Optimal Feedback Quantization Schemes for Multiuser Diversity Systems

Optimal Feedback Quantization Schemes for Multiuser Diversity Systems _________________ Alan Pak Tao Lau Supervisor: Prof. F. R. Kschischang Date: April 2 nd, 2004 Alan P. T. Lau

Wireless Fading Channels • Fluctuations of channel quality over time • Constructive and destructive interference due to multi-paths Alan P. T. Lau 2

Downlink Multiuser Fading Channel • Operates on a time-division basis (e. g. GSM, HDR) • Transmission sometimes scheduled to users in deep fade Alan P. T. Lau 3

Multiuser Diversity • Each user measures and feeds back instantaneous channel quality for scheduling • Long term throughput maximized by always serving the user with the best channel quality Alan P. T. Lau 4

Feedback Quantization • Each user digitizes and feeds back their current channel quality through their feedback channel • What should they feedback? Alan P. T. Lau 5

Feedback Quantization • Each user digitizes and feeds back their current channel quality through their feedback channel • What should they feedback? • Information rate, channel coefficient, SNR etc. Alan P. T. Lau 6

Feedback Quantization • Each user digitizes and feeds back their current channel quality through their feedback channel • What should they feedback? • Information rate, channel coefficient, SNR etc. • Any quantity can be fed back if is any monotonically increasing function Alan P. T. Lau 7

Channel Quality Index • • where is the c. d. f. of is uniformly distributed in [0, 1] Denote as the channel quality index for user i Multiuser diversity Alan P. T. Lau 8

Probability of Error • Number of users K=2 • Number of quantization levels per user L=2 • Assumptions: independent fading, perfect estimation of s for users, perfect feedback channel Alan P. T. Lau 9

Probability of Error • Number of users K=2 • Number of quantization levels per user L=2 • Assumptions: independent fading, perfect estimation of s for users, perfect feedback channel • Probability of error Alan P. T. Lau 10

Problem Statement • Given independent and uniformly distributed in [0, 1] and L quantization levels for each index, design quantization rules Qk, together with a decision rule D that will optimize a certain performance criterion • Criterion: minimize • The set of boundaries for all K users uniform quantization scheme Alan P. T. Lau 11

for 2 users, 2 levels • Decision rule D Maximum A Postereri (MAP) rule • Minimum when Alan P. T. Lau sdaffdsaadf

for 2 users, L levels • while • Optimal scheme saves 1 bit as L goes large Alan P. T. Lau 13

Interleaving Property • Theorem 1: In a system of K users and L levels with quantization boundaries , the set user i for minimum Alan P. T. Lau 14

for K users, L levels Alan P. T. Lau 15

Performance for K=5 • Optimal scheme saves more than 1 bit Alan P. T. Lau 16

Approximation Scheme Alan P. T. Lau 17

Approximation Scheme Alan P. T. Lau 18

Approximation Scheme • For K users, L levels, approximation scheme Alan P. T. Lau 19

Numerical Results • At K=30, L=16, optimal scheme requires L=3 while approximation scheme requires L=10 Alan P. T. Lau 20

Quantizing for Maximum Throughput _________________________ • Minimize = minimize • Maximize throughput = minimize Alan P. T. Lau 21

Optimal Weighting Function • Maximize expected throughput = minimize Alan P. T. Lau 22

for K users and L levels • For a system with i. i. d Rayleigh fading Alan P. T. Lau 23

Numerical Results • At K=30, L=16, optimal scheme requires L=3 while approximation scheme requires L=8 Alan P. T. Lau 24

Location of Boundaries • Generally skewed towards 1 • Boundaries for more skewed towards 1 Alan P. T. Lau 25

Implementation Issues • Base station updates K, user identity known for each user • Adding bias for approximation scheme • Only quantization for minimal is possible if distributions not identical, but it ensures proportional fairness Alan P. T. Lau 26

Summary • Distributed scalar quantization schemes to minimize and maximize throughput • Designed jointly, implemented separately • Substantial improvements over uniform quantization scheme Alan P. T. Lau 27

Summary (cont’d) • Low complexity approximation scheme shown to outperform the uniform quantization scheme • Implementation issues of optimal quantization schemes Alan P. T. Lau 28