Low-Complexity Hybrid Precoding and Combining Scheme Based on Array Response Vectors

The hybrid precoding and combining algorithms for mmWave massive multiple-input multiple-output (MIMO) systems must consider the trade-off between the complexity and performance of the system. Unfortunately, because of the unit-norm constraint imposed by the use of phase shifters, the optimization of the radio frequency (RF) precoder and combiner becomes a non-convex problem. As a consequence, the algorithm for hybrid precoding and combining design often incurs high complexity. This paper proposes a low-complexity algorithm for hybrid precoding and combining design based on array response vectors. The proposed algorithm considers a decoupled optimization scheme between the RF and baseband domains for the spectral efficiency-maximization problem. In the RF domain, we propose an incremental successive selection method to find a subset of array response vectors from a dictionary, which forms the RF precoding/combining matrices. For the digital domain, we employ singular-value decomposition (SVD) of the low-dimensional effective channel matrix to generate the digital baseband precoder and combiner. Through numerical simulation, we show that the proposed algorithm achieves near-optimal performance with 89.9% - 99.4% complexity reduction compared to the conventional state-of-the-art hybrid precoding and combining algorithm.