Low complexity asymptotically unitary algorithm for hybrid beamforming in mmWave communication systems

In millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, because of the high hardware cost and high power consumption, the traditional fully digital beamforming (DBF) cannot be implemented easily. Meanwhile, analog beamforming which is implemented with phase shifters has high availability but suffers poor performance. Considering the advantages of above two, a potential solution is to design an appropriate hybrid analog and digital beamforming structure, where the available iterative optimization algorithm can get performance close to fully digital processing, but solving this sparse optimization problem faces with a high computational complexity. The key challenge of seeking out hybrid beamforming (HBF) matrices lies in leveraging the trade-off between the spectral efficiency performance and the computational complexity. In this paper, we propose an asymptotically unitary hybrid precoding (AUHP) algorithm based on antenna array response (AAR) properties to solve the HBF optimization problem. Firstly, we get the optimal orthogonal analog and digital beamforming matrices relying on the channel's path gain in absolute value by taking into account that the AAR matrices are asymptotically unitary. Then, an improved simultaneously orthogonal matching pursuit (SOMP) algorithm based on recursion is adopted to refine the hybrid combining. Numerical results demonstrate that our proposed AUHP algorithm enables a lower computational complexity with negligible spectral efficiency performance degradation.