1

Power Control,Interference Suppression

and Interference Avoidance

in Wireless Systems

Roy Yates(with S. Ulukus and C. Rose)WINLAB, Rutgers University

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CDMA System Model

11 sp

22 sp

33 sp

1kh BS k

2kh 3kh44 sp

55 sp

66 sp

14h BS 1

15h 16h

4kh

5kh

3

CDMA Receivers

3c

1c

2c11 sp

22 sp

33 sp

SIR1

SIRi

SIRN

4

CDMA Signals

ijj

tkijkj

itkiiki

ki

ktki

ijj

tkijjkji

tkiiikiki

jkjjjkjk

ph

phSIR

bphbphy

bph

22

2

noiseceInterferen

Signal Desired

][sc

scp

ncscsc

nsr

• Power Control: pi • Interference suppression: cki

• Interference Avoidance: si

5

22

2 :constraint SIR ij

jjtkikj

itki

ii psch

scp

1 iff Feasible G

Gpp :formVector

SIR Constraints

• Feasibility depends on link gains, receiver filters

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SIR Balancing

• SIR low Increase transmit power• SIR high Decrease transmit power

• [Aein 73, Nettleton 83, Zander 92, Foschini&Miljanic 93]

)())((

)1( tptSIR

tp iki

ii p

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Power Control + Interference Suppression

• 2 step Algorithm: – [Rashid-Farrokhi, Tassiulas, Liu], [Ulukus, Yates]

– Adapt receiver filter ckj for 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

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Interference Avoidance

• Old Assumption: Signatures never change

• New Approach: Adapt signatures si to improve SIR– Receiver feedback tells transmitter how to

adapt.

• Application: – Fixed Wireless – Unlicensed Bands

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MMSE Signature Optimization

ci MMSE receiver filter

Interference

si transmit signal

Capture MoreEnergy

InterferenceSuppressionis unchanged

Match si to ci

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Optimal Signatures

• IT Sum capacity: [Rupf, Massey]

• User Capacity [Viswanath, Anantharam, Tse]

• BW Constrained Signatures [Parsavand, Varanasi]

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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

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Sum Capacity [Rupf, Massey]

• CDMA sum capacity

SSISSI t

Nt

G

ppC 22sum det(log

21

det(log21

• 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

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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

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User Capacity II

• Max achieved withequal rec’d powers pi = pWBE sequences: SSt = (N/G) IG

• MMSE filters: ci=gi(SSt+I) -1si

– gi used to normalize ci

• MMSE filters are matched filters!

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Welch’s Bound

• For unit energy vectors, a lower bound for maxi,j(si

tsj)2 derived using

k

kGk

j

N

i

N

j

ti

N1

22

1 1

)(

ss

• For k=1, a lower bound on Total Squared Correlation (TSC):

GNj

N

i

N

j

ti /)(TSC 22

1 1

ss

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Welch’s Bound

GNj

N

i

N

j

ti /)(TSC 22

1 1

ss

• 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

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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.

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Reducing TSC

22 )(2)(TSC jki kj

tik

kj

tjj

tkk

tk

k

sss

A

sssss

• To reduce TSC, replace sk with

– eigenvector of Ak with min eigenvalue (C. Rose)• Ak is the interference covariance matrix and can be

measured

– generalized MMSE filter: (S. Ulukus)

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MMSE Signature Optimization Algorithm

ci MMSE receiver filter

Interference

si transmit signal

Iterative Algorithm:

Match si to ci

Convergence?

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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

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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

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MMSE Iteration

• S(n-1), TSC(n-1) At stage n:– replace s1 TSC1(n)

– replace s2 TSC2(n)…replace sN TSCN(n) = TSC(n)

• TSC(n) is decreasing and lower bounded– TSC(n) converges S(n) S

• Does TSC reach global minimum?

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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)

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MMSE Convergence Example

Eigenvalues TSC

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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.

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EigenAlgorithm

• Replace sk with eigenvector ek of Ak with 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)

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EigenAlgorithm Iteration

• S(n-1), TSC(n-1) At stage n:– replace s1 TSC1(n)

– replace s2 TSC2(n)…replace sN TSCN(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?

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EigenAlgorithm Properties

• If N G, – S orthonormal set (in N steps)

• Each ek is a decorrelating filter

• If N > G, S WBE sequences (in practice)– EigenAlgorithm has local minima – Initial partitioning not a problem

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Stuff to Do

• Asynchronous systems• Multipath Channels• Implementation with blind

adaptive detectors• Multiple receivers

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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