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Wireless Communication Low Complexity Multiuser Detection. Rami Abdallah University of Illinois at Urbana Champaign 12/06/2007. Outline. Introduction. Multiuser Detection (MUD): canceling or suppressing interfering users from the desired signals Benefits: Capacity Improvement - PowerPoint PPT Presentation
1
Wireless Communication
Low Complexity Multiuser DetectionRami Abdallah
University of Illinois at Urbana Champaign
12/06/2007
2
Outline
Multiuser Detectors
OptimalJoint-ML Suboptimal
LinearInterference Cancellation
Near-ML
Sphere Decoder
Semi-DefiniteRelaxation
ProbabilisticData
Association
Parallel
Succesive
Decision Feedback
MMSE
Decorrelator
PolynomialExpansion
3
Introduction
• Multiuser Detection (MUD): canceling or suppressing interfering users from the desired signals
• Benefits: – Capacity Improvement– Reduced requirement for power control
• Limitations:– Complexity– Intercell interference– Spreading – Coding tradeoff
4
Problem Definition
• Optimum Multiuser Detection
– Search space exponential in number of users
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5
System Representation
• Matched Filter (MF)– Received Signal for user k:
– System Representation after MF:
• Noise Whitening– Cholesky Decomposition to decorrelate noise
– Enables layered decoding
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Multiple-Access Interference (MAI)
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LLR nzyy
LAL1~ 0,0 NCNn
6
Linear Detectors (1)
• Decorrelating Detector– Solve for z by inverting R– Independent User Decoding– Best near-far resistance– Noise enhancement
• Optimal Linear Detector (MMSE) – Trade-off between MAI elimination and noise enhancement
wzyx
kkkk wzAx
RAR~
11
120
ANRT
T
MMSE
MMSE yx
7
Linear Detectors (2)
• Polynomial Expansion (PE) Detector :
– Weighted sum of MF output (R)– Weights (W) chosen depending on a performance
criterion and can be adaptively updated– Can approximate decorrelating and MMSE detector
(Cayley-Hamilton Theorem)– Regular architecture avoiding Matrix inversion
N
i
iiPE
PE
RwTwhere
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0
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8
Interference Cancellation
• Successive Interference Cancellation (SIC)
– Order users according to descending power
– Start detection with the highest power first and subtract its effect from the received signal
– Successive users benefits more for MAI cancellation
• Problems:
– Latency
– Decision error propagation
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Receiver 1
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Receiver 2
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Receiver K
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9
Interference Cancellation (2)
Stage 1
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Stage N
r(t)
• Parallel Interference Cancellation (PIC) – Every stage use previous estimates to subtract
MAI for each user in parallel– Tradeoff between complexity and performance
z.yz iGAi ˆ1ˆ
10
Performance Comparison
– PIC superior over SIC in well-power controlled environment
Power Controlled
11
• Multistage decision feed-back detector: – In each stage use the already detected bits to improve detection of remaining bits in the same stage
• Partial interference cancellation– Decision is based on
– Partially cancel MAI with the amount being cancelled increasing with each stage
Variations of PIC
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ipiGApi ii zz.yz ˆ1ˆsgn1ˆ
iiGAip zz.yz ˆ,ˆ,1ˆ
12
• Decision feed-back detector:– User ordering in terms of descending power– Noise whitening – SIC to cancel MAI among user (F is lower triangular)
Decision Feedback MUD
r(t)
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13
• Sphere Decoders (SD) in AWGN Channel
– ML: Search over all
– SD: Restrict search within a sphere of center s and radius R
• Complexity tradeoff in terms of choosing radius R
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z~
Sphere (lattice) Decoder
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14
Preprocessing for SD
• Triangularization in AWGN– QR Decomposition: a unitary matrix (Q) and an upper triangular matrix
• Triangularization in MUD – Noise Whitening
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New received vector
Still AWGN with equal variance
Channel Normalization
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15
• Layered/ Tree-based Decoding – Partial Euclidean Distance Accumulations by taking advantage of
channel triangularization
• Search Constraint: Radius or Best Candidates
Sphere Decoders
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16
Constrained SD Z1
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C(z
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z 3)
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1
1 1
1
11
0 0
0
0 0 00
d(z1,z2,z3)
• Depth First SD– Search the tree in downward and upward manner– Update the search radius after each pass
• Breadth First (K-best SD)– Search in downward direction only– K best candidates are retained at each level in the tree
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Performance Comparison
• 1000X reduction in complexity
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• SD limits search space• Relaxation increases search space by dropping certain constraints so that the search is
easier to implement• Unconstrained Relaxation (UR)
– Remove constraint on Alphabet
– Penalized UR:
Compare to MF, Decorrelator, MMSE
Relaxations and Heuristics
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19
• Problem Setup:
• Semi-Definite Relaxation (SDR):
– Drop rank 1 constraint on X with X still symmetric positive semi definite:
– An efficient solution can be found in
Semi-Definite Relaxation
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1,.max
max1,1
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QK
,x xxX X
xx x
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20
• Approximate Boolean solution by randomization
– Randomize to approximate xi from vi
Semi-definite Relaxation (2)
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21
SDR for MUD
SNR3=11dB
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y z
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22
• Problem Setup:
• PDA
– Order users in decreasing power
– Belief on the decision of user k at stage i
– Update this belief by treating MAI as AWGN:
– Stop when belief converges, Decide by comparing p to 0.5
Probabilistic Data Association
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1)()(
ik
i zppkz
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)1,()()(
14,12~
,1
23
Performance Comparison
Average BER with K=29 with gold codes
24
Conclusions
• Multiuser Detection (MUD): canceling or suppressing interfering users from the desired signals
• Different techniques exist that trade-off complexity with performance
• Detection techniques can be applied to other detection problems (ex. MIMO)
• Viterbi Algorithm can be applied to MUD, How would low complexity “Viterbi algorithm” behave under MUD?