Sparse Phased Array Optimization Using Deep Learning

TL;DR

This work tackles grating lobes in sparse planar phased arrays by reframing the design as a non-convex optimization problem and solving it with a deep-learning surrogate. A data-driven workflow generates candidate sub-array configurations via local periodicity, then trains neural surrogates (a Feedforward Neural Network and a Set Transformer) to approximate the main-lobe to side-lobe energy cost, enabling efficient gradient descent on the two optimization coordinates $u_y$ and $u_z$. A penalty mechanism enforcing minimum element spacing guides the optimizer toward physically feasible designs, yielding substantial cost reductions: on the ten lowest-cost configurations, average improvements of about 552% with penalty (peak 643% for the FNN) versus 59% without penalty. The approach is general, scalable, and applicable to both planar and non-planar arrays, with potential extensions to phase tapering and beam shaping for next-generation wireless and radar systems.

Abstract

Antenna arrays are widely used in wireless communication, radar systems, radio astronomy, and military defense to enhance signal strength, directivity, and interference suppression. We introduce a deep learning-based optimization approach that enhances the design of sparse phased arrays by reducing grating lobes. This approach begins by generating sparse array configurations to address the non-convex challenges and extensive degrees of freedom inherent in array design. We use neural networks to approximate the non-convex cost function that estimates the energy ratio between the main and side lobes. This differentiable approximation facilitates cost function minimization through gradient descent, optimizing the antenna elements' coordinates and leading to an improved layout. Additionally, we incorporate a tailored penalty mechanism that includes various physical and design constraints into the optimization process, enhancing its robustness and practical applicability. We demonstrate the effectiveness of our method by applying it to the ten array configurations with the lowest initial costs, achieving further cost reductions ranging from 411% to 643%, with an impressive average improvement of 552%. By significantly reducing side lobe levels in antenna arrays, this breakthrough paves the way for ultra-precise beamforming, enhanced interference mitigation, and next-generation wireless and radar systems with unprecedented efficiency and clarity.

Figures (5)

• Figure 1: Example of a periodic sub-array configuration.
• Figure 2: Flowchart illustrating iterative optimization process
• Figure 3: Example of an optimized array configuration.
• Figure 4: The $u_y$ and $u_z$ cuts are derived using both the FNN and the Set Transformer. Solid lines indicate the results from the FNN, whereas dashed lines represent those obtained with the Set Transformer.
• Figure 5: The $u_y$ and $u_z$ cuts are derived using the FNN, both with and without the penalty mechanism. Solid lines indicate the results from the FNN without penalty, whereas dashed lines represent those obtained with penalty.