Evaluation of SVM decoder for DS-CDMA system

Evaluation of SVM decoder for DS-CDMA system Ramkumar Gowrishankar EE645 Final Project

Introduction • Goal • To reduce the BER of a single user in an interference limited multi-user system • Method • DS-CDMA system with 8 bit spreading code • Support Vector Machine decoder • Linear, Polynomial and Gaussian kernels • Applications • Cellular systems • Problems considered • Performance comparison with increasing number of users • Performance with increasing correlation • Effect of polynomial and RBF kernels • Near-Far problem

Outline of Presentation • PART 1 • SSMA system • Introduction to SSMA systems • Types of SSMA systems • Synchronous vs. Asynchronous model • Near-Far problem • PART 2 • Conventional Decoders • Match Filter decoding • Decorrelating Detector • Optimum Detector • PART 3 • Support Vector Machines • PART 4 • Simulation parameters • Results • Conclusion

SSMA system • Spread Spectrum Multiple Access • Wideband system • Pseudo-Noise (PN) sequence converts narrowband signal to wideband noise like signal • Advantages • Robust multiple access capability • Immunity to multipath interference • Efficient bandwidth use in multiuser environment

Types of SSMA system • Direct Sequence Spread Spectrum (DS-CDMA) • Orthogonal pseudo-random codes are used to “spread” the bit sequence to be transmitted • All signals use the same carrier frequency and transmit simultaneously • MultiCarrier CDMA • Using carriers that are orthogonal in the frequency domain instead of time domain • Frequency Hopping SSMA • In this model the frequency of transmission is randomly changed based on a chip sequence • A wideband channel is split into several narrowband channels and each narrowband channel is associated with a PN sequence

Asynchronous Model Where is the random offset of kth user with respect to 1st user 2M+1 is the length of each frame transmitted by a user Analysis more rigorous Decoding based on full length of frame and not just the length of the PN sequence Synchronous Model sk(t)-spreading sequence bk-bit of kth user Ak-Amplitude of kth user N(t)-noise σ-Standard Deviation of noise Assumes all users are synchronized at receiver Decoding is only based on the length of the code used Synchronous vs. Asynchronous Model

Near-Far Problem • Refers to problem of decoding weak user signal in presence of strong interferers • Occurs when many mobile users share the same channel • Strongest received mobile signal will capture the demodulator • Consequence: Noise floor for weaker signals raised

Fig 1 • Consider 2 users that are using the same time-frequency slot with different spreading codes • The propagation environment is inversely proportional to d4 where d is the distance of separation • The transmitted powers are assumed to be equal • If they are at equal distance from base station then received power of both users is the same and they can be decoded

Fig 2 • If user 2 moves closer to base station, there will be increase in received power • User 2 will become dominant and will start masking user 1 • Performance of user 1 will degrade significantly Figures from: http://www.cdmaonline.com/members/2ginteractive/3000/index.html

Outline of Presentation • PART 1 • SSMA system • Introduction to SSMA systems • Types of SSMA systems • Synchronous vs. Asynchronous model • Near-Far problem • PART 2 • Conventional Decoders • Match Filter decoding • Decorrelating Detector • Optimum Decoder • PART 3 • Support Vector Machines • PART 4 • Simulation parameters • Results • Conclusion

Match Filter Decoder Matched Filter User 1 • Simplest Decoder for CDMA systems • In case of perfectly orthogonal codes and synchronous system the optimum detector is match filter Matched Filter User 2 y (t) Matched Filter User k Correlation between the codes=0 for perfect orthogonal codes

Decorrelating Detector • The performance of the matched filter detector is bad in presence of correlation • A better receiver is the decorrelating detector • Problem with matched filter Solution

Optimum Detector • Detection using Maximum-Likelihood detector • Log likelihood function given below • where • b (Kx1) is the vector of transmitted bits from K users, • y (Kx1) is the vector of outputs from K matched filters • A is the (KxK) Amplitude matrix • R is (KxK) correlation matrix • The data set that yields maximum L(b) is the transmitted data set • Complexity is O(2K/K) for each bit. • Not practically feasible for large number of users

Support Vector Machines • Support Vector Machines classify data based on finding an optimum hyperplane • Popularity?? • Non-linear classifier (using kernel trick) • Avoid over-fitting by maximizing margin • Low number of support vectors

Why use SVM??? • Drawbacks of Conventional decoders • Performance degradation when • codes are non-orthogonal • interfering users are present • unfavorable near-far conditions are present • Need to know codes of other users • Advantage of SVM • NO need to know code of other users • More resilience in presence of noise and interference • More resistant to near-far problem • Better classification using Gaussian kernels

Simulation parameters • Goal: To compare performance of various SVM kernels with variation in • Number of users • Correlation between users • Simulation parameters: • Code length:8 • SNR-0:20 dB • Noise: AWGN • Ideal Channel • Number of users:2-5 • Correlation between detected user and interferers: 0.25, 0.5, 0.75 • Near-Far problem • Correlation:0.5 • Number of users:3 • Near-Far factor:1,4,9,16

Results 1: Correlation 0.25 2 users 3 users 4 users 5 users

Results 1: Correlation 0.25 • Performance of match filter degrades with increasing number of users • Gaussian Kernel, Decorrelating and Optimum detector performance similar • Polynomial kernels do not work well • Better to use conventional decorrelating detector

Results 2: Correlation 0.5 • Optimum detector shows better performance than rest • Gaussian kernel performance is better than decorrelating receiver • Match filter performance is bad • Correlating detector better than linear and polynomial kernel based SVM • Difference in performance of linear from decorrelating detector decreases with increasing number of users

Results 3: Correlation 0.75 • Gaussian kernel performance is very close to optimum detector • Linear kernel and decorrelating detector performance same • Performance of polynomial kernel improves • For a full user set with high correlation polynomial kernels may work better

Result 4: Near-Far problem NFR=1:1 NFR=4:1 NFR=9:1 NFR=16:1

Result 4: Near-Far problem • The overall performance degrades as the NFR increases • Gaussian kernel has a worse BER than linear kernel or decorrelating receiver at low SNRs • At high SNRs the Gaussian kernel closely matches the performance of optimum detector • At a BER of 10-2 there is less than 1dB of difference between Gaussian kernels and decorrelating detector for NFR=1 • At same BER with NFR=4, the Gaussian kernel is better by around 1.5 dB

Conclusion • Gaussian kernel based SVM can almost match the performance of the optimum detector • As the number of users increases the relative performance of the Gaussian kernel with respect to decorrelating detector improves • Gaussian kernel is able to withstand the near-far effect at moderate and high SNRs and give good performance

Evaluation of SVM decoder for DS-CDMA system