Due to the high cost and power consumption of the radio frequency(RF) chains, it is difficult to implement the full digital beamforming in millimeter-wave(mm Wave) multiple-input multiple-output(MIMO) systems. Fortunately, the hybrid beamforming(HBF) is proposed to overcome these limitations by splitting the beamforming process between the analog and digital domains. In recent works, most HBF schemes improve the spectral efficiency based on greedy algorithms. However, the iterative process in greedy algorithms leads to high computational complexity. In this paper, a new method is proposed to achieve a reasonable compromise between complexity and performance. The novel algorithm utilizes the low-complexity Gram-Schmidt method to orthogonalize the candidate vectors. With the orthogonal candidate matrix, the slow greedy algorithm is avoided. Thus, the RF vectors are found simultaneously without any iteration. Additionally, the phase extraction is applied to satisfy the element-wise constant-magnitude constraint on the RF matrix. Simulation results demonstrate that the new HBF algorithm can make substantial improvements in complexity while maintaining good performance.
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