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

On the performance of semidefinite relaxation MIMO detectors for QAM constellations

Due to their computational efficiency and strong empirical perfor-mance, semidefinite relaxation (SDR)–based algorithms have gained much attention in multiple–input multiple–output (MIMO) detec-tion. In the case of a binary phase–shift keying (BPSK) constella-tion, the theoretical performance of the SDR approach is relatively well–understood. However, little is known about the case of quadra-ture amplitude modulation (QAM) constellations, although simula-tion 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 al-gorithms 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