Wireless Communication Low Complexity Multiuser Detection Rami Abdallah
Wireless Communication Low Complexity Multiuser Detection Rami Abdallah University of Illinois at Urbana Champaign 12/06/2007
Outline 2
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 3
Problem Definition • Optimum Multiuser Detection – Search space exponential in number of users 4
System Representation • Matched Filter (MF) – Received Signal for user k: Multiple-Access Interference (MAI) – System Representation after MF: • Noise Whitening – Cholesky Decomposition to decorrelate noise – Enables layered decoding 5
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 6
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 7
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 8
Interference Cancellation (2) • Parallel Interference Cancellation (PIC) – Every stage use previous estimates to subtract MAI for each user in parallel – Tradeoff between complexity and performance 9
Performance Comparison Power Controlled – PIC superior over SIC in well-power controlled environment 10
Variations of PIC • 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 11
Decision Feedback MUD • Decision feed-back detector: – User ordering in terms of descending power – Noise whitening – SIC to cancel MAI among user (F is lower triangular) 12
Sphere (lattice) Decoder • Sphere Decoders (SD) in AWGN Channel H: channel, n : AWGN – ML: Search over all – SD: Restrict search within a sphere of center s and radius R • Complexity tradeoff in terms of choosing radius R 13
Preprocessing for SD New received vector Still AWGN with equal variance • Triangularization in AWGN – QR Decomposition: a unitary matrix (Q) and an upper triangular matrix • Triangularization in MUD – Noise Whitening 14
Sphere Decoders • Layered/ Tree-based Decoding – Partial Euclidean Distance Accumulations by taking advantage of channel triangularization • Search Constraint: Radius or Best Candidates 15
Constrained SD • 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 16
Performance Comparison • 1000 X reduction in complexity 17
Relaxations and Heuristics • 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 18
Semi-Definite Relaxation • 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 19
Semi-definite Relaxation (2) • Approximate Boolean solution by randomization – Randomize to approximate xi from vi 20
SDR for MUD SNR 3=11 d. B 21
Probabilistic Data Association • 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 22
Performance Comparison Average BER with K=29 with gold codes 23
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? 24
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