MIMO Integrated Sensing and Communication with Extended Target: CRB-Rate Tradeoff

TL;DR

This paper explores the fundamental tradeoff between sensing accuracy and communication rate in a MIMO ISAC system with an extended target, proposing an optimal transmit covariance solution to balance both objectives.

Contribution

It introduces a new MIMO rate maximization framework with a CRB constraint, deriving a semi-closed form optimal transmit covariance that unifies rate maximization and sensing accuracy.

Findings

Optimal transmit covariance is full rank, combining water-filling and isotropic transmission.

The proposed design outperforms benchmark schemes in numerical simulations.

The Pareto boundary of the CRB-rate region is characterized.

Abstract

This paper studies a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system, in which a multi-antenna base station (BS) sends unified wireless signals to estimate an extended target and communicate with a multi-antenna communication user (CU) at the same time. We investigate the fundamental tradeoff between the estimation Cram\'er-Rao bound (CRB) for sensing and the data rate for communication, by characterizing the Pareto boundary of the achievable CRB-rate (C-R) region. Towards this end, we formulate a new MIMO rate maximization problem by optimizing the transmit covariance matrix at the BS, subject to a new form of maximum CRB constraint together with a maximum transmit power constraint. We derive the optimal transmit covariance solution in a semi-closed form, by first implementing the singular-value decomposition (SVD) to diagonalize the communication channel and then properly allocating the transmit power over these subchannels for communication and other orthogonal subchannels (if any) for dedicated sensing. It is shown that the optimal transmit covariance is of full rank, which unifies the conventional rate maximization design with water-filling power allocation and the CRB minimization design with isotropic transmission. Numerical results are provided to validate the performance achieved by our proposed optimal design, in comparison with other benchmark schemes.