Low-Complexity Joint Communication and Sensing Beamforming for ISAC Systems: A Bisection Search Approach

We investigate the problem of joint sensing and communication beamforming for multiple-input-multiple-output integrated sensing and communication (MIMO-ISAC) systems. The objective is to minimize the Cramér-Rao bound (CRB) of the direction-of-arrival of a point target or the CRB of the target response matrix of an extended target, subject to a number of communication signal-to-interference-plus-noise-ratio (SINR) constraints. Although such a problem has been studied in prior works, existing methods, such as semidefinite programming (SDP) suffer a prohibitively high computational complexity. To address this issue, we first employ a bisection search framework to transform the nonconvex problem into a series of feasibility-checking problems, and then develop an efficient gradient-based algorithm for feasibility checking. Unlike the SDP method which needs to lift the problem to a high-dimensional space, our proposed method directly works on the original beamformer domain. Our analysis and numerical results show that the proposed algorithm presents a significant advantage over the SDP method in terms of computational efficiency, meanwhile achieving the same communication/sensing performance.