Optimal Sequence Allocation and Multi-rate CDMA Systems Krishna Kiran Mukkavilli, Sridhar Rajagopal, Tarik Muharemovic, Vikram Kanodia

Motivation 3rd Generation Comm. Systems Multi-Rate Detection Multimedia(Data, Voice, Video) Multiple Rate Comm. Multi-Rate Detection Users entering/leaving the system Optimal Sequence Allocation to achieve Capacity.

Outline Conventional CDMA multiuser system Discussion of multirate systems Methods of multirate CDMA access Performance of multiuser detectors Interference avoidance Application to variable number of users

Multi-rate CDMA systems Multi code access (MC) Give more Codes Variable spreading length (VSL) Change Spreading Length Variable chip rate(VCR) Change Chip Frequency

Multi code (MC) Higher Rate users assigned more codes Data transmitted in parallel “Virtual User” Concept Same Spreading for all users.

Multi Code Code 1 Code 2 User Rate R User Rate 2R T Code 3

Variable spreading length(VSL) Higher Rate Users allocated smaller spreading lengths For detection, rate of slowest user is considered. More bits of higher rate users detected per bit of lower rate users For detection, put 0’s

Variable Spreading Length User Rate R T User Rate 2R 2T

Variable Chip Rate(VCR) User allocated different chip rates Larger Bandwidth required Requires more RF hardware Oscillators Not practical for implementation

Variable Chip Rate User Rate R T User Rate 2R 2T

Implementation Aspects VSL and VCR have a sparse correlation matrix VCR requires larger bandwidth MC requires more codes VSL proposed for next generation systems

Multiuser Detectors Maximum likelihood detector (MLD) Conventional single user detector (SUD) MMSE detector Decorrelating detector

Simulations Four users Random Codes Spread length 32 for low rate user 2 users at rate R 2 users at rate 2R Random Codes Spread length 32 for low rate user 10000 bits Channels AWGN Fading - Jakes Model

Investigate... Performance of multiuser detectors Near far problem in detectors Performance of high rate and low rate users in MC and VSL systems All users with equal power Users with unequal power

BER comparison for different detectors in multi code system 10 MLD 10 MLD MMSE Decorrelator Single user detector -1 10 -2 BER 10 -3 10 -4 10 2 3 4 5 6 7 8 9 10 11 12 SNR

BER comparison for detectors with unequal powers 10 MLD Equal Power 10 MLD Equal Power MLD Unequal Power SUD Equal Power SUD Unequal Power -1 10 -2 BER 10 -3 10 -4 10 2 3 4 5 6 7 8 9 10 11 12 SNR

Comparison of Different Rate Users in MC and VSL 10 High rate MC 10 High rate MC High rate VSL Low rate MC Low rate VSL -1 10 -2 BER 10 -3 10 -4 10 2 3 4 5 6 7 8 9 10 11 12 SNR

VSL System Virtual user from high rate user High rate user lower spreading length lower interference (other virtual users are orthogonal) High rate user interference from same number of virtual users with lower spread length

Variable Spreading Length User Rate R T User Rate 2R 2T

Near Far effect for Different Rate Users in MC and VSL 10 Low rate MC 10 Low rate MC Low rate VSL High rate MC High rate VSL -1 10 -2 BER 10 -3 10 -4 10 2 3 4 5 6 7 8 9 10 11 12 SNR

Results Multi Code High rate and low rate users have same performance (both BER and NFR) VSL Low rate users have bad BER and NFR High rate users’ performance is similar to multicode access system.

Interference Avoidance in Wireless Multiuser Systems Interference Avoidance  send where there is less noise Fixed modulation - traditional approach TDMA FDMA CDMA CWMA Future wireless systems - dynamically adapt to the changing interference pattern

Preliminaries for Multiuser Systems (class notes pg. 5-12) System model: Capacity region:  X1 XM N Y R1 R2

Total Square Correlation vs Iteration Number 9.5 Optimum Lower Bound 9 8.5 Total Square Correlation 8 7.5 7 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Iteration Number

Preliminaries for Multiuser Systems (class notes pg. 5-12) Sum Capacity: W : channel bandwidth Pi : power of i-th user N0 : noise power spectrum

Multiuser Spread Spectrum Systems System model Y sM  X1 XM N  s1

Multiuser Spread Spectrum Systems Sum Capacity: Optimum sequences maximize Sum Capacity Total Square Correlation (TSC): Max. Sum Capacity  Min. TSC

Eigen-Algorithm Iterative reduction of TSC User k updates his spreading sequence Rayleigh quotient Choose sk to be eigenvector with smallest eigenvalue

Performance comparison of optimal codes with random codes 10 10 Random Code Allocation Optimal Code Allocation -1 10 -2 BER 10 -3 10 -4 10 8 10 12 14 16 18 20 22 SNR

BER Performance with an Incoming User 10 Random Code to new user 10 Random Code to new user Iteration for new user only Optimal Code Allocation -1 10 BER -2 10 -3 10 6 7 8 9 10 11 12 13 14 15 16 SNR

Conclusions Significant improvement in performance with optimal codes Iterative algorithm compatible with user dynamics Good sub-optimal schemes for user addition Can be combined with the multi-rate schemes