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