This paper studies transmit beamforming design in an integrated sensing and communication (ISAC) system, where a base station sends symbols to perform downlink multi-user communication and sense an extended target simultaneously. We first model the extended target contour with truncated Fourier series. By considering echo signals as reflections from the valid elements on the target contour, a novel Cram\'er-Rao bound (CRB) on the direction estimation of extended target is derived. We then formulate the transmit beamforming design as an optimization problem by minimizing the CRB of radar sensing, and satisfying a minimum signal-to-interference-plus-noise ratio requirement for each communication user, as well as a 3-dB beam coverage requirement tailored for the extended sensing target under a total transmit power constraint. In view of the non-convexity of the above problem, we employ semidefinite relaxation (SDR) technique for convex relaxation, followed by a rank-one extraction scheme for non-tight relaxation circumstances. Numerical results show that the proposed SDR beamforming scheme outperforms benchmark beampattern design methods with lower CRBs for the circumstances considered.

翻译：本文研究了一体化感知与通信(ISAC)系统中发射波束赋形设计问题，其中基站同时发送符号以实现下行多用户通信并感知扩展目标。首先，我们采用截断傅里叶级数对扩展目标轮廓进行建模。通过将回波信号视为目标轮廓上有效单元的反射，推导了扩展目标方向估计的新型克拉美罗界(CRB)。随后，我们将发射波束赋形问题建模为优化问题，目标是在满足每个通信用户最小信干噪比要求、针对扩展感知目标的3分贝波束覆盖要求，以及总发射功率约束的条件下，最小化雷达感知的CRB。针对上述问题的非凸性，我们采用半定松弛(SDR)技术进行凸松弛，并针对非紧松弛情形设计了秩一提取方案。数值结果表明，在所考虑的场景下，所提出的SDR波束赋形方案相比基准波束图设计方法具有更低的CRB性能。