Bi-Level Deep Unfolding Based Robust Beamforming Design for IRS-Assisted ISAC System

Abstract

In this paper, an intelligent reflecting surface (IRS)-assisted integrated sensing and communication (ISAC) system is considered, where the ISAC base station (BS) serves the communication user equipments (UEs) and tracks sensing targets simultaneously. Unfortunately, it is challenging to obtain the perfect channel state information (CSI) of user equipments (UEs)-related links and target directions in practice. To address the imperfection, we investigate the robust beamforming design under the statistical CSI and bounded target direction uncertainty models. With these considerations, we formulate a Cramér-Rao bound (CRB) of sensing targets minimization problem, subject to the signal-to-interference-plus-noise ratio (SINR) outage probability constraint, the maximum transmit power limits and the unit-modulus constraint of each IRS element. In order to solve this non-convex problem, we formulate the robust beamforming design as a bi-level optimization (BLO) problem and then apply the double-loop deep unfolding (DU) approach to solve this problem. Specifically, we formulate the problem into a primal-dual problem by integrating the SINR outage probability constraint into the objective function which is further approximated by using the worst-case SINR. The projection method and Riemannian manifold optimization method are used to deal with the maximum transmit power constraint and the unit-modulus constraint, respectively. Therefore, the problem can be reformulated as the bi-level optimization (BLO) problem. The lower level (LL) problems aim to find the worst-case CSI and angle of sensing targets. The upper level (UL) problem is the primal-dual problem solved by beamforming design and the Lagrange multipliers optimization with the certain CSI and angle. Then, we apply double-loop DU neural network which unfolds the iterative gradient descent into multi-layer structure, and each layer consists of UL loop and LL loop. In addition, the trainable step sizes and offset parameters are introduced as the network parameters, and the network ultimately outputs optimal optimization variables. Simulation results demonstrate the effectiveness of the proposed robust beamforming design algorithm.

Keywords

• Integrated sensing and communication system
• intelligent reflecting surface
• robust beamforming
• bi-level optimization
• deep unfolding
• worst-case CRB