Pencil and Shaped Beam Patterns Synthesis Using a Hybrid GA/l₁ Optimization and Its Application to Improve Spectral Efficiency of Massive MIMO Systems

The synthesis of pencil beam and arbitrarily shaped beam patterns of linear antenna arrays (LAA) using reduced number of antenna elements attracts the attention of researchers in recent years. In this paper, a hybrid beamforming technique based on the combination of the genetic algorithm (GA) optimization technique and the $l_{1}$ minimization method denoted as (GA/ $l_{1}$ ) is introduced for LAAs synthesis. The proposed GA/ $l_{1}$ beamforming technique optimizes both the elements excitations and interelement spacing to synthesize the desired LAA pattern with a minimum number of antenna elements. The GA/ $l_{1}$ technique provides an excellent approximation to the desired radiation pattern with high accuracy and low complexity (less number of iterations and computational time) compared to the other synthesis approaches introduced in the literature. In addition, as an application of this work, the proposed GA/ $l_{1}$ technique is used to build up a proposed hybrid precoding and beamforming (HP-BF) structure for Massive Multi-input Multi-output (M-MIMO) systems. In this structure, the transmit antenna array is synthesized for maximum gain realization using the existing number of antenna elements. In the HP-BF structure, the proposed GA/ $l_{1}$ technique is used to make full use of the existing transmit array elements to synthesize the radiation pattern of much larger size and higher gain arrays without the need for additional elements. Thereby, significant savings in the number of antenna elements and their corresponding radio frequency (RF) chains are achieved, which reduces the system complexity. In addition, the array gain maximization will maximize the received signal to noise ratio (SNR) giving rise to higher system performance in terms of spectral efficiency (SE) and power utilization.