CRB-Rate Tradeoff for Bistatic ISAC with Gaussian Information and Deterministic Sensing Signals

Abstract

In this paper, we investigate a bistatic integrated sensing and communications (ISAC) system, consisting of a multi-antenna base station (BS), a multi-antenna sensing receiver, a single-antenna communication user (CU), and a point target to be sensed. Specifically, the BS transmits a superposition of Gaussian information and deterministic sensing signals. The BS aims to deliver information symbols to the CU, while the sensing receiver aims to estimate the target's direction-of-arrival (DoA) with respect to the sensing receiver by processing the echo signals. For the sensing receiver, we assume that only the sequences of the deterministic sensing signals and the covariance matrix of the information signals are perfectly known, whereas the specific realizations of the information signals remain unavailable. Under this setup, we first derive the corresponding Cramér-Rao bounds (CRBs) for DoA estimation and propose practical estimators to accurately estimate the target's DoA. Subsequently, we formulate the transmit beamforming design as an optimization problem aiming to minimize the CRB, subject to a minimum signal-to-interference-plus-noise ratio (SINR) requirement at the CU and a maximum transmit power constraint at the BS. When the BS employs only Gaussian information signals, the resulting beamforming optimization problem is convex, enabling the derivation of an optimal solution. In contrast, when both Gaussian information and deterministic sensing signals are transmitted, the resulting problem is non-convex and a locally optimal solution is acquired by exploiting successive convex approximation (SCA). Finally, numerical results demonstrate that employing Gaussian information signals leads to a notable performance degradation for target sensing and the proposed transmit beamforming design achieves a superior ISAC performance boundary compared with various benchmark schemes.