Compressed sensing based semidefinite relaxation detection algorithm for overloaded uplink multiuser massive MIMO system

The research on detection algorithms for uplink multiuser Massive multi input multi output (MIMO) system is a hot-spot for 5G. The recent detection algorithms are constrained by the assumed condition that the receiving antennas' number should be equal to or larger than the transmitting antennas' number. For the overloaded case that the total number of transmitting antennas of users in a cell is larger than that of receiving antennas at base station(BS), they fail to detect with a bad performance. Thus, this paper presents a compressed sensing based semidefinite relaxation (CSR) detection algorithm for this case, which is based on a sparse overloaded detection model where users select to access randomly and autonomously and the accessed state is unknown at BS. Simulation results shows its efficiency. Along with low polynomial computational complexity of O(N^2.5_K) per symbol, the proposed CSRD obtains an approximate optimum bits error rate performance of 10^-5 and a high correct detection rate of the users' accessed state at medium low average received signal to noise ratio for combined 4-quadrature amplitude modulation (QAM) and 16QAM signal without known users' accessed state at BS in the overloaded case of N_k > N_r, where N_K and N_r denote the users' and receiving antennas' numbers, respectively.