Optimal Resource Allocation Design for Wideband Integrated Sensing and Communication Systems

This paper investigates resource allocation design for wideband integrated sensing and communication (ISAC) systems. To tackle the severe propagation attenuation issue in designing high-frequency ISAC systems, we adopt the hybrid beamformer at the transmitter to achieve substantial beamforming gains by generating highly directional beams. However, the well-known beam-split effect introduces multiple spatial directions at each subcarrier, due to the employment of wider bandwidth and a larger number of antennas, which may lead to system performance degradation. Fortunately, the notion of a true-time-delayer (TTD) has emerged as a crucial solution for compensating for the beam split by generating frequency-dependent phase shifts. To fully unleash its potential, we aim to minimize the Cramér-Rao Bound (CRB) for target estimation by jointly optimizing subcarrier allocation, digital beamforming matrices, and frequency-independent and frequency-dependent analog beamforming matrices at base station (BS). We formulate the optimization design as a non-convex mixed-integer non-linear programming (MINLP) problem, subject to the transmit power budget constraint of the BS, the rate quality-of-service (QoS) constraints for users, and the discrete nature of the analog beamformer. To achieve a globally optimal solution for the complex design problem, an iterative resource allocation algorithm is proposed by exploiting the generalized Bender's decomposition (GBD) method. Moreover, we develop a computationally-efficient suboptimal algorithm to strike an effective balance between system performance and complexity. Our simulation results demonstrate the crucial importance of simultaneously optimizing all available degrees-of-freedom (DoFs) in wideband ISAC systems jointly and optimally. Furthermore, our proposed schemes are able to significantly improve the sensing accuracy over the traditional alternating optimization (AO) scheme adopted in existing solutions. Besides, our results unveil that deploying TTD units with limited bit-resolution time delays can achieve substantial gains in both communication and sensing performances.