Random ISAC Signals Deserve Dedicated Precoding

TL;DR

This paper introduces new precoding schemes for random ISAC signals, optimizing sensing performance through a novel metric and demonstrating significant gains over traditional methods.

Contribution

It proposes both data-dependent and data-independent precoding schemes for random ISAC signals, with optimized structures and an extension to ISAC scenarios, improving sensing performance.

Findings

Proposed DDP and DIP schemes outperform conventional ISAC signaling.

ELMMSE metric effectively characterizes sensing performance with random signals.

Dedicated precoding designs significantly enhance ISAC system performance.

Abstract

Radar systems typically employ well-designed deterministic signals for target sensing, while integrated sensing and communications (ISAC) systems have to adopt random signals to convey useful information. This paper analyzes the sensing and ISAC performance relying on random signaling in a multi-antenna system. Towards this end, we define a new sensing performance metric, namely, ergodic linear minimum mean square error (ELMMSE), which characterizes the estimation error averaged over random ISAC signals. Then, we investigate a data-dependent precoding (DDP) scheme to minimize the ELMMSE in sensing-only scenarios, which attains the optimized performance at the cost of high implementation overhead. To reduce the cost, we present an alternative data-independent precoding (DIP) scheme by stochastic gradient projection (SGP). Moreover, we shed light on the optimal structures of both sensing-only DDP and DIP precoders. As a further step, we extend the proposed DDP and DIP approaches to ISAC scenarios, which are solved via a tailored penalty-based alternating optimization algorithm. Our numerical results demonstrate that the proposed DDP and DIP methods achieve substantial performance gains over conventional ISAC signaling schemes that treat the signal sample covariance matrix as deterministic, which proves that random ISAC signals deserve dedicated precoding designs.