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Spherical Coordinates

Spherical Coordinates

Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...

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On Difference Pattern Synthesis for Spherical Sensor Arrays.

Zhijiang Huang¹, Maolin Chen¹, Xianglu Li¹

¹Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621999, China.

Sensors (Basel, Switzerland)

|April 13, 2024

Summary

This summary is machine-generated.

This study introduces a novel method for synthesizing optimal spherical sensor array difference patterns using spherical harmonics and enhancing the Zolotarev pattern for linear arrays with odd elements. The approach improves sidelobe tapering and extends pattern synthesis capabilities.

Keywords:

difference pattern phase-mode processing sidelobe suppression spherical harmonics spherical sensor array

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Area of Science:

Signal Processing
Array Signal Processing
Electromagnetics

Background:

Traditional methods for synthesizing difference patterns in spherical sensor arrays are limited.
Existing techniques for linear arrays often require an even number of elements.
Sidelobe control is crucial for array performance in various applications.

Purpose of the Study:

To develop an innovative method for synthesizing optimum difference patterns of spherical sensor arrays.
To extend the applicability of pattern synthesis techniques to uniformly spaced linear arrays (ULA) with odd-numbered elements.
To introduce a sidelobe tapering technique for improved array performance.

Main Methods:

Utilizing spherical harmonics of degree ±1 for spherical array difference pattern synthesis.
Establishing a mapping relationship between spherical array and uniformly spaced linear array (ULA) difference patterns.
Enhancing the Zolotarev difference pattern for ULA with odd-numbered elements and proposing a generalized Bayliss method.

Main Results:

Successful synthesis of optimum difference patterns for spherical sensor arrays.
Demonstrated applicability of the enhanced Zolotarev pattern to ULA with odd-numbered elements.
Validation of the generalized Bayliss method through experimental simulations.

Conclusions:

The proposed method offers an effective approach for synthesizing optimum difference patterns in spherical and linear arrays.
The sidelobe tapering technique and pattern enhancement provide improved performance characteristics.
The study expands the capabilities of array pattern synthesis for configurations with odd-numbered elements.