ISAC Super-Resolution Receiver via Lifted Atomic Norm Minimization

TL;DR

This paper presents a novel off-the-grid estimator using lifted atomic norm minimization for ISAC systems, enabling simultaneous radar target localization and communication decoding even with unknown signals and channels.

Contribution

It introduces a new LANM-based off-the-grid estimator for ISAC that handles unknown signals and channels, extending super-resolution techniques to integrated sensing and communication.

Findings

LANM achieves simultaneous localization and decoding.

Estimator performs well under noise and jamming.

Complexity comparable to traditional channel estimation methods.

Abstract

This paper introduces an off-the-grid estimator for integrated sensing and communication (ISAC) systems, utilizing lifted atomic norm minimization (LANM). The key challenge in this scenario is that neither the transmit signals nor the radar-and-communication channels are known. We prove that LANM can simultaneously achieve localization of radar targets and decoding of communication symbols, when the number of observations is proportional to the degrees of freedom in the ISAC systems. Despite the inherent ill-posed nature of the problem, we employ the lifting technique to initially encode the transmit signals. Then, we leverage the atomic norm to promote the structured low-rankness for the ISAC channel. We utilize a dual technique to transform the LANM into an infinite-dimensional search over the signal domain. Subsequently, we use semidefinite relaxation (SDR) to implement the dual problem. We extend our approach to practical scenarios where received signals are contaminated by additive white Gaussian noise (AWGN) and jamming signals. Furthermore, we derive the computational complexity of the proposed estimator and demonstrate that it is equivalent to the conventional pilot-aided ANM for estimating the channel parameters. Our simulation experiments demonstrate the ability of the proposed LANM approach to estimate both communication data and target parameters with a performance comparable to traditional radar-only super-resolution techniques.