# Directivity Maximization of Difference Patterns for Monopulse Microstrip Patch Arrays with Sidelobe Constraints

## TL;DR

This paper introduces a new method to improve the performance of microwave antenna arrays used in tracking and scanning applications.

## Contribution

A novel nonconvex optimization method is proposed to maximize directivity of monopulse arrays with low sidelobes.

## Key findings

- The proposed method decomposes nonconvex problems into convex subproblems for efficient solution.
- Numerical examples show high directivity and symmetric main lobes in monopulse array designs.
- The method enhances performance without changing the array's geometric configuration.

## Abstract

High-performance difference patterns (DPs) are critical for compact and integrated microwave array systems, particularly in monopulse tracking and beam-scanning applications. However, the design of monopulse phased arrays with steep slopes, high directivity, low sidelobes, and symmetric main lobes remains challenging due to constraints imposed by the array aperture and radome structure. In this paper, a novel design method is proposed to maximize the DP directivities for monopulse linear and planar phased arrays composed of microstrip patch antennas. The DP synthesis problem is first formulated as a nonconvex optimization model for directivity maximization. By fixing the reference phase of the DP slope and applying a first-order Taylor expansion of the quadratic function, the original problem is decomposed into a sequence of convex subproblems that can be solved efficiently. The proposed method fully exploits the flexibility of the phased array feed network, enabling directivity enhancement without altering the geometric configuration of the monopulse array. Finally, three numerical examples employing a radome-enclosed linear array, a uniform planar array, and a radome-enclosed planar array are presented to demonstrate the effectiveness of the proposed method in achieving the monopulse array DP synthesis with high directivity and symmetric main lobes.