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.

翻译：本文提出了一种基于提升原子范数最小化（LANM）的ISAC系统离网估计器。ISAC系统的主要挑战在于发射信号与雷达通信信道均具有未知特性。我们使用已知字典对发射信号进行编码，并证明当观测数量与系统自由度及字典矩阵相干性成正比时，LANM能够实现雷达目标定位与通信符号解码。通过采用对偶方法重构LANM，并针对不同字典矩阵使用半定松弛（SDR）求解，我们降低了接收端所需的观测数量。仿真结果表明，通过选择不同的字典矩阵，所提出的LANM方法能够在不同复杂度条件下准确估计通信数据与目标参数。