1. 1 Wireless Communication Low Complexity Multiuser Detection Rami Abdallah University of Illinois at Urbana Champaign 12/06/2007

2. 2 Outline

3. 3 Introduction Multiuser Detection (MUD): canceling or suppressing interfering users from the desired signals Benefits: –Capacity Improvement –Reduced requirement for power control Limitations: –Complexity –Intercell interference –Spreading – Coding tradeoff

4. 4 Problem Definition Optimum Multiuser Detection –Search space exponential in number of users

5. 5 System Representation Matched Filter (MF) –Received Signal for user k: –System Representation after MF: Noise Whitening –Cholesky Decomposition to decorrelate noise –Enables layered decoding Multiple-Access Interference (MAI)

6. 6 Linear Detectors (1) Decorrelating Detector –Solve for z by inverting R –Independent User Decoding –Best near-far resistance –Noise enhancement Optimal Linear Detector (MMSE) –Trade-off between MAI elimination and noise enhancement

7. 7 Linear Detectors (2) Polynomial Expansion (PE) Detector : –Weighted sum of MF output (R) –Weights (W) chosen depending on a performance criterion and can be adaptively updated –Can approximate decorrelating and MMSE detector (Cayley-Hamilton Theorem) –Regular architecture avoiding Matrix inversion

8. 8 Interference Cancellation Successive Interference Cancellation (SIC) –Order users according to descending power –Start detection with the highest power first and subtract its effect from the received signal –Successive users benefits more for MAI cancellation Problems: –Latency –Decision error propagation

9. 9 Interference Cancellation (2) Parallel Interference Cancellation (PIC) –Every stage use previous estimates to subtract MAI for each user in parallel –Tradeoff between complexity and performance

10. 10 Performance Comparison –PIC superior over SIC in well-power controlled environment Power Controlled

11. 11 Multistage decision feed-back detector: –In each stage use the already detected bits to improve detection of remaining bits in the same stage Partial interference cancellation –Decision is based on –Partially cancel MAI with the amount being cancelled increasing with each stage Variations of PIC

12. 12 Decision feed-back detector: –User ordering in terms of descending power –Noise whitening –SIC to cancel MAI among user (F is lower triangular) Decision Feedback MUD

13. 13 Sphere Decoders (SD) in AWGN Channel –ML: Search over all –SD: Restrict search within a sphere of center s and radius R Complexity tradeoff in terms of choosing radius R Sphere (lattice) Decoder H : channel, n : AWGN

14. 14 Preprocessing for SD Triangularization in AWGN –QR Decomposition: a unitary matrix (Q) and an upper triangular matrix Triangularization in MUD –Noise Whitening New received vector Still AWGN with equal variance

15. 15 Layered/ Tree-based Decoding –Partial Euclidean Distance Accumulations by taking advantage of channel triangularization Search Constraint: Radius or Best Candidates Sphere Decoders

16. 16 Constrained SD Depth First SD –Search the tree in downward and upward manner –Update the search radius after each pass Breadth First (K-best SD) –Search in downward direction only –K best candidates are retained at each level in the tree

17. 17 Performance Comparison 1000X reduction in complexity

18. 18 SD limits search space Relaxation increases search space by dropping certain constraints so that the search is easier to implement Unconstrained Relaxation (UR) –Remove constraint on Alphabet –Penalized UR: Compare to MF, Decorrelator, MMSE Relaxations and Heuristics

19. 19 Problem Setup: Semi-Definite Relaxation (SDR): –Drop rank 1 constraint on X with X still symmetric positive semi definite: –An efficient solution can be found in Semi-Definite Relaxation

20. 20 Approximate Boolean solution by randomization –Randomize to approximate xi from vi Semi-definite Relaxation (2)

21. 21 SDR for MUD SNR3=11dB

22. 22 Problem Setup: PDA –Order users in decreasing power –Belief on the decision of user k at stage i –Update this belief by treating MAI as AWGN: –Stop when belief converges, Decide by comparing p to 0.5 Probabilistic Data Association

23. 23 Performance Comparison Average BER with K=29 with gold codes

24. 24 Conclusions Multiuser Detection (MUD): canceling or suppressing interfering users from the desired signals Different techniques exist that trade-off complexity with performance Detection techniques can be applied to other detection problems (ex. MIMO) Viterbi Algorithm can be applied to MUD, How would low complexity “Viterbi algorithm” behave under MUD?