A New Array Synthesizer Based on Slepian Functions

TL;DR

This paper presents a novel array synthesizer utilizing Slepian functions to optimize beamforming gain within specific spatial regions, enhancing capacity and providing a new optimization approach for multi-antenna systems.

Contribution

It introduces a new array synthesizer based on Slepian functions, combining bounds into a superior capacity approximation and formulating a solvable optimization problem.

Findings

The synthesizer effectively concentrates beamforming gain within targeted regions.

Simulation results demonstrate improved capacity performance.

The method adapts to different angular region widths.

Abstract

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 Shannon capacity of the targeted region, which is suitable for codebook-based analog BF. Starting with the mean capacity formula incorporating the effect of BF, Jensen inequality was used to set upper and lower bounds of the mean capacity. Then, a novel method was introduced by combining the two bounds into a new approximation of the mean capacity that outperform both bounds. Finally, the approximation was formulated to a solvable Slepian optimization problem that yielded the weights of the synthesizer. The properties of the synthesizer were listed, including a discussion on how it behaves by changing the width of the targeted region. The steering method was derived, and simulation results were presented.