Active MIMO Sensing With Exploration-Exploitation Tradeoff

This paper develops an active sensing framework for designing the transmit and receive beamformers of a multiple-input multiple-output (MIMO) radar system. In the proposed technique, the beamformers are adaptively designed in each sensing stage based on the measurements made in the previous sensing stages. The beamformers are determined by minimizing the Bayesian Cram{é}r-Rao bound (BCRB) for the estimation of the unknown sensing parameters at each stage via Lagrangian dual optimization. To address the exploration-exploitation tradeoff that is inherent to such an adaptive design, this paper proposes two variants of the BCRB optimization problem: an exploration-centric variant, that ensures that multiple orthogonal beamforming directions are probed in each sensing stage, and an exploitation-centric variant, that does not restrict the number of optimal beamformers. Each variant of the optimization problem is solved via an alternating optimization algorithm that alternates between solving for the transmit beamformers and solving for the receive beamformers. The algorithm is shown to converge to a stationary point provided that each optimization problem is solved to global optimality. Moreover, this paper studies each of the two BCRB optimization sub-problems in the Lagrangian dual domain and shows that despite the non-convexity, global optimality is guaranteed provided that certain sufficient conditions hold. The conditions pertain to the multiplicity of the eigenvalues of a specific direction matrix that can be analytically written in terms of the optimal dual variables. These conditions further imply the tightness of the semidefinite relaxation of the optimization problems. Simulation results demonstrate the benefits of the proposed BCRB-based design compared to state-of-the-art adaptive beamforming strategies.

RIS-Assisted Joint Sensing and Communications via Fractionally Constrained Fractional Programming

This paper studies an uplink dual-functional sensing and communication system aided by a reconfigurable intelligent surface (RIS), whose reflection pattern is optimally configured to trade-off sensing and communication functionalities. Specifically, the Bayesian Cram\'er-Rao lower bound (BCRLB) for estimating the azimuth angle of a sensing user is minimized while ensuring the signal-to-interference-plus-noise ratio constraints for communication users. We show that this problem can be formulated as a novel fractionally constrained fractional programming (FCFP) problem. To deal with this highly nontrivial problem, we extend a quadratic transform technique, originally proposed to handle optimization problems containing ratio structures only in objectives, to the scenario where the constraints also contain ratio structures. First, we consider the case where the fading coefficient is known. Using the quadratic transform, the FCFP problem is turned into a sequence of subproblems that are convex except for the constant-modulus constraints which can be tackled using a penalty-based method. To further reduce the computational complexity, we leverage the constant-modulus conditions and propose a novel linear transform. This new transform enables the FCFP problem to be turned into a sequence of linear programming (LP) subproblems, which can be solved with linear complexity in the dimension of reflecting elements. Then, we consider the case where the fading coefficient is unknown. A modified BCRLB is used to make the problem more tractable, and the proposed quadratic transform-based algorithm is used to solve the problem. Finally, numerical results unveil nontrivial and effective reflection patterns that the RIS can be configured to generate to facilitate both functionalities.