A Near-Maximum-Likelihood Decoding Algorithm for MIMO Systems Based on Semi-Definite Programming

Mobasher, Amin; Taherzadeh, M.; Sotirov, Renata; Khandani, Amir K.

doi:10.1109/tit.2007.907472

Cited by 80 publications

(71 citation statements)

References 45 publications

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“…Given an observed noisy output vector y ∈ R m , problem (31) must be solved for decoding the binary input vector x ∈ {−1, +1} n for a matrix Q ∈ R m×n [22,23,26]. Letting z = 1 2 (1 + x) and b = 1 2 Q1 + y, we can state (31) in the conic quadratic form min t : ||Qz − b|| ≤ t, z ∈ {0, 1} n , t ∈ R + .…”

Section: 3mentioning

confidence: 99%

Conic mixed-integer rounding cuts

2008

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Abstract. A conic integer program is an integer programming problem with conic constraints. Many problems in finance, engineering, statistical learning, and probabilistic optimization are modeled using conic constraints.Here we study mixed-integer sets defined by second-order conic constraints. We introduce general-purpose cuts for conic mixed-integer programming based on polyhedral conic substructures of second-order conic sets. These cuts can be readily incorporated in branch-and-bound algorithms that solve either secondorder conic programming or linear programming relaxations of conic integer programs at the nodes of the branch-and-bound tree.Central to our approach is a reformulation of the second-order conic constraints with polyhedral second-order conic constraints in a higher dimensional space. In this representation the cuts we develop are linear, even though they are nonlinear in the original space of variables. This feature leads to a computationally efficient implementation of nonlinear cuts for conic mixed-integer programming. The reformulation also allows the use of polyhedral methods for conic integer programming.We report computational results on solving unstructured second-order conic mixed-integer problems as well as mean-variance capital budgeting problems and least-squares estimation problems with binary inputs. Our computational experiments show that conic mixed-integer rounding cuts are very effective in reducing the integrality gap of continuous relaxations of conic mixed-integer programs and, hence, improving their solvability.

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Section: 3mentioning

confidence: 99%

Conic mixed-integer rounding cuts

2008

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“…There are many ways to relax problem (4) into an SDP; see, e.g., [17,10,7,8,18]. For the sake of simplicity, we shall follow the approach of Mao et al [7].…”

Section: Semidefinite Relaxation Of the ML Detection Problemmentioning

confidence: 99%

“…As a result, many sub-optimal but efficient heuristics have been proposed for solving the ML detection problem (see, e.g., [1] for a brief overview). One such heuristiccalled the semidefinite relaxation (SDR) detector -has attracted a lot of interest recently (see, e.g., [12,5,17,1,10,8,7,18,6]). Roughly speaking, the SDR detector solves a convex relaxation of * E-mail: manchoso@se.cuhk.edu.hk.…”

Section: Introductionmentioning

confidence: 99%

On the performance of semidefinite relaxation MIMO detectors for QAM constellations

2009

2009 IEEE International Conference on Acoustics, Speech and Signal Processing

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Due to their computational efficiency and strong empirical performance, semidefinite relaxation (SDR)-based algorithms have gained much attention in multiple-input multiple-output (MIMO) detection. In the case of a binary phase-shift keying (BPSK) constellation, the theoretical performance of the SDR approach is relatively well-understood. However, little is known about the case of quadrature amplitude modulation (QAM) constellations, although simulation results suggest that the SDR approach should work well in the low signal-to-noise ratio (SNR) region. In this paper we make a first step towards explaining such phenomenon by showing that in the case of QAM constellations, several commonly used SDR-based algorithms will provide a constant factor approximation to the optimal log-likelihood value in the low SNR region with exponentially high probability. Our result gives some theoretical justification for using SDR-based algorithms for the MIMO detection of QAM signals, at least in the low SNR region.

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“…However, this is achieved at the cost of huge computational complexity, which increases exponentially with the number of users. In the last decade, a variety of multiuser detectors with low complexity and sub-optimum performance were proposed, such as linear detectors [33], subtractive interference canceling [25], semidefinite programming approach by using interior-point methods [22,24,31,34], sphere decoder [14] and heuristic methods [7,8,21,27,28]. The last three methods have been used for solving different detection models and obtaining near-maximum likelihood (near-ML) performance at cost of polynomial computational complexity, except for the sphere decoder algorithm whose expected complexity increases exponentially according to the number of users for large size problems [14].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, heuristic algorithms have been applied to symbol detection in non-spreading multiple-input multiple-output systems [4,24]. PSO heuristic method has been applied to non-spreading MIMO multiuser detection on 16-and 64-QAM modulation [19,37].…”

Section: Introductionmentioning

confidence: 99%

S/MIMO MC-CDMA Heuristic Multiuser Detectors Based on Single-Objective Optimization

Abrão

Oliveira

Ciriaco

et al. 2009

Wireless Pers Commun

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This paper analyzes the complexity-performance trade-off of several heuristic near-optimum multiuser detection (MuD) approaches applied to the uplink of synchronous single/multiple-input multiple-output multicarrier code division multiple access (S/MIMO MC-CDMA) systems. Genetic algorithm (GA), short term tabu search (STTS) and reactive tabu search (RTS), simulated annealing (SA), particle swarm optimization (PSO), and 1-opt local search (1-LS) heuristic multiuser detection algorithms (Heur-MuDs) are analyzed in details, using a single-objective antenna-diversity-aided optimization approach. MonteCarlo simulations show that, after convergence, the performances reached by all nearoptimum Heur-MuDs are similar. However, the computational complexities may differ substantially, depending on the system operation conditions. Their complexities are carefully analyzed in order to obtain a general complexity-performance framework comparison and to show that unitary Hamming distance search MuD (uH-ds) approaches (1-LS, SA, RTS and STTS) reach the best convergence rates, and among them, the 1-LS-MuD provides the best trade-off between implementation complexity and bit error rate (BER) performance.

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A Near-Maximum-Likelihood Decoding Algorithm for MIMO Systems Based on Semi-Definite Programming

Cited by 80 publications

References 45 publications

Conic mixed-integer rounding cuts

Conic mixed-integer rounding cuts

On the performance of semidefinite relaxation MIMO detectors for QAM constellations

S/MIMO MC-CDMA Heuristic Multiuser Detectors Based on Single-Objective Optimization

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