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

Dec 20, 2015

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

1

Power Control,Interference Suppression

and Interference Avoidance

in Wireless Systems

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

Page 2: 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

11 sp

22 sp

33 sp

1kh BS k

2kh 3kh44 sp

55 sp

66 sp

14h BS 1

15h 16h

4kh

5kh

Page 3: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

3

CDMA Receivers

3c

1c

2c11 sp

22 sp

33 sp

SIR1

SIRi

SIRN

Page 4: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

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

Page 5: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

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

Page 6: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

6

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

Page 7: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

7

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

Page 8: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

8

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

Page 9: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

9

MMSE Signature Optimization

ci MMSE receiver filter

Interference

si transmit signal

Capture MoreEnergy

InterferenceSuppressionis unchanged

Match si to ci

Page 10: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

10

Optimal Signatures

• IT Sum capacity: [Rupf, Massey]

• User Capacity [Viswanath, Anantharam, Tse]

• BW Constrained Signatures [Parsavand, Varanasi]

Page 11: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

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

Page 12: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

12

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

Page 13: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

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

Page 14: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

14

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!

Page 15: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

15

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

Page 16: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

16

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

Page 17: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

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.

Page 18: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

18

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)

Page 19: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

19

MMSE Signature Optimization Algorithm

ci MMSE receiver filter

Interference

si transmit signal

Iterative Algorithm:

Match si to ci

Convergence?

Page 20: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

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

Page 21: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

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

Page 22: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

22

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?

Page 23: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

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)

Page 24: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

24

MMSE Convergence Example

Eigenvalues TSC

Page 25: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

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.

Page 26: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

26

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)

Page 27: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

27

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?

Page 28: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

28

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

Page 29: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

29

Stuff to Do

• Asynchronous systems• Multipath Channels• Implementation with blind

adaptive detectors• Multiple receivers

Page 30: 1 Power Control, Interference Suppression and Interference Avoidance in Wireless Systems Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University.

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