Combined Radar and Communications with Phase-Modulated Frequency Permutations

TL;DR

This paper investigates the integration of radar and communication systems using phase-modulated frequency permutations, analyzing the impact on sensing accuracy and proposing efficient encoding and detection schemes.

Contribution

It introduces a novel waveform scheme using frequency permutations and a combinatorial transform, along with analytical tools for assessing radar and communication performance.

Findings

MPSK modulation minimally affects radar local accuracy.

The proposed Lehmer code-based scheme enables efficient data-to-waveform mapping.

Analytical bounds for error probabilities are derived and validated.

Abstract

This paper focuses on the combined radar and communications problem and conducts a thorough analytical investigation on the effect of phase and frequency change on the communication and sensing functionality. First, we consider the classical stepped frequency radar waveform and modulate data using M-ary phase shift keying (MPSK). Two important analytical tools in radar waveform design, namely the ambiguity function (AF) and the Fisher information matrix (FIM) are derived, based on which, we make the important conclusion that MPSK modulation has a negligible effect on radar local accuracy. Next, we extend the analysis to incorporate frequency permutations and propose a new signalling scheme in which the mapping between incoming data and waveforms is performed based on an efficient combinatorial transform called the Lehmer code. We also provide an efficient communications receiver based on the Hungarian algorithm. From the communications perspective, we consider the optimal maximum likelihood (ML) detector and derive the union bound and nearest neighbour approximation on the block error probability. From the radar sensing perspective, we discuss the broader structure of the waveform based on the AF derivation and quantify the radar local accuracy based on the FIM. Extensive numerical examples are provided to illustrate the accuracy of our results.