Low-Complexity Multistage Optimal Detection for SVD-Based Hybrid Millimeter Wave MIMO Systems

The singular value decomposition (SVD) based hybrid processing for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems attempts to eliminate mutual interference between data streams by processing the original channel matrix to an approximate diagonal matrix. However, the non-zero off-diagonal entries will result in performance loss. To improve the performance with low-complexity, we propose a multistage optimal detection algorithm for SVD-based hybrid mmWave MIMO systems. At the first stage, a decision criterion is proposed by effectively exploiting the characteristic that the magnitudes of off-diagonal entries of the baseband channel matrix are relatively small. Through this decision criterion, some elements of global optimal solution can be determined. The ratio of the determined elements to all elements is analyzed to reveal the advantage of proposed decision criterion. At the second stage, we further propose a decision feedback algorithm to detect more elements of global optimal solution. If all elements are determined, the detection is complete, otherwise it enters the third stage. In the case of third stage, we apply the maximum likelihood (ML) detection algorithm to solve the residual small-scale optimization problem containing only few undetermined elements. Numerical experiments show that the number of elements required to be determined by ML detection is relatively very small or zero, in most situations, that is why the algorithm has a significantly lower complexity.