Robust Transceiver Design for ISAC Systems via Product Complex Circle-Sphere Manifold Method

The transceiver design with constant modulus constraints (CMCs) is the key issue in integrated sensing and communication (ISAC) systems. Usually, existing methods assume the prior knowledge of the target and clutter for sensing is precisely known, which brings challenges to the imprecise scenarios in practical applications. To address the issue, a robust ISAC transceiver design is proposed. We jointly maximize the averaged signal-to-interference-plus-noise ratio (SINR) for sensing and the achievable sum rate (ASR) for communication, subject to CMC for transmit codes and spherical constraints (SPCs) for the receive filter. The resulting problem is nonconvex and NP-hard due to CMC and the coupling between transmit codes and the receive filter. Existing methods address it using relaxation and matrix inversion, resulting in performance degradation and computationally unaffordable. To solve the problem, a product complex circle-sphere manifold (PCCSM) method without relaxation and matrix inversion is proposed. First, the PCCSM is constructed to satisfy the CMC and SPC. Then, the problem is converted to an unconstrained coupled fractional programming (UCFP) problem over the PCCSM. Finally, the parallel limited-Broyden-Fletcher-Goldfarb-Shanno (PL-BFGS) method is derived to optimize transmit codes and receive filters in parallel. Compared with the existing methods, the proposed method has the following advantages: 1) complexity reduction by over 50% while improving sensing SINR by 0.31 dB and communication ASR by 0.4827 bits/s/Hz and 2) improvement of sensing SINR by 0.19 dB and communication ASR by 0.613 bits/s/Hz over nonrobust designs.