# On Difference Pattern Synthesis for Spherical Sensor Arrays

## TL;DR

This paper introduces a new method for optimizing spherical sensor array difference patterns and adapting them for linear arrays with odd-numbered elements.

## Contribution

The novel contribution is extending the Zolotarev difference pattern to work with odd-numbered linear arrays and proposing a generalized synthesis method.

## Key findings

- Spherical harmonics of degree ±1 are effective for synthesizing spherical array difference patterns.
- A mapping relationship between spherical and linear array difference patterns was established.
- The modified Zolotarev pattern successfully synthesizes difference patterns for odd-numbered ULAs.

## Abstract

An innovative method for synthesizing optimum difference patterns of the spherical sensor array is introduced, along with a sidelobe tapering technique. Firstly, we suggest employing the spherical harmonics of degree ±1 to synthesize the spherical array difference pattern; secondly, we study the mapping relationship between the difference pattern of the spherical sensor array and the difference pattern of the uniformly spaced linear array (ULA) with odd-numbered elements; finally, we enhance the Zolotarev difference pattern, which is a counterpart to the Dolph–Chebyshev sum pattern that traditionally allows synthesis only for ULA with even-numbered elements. Our modification extends its applicability to synthesize difference patterns for ULA with odd-numbered elements. Leveraging the optimal difference pattern, a generalized Bayliss difference pattern synthesis method designed for the ULA with odd-numbered elements is further proposed. To illustrate the effectiveness of our approach, we present several design examples through experimental simulation.