Power Control, Interference Suppression and Interference Avoidance in Wireless Systems

1. Power Control,Interference Suppression and Interference Avoidancein Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University

2. CDMA System Model BS k BS 1

3. CDMA Receivers SIR1 SIRi SIRN

4. CDMA Signals • Power Control:pi • Interference suppression: cki • Interference Avoidance: si

5. SIR Constraints • Feasibility depends on link gains, receiver filters

6. SIR Balancing • SIR low  Increase transmit power • SIR high  Decrease transmit power • [Aein 73, Nettleton 83, Zander 92, Foschini&Miljanic 93]

7. Power Control + Interference Suppression • 2 step Algorithm: • [Rashid-Farrokhi, Tassiulas, Liu], [Ulukus, Yates] • Adapt receiver filter ckjfor max SIR • Given p, use MMSE filter [Madhow, Honig 94] • Given ckj, use min power to meet SIR target • Converges to min powers, corresponding MMSE receivers

8. Interference Avoidance • Old Assumption: Signatures never change • New Approach: Adapt signatures sito improve SIR • Receiver feedback tells transmitter how to adapt. • Application: • Fixed Wireless • Unlicensed Bands

9. MMSE Signature Optimization ci MMSE receiver filter Matchsito ci si transmit signal Capture More Energy Interference Suppression is unchanged Interference

10. Optimal Signatures • IT Sum capacity: [Rupf, Massey] • User Capacity[Viswanath, Anantharam, Tse] • BW Constrained Signatures [Parsavand, Varanasi]

11. Simple Assumptions • N users, processing gain G, N>G • Signature set: S =[s1 | s2 | … |sN] • Equal Received Powers: pi = p • 1 Receiver/Base station • Synchronous system

12. Sum Capacity [Rupf, Massey] • CDMA sum capacity • To maximize CDMA sum capacity • If N G, StS = IN • N orthonormal sequences • If N > G, SSt = (N/G) IG • N Welch Bound Equality (WBE) sequences

13. User Capacity • [Viswanath, Anantharam, Tse] • Max number of admissible users given • proc gain G, SIR target  • With MMSE receivers: • N < G (1 + 1/ ) • Max achieved with • equal rec’d powers, WBE sequences

14. User Capacity II • Max achieved with equal rec’d powers pi = p WBE sequences: SSt = (N/G) IG • MMSE filters: ci=gi(SSt+s2I)-1si • gi used to normalize ci • MMSE filters are matched filters!

15. Welch’s Bound • For unit energy vectors, a lower bound for maxi,j(sitsj)2 derived using • For k=1, a lower bound on Total Squared Correlation (TSC):

16. Welch’s Bound • For k=1, a lower bound on TSC: • If N  G, bound is loose • N orthonormal vectors, TSC=N • If N>G, bound is achieved iff SSt = (N/G)IG

17. WBE Sequences, Min TSC, Optimality • Min TSC sequences • N orthonormal vectors for N  G • WBE sequences for N > G • For a single cell CDMA system, min TSC sequences maximize • IT sum capacity • User capacity • Goal: A distributed algorithm that converges to a set of min TSC sequences.

18. Reducing TSC • To reduce TSC, replace sk with • eigenvector of Akwith min eigenvalue (C. Rose) • Ak is the interference covariance matrix and can be measured • generalized MMSE filter: (S. Ulukus)

19. MMSE Signature Optimization Algorithm Iterative Algorithm: Matchsito ci Convergence? ci MMSE receiver filter si transmit signal Interference

20. MMSE Algorithm • Replace sk with MMSE filter ck • Old signatures: S=[s1,…,sk-1,sk,sk, sk+1,…, sN] • New signatures: S'=[s1,…,sk-1,sk,ck, sk+1,…, sN] • Theorem: • TSC(S’)  TSC(S) • TSC(S’) =TSC(S) iff ck = sk

21. MMSE Implementation • Use blind adaptive MMSE detector • RX i converges to MMSE filter ci • TX i matches RX: si = ci • Some users see more interference, others less • Other users iterate in response • Longer timescale than adaptive filtering

22. MMSE Iteration • S(n-1), TSC(n-1) At stage n: • replace s1TSC1(n) • replace s2 TSC2(n)…replace sNTSCN(n) = TSC(n) • TSC(n) is decreasing and lower bounded • TSC(n) converges S(n)  S • Does TSC reach global minimum?

23. MMSE Iteration Properties • Assumption: Initial S cannot be partitioned into orthogonal subsets • MMSE filter ignores orthogonal interferers • MMSE algorithm preserves orthogonal partitions • If N  G, S  orthonormal set • If N >G, S  WBE sequences (apparently)

24. MMSE Convergence Example Eigenvalues TSC

25. MMSE Iteration: Proof Status • Theorem: No orthogonal splitting in S(0) no splitting in S(n) for all finite n • doesn’t say that the limiting S is unpartitioned • In practice, fixed points of orthogonal partitions are unstable.

26. EigenAlgorithm • Replace sk with eigenvector ekof Akwith min eigenvalue • Old signatures: S=[s1,…,sk-1,sk,sk, sk+1,…, sN] • New signatures: S'=[s1,…,sk-1,sk,ek, sk+1,…, sN] • Theorem: • TSC(S’)  TSC(S)

27. EigenAlgorithm Iteration • S(n-1), TSC(n-1) At stage n: • replace s1TSC1(n) • replace s2 TSC2(n)…replace sNTSCN(n) = TSC(n) • TSC(n) is decreasing and lower bounded • TSC(n) converges • Wihout trivial signature changes, S(n)  S • Does TSC reach global minimum?

28. EigenAlgorithm Properties • If N  G, • S  orthonormal set (in N steps) • Each ekis a decorrelating filter • If N >G, S  WBE sequences (in practice) • EigenAlgorithm has local minima • Initial partitioning not a problem

29. Stuff to Do • Asynchronous systems • Multipath Channels • Implementation with blind adaptive detectors • Multiple receivers

30. Unlicensed Bands • FCC allocated 3 bands (each 100 MHz) around 5 GHz • Minimal power/bandwidth rules • No required etiquette • How can or should it be used? • Dominant uses? • Non-cooperative system interference