# Robust Hybrid Beamforming Scheme for Millimeter-Wave Massive-MIMO 5G Wireless Networks
## 1 Introduction
The RF link and all antennas in the fully connected hybrid beamforming structure are so that the full beamforming gain of the antenna can be obtained. On the basis of the sparsity of mmWave channels, a phase-pursuit (PP) algorithm was proposed in [18] that utilizes the idea of decomposing the hybrid precoding problem into several subproblems for optimization. It considered the unit-modulus constraint on the analog precoding part to find the optimal solution that is used as a reference for finding the digital part. However, as this algorithm only considers the phase aspect and no other aspects of optimization, it has high computational complexity and a large number of iterations requirements. In [19], the authors proposed a low-complexity hybrid precoding scheme that was based on a partly connected architecture and deployed successive interference cancellation (PC-SIC). It utilized partial singular-value decomposition (SVD) to realize subrate optimization and reduce complexity. However, this algorithm requires more complete information of subantenna arrays, and its performance degrades quickly with an increasing number of subantenna arrays, which results in high energy consumption as complexity increases. Another study [20] proposed an orthogonal matching pursuit (OMP) hybrid beamforming algorithm that uses the error matrix of a pure digital beamforming matrix and hybrid beamforming matrix from the candidate set. The analog beamforming matrix is iteratively updated, and finally, a hybrid beamforming algorithm with better performance is obtained. However, there is a big difference between rate and theoretical value obtained when the channel does not satisfy sparsity. The authors in [21] proposed a low-complexity hybrid beamforming algorithm based on the orthogonal characteristics of a digital beamforming matrix that avoided the pseudoinverse operation of the matrix and had low algorithm complexity, but its energy consumption was high. The authors in [22] proposed a hybrid beamforming algorithm based on beam training, but due to the limited accuracy of the phase shifter in practical systems, the algorithm did not achieve optimal performance. In [23], the authors studied the effect on system performance of the relationship between the number of data streams and the number of RF links, and pointed out that, when the number of RF links is equal to twice the number of data streams, hybrid beamforming can be approximated to pure numbers for beamforming. Another study [24] proposed a matrix decomposition-based hybrid processing (MD-HP) scheme. The method achieved similar system performance to that of pure digital beamforming by continuously converging the phase of the analog matrix, and updating the digital matrix and the analog matrix. At present, there is relatively little research on partially connected hybrid beamforming. Some connection structures are characterized by the RF link only being connected to some antennas, so the hybrid beamforming algorithm based on structure-shaping gain is less than that of a full connection, but due to antenna grouping, the hybrid beamforming of a partial-connection mode is to sacrifice the partial gain for lower complexity. In [25], the authors proposed a codebook-based hybrid beamforming design. Although the algorithm was less complex, system performance was lost. On the basis of successive interference cancellation (SIC), [26] proposed a partially connected hybrid beamforming algorithm, but the full gain of the algorithm came from the analog matrix, so only suboptimal performance could be achieved. The SDR-AltMin algorithm proposed in [21] had improved performance compared to the algorithm in [20], but it still could not achieve optimal performance due to harsh design conditions. On the basis of the above analysis, in order to obtain better system performance, an alternating minimum mean square error (Alt-MMSE) algorithm is proposed for a fully connected structure. The algorithm aims to minimize the mean square error (MSE) of the transmitted and received signals.