NEURAL NETWORK BASED MULTIUSER DETECTORS FOR DS-CDMA BIJAYA NEPAL (B Eng., Tianjin University, P R China) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2003 Acknowledgement August 2003 I would like to express my sincere gratitude towards my supervisor Professor Dr Tjhung Tjeng Thiang for his invaluable guidance and continuous encouragement throughout the course of this research work Especially I thank him for the inspiration he provided to me during the hard time of the research work I will always remember his supports on academic as well as on personal matters I would also like to express my sincere gratitude to Dr Chew Yong Huat for providing me a lot of suggestions plus showing me the mistakes on my work Finally I would like to thank the National University of Singapore for providing me the research scholarship to pursue my Master of Engineering Degree in this prestigious University Bijaya Nepal i Table of Contents Acknowledgements i Table of Contents ii List of Figures vi List of Symbols ix List of Abbreviations xii Summary xiii Chapter 1: Introduction 1.1 Background ………………………………………………… 1.2 Spread Spectrum Communications Principle ………………… 1.3 DS-CDMA ………………………………………………… 1.3.1 Multiple Access Interference ………………………… 1.3.2 Performance of DS-CDMA ………………………… 1.3.3 Simple Illustration of Near-far Problem in DS-CDMA … 1.3.4 Power Control ………………………………………… 10 1.3.5 Multiuser Detection ………………………………… 11 ………………………………………………… 12 1.4 Motivation 1.5 Contribution of this Thesis ………………………………… 13 1.6 Organization of the Thesis ………………………………… 14 ii Chapter 2: Multiuser Detection Strategies 2.1 17 DS-CDMA Received Signal Model ………………………… 17 2.1.1 Synchronous Transmission ………………………… 20 2.1.2 Asynchronous Transmission ………………………… 21 2.2 Output of Matched Filter Detector - Matrix – Vector Notation … 21 2.3 2.2.1 Synchronous System ………………………………… 22 2.2.2 Asynchronous System ………………………………… 24 Established Multiuser Detectors 28 2.3.1 Conventional Matched Filter Detector (CD) …………… 28 2.3.2 Optimum Multi-user Detector (OMD) …………………… 29 2.3.3 Decorrelating Detector 2.3.4 Multistage Detector 2.3.4 2.4 ………………………… …………………………… 31 …………………………………… 33 Minimum Mean Square Error (MMSE) Detector ………… Summary …………………………………………………… Chapter 3: Hybrid-MGNANN Multiuser Detector for DS-CDMA 3.1 Neural Network in DS-CDMA Multiuser Detection 3.2 Hopfield Neural Network (HNN) for Multiuser Detection 3.3 Problems with HNN 3.4 Solution of Local Minima Problem 34 35 37 …………… 37 …… 39 …………………………………………… 43 …………………………… 43 3.4.1 Annealed Neural Network Multiuser Detector …………… 43 3.4.2 Matrix Graduated Non-Convexity Technique …………… 3.5 Complexity Reduction by Using Reduced Detector …………… 44 46 iii 3.6 Simulation Parameters, Results and Discussions 3.6.1 Simulation Parameters ………………………………… 3.6.1.1 3.6.1.2 3.6.1.4 53 noise Generation ………………………… 54 Spreading Codes ………………………… 54 ………………………… 56 Gain of the Sigmoid function and Time Constant value in HNN 3.6.1.5 53 User bits, Phase angle, Delay and Gaussian 3.6.1.3 Packet Size 3.6.2 …………… ………………… Initial Temperature for Annealing Process … 57 57 Flowchart of the Simulation Programs for the Multiuser Detection …………………………… 58 3.6.2.1 Synchronous Transmission …………………… 58 3.6.2.2 Asynchronous Transmission …………………… 59 3.6.3 Simulation Results and Discussions for Hybrid-MGNANN Multiuser Detector 3.7 …………………………………… 60 3.6.3.1 Synchronous DS-CDMA Simulation Examples … 60 3.6.3.2 Asynchronous DS-CDMA Simulation Examples … 66 Summary …………………………………………………… 69 Chapter 4: Hybrid-RBFN Multiuser Detector for DS-CDMA 4.1 Radial Basis Function Networks (RBFN) 4.2 Bayesian Decision Rule 4.3 Complexity Reduction Techniques 70 …………………… 70 …………………………………… 73 …………………………… 74 iv 4.4 Proposed Hybrid Detector …………………………………… 76 4.5 Simulation Results and discussions for Hybrid-RBFN Multiuser Detector 4.6 ………………………………………… 78 4.5.1 Synchronous DS-CDMA Simulation Examples … 78 4.5.2 Asynchronous DS-CDMA Simulation Examples … 82 ………………………………………………… 85 Summary Chapter 5: Conclusions and Future Research Directions 86 5.1 Conclusion …………………………………………………… 86 5.2 Future Work …………………………………………………… 88 List of References 90 v List of Figures Chapter 1: Introduction Figure 1.1 Multiaccess Channel – Signals from K users Figure 1.2 Basic spread spectrum technique Figure 2.1 K asynchronous users over an AWGN channel Figure 2.2 Relative time delays between user bits (assuming τ = ) Figure 2.3 K - user detector employing matched filter detector at the front end …………… …………………………… …………… 19 …… 21 …………………………………………… 23 Figure 2.4 The decorrelator for synchronous CDMA …………………… 32 Figure 2.7 n stage multistage detector …………………………………… 34 Figure 3.1 Additive model of a neuron …………………………………… 40 Figure 3.2 A simple Hopfield Neural Network of neurons Figure 3.3 Hybrid MUD …………………………………………………… 47 Figure 3.4 Flowchart for simulation in synchronous transmission …… 58 Figure 3.5 Flowchart for simulation in asynchronous transmission …… 59 Figure 3.6 Cumulative BER versus SNRi ( K = 7, L = , NFR = 10 dB ) …… 60 Figure 3.7 Weakest user’s BER versus SNR ( K = 7, L = , NFR = dB ) … 61 Figure 3.8 Cumulative BER versus SNR ( K = 7, L = , E1 = 10, E = 20, E i = 1, i = 3, ,7 ) Figure 3.9 …………… 41 …………… 62 Cumulative BER versus SNR ( K = 5, L = Gold Codes E1 = 10, E i = 1, i = 2, ,5 ) …………………………… 63 vi Figure 3.10 Cumulative BER versus number of users ( E1 E i = 10 dB, SNRi = dB ) Figure 3.11 …………………………… 64 Weakest user’s BER versus NFR ( K = 5, L = , NFR = E i E1 , SNR1 = 8dB ) …………………… 65 Figure 3.12 Weakest user’s BER versus SNR ( K = 3, L = , NFR = E i E1 = 8dB, i = 2,3 , delay fixed at [0; 0.5T ; 0.75T ] ) …… 66 Figure 3.13 Cumulative BER versus SNRi ( K = 5, L = , NFR = 10 dB , delay changed at every 300 transmissions) …………………… 67 Figure 3.14 Weakest user BER versus SNR ( K = 5, L = Gold Codes, NFR = dB ) …………………………………………………… 68 Figure 4.1 A Radial Basis Function Network for DS-CDMA …………… 72 Figure 4.2 Hybrid RBF Receiver with preprocessing stage …………… 76 Figure 4.3 Cumulative BER performance of different detectors ( K = 5, L = ) Figure 4.4 Weakest user BER Performance of different detectors ( K = 7, L = ) Figure 4.5 …………………………………… 78 …………………………………… 79 Cumulative BER versus number of users ( E1 E i = 10 dB, SNRi = dB ) …………………………… 80 Figure 4.6 Cumulative BER versus NFR ( K = 5, L = 7, SNRi = 8dB) ……… 81 Figure 4.7 Cumulative BER versus SNR ( K = , L = , E1 / E i = 10dB , delay fixed at [0;0.5Tb ;0.75Tb ] ) …………………………… 82 vii Figure 4.8 Weakest user BER Performance of different detectors K = , L = , E1 = 1, E = 6, E = 10 , delay fixed at [0;0.5Tb ;0.75Tb ] … 83 Figure 4.9 Cumulative BER versus SNR( K = , L = , E / E i = 10dB ) … 84 viii List of Symbols Ak A a k (t ) a k ,l ak bk(i ) bˆ ( i ) k b br bw Cj Cj E E[⋅] Ep E Eb Ek e F (y ) H ~ H H rr k th user’s signal amplitude diagonal matrix of all users received amplitudes k th user spreading waveform l th chip of k th user spreading sequence k th user’s spreading sequence vector of length L k th user’s data bit for i th interval estimated data bit of k th user in i th interval transmitted data bit vector determined users bit vector after an iteration of reduced algorithm undetermined users bit vector after an iteration of reduced algorithm leakage capacitance of the RC circuit connected to neuron j j th center vector of RBF network energy function of Hopfield neural network expected value constraint energy term in matrix graduated nonconvexity Ij diagonal matrix with elements as signal energies bit energy k th user’s signal energy per bit a constant soft output from the RBFN cross correlation matrix cross correlation matrix for asynchronous transmission cross-correlation matrix of the determined users (or elements) after an iteration of reduced algorithm cross-correlation matrix of the undetermined users (or elements) after an iteration of reduced algorithm cross-correlation matrix related with the determined and undetermined users after an iteration of reduced algorithm externally supplied bias for j th neuron K k L L(r ) I N number of transmitting users penalty parameter in matrix graduated nonconvexity length of spreading sequence (number of chips) likelihood ratio identity matrix number of neurons in HNN H ww H rw ix Chapter 4: Hybrid-RBFN Multiuser Detector for DS-CDMA _ 4.5.2 Asynchronous DS-CDMA Simulation Examples Example 4.5 In our first asynchronous CDMA example for Hybrid-RBFN MUD, we have K = asynchronous users employing L = poor signature sequence The codes are: a (1) = [1,1,1,1], a ( ) = [1,1,−1,−1], a ( ) = [−1,1,−1,1] The relative delays of each user are: τ = 0, τ = 0.5Tb , τ = 0.75Tb The first user’s energy is 10 times bigger than the rest of the users Figure 4.7 shows the cumulative BER performance of different detectors versus the SNR of the weaker users Due to the use of poor signature sequence, the size of the remaining optimization problem was generally found very big Nevertheless our proposed detector performed better than other sub-optimum detectors -0 -1 -1 Cumulative BER -2 -2 -3 -3 cd dec o re d u c e d m s 10 h rb f -4 -4 -5 4.5 5.5 6.5 S N R (i)(d B ) i= , 7.5 8.5 Figure 4.7 Cumulative BER versus SNR ( K = , L = , E1 / E i = 10dB , delay fixed at [0;0.5Tb ;0.75Tb ] ) 82 Chapter 4: Hybrid-RBFN Multiuser Detector for DS-CDMA _ Example 4.6 This asynchronous CDMA experiment also involves the same set of users with same poor signature sequence and relative delays Instead of one strong user, we now have two strong users: E1 = 1, E = 6, E = 10 We are now interested with the weakest user BER performance Figure 4.8 shows the weakest user BER Performance of different detectors when we increase the SNR of that user We can see that the hybrid RBF detector performs best among the sub-optimum detectors -0.5 -1 Weakest User BER -1.5 -2 -2.5 -3 -3.5 cd deco reduced ms10 hrbf -4 -4.5 4.5 5.5 6.5 SNR1 (dB) 7.5 8.5 Figure 4.8 Weakest user BER performance of different detectors( K = , L = , E1 = 1, E = 6, E = 10 , delay fixed at [0;0.5Tb ;0.75Tb ] ) 83 Chapter 4: Hybrid-RBFN Multiuser Detector for DS-CDMA _ Example 4.7 In our final asynchronous example, we have K = users with L = Gold codes The energy of one user is 10 times larger than the energy of the rest of the users The delays of the users were changed every 100 test cases to obtain an estimate of the average performance over all the possible delays As, we used well designed Gold codes in this simulation example, the size of the residual problem was generally small In Figure 4.9, we compare the performance of the hybrid RBF detector to that of MS10, reduced, CD and Deco It is shown that the hybrid RBF performs best amongst these detectors -1 -1.5 Cumulative BER -2 -2.5 -3 -3.5 cd deco reduced ms10 hrbf -4 -4.5 4.5 5.5 6.5 SNR(i)(dB), i=1,2,3 7.5 8.5 Figure 4.9 Cumulative BER versus SNR ( K = , L = , E / E i = 10dB ) 84 Chapter 4: Hybrid-RBFN Multiuser Detector for DS-CDMA _ 4.6 Summary We have proposed a sub-optimum hybrid radial basis function network (HRBF) multiuser detector for DS-CDMA system and have investigated its BER performance in AWGN channel We performed various experiments implementing different spreading codes, near-far ratio and number of users to analyse the performance of our proposed detector in a broader view We show from simulations that the proposed MUD in synchronous scenarios outperforms other sub-optimal detectors and approaches the performance of the OMD but with much lesser computational complexity than the OMD In the asynchronous scenario, if we use well designed spreading codes, the size of the residual problem will generally be small, but if we implement the poorly designed codes, then the size of the residual problem that has to be solved by the RBF network will be big, involving comparatively high computational complexity Since the cross-correlation matrix in asynchronous scenario is sparse (as most of the (2 P + 1) K bits in a typical message length (2 P + 1) not overlap with each other), it still may be possible to breakup the residual cross-correlation matrix into small size matrices to reduce the complexity in the RBF stage 85 Chapter Conclusions and Future Research Directions In this thesis, we considered the problem of demodulating spread-spectrum signals in a multiple-access Gaussian channel Multi-user detection has been viewed as an optimization problem We described and evaluated the performances of two novel neural network based sub-optimum multiuser receivers to improve the performance of DSCDMA communications system The Bit error probabilities of the proposed receivers were compared with other sub-optimum receivers as well as with conventional and optimum receivers in synchronous and asynchronous systems 5.1 Conclusion We have proposed reduced complexity Hopfield Neural Network (HNN) based multiuser detector with annealing and matrix graduated non-convexity capabilities HNN is well known for its ability to provide fast sub-optimum solutions to the combinatorial optimization problem The main attractions of this type of network are that the hardware complexity is linear in the number of users, it does not require training and it has high convergence speed However, the HNN has a major drawback, i.e it is only guaranteed to converge to a local minimum of the OMD objective function It requires knowledge of the optimal values of parameters for the network to yield optimum decision But the optimal values of parameters change with the number of users and channel conditions 86 Chapter 5: Conclusions and Future Research Directions _ Annealing