Semi-Blind Beamforming in Beam Space MIMO NOMA for mmWave Communications

Non-orthogonal multiple access (NOMA) scheme has gained remarkable consideration from researchers as it is a favorable technique for the future release of 5G and beyond. Recently proposed beamspace MIMO NOMA for mmWave communication has shown further improvement in its spectrum efficiency by employing beamforming with the aid of instantaneous channel state estimation. But, practically the downlink and the uplink channel state information (CSI) are not identical as the channel reciprocity is no more valid in the fast-varying environment of mmWave communication. Thus, this increases the transmission overhead due to pilot transmission in both uplink and downlink communication. To overcome this issue, we propose a semi-blind technique to design beamforming in downlink power-domain NOMA for mmWave communication which only requires statistical CSI. In the first step, the sum outage probability is derived by using the exact characterization of ratio of the indefinite quadratic form (IQF). In the second step, a heuristic approach with the aid of the interior point (IP) algorithm is developed to find the optimal solution for beam vectors by minimizing the derived sum outage probability. Moreover, a closed-form statistical beamforming solution is derived which is established on statistical signal-to-leakage-noise-ratio (SLNR) maximization. These two proposed methods are compared with the classical principle eigenvector-based solution. Monte Carlo simulations are used to validate the derived analytical expression of outage probability. The results of optimization demonstrate that the performance of both proposed beamforming is higher than the classical eigenvector-based solution. However, the heuristic-based beamforming algorithm via interior-point optimization is significantly better than the SLNR-based solution.