Linear Programming Detection and Decoding for MIMO Systems

We develop an efficient linear programming detector (LPD) for multiple-input multiple-output (MIMO) systems. Instead of using the usual l2 norm, our proposed LPD uses the l1 norm as the detection metric, resulting in a mixed-integer linear program (MILP). Two branch-and-bound algorithms are proposed to solve the MILP. The solution of the MILP achieves the same full diversity order as the maximum likelihood detector. The MILP is further relaxed to a linear program (LP), which can be readily solved using the standard simplex method. We show that in some cases the solution of the LP is guaranteed to be that of the MILP. The LPD is also extended to the joint detection and decoding of linear block coded MIMO systems. Our LPD can be immediately implemented using mature circuits design for the simplex algorithm

A new exact closest lattice point search algorithm using linear constraints

The problem of finding the closest lattice point arises in several communications scenarios and is known to be NP-hard. We propose a new closest lattice point search algorithm which utilizes a set of new linear inequality constraints to reduce the search of the closest lattice point to the intersection of a polyhedron and a sphere. This set of linear constraints efficiently leverage the geometric structure of the lattice to reduce considerably the number of points that must be visited. Simulation results verify that this algorithm offers substantial computational savings over standard sphere decoding when the dimension of the problem is large

MIMO Detection for High-Order QAM Based on a Gaussian Tree Approximation

This paper proposes a new detection algorithm for MIMO communication systems employing high order QAM constellations. The factor graph that corresponds to this problem is very loopy; in fact, it is a complete graph. Hence, a straightforward application of the Belief Propagation (BP) algorithm yields very poor results. Our algorithm is based on an optimal tree approximation of the Gaussian density of the unconstrained linear system. The finite-set constraint is then applied to obtain a loop-free discrete distribution. It is shown that even though the approximation is not directly applied to the exact discrete distribution, applying the BP algorithm to the loop-free factor graph outperforms current methods in terms of both performance and complexity. The improved performance of the proposed algorithm is demonstrated on the problem of MIMO detection

Generalized feedback detection for spatial multiplexing multi-antenna systems

We present a unified detection framework for spatial multiplexing multiple-input multiple-output (MIMO) systems by generalizing Heller’s classical feedback decoding algorithm for convolutional codes. The resulting generalized feedback detector (GFD) is characterized by three parameters: window size, step size and branch factor. Many existing MIMO detectors are turned out to be special cases of the GFD. Moreover, different parameter choices can provide various performance-complexity tradeoffs. The connection between MIMO detectors and tree search algorithms is also established. To reduce redundant computations in the GFD, a shared computation technique is proposed by using a tree data structure. Using a union bound based analysis of the symbol error rates, the diversity order and signal-to-noise ratio (SNR) gain are derived analytically as functions of the three parameters; for example, the diversity order of the GFD varies between 1 and N. The complexity of the GFD varies between those of the maximum-likelihood (ML) detector and the zero-forcing decision feedback detector (ZFDFD). Extensive computer simulation results are also provided