ISAC Super-Resolution Receivers: The Effect of Different Dictionary Matrices

This paper presents an off-the-grid estimator for ISAC systems using lifted atomic norm minimization (LANM). The main challenge in the ISAC systems is the unknown nature of both transmitted signals and radar-communication channels. We use a known dictionary to encode transmit signals and show that LANM can localize radar targets and decode communication symbols when the number of observations is proportional to the system's degrees of freedom and the coherence of the dictionary matrix. We reformulate LANM using a dual method and solve it with semidefinite relaxation (SDR) for different dictionary matrices to reduce the number of observations required at the receiver. Simulations demonstrate that the proposed LANM accurately estimates communication data and target parameters under varying complexity by selecting different dictionary matrices.

ISAC Super-Resolution Receiver via Lifted Atomic Norm Minimization

This paper introduces an off-the-grid estimator for integrated sensing and communication (ISAC) systems, utilizing lifted atomic norm minimization (LANM). The key challenge in this scenario is that neither the transmit signals nor the radar-and-communication channels are known. We prove that LANM can simultaneously achieve localization of radar targets and decoding of communication symbols, when the number of observations is proportional to the degrees of freedom in the ISAC systems. Despite the inherent ill-posed nature of the problem, we employ the lifting technique to initially encode the transmit signals. Then, we leverage the atomic norm to promote the structured low-rankness for the ISAC channel. We utilize a dual technique to transform the LANM into an infinite-dimensional search over the signal domain. Subsequently, we use semidefinite relaxation (SDR) to implement the dual problem. We extend our approach to practical scenarios where received signals are contaminated by additive white Gaussian noise (AWGN) and jamming signals. Furthermore, we derive the computational complexity of the proposed estimator and demonstrate that it is equivalent to the conventional pilot-aided ANM for estimating the channel parameters. Our simulation experiments demonstrate the ability of the proposed LANM approach to estimate both communication data and target parameters with a performance comparable to traditional radar-only super-resolution techniques.

Robust Joint Active-Passive Beamforming Design for IRS-Assisted ISAC Systems

The idea of Integrated Sensing and Communication (ISAC) offers a promising solution to the problem of spectrum congestion in future wireless networks. This paper studies the integration of intelligent reflective surfaces (IRS) with ISAC systems to improve the performance of radar and communication services. Specifically, an IRS-assisted ISAC system is investigated where a multi-antenna base station (BS) performs multi-target detection and multi-user communication. A low complexity and efficient joint optimization of transmit beamforming at the BS and reflective beamforming at the IRS is proposed. This is done by jointly optimizing the BS beamformers and IRS reflection coefficients to minimize the Frobenius distance between the covariance matrices of the transmitted signal and the desired radar beam pattern. This optimization aims to satisfy the signal-to-interference-and-noise ratio (SINR) constraints of the communication users, the total transmit power limit at the BS, and the unit modulus constraints of the IRS reflection coefficients. To address the resulting complex non-convex optimization problem, an efficient alternating optimization (AO) algorithm combining fractional programming (FP), semi-definite programming (SDP), and second order cone programming (SOCP) methods is proposed. Furthermore, we propose robust beamforming optimization for IRS-ISAC systems by adapting the proposed optimization algorithm to the IRS channel uncertainties that may exist in practical systems. Using advanced tools from convex optimization theory, the constraints containing uncertainty are transformed to their equivalent linear matrix inequalities (LMIs) to account for the channels' uncertainty radius. The results presented quantify the benefits of IRS-ISAC systems under various conditions and demonstrate the effectiveness of the proposed algorithm.