Waveform Design for ISAC Systems Via the Riemannian Geometric Optimization Network

In this paper, we focus on designing a dual-functional constant modulus (CM) waveform for integrated sensing and communication (ISAC) systems. The design aims to match a desired beampattern for radar sensing and minimize transmission distortion for communication. Due to the constant modulus constraint (CMC), the problem is non-convex and thus difficult to solve. Among current studies, the Riemannian conjugate gradient (RCG) method can effectively address the CMC problem with notable performance. However, the existing RCG method utilizes constant step sizes and scalar parameters during optimization, which often leads to results falling into a bad local optimum, consequently degrading both radar detection ability and communication quality. To alleviate these drawbacks, we develop a model-driven network named the Riemannian geometric optimization network (RGON). It is constructed by unfolding the iterative RCG method into the network layers. In the network, we transform the step sizes and scalar parameters into learnable parameters and learn their values in an unsuper-vised manner. Through this adaptive learning, the network can obtain the most appropriate step sizes and scalar parameters for each iteration. Numerical results show that the proposed network with trainable step sizes and scalar parameters achieves better performance in terms of convergence speed, beampattern matching and average sum rate compared with other related methods.