Integrated sensing and communication (ISAC) is widely recognized as a fundamental enabler for future wireless communications. In this paper, we present a joint communication and radar beamforming framework for maximizing a sum spectral efficiency (SE) while guaranteeing desired radar performance with imperfect channel state information (CSI) in multi-user and multi-target ISAC systems. To this end, we adopt either a radar transmit beam mean square error (MSE) or receive signal-to-clutter-plus-noise ratio (SCNR) as a radar performance constraint of a sum SE maximization problem. To resolve inherent challenges such as non-convexity and imperfect CSI, we reformulate the problems and identify first-order optimality conditions for the joint radar and communication beamformer. Turning the condition to a nonlinear eigenvalue problem with eigenvector dependency (NEPv), we develop an alternating method which finds the joint beamformer through power iteration and a Lagrangian multiplier through binary search. The proposed framework encompasses both the radar metrics and is robust to channel estimation error with low complexity. Simulations validate the proposed methods. In particular, we observe that the MSE and SCNR constraints exhibit complementary performance depending on the operating environment, which manifests the importance of the proposed comprehensive and robust optimization framework.

翻译：集成感知与通信（ISAC）被广泛认为是未来无线通信的基础性使能技术。本文提出了一种联合通信与雷达波束赋形框架，旨在多用户多目标ISAC系统中，在保证期望雷达性能的前提下，最大化总和频谱效率（SE），且考虑信道状态信息（CSI）不完美的情况。为此，我们分别采用雷达发射波束均方误差（MSE）或接收信号杂波加噪声比（SCNR）作为总和SE最大化问题的雷达性能约束。为应对非凸性和不完美CSI等固有挑战，我们重新表述问题，并推导出联合雷达与通信波束赋形器的一阶最优性条件。将该条件转化为具有特征向量依赖性的非线性特征值问题（NEPv）后，我们开发了一种交替方法，通过幂迭代求解联合波束赋形器，并通过二分搜索求解拉格朗日乘子。该框架可兼容两种雷达度量指标，对信道估计误差具有鲁棒性，且复杂度低。仿真验证了所提方法的有效性。特别地，我们观察到MSE约束和SCNR约束的性能在不同运行环境下呈现互补特性，这凸显了所提出的全面且鲁棒优化框架的重要性。