and matrix graduated non-convexity (MGN) techniques are considered effective tools to overcome the local minima problem of HNN In this thesis, we have employed both these tools and shown that we can achieve better BER performance for the DS-CDMA system To reduce the hardware complexity for the HNN, we further implemented digital signal processing stage (Reduced detector) at the front end This was particularly effective in asynchronous DS-CDMA where the size of the optimization problem that needs to be solved is very big The front-end reduced detector reduces the size of the original optimization problem by employing an efficient algorithm recursively The remaining reduced size optimization problem is then forwarded to the HNN with annealing and matrix graduated non-convexity capabilities for further processing The performance of the hybrid MGNANN was found to be comparable to that of the optimum receivers in most of the simulation examples considered for the synchronous system However, due to the high complexity involved, we could not perform simulation for the OMD in asynchronous system and we could only compare the performance of our proposed detector with the performance of other sub-optimum detectors Hybrid Radial Basis Function Network (Hybrid RBFN) is another novel approach we have considered for multiuser detection problem In our work, we have assumed that the spreading codes of all the users are known to the receiver In such instance, there is no need of training The main drawback that lies with this type of network is its hardware complexity The number of centres (nodes) increases exponentially with the increase in the number of users To reduce the complexity, we have used pre-processing stage RBFN so that the length of the input vector to the RBF is equal to the number of users (this will 87 Chapter 5: Conclusions and Future Research Directions _ be particularly beneficial when K < L ) Furthermore, as in the case of MGNANN, we have also used reduced detector at the front end so that the RBFN has to deal with smaller size remaining optimization problem The presented hybrid RBFN receiver has a moderate complexity If the employed spreading codes are poorly designed, then the size of the residual problem from the reduced detector which has to be solved by the RBFN might be big involving high computational complexity, specially in the asynchronous DS-CDMA In such cases, most of the time, we can still split the remaining cross-correlation matrix and the matched filter output vector into smaller sizes and process the data separately If that is also not possible, then we need to bypass the RBFN and need to employ other sub-optimum detector The two proposed receivers are much less complex than the optimal detector, yet they perform nearly as well as the optimal detector Thus, these two receivers appear to offer an attractive tradeoff between complexity and performance in many multiuser communications scenarios 5.2 Future Work Although the performance was evaluated assuming only AWGN, the effect of time varying nature of the fading communication channels may be considered in future work We can simulate our proposed detectors to evaluate their performances under multipath fading condition For RBF network, in this thesis we assumed full knowledge of all the user’s spreading codes, so it is applicable for uplink transmission only We can extend our 88 Chapter 5: Conclusions and Future Research Directions _ work to the downlink transmission by applying training algorithms to train the center and weight vector 89 List of References [1] A Cichocki and R Unbehauen, “Neural Networks for Optimization and Signal Processing”, John Wiley & Sons Ltd., 1993 [2] A Duel-Hallen, J Holzman and Z Zvonar, “Multiuser Detection for CDMA Systems”, IEEE Personal Communications Magazine, Vol 2, No 2, April 1995, pp 46-58 [3] A J Viterbi, “Spread Spectrum Communications: Myths and Realities”, IEEE Communications Magazine, 50th Anniversary Commemorative Issue, May 2002 [4] A Makki and P Siy, “Hopfield Neural Networks Control for Optimal Solutions”, Int Joint Conference on Neural Network, Vol 4, June 1992, pp 462-467 [5] B Aazhang, B.P Paris, G.C Orsak, “Neural Networks for Multiuser Detection in Code-Division Multiple-Access 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ANNMD BER BPSK CD CDMA CLB DS DS -CDMA DSP DS- SS DSSS-BPSK DECO FDMA FH FH -CDMA HNN HNNMD H-RBFN H-MGNANN MAI MAP MF MLP MLSD MRBF MSD MUD NFR OMD NN PG PN PPB PSK RD RBF RBFN SNR SS TDMA