Flexible Hierarchical Multi-Beam Search Algorithm for Millimeter-Wave 3D MIMO Systems With Uniform Planar Arrays

Massive multiple-input multiple-output (MIMO) systems and millimeter-wave (mmWave) spectrum are key technologies for enabling next-generation wireless communications. To fully exploit the array and multiplexing gains, beamforming or precoding strategies require accurate information about the multiple multipath components (MPCs) in the mmWave channel. In this paper, we propose a novel hierarchical multi-beam search algorithm for channel estimation in mmWave MIMO systems aiming to enhance beamforming performance. The proposed algorithm enables efficient channel estimation and precoding design in massive MIMO systems with uniform planar arrays with any composite number of horizontal and vertical elements. Thus, it overcomes the limitations of existing hierarchical codebooks, which mostly support uniform linear arrays with an antenna count that is a power of an integer. The proposed algorithm reduces training overhead using a low-complexity least-squares-based refinement approach. The simulation results show that the failure rate of the proposed algorithm is comparable to that of current methods but with a lower training cost and complexity. Moreover, the simulation results also show that the spectral efficiency of the precoding scheme determined using the proposed search algorithm and codebook is the highest compared to existing methods. Numerical results show that the proposed method achieves more accurate spatial angle estimation than existing approaches, even in the presence of hardware impairments, highlighting its superior flexibility and robustness in practical scenarios.