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.

翻译：本文介绍了一种用于集成感知与通信（ISAC）系统的离网估计器，该方法利用了提升原子范数最小化（LANM）技术。该场景中的关键挑战在于发射信号与雷达-通信信道均未知。我们证明，当观测数量与ISAC系统的自由度成比例时，LANM能够同时实现雷达目标定位与通信符号解码。尽管问题本身具有不适定性，我们采用提升技术对发射信号进行初步编码，随后利用原子范数促进ISAC信道的结构化低秩特性。通过引入对偶技巧，我们将LANM转化为信号域上的无限维搜索问题，进而使用半定松弛（SDR）实现对偶问题的求解。我们将该方法扩展到实际场景中，其中接收信号受到加性高斯白噪声（AWGN）与干扰信号的污染。此外，我们推导了所提估计器的计算复杂度，并证明其与传统导频辅助ANM在信道参数估计方面具有等效性。仿真实验表明，所提出的LANM方法能够以与传统纯雷达超分辨率技术相当的性能，同时估计通信数据与目标参数。