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Power Control, Interference Suppression and Interference Avoidance in Wireless Systems. Roy Yates (with S. Ulukus and C. Rose) WINLAB, Rutgers University. CDMA System Model. BS k. BS 1. CDMA Receivers. SIR 1. SIR i. SIR N. CDMA Signals. Power Control: p i - PowerPoint PPT Presentation
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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
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
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
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
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
9
MMSE Signature Optimization
ci MMSE receiver filter
Interference
si transmit signal
Capture MoreEnergy
InterferenceSuppressionis unchanged
Match si to ci
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
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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
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 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!
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
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
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
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)
19
MMSE Signature Optimization Algorithm
ci MMSE receiver filter
Interference
si transmit signal
Iterative Algorithm:
Match si to ci
Convergence?
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 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?
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 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)
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?
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
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