This paper investigates the joint channel estimation and localization problem for integrated sensing and communication (ISAC) systems assisted by a reconfigurable intelligent surface (RIS). The key technical challenges involve addressing the computational complexity of high-dimensional sparse recovery while effectively exploiting geometric relationships in parameter estimation. To begin with, we formulate the joint estimation problem as a geometrically-constrained sparse recovery task based on maximum a posteriori estimation principles, incorporating physical feasibility constraints. Then, we propose the geometrically-constrained separable multidimensional orthogonal matching pursuit (GSMOMP) algorithm, which iteratively executes three key procedures: (1) coarse candidate selection via separable projections to avoid high-dimensional tensor construction; (2) geometric feasibility filtering to eliminate physically implausible propagation paths; and (3) refined atom selection with joint parameter updates that concurrently optimize both channel estimates and location parameters. The convergence is ensured by analytically demonstrating the monotonic decrease of the residual error. Finally, numerical results verify the effectiveness of the proposed algorithm, which achieves substantial computational efficiency improvement compared to conventional MOMP while maintaining comparable localization and angular estimation accuracy.

This article investigates the joint design problem of the hybrid/reflective beamforming for the dual-function radar-communication (DRC) system with the help of an intelligent reflecting surface (IRS). The degrees of freedom for beamformer design are the analog and digital beamformers (DBF) at the base station (BS), and the reflective beamformer (RBF) at the IRS. To begin with, we formulate the beamformer design problem as a weighted sum-rate (WSR) maximization problem subject to the transmit power and similarity between the designed beamformer and the reference one with desired beampattern property. Then, utilizing equivalent reformulation of the preceding design problem, we conceive an alternating direction sequential programming (ADSP)-based algorithm that iteratively updates the following low-complexity subproblems: 1) DBF at the BS through the Powell–Hestenes–Rockafellar (PHR) method; 2) analog beamformer at the BS using the Riemannian conjugate gradient method; and 3) RBF at the IRS by the successive convex approximation (SCA) technique. The convergence is ensured by analytically offering the nondecreasing and boundary of the WSR value. Finally, numerical results verify the effectiveness of the proposed algorithm, which achieves superior WSR performance while ensuring the radar requirement.

For the intelligent reflecting surface (IRS) assisted sensing system, this letter investigates the joint design problem of active and passive beamforming with imperfect channel state information (CSI). To begin with, the beamformer design problem is formulated as a stochastic optimization problem with inner-layer variable (active beamforming vector) and outer-layer variable (passive phase-shift matrix), subject to the available transmit power and constant modulus constraints. Then, utilizing equivalent reformulation of the preceding design problem, we conceive a stochastic successive inner-outer programming (SSIOP) algorithm that updates the inner-layer and outer-layer variables in sequence and returns the corresponding closed-form solutions. Finally, numerical results assess the dependability of the SSIOP algorithm under an imperfect CSI scenario.