Hybrid beamforming with impaired elements: Design of optimized beam pattern

Abstract

Millimeter-wave (mmWave) multi-input multi-output systems, affected by atmospheric conditions and hardware failure, are vulnerable to antenna element blockages and failures. The authors consider the hybrid beamforming (HBF) optimization problem for systems with impaired elements to approximate the performance of a fault-free system. Especially, the impaired coefficient of elements is estimated rather than simply assuming it is completely invalid. Firstly, to ensure that radiation power is within the desired angle, the impaired coefficients are estimated and the beamforming vector basis is designed. Then, by using the derived basis and semidefinite relaxation (SDR) technique, a minimax optimization problem is solved to smooth the passband response. Finally, a hybrid decomposition is conducted to be compatible with HBF structures. Numerical results indicate that the proposed algorithm improves the average data rate of the mmWave system with three impaired elements by about 40%, which is almost 93% of the performance of a fault-free system.