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

2 CDMA System Model BS k BS 1

3 CDMA Receivers SIR 1 SIR i SIR N

4 CDMA Signals Power Control: p i Interference suppression: c ki Interference Avoidance: s i

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 c kj for max SIR Given p, use MMSE filter [Madhow, Honig 94] –Given c kj, 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 s i to improve SIR –Receiver feedback tells transmitter how to adapt. Application: –Fixed Wireless –Unlicensed Bands

9 MMSE Signature Optimization c i MMSE receiver filter Interference s i transmit signal Capture More Energy Interference Suppression is unchanged Match s i to c i

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 =[s 1 | s 2 | … |s N ] Equal Received Powers: p i = p 1 Receiver/Base station Synchronous system

12 Sum Capacity [Rupf, Massey] CDMA sum capacity To maximize CDMA sum capacity –If N  G, S t S = I N N orthonormal sequences –If N > G, SS t = (N/G) I G 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 p i = p WBE sequences: SS t = (N/G) I G MMSE filters: c i =g i (SS t +   I) -1 s i –g i used to normalize c i MMSE filters are matched filters!

15 Welch’s Bound For unit energy vectors, a lower bound for max i,j (s i t s j ) 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 SS t = (N/G) I G

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 s k with –eigenvector of A k with min eigenvalue (C. Rose) A k is the interference covariance matrix and can be measured –generalized MMSE filter: (S. Ulukus)

19 MMSE Signature Optimization Algorithm c i MMSE receiver filter Interference s i transmit signal Iterative Algorithm: Match s i to c i Convergence?

20 MMSE Algorithm Replace s k with MMSE filter c k –Old signatures: S=[s 1,…, s k-1,s k,s k, s k+1,…, s N ] –New signatures: S ' =[s 1,…, s k-1,s k,c k, s k+1,…, s N ] Theorem: –TSC(S ’ )  TSC(S) –TSC(S ’ ) =TSC(S) iff c k = s k

21 MMSE Implementation Use blind adaptive MMSE detector RX i converges to MMSE filter c i TX i matches RX: s i = c i –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 s 1 TSC 1 (n) –replace s 2 TSC 2 (n) … replace s N TSC N (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 s k with eigenvector e k of A k with min eigenvalue –Old signatures: S=[s 1,…, s k-1,s k,s k, s k+1,…, s N ] –New signatures: S ' =[s 1,…, s k-1,s k,e k, s k+1,…, s N ] Theorem: –TSC(S ’ )  TSC(S)

27 EigenAlgorithm Iteration S(n-1), TSC(n-1) At stage n: –replace s 1 TSC 1 (n) –replace s 2 TSC 2 (n) … replace s N TSC N (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 e k is 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