Fundamental CRB-Rate Tradeoff in Multi-Antenna ISAC Systems With Information Multicasting and Multi-Target Sensing

This paper investigates the performance tradeoff for a multi-antenna integrated sensing and communication (ISAC) system with simultaneous information multicasting and multi-target sensing, in which a multi-antenna base station (BS) sends the common information messages to a set of single-antenna communication users (CUs) and estimates the parameters of multiple sensing targets based on the echo signals concurrently. We consider two target sensing scenarios without and with prior target knowledge at the BS, in which the BS is interested in estimating the complete multi-target response matrix and the target reflection coefficients/angles, respectively. First, we consider the capacity-achieving transmission and characterize the fundamental tradeoff between the achievable rate and the multi-target estimation Cramér-Rao bound (CRB) accordingly. To this end, we design the optimal transmit signal covariance matrix at the BS to minimize the estimation CRB for each of the two scenarios, subject to the minimum multicast rate requirement and the maximum transmit power constraint. It is shown that the optimal covariance matrix consists of two parts for ISAC and dedicated sensing, respectively. Next, we consider the transmit beamforming designs, in which the BS sends one information beam together with multiple a-priori known dedicated sensing beams for effective ISAC and each CU can cancel the interference caused by the sensing signals. By exploiting the successive convex approximation (SCA) technique, we develop efficient algorithms to obtain the joint information and sensing beamforming solutions to the resultant rate-constrained CRB minimization problems. Finally, we provide numerical results to validate the CRB-rate (C-R) tradeoff achieved by our proposed designs, as compared to two benchmark schemes, namely the isotropic transmission and the joint beamforming without sensing interference cancellation. It is shown that the proposed optimal transmit covariance solution achieves much better C-R performance than the benchmark schemes and the proposed joint beamforming with sensing interference cancellation performs close to the optimal transmit covariance solution when the number of CUs is small. We also conduct simulations to show the practical estimation performance achieved by our proposed designs, by considering randomly generated information signals and practical estimators.