. The same process of estimating spectrum is repeated for many blocks and an average is considered over them to obtain the estimate of Capon s spectrum. The peaks in the spectrum determine the transmitting user location. The method requires estimation of matrix inverse, which could be highly complex in case of large arrays. 53

66 3.6.2 MUSIC algorithm Schmidt proposed the subspace based method, MUltiple SIgnal Classification (MUSIC) algorithm, as a technique based on exploiting the eigen structure of the input covariance matrix. Eigen decomposition on ˆ gives Ruu R ˆ uu V = V -- (eq. 3.8) Where = diag{ 0, λ 1... λ M 1 } [ q q q ] λ, λ0 λ1... λm 1 are the eigenvalues V = 0, 1... M 1 are the corresponding eigenvectors of Ruu ˆ If there are D input signals from different directions (such that M>D), then the noise subspace is given by V n = [ qd, qd qm 1 ]. The noise subspace and signal subspace are orthogonal to each other. The steering vectors corresponding to the direction of arrival of the signals lie in the signal subspace and are orthogonal to the noise subspace. H H Hence, a ( θ ) VnVn a( θ ) = 0 whenθ corresponds to the direction of arrival of the incident signal. The DOAs can be computed by using the MUSIC spectrum, given as P ( θ ) a H ( θ ) a( θ ) H ( θ ) V V a( θ ) a MU = -- (eq. 3.9) H n n The DOA corresponds to a peak in the spectrum, resulting due to denominator approaching zero The numerator results in a constant value equal to the number of antennas in the array hence can be removed. Another significant improvement can be gained by avoiding the reciprocal in the equation and by doing so the DOA is represented by a dip in the spectrum, instead of a peak. 3.7 Simulation results The ranging MSS is located at 90 degrees and other MSS, transmitting data, is located at 95 degrees. Since the ranging MSS is transmitting signal at a very low power compared to the power of other MSS, transmitting data, the Music algorithm detects it but with a very low power (figure 3.9). The same is not detected by Capon s method (figure 3.8), showing that the MUSIC algorithm has better resolution. It was observed from the simulation results that the resolution is good when the SNR is high, additionally it was seen that the amplitude of the signal has an effect on its detection probability. Signals with high amplitude mask out the signal with low amplitude, if they are located close to each other. In a fading channel, the amplitude of the signal can get boosted or 54

67 attenuated; hence the performance is affected by fading, if the users are located close to each other. Figure 3.8: Capon s method for DOA computation (DOA of signals from two MSS is not distinguished). Figure 3.9: MUSIC method for DOA computation, DOA of signals from two MSS is seen 55

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