# Spatio-Temporal Waveform Design in Active Sensing Systems with Multilayer Targets

## TL;DR

This paper develops a method for designing optimal spatio-temporal waveforms in active radar systems to improve detection and classification of multilayer targets by maximizing backscattered signal power through semidefinite programming.

## Contribution

It introduces a novel waveform design framework that adapts to multilayer target responses and considers angle uncertainties, enhancing detection performance in active sensing.

## Key findings

- Significant increase in backscattered signal power with optimal waveforms.
- Multiple temporal dimensions reduce the number of antennas needed.
- Effective in single and multiple target scenarios with clutter.

## Abstract

In this paper, we study the optimal spatio-temporal waveform design for active sensing applications. For this purpose a multi-antenna radar is exploited. The targets in the radar vision are naturally composed of multiple layers of different materials. Therefore, the interaction of these layers with the incident wave effects targets detection and classification. In order to enhance the quality of detection, we propose to exploit space-time waveforms which adapt with the targets multilayer response. We consider the backscattered signal power as the utility function to be maximized. The backscattered signal power maximization under transmit signal power constraint is formulated as a semidefinite program (SDP). First, we assume a single-target scenario, where the resulting SDP yields an analytical solution. Second, we study the optimal waveform which considers the angle uncertainties of a target in the presence of a clutter. Third, having multiple targets and multiple clutters, the weighted sum of the backscattered signals power from the targets is maximized to deliver the backscattered power region outermost boundary. We observe that, when the targets material is given, the backscattered signal power can be significantly increased by optimal spatio-temporal waveform design. Moreover, we observe that by utilizing multiple temporal dimensions in the waveform design process, the number of exploited antennas can be significantly decreased.