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
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
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
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
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
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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
9
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 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