A New Array Synthesizer Based on Slepian Functions

This study introduces a new multi-antenna array synthesizer based on Slepian functions. The synthesizer concentrates beamforming (BF) gain within a spatial region (i.e., an angular sector), optimizing the spectral efficiency of the given region, which is suitable for codebook-based analog BF. Starting with the spectral efficiency formula incorporating the effect of BF, Jensen’s inequality was used to set upper and lower bounds of the spectral efficiency. Then, a novel method was introduced to combine the bounds into an approximation called Hesham’s approximation. Finally, Hesham’s approximation was formulated into a solvable Slepian optimization problem that yielded the weights of the synthesizer. The properties of the synthesizer were listed, including a discussion of how it behaves by changing the width of the targeted region. The steering method was derived, and simulation results were presented.