2 research outputs found
Tightness of a new and enhanced semidefinite relaxation for MIMO detection
In this paper, we consider a fundamental problem in modern digital
communications known as multi-input multi-output (MIMO) detection, which can be
formulated as a complex quadratic programming problem subject to unit-modulus
and discrete argument constraints. Various semidefinite relaxation (SDR) based
algorithms have been proposed to solve the problem in the literature. In this
paper, we first show that the conventional SDR is generally not tight for the
problem. Then, we propose a new and enhanced SDR and show its tightness under
an easily checkable condition, which essentially requires the level of the
noise to be below a certain threshold. The above results have answered an open
question posed by So in [35]. Numerical simulation results show that our
proposed SDR significantly outperforms the conventional SDR in terms of the
relaxation gap.Comment: 24 pages, 2 figures, accepted for publication in SIAM Journal on
Optimizatio
An Efficient Sparse Quadratic Programming Relaxation Based Algorithm for Large-Scale MIMO Detection
Multiple-input multiple-output (MIMO) detection is a fundamental problem in
wireless communications and it is strongly NP-hard in general. Massive MIMO has
been recognized as a key technology in the fifth generation (5G) and beyond
communication networks, which on one hand can significantly improve the
communication performance, and on the other hand poses new challenges of
solving the corresponding optimization problems due to the large problem size.
While various efficient algorithms such as semidefinite relaxation (SDR) based
approaches have been proposed for solving the small-scale MIMO detection
problem, they are not suitable to solve the large-scale MIMO detection problem
due to their high computational complexities. In this paper, we propose an
efficient sparse quadratic programming (SQP) relaxation based algorithm for
solving the large-scale MIMO detection problem. In particular, we first
reformulate the MIMO detection problem as an SQP problem. By dropping the
sparse constraint, the resulting relaxation problem shares the same global
minimizer with the SQP problem. In sharp contrast to the SDRs for the MIMO
detection problem, our relaxation does not contain any (positive semidefinite)
matrix variable and the numbers of variables and constraints in our relaxation
are significantly less than those in the SDRs, which makes it particularly
suitable for the large-scale problem. Then we propose a projected Newton based
quadratic penalty method to solve the relaxation problem. By extensive
numerical experiments, when applied to solve large-scale problems, the proposed
algorithm achieves better detection performance and is more robust to the
choice of the initial point than a recently proposed generalized power method.Comment: 25pages, 6 figure