Multiuser Detection
Approximation algorithms for MAX-3-CUT and other problems via complex semidefinite programming
Journal of Computer and System Sciences - STOC 2001
Fundamentals of wireless communication
Fundamentals of wireless communication
On approximating complex quadratic optimization problems via semidefinite programming relaxations
Mathematical Programming: Series A and B
On the performance of semidefinite relaxation MIMO detectors for QAM constellations
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Semidefinite relaxation based multiuser detection for M-ary PSK multiuser systems
IEEE Transactions on Signal Processing - Part I
IEEE Transactions on Signal Processing
A Near-Maximum-Likelihood Decoding Algorithm for MIMO Systems Based on Semi-Definite Programming
IEEE Transactions on Information Theory
The Diversity Order of the Semidefinite Relaxation Detector
IEEE Transactions on Information Theory
The application of semidefinite programming for detection in CDMA
IEEE Journal on Selected Areas in Communications
Multireference alignment using semidefinite programming
Proceedings of the 5th conference on Innovations in theoretical computer science
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We consider the problem of detecting a vector of symbols that is being transmitted over a fading multiple--input multiple--output (MIMO) channel, where each symbol is an M--th root of unity for some fixed M ≥ 2. Although the symbol vector that minimizes the error probability can be found by the so-called maximum--likelihood (ML) detector, its computation is intractable in general. In this paper we analyze a popular polynomial--time heuristic, called the semidefinite relaxation (SDR) detector, for the problem and establish its first non--asymptotic performance guarantee. Specifically, in the low signal--to--noise ratio (SNR) region, we show that for any M ≥ 2, the SDR detector will yield a constant factor approximation to the optimal log-likelihood value with a probability that increases exponentially fast to 1 as the channel size increases. In the high SNR region, it is known that for M = 2, the SDR detector will yield an exact solution to the ML detection problem with a probability that converges to 1. We refine this result by establishing the rate of convergence. Our work can be viewed as an average-case analysis of a certain SDP relaxation, and the input distribution we use is motivated by physical considerations. Our results also refine and extend those in previous work, which are all asymptotic in nature and apply only to the problem of detecting binary (i.e., when M = 2) vectors. In particular, our results can give better insight into the performance of the SDR detector in practical settings.