Efficient Algorithms for Constant-Modulus Analog Beamforming


For the purpose of achieving beamforming gains in multi-antenna Communication systems, such as those used in the design of millimeter-wave (mmWave) systems to combat severe propagation losses, the application of a large-scale antenna array, abbreviated as LSAA, has emerged as an important characteristic. In these types of applications, the implementation of fully-digital beamformers requires that each antenna element be driven by a radio frequency (RF) chain. This results in a significant increase in the complexity of the hardware, as well as the cost and amount of power it consumes. As a result, constant-modulus analog beamforming (CMAB) emerges as an option worthy of consideration. In this paper, we take into consideration the scaled analog beamforming (SAB) or the constant-modulus analog beamforming (CMAB) architecture. We then design the system parameters by solving two different variants of the beampattern matching problem. In the first scenario, the magnitude and phase of the beampattern are both matched to the specific desired beampattern. In the second scenario, however, only the magnitude of the beampattern is matched to the desired beampattern. Both of the beampattern matching problems can be recast as different iterations of the same problem known as the constant-modulus least-squares (CLS) problem. We offer effective algorithms for solving the problem, all of which are based on the alternating majorization-minimization (AMM) framework. This framework combines the alternating minimization and the MM frameworks, as well as the conventional-cyclic coordinate descent (C-CCD) algorithms. We also propose algorithms that are based on a new approach that is based on modified CCD (M-CCD). Convergence to a Karush-Kuhn-Tucker (KKT) point is demonstrated for each of the algorithms that were developed by us (or a stationary point). The numerical results show that the proposed algorithms converge more quickly than the solutions that are currently considered to be state-of-the-art. The M-CCD-based algorithms are the ones with the quickest convergence when measured in terms of the number of iterations, whereas the AMM-based algorithms are the ones with the lowest complexity.

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