1-bit Massive MIMO Signal Detector Based on Convex Integral Quadratic Programming

With discrete modulation techniques, such as quadrature amplitude modulation and phase-shift keying, maximum likelihood (ML) signal detection in massive multi-input multi-output (MIMO) systems fundamentally relies on convex integer programming, executed efficiently through linear operations. However, for 1-bit massive MIMO systems, the nonlinearity introduced by 1-bit quantization impedes the linear realization of the ML detector. To achieve ML detector performance with manageable computational costs, researchers have proposed a two-stage strategy consisting of relaxed continuous convex programming followed by refinement using discrete search within the candidate solution set surrounding the optimal solution of the relaxed continuous convex programming. This article specifically examines the refinement stage. We demonstrate that it is possible to approximate the ML detection's log-likelihood function using a 1-degree freedom quadratic function. We subsequently modify the decomposition algorithm for convex integer quadratic programming (CIQP) with a d -degree freedom matrix and box constraint. Finally, we employ the modified decomposition algorithm for refinement to obtain an initial candidate solution set, which is then expanded and pruned. This method is referred to as the improved CIQP-based algorithm. Numerical results indicate that the improved CIQP-based algorithm outperforms existing approaches in this domain.