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 (P2C2M) 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 P2C2M. Based on the P2C2M, 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.

The transceiver design with constant modulus constraints (CMC) is the key issue in the integrated sensing and communication (ISAC) systems. Usually, existing methods assume the prior knowledge of the target and clutter for sensing is precisely known, which brings challenges to the imprecise scenarios in practical applications. To address the issue, the robust ISAC transceiver design is proposed. We jointly maximize the averaged signal-to-interference-plus-noise ratio (SINR) for sensing and the achievable sum-rate (ASR) for communication, subject to CMC for transmit codes and spherical constraints (SPC) for receive filter. The resulting problem is non-convex and NP-hard due to CMC and the coupling between transmit codes and receive filter. Existing methods address it using relaxation and matrix inversion, resulting in performance degradation and computationally unaffordable. To solve the problem, a product complex circle-sphere manifold (PCCSM) method without relaxation and matrix inversion is proposed. Firstly, the PCCSM is constructed to satisfy the CMC and SPC. Then, the problem is converted to an Unconstrained coupled fractional programming (UCFP) problem over the PCCSM. Finally, the Parallel Limited-Broyden-Fletcher-Goldfarb-Shanno (PL-BFGS) method is derived to optimize transmit codes and receive filter in parallel. Compared with the existing methods, the proposed method has the following advantages: (1) Complexity reduction by over 50% while improving sensing SINR by 0.31 dB and communication ASR by 0.4827 bits/s/Hz. (2) Improvement of sensing SINR by 0.19 dB and communication ASR by 0.613 bits/s/Hz over non-robust designs.

Polarization adds an additional dimension to the radar signals, contributing to waveform diversity. Codesign of unimodular waveforms and filters with polarimetric power allocation for maximizing the signal-to-interference plus noise ratio (SINR) plays a key role in the polarimetric radar system. The problem is challenging to solve due to the non-convex nature of the objective function and constraints, coupled with the interdependence of multiple variables. Existing methods mainly solve this problem by fixing the power allocation or relaxing the objective function, and obtain the receive filters with matrix inversion. We directly address this problem without matrix inversion by using the proposed Adaptive Unified Manifold Optimization (AUMO) framework. Specifically, a unified manifold space is constructed to satisfy the constraints of unimodular waveform, filters and power, transforming the problem to an unconstrained optimization problem over the manifold. To solve this problem, a parallel conjugate gradient algorithm is derived. This algorithm can adaptively change the step size by exploring the local features of the manifold space. The experimental results based on the measured data show that the proposed method outperforms existing methods in terms of SINR gain and execution time.

he waveform design with constant- modulus (CM) constraint is a key issue in the dual function radar-communication (DFRC) systems. Usually, existing methods optimize DFRC waveform by considering radar signal to interference plus noise ratio (SINR) and communication multi-user interference (MUI). We have noticed that existing methods ignore MUI in the time or per-user dimension, resulting in dynamically uncontrollable communication QoS. To this end, a per-user dynamically controllable waveform design is proposed. We jointly design waveforms and filters to enhance radar detection under the per-user dynamic controllable communication QoS constraint . The problem is non-convex and NP-hard due to the CM constraint and waveform-filter coupling. Existing methods tackle it via relaxation and matrix inversion, leading to degraded performance and computational complexity. We observe that the problem is separable in time and user dimensions, and therefore propose a stacked-product riemannian manifold (S-PRM) space to satisfy CM and per-user dynamic controllable communication QoS constraint. Then, we propose a stacked-product riemannian manifold penalty (S-PRMP) method without relaxation and matrix inversion. Compared to existing works, the proposed method offers the following contributions: (1) computational burden reduction by over $80 \%$ while improving radar SINR by 0.83dB and reducing MUI by one order of magnitude. (2) more reliable per-user dynamically controllable communication QoS.

This paper tackles the challenge of designing nonconvex unimodular waveforms under spectral constraints to minimize the spatial Integrated Sidelobe Level Ratio (ISLR) in Multiple Input Multiple Output (MIMO) radar systems. While existing methods primarily rely on the Semidefinite Programming (SDP) framework with prohibitive computational cost or the Alternating Directions Method of Multipliers (ADMM) by relaxing the unimodular constraint or objective function, leading to non-strict unimodular waveforms or performance degradation. We observe that the complex circle manifold (CCM) inherently satisfies the unimodular constraint, and using a non-negative smooth function better adheres to the shape of spectral inequality constraints. Leveraging these insights, we propose the Adaptive Smooth Penalty-Inequality Constrained Manifold Optimization (ASP-ICMO) framework. ASP-ICMO directly addresses the problem without relaxing the objective function, while adaptively adjusting the penalty factor. Our approach combines direct problem solving on manifold space with adaptive penalty factor updates, facilitating quicker convergence compared to the ADMM method, which sequentially solves multiple subproblems with a fixed penalty factor. Furthermore, ASP-ICMO ensures that the Karush-Kuhn-Tucker (KKT) conditions for the converged solution are satisfied. Simulation results demonstrate that the proposed method achieves superior comprehensive system performance with reduced computational cost compared to existing methods.