MIMO Integrated Sensing and Communication: CRB-Rate Tradeoff

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 one sensing target and communicate with a multi-antenna communication user (CU) simultaneously. We consider two sensing target models, namely the point and extended targets, respectively. For the point target case, the BS estimates the target angle and the reflection coefficient as unknown parameters, and we adopt the Cramér-Rao bound (CRB) for angle estimation as the sensing performance metric. For the extended target case, the BS estimates the complete target response matrix, and we consider three different sensing performance metrics including the trace, the maximum eigenvalue, and the determinant of the CRB matrix for target response matrix estimation. For each of the four scenarios with different CRB measures, we investigate the fundamental tradeoff between the estimation CRB for sensing and the data rate for communication, by characterizing the Pareto boundary of the achievable CRB-rate (C-R) region. In particular, we formulate a new MIMO rate maximization problem for each scenario, by optimizing the transmit covariance matrix at the BS, subject to a different form of maximum CRB constraint and its maximum transmit power constraint. For these problems, we obtain the optimal transmit covariance solutions in semi-closed forms by using advanced convex optimization techniques. For the point target case, the optimal solution is obtained by diagonalizing a composite channel matrix via singular value decomposition (SVD) together with water-filling-like power allocation over these decomposed subchannels. For the three scenarios in the extended target case, the optimal solutions are obtained by diagonalizing the communication channel via SVD, together with proper power allocation over two orthogonal sets of subchannels, one for both communication and sensing, and the other for dedicated sensing only. Finally, numerical results show the C-R region achieved by the optimal design in each scenario, which significantly outperforms that by other benchmark schemes such as time switching.