Joint communications and sensing (JCAS) is envisioned as a key feature in future wireless communications networks. In massive MIMO-JCAS systems, hybrid beamforming (HBF) is typically employed to achieve satisfactory beamforming gains with reasonable hardware cost and power consumption. Due to the coupling of the analog and digital precoders in HBF and the dual objective in JCAS, JCAS-HBF design problems are very challenging and usually require highly complex algorithms. In this paper, we propose a fast HBF design for JCAS based on deep unfolding to optimize a tradeoff between the communications rate and sensing accuracy. We first derive closed-form expressions for the gradients of the communications and sensing objectives with respect to the precoders and demonstrate that the magnitudes of the gradients pertaining to the analog precoder are typically smaller than those associated with the digital precoder. Based on this observation, we propose a modified projected gradient ascent (PGA) method with significantly improved convergence. We then develop a deep unfolded PGA scheme that efficiently optimizes the communications-sensing performance tradeoff with fast convergence thanks to the well-trained hyperparameters. In doing so, we preserve the interpretability and flexibility of the optimizer while leveraging data to improve performance. Finally, our simulations demonstrate the potential of the proposed deep unfolded method, which achieves up to 33.5% higher communications sum rate and 2.5 dB lower beampattern error compared with the conventional design based on successive convex approximation and Riemannian manifold optimization. Furthermore, it attains up to a 65% reduction in run time and computational complexity with respect to the PGA procedure without unfolding.

翻译：联合通感（JCAS）被视为未来无线通信网络的关键特性。在大规模MIMO-JCAS系统中，通常采用混合波束赋形（HBF）以在合理的硬件成本和功耗下获得满意的波束赋形增益。由于HBF中模拟与数字预编码器的耦合以及JCAS的双重目标，JCAS-HBF设计问题极具挑战性，通常需要高度复杂的算法。本文提出一种基于深度展开的JCAS快速HBF设计方法，以优化通信速率与感知精度之间的权衡。我们首先推导出通信与感知目标函数关于预编码器的梯度闭式表达式，并证明模拟预编码器相关梯度的幅值通常小于数字预编码器对应的梯度。基于此发现，我们提出一种改进的投影梯度上升（PGA）方法，显著提升了收敛速度。随后，我们开发了一种深度展开的PGA方案，借助训练良好的超参数，在快速收敛的同时高效优化通感性能权衡。该方法在保持优化器可解释性与灵活性的基础上，利用数据提升性能。仿真结果表明，所提出的深度展开方法相比基于连续凸近似与黎曼流形优化的传统设计，通信和速率提升高达33.5%，波束方向图误差降低2.5 dB。此外，相较于未展开的PGA过程，该方法运行时间与计算复杂度可降低65%。