An Overloaded MU-MIMO Signal Detection Method Using Piecewise Continuous Nonconvex Sparse Regularizer

In this paper, we consider the signal detection problem of overloaded massive multi-user multi-input multi-output (MU-MIMO) orthogonal frequency division multiplexing (OFDM) and single carrier block transmission with cyclic prefix (SC-CP) systems. For the systems, we employ iterative weighted sum of complex sparse regularizers with group sparsity (IWSCSR-GS) optimization, which is a complex discrete-valued vector reconstruction method that uses discreteness of symbols to estimate unknown vectors, and propose a signal reconstruction method using piecewise continuous nonconvex sparse regularizers, such as smoothly clipped absolute deviation (SCAD) or minimax concave penalty (MCP), in the optimization problem. Computer simulation results demonstrate that the proposed signal reconstruction method with MCP achieves better symbol error rate (SER) performance than that of not only IWSCSR-GS with l
1
norm but also that with l
p
norm (p=0,1/2,2/3) or l
1
-l
2
difference, which are nonconvex sparse regularizers, and the proposed signal reconstruction method with SCAD achieves the best performance among the methods for large systems with high signal-to-noise ratio (SNR) region.