P2C2M: Parallel Product Complex Circle Manifold for RIS-Aided ISAC Waveform Design

The unimodular waveform design for simultaneous sensing and communication plays an important role in the integrated sensing and communication (ISAC) systems. The existing studies mainly include the trade-off waveform design without Reconfigurable Intelligent Surface (RIS); or the RIS-aided waveform design with optimal performance in a certain aspect, which usually degrade the comprehensive performance. To address these issues, the comprehensive waveform design with RIS is proposed, in which the waveform and RIS are coupled. The existing decoupled methods are mainly Alternating Optimization (AO), which are usually computationally unaffordable. To solve the problem efficiently, the Parallel Product Complex Circle Manifold ((PCM)-C-2-M-2) framework is devised using the natural constant modulus characteristic of both the waveform and RIS. Concretely, the problem is converted to the Unconstrained Coupling Quartic Problem (UCQP) over the (PCM)-C-2-M-2. Based on the (PCM)-C-2-M-2, the Parallel Conjugate Gradient algorithm is derived to optimize the waveform and RIS in parallel. Compared with the existing methods, the proposed method achieves better comprehensive performance with less computational cost.