Efficient Algorithms for Constant-Modulus Analog Beamforming

The use of a large-scale antenna array (LSAA) has become an important characteristic of multi-antenna communication systems to achieve beamforming gains. For example, in millimeter wave (mmWave) systems, an LSAA is employed at the transmitter/receiver end to combat severe propagation losses. In such applications, each antenna element has to be driven by a radio frequency (RF) chain for the implementation of fully-digital beamformers. This strict requirement significantly increases the hardware cost, complexity, and power consumption. Therefore, phase-only analog beamforming becomes a viable solution. In this paper, we consider the scaled analog beamforming (SAB) architecture and design the system parameters by solving the beampattern matching problem. We consider two beampattern matching problems. In the first case, both the magnitude and phase of the beampattern are matched to the given desired beampattern whereas in the second case, only the magnitude of the beampattern is matched. Both the beampattern matching problems are cast as a variant of the constant-modulus least-squares problem. We provide efficient algorithms based on the alternating majorization-minimization (AMM) framework that combines the alternating minimization and the MM frameworks and the conventional-cyclic coordinate descent (C-CCD) framework to solve the problem in each case. We also propose algorithms based on a new modified-CCD (M-CCD) based approach. For all the developed algorithms we prove convergence to a {\color{red} Karush-Kuhn-Tucker (KKT) point (or a stationary point)}. Numerical results demonstrate that the proposed algorithms converge faster than state-of-the-art solutions. Among all the algorithms, the M-CCD-based algorithms have faster convergence when evaluated in terms of the number of iterations and the AMM-based algorithms offer lower complexity.