Additive White Gaussian Noise Annealed Neural Network Annealed Neural Network Multiuser Detector Bit Error Rate Binary Phase Shift Keying Conventional Detector Code Division Multiple Access Chip Level Based Direct Sequence... _ proposed a multiuser receiver using a radial basis function (RBF) network Similarly, Ketchriotis et al [10] and Miyajima [35] have proposed Hopfield neural network (HNN) based multiuser receiver Though all these neural network based MUDs’ perform better than the conventional matched filter detector and at par with OMD, they all suffer from one or other problems In the MLP based MUD, the number... they are well suited for the pattern classification problem We carried out extensive simulations for synchronous and asynchronous DS- CDMA systems with various operating conditions in order to compare the error probability performance of our proposed detectors with other competing multiuser detectors, which are based on conventional matched filter detector (CD), Hopfield Neural Network (HNN), multistage... of spread spectrum and DS- CDMA systems We reviewed the role of MAI in performance degradation of DSCDMA The need for multi-user detection as well as sub-optimum multi-user detectors has been mentioned The motivation and objective of our work have been provided Chapter 2 reviews the system model of DS- CDMA followed by a detailed background of some of the established multiuser detectors such as conventional... practical implementation For this purpose, we propose hybrid matrix graduated non convexity annealed neural network (Hybrid-MGNANN) and hybrid radial basis function network (Hybrid-RBFN) multiuser detectors and investigate and discuss the performance of these detectors in comparison with other sub-optimal detectors 1.5 Contributions of this Thesis In this thesis, we investigate the performance of various... and annealed neural network (ANNMD) We also use the optimum multiuser detector (OMD) as comparison benchmark for all the MUDs To have broader view to the proposed detectors performances, we vary parameters such as spreading codes, user power ratio, and number of users in the system etc Simulations for the AWGN channel, performed using MATLAB 6.1, have shown that the error probability performances of... Frequency Hopping Code Division Multiple Access Hopfield Neural Network Hopfield Neural Network Multiuser Detector Hybrid Radial Basis Function Network Hybrid Matrix Graduated Non-Convexity Annealed Neural Network Multiple Access Interference Maximum a posteriori Matched Filter Multilayer Perceptron Maximum Likelihood Sequence Detection Radial Basis Function based on Mahalanobis Distance Measure Multistage... increasing the number of users and so does the training time RBF based MUD performs optimally in AWGN but its complexity in terms of centers (nodes) grows exponentially In the same way HNN based MUD suffers from local minima problem The main objective of this thesis is to address the need for sub-optimum multiuser detector for DS- CDMA that performs reliably in high bandwidth efficiency situations and is... hopping pattern of the signal FH -CDMA is primarily concerned with evading eavesdropping and interception of signal and data, so it is suitable for the military application In our work, we are only considering DS- CDMA 1.3 DS- CDMA The performance gain obtained from a Direct Sequence Spread Spectrum (DS- SS) signal through the processing gain can be used to enable many DS- SS signals to occupy the same... has attractive bit error rate performance with low complexity • Performance of hybrid radial basis function multi-user detector (Hybrid-RBFN): This detector is based on digital signal processing and radial basis function neural network and performs very well in synchronous CDMA with complexity a little higher than the Hybrid-MGNANN But in the asynchronous CDMA, the performance of this detector is comparatively ... …………………………………………………… Chapter 3: Hybrid-MGNANN Multiuser Detector for DS-CDMA 3.1 Neural Network in DS-CDMA Multiuser Detection 3.2 Hopfield Neural Network (HNN) for Multiuser Detection 3.3 Problems with... Multiple Access Hopfield Neural Network Hopfield Neural Network Multiuser Detector Hybrid Radial Basis Function Network Hybrid Matrix Graduated Non-Convexity Annealed Neural Network Multiple Access... sub-optimum multiuser detector that has lower complexity and can achieve near optimum performance Basically we are interested in using some neural network models for this purpose as neural networks