A low complexity detection for the binary MIMO system using Lagrange multipliers

Maximum-likelihood (ML) detection for binary Multiple-Input-Multiple-Output (MIMO) systems can be posed as a binary quadratic programming (BQP) which belongs to a nondeterministic polynomial-time hard (NP-hard) problem in general. In this paper, we translate the binary constraints of BQP into the equivalent quadratic equality constraints and employ the Lagrange multipliers method to deal these equivalent constraints. We derive the relation among the Lagrange multiplier, transmitting signal and noise. Since both transmitting signal and noise are unknown, it is impossible to solve the Lagrange multipliers exactly. However, in this paper, an estimation method is proposed to obtain the approximations of the Lagrange multipliers with low computational complexity. Numerical experiments show that the performance of the proposed method is very near to that of the ML detection.