A New Array Synthesizer Based on Slepian Functions

TL;DR

The paper tackles region-focused analog beamforming by employing Slepian (DPSS) functions to concentrate beamformer gain within a designated angular sector, enabling region-based codebooks and improved spectral efficiency. It introduces a new capacity approximation  that outperforms traditional upper and lower bounds and formulates an optimization in the Rayleigh-quotient form using the matrix A(W); the solution yields synthesizer weights as the leading eigenvector of A(W), with steering achieved by phase-multiplication corresponding to the target region. The approach provides insight into the effect of the target region width, demonstrates improved mean and outage capacity in simulations versus standard synthesizers, and offers practical implementation paths (offline codebooks, steering via element-wise phases, and potential DPSS-based realizations). Overall, the region-centric Slepian-based synthesizer shows promise for higher SINR and data rates in codebook-based analog beamforming, with extensions to more complex array geometries and subwavelength spacing discussed for future work.

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.

Figures (9)

• Figure 1: A ULA placed along the z-axis.
• Figure 2: The angular coverage divided into angular regions instead of discrete directions.
• Figure 3: PDF of phase for desired and interfereing signals.
• Figure 4: Arbitrary directivity gain in the phase domain showing signal/interference sections of the curve ($W=0.2$).
• Figure 5: Arbitrary directivity gain ($M=4$, $kd=\pi$, $W=0.3$) in the phase domain showing area under signal/interference regions.