Evaluation of SVM decoder for DSCDMA system

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Evaluation of SVM decoder for DS-CDMA system

• Ramkumar Gowrishankar
• EE645 Final Project

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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

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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

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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

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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

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Synchronous vs. Asynchronous Model

• Asynchronous Model
• Where is the random offset of kth user
  with respect to 1st user
• 2M1 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
• s-Standard Deviation of noise
• Assumes all users are synchronized at receiver
• Decoding is only based on the length of the code
  used

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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

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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

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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/2g
interactive/3000/index.html
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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

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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 codes0 for perfect
orthogonal codes
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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
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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

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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

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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

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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

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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

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Simulation parameters

• Goal To compare performance of various SVM
  kernels with variation in
• Number of users
• Correlation between users
• Simulation parameters
• Code length8
• SNR-020 dB
• Noise AWGN
• Ideal Channel
• Number of users2-5
• Correlation between detected user and
  interferers 0.25, 0.5, 0.75
• Near-Far problem
• Correlation0.5
• Number of users3
• Near-Far factor1,4,9,16

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

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Results 2 Correlation 0.5
3 users
2 users
4 users
5 users
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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

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Results 3 Correlation 0.75
3 users
2 users
4 users
5 users
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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

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Result 4 Near-Far problem
NFR11
NFR41
NFR91
NFR161
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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 NFR1
• At same BER with NFR4, the Gaussian kernel is
  better by around 1.5 dB

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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