谱压缩感知的非凸低秩矩阵优化模型与方法综述

Nonconvex low-rank matrix recovery models and methods for spectral compressed sensing:An overview

谱压缩感知研究有限样本下谱稀疏信号及其连续频率参数的恢复问题,是经典的信号频谱分析问题的拓展,在阵列与雷达信号处理和无线通信等信息技术领域中有着广泛应用.谱压缩感知的经典方法和本世纪诞生的凸松弛方法由于适用范围、估计精度或算法速度的制约,无法满足当下5G和未来6G无线通信等技术对于高精度、高速度的迫切需求.近期,一系列基于结构低秩矩阵的非凸优化模型被提出,这些模型通过精确刻画谱稀疏信号的几何结构,将具有严重非凸性的原参数域优化问题等价刻画为信号域中的结构低秩矩阵恢复问题,为谱压缩感知问题提供了全新的求解思路,带来了算法精度的本质提升.本文系统性地综述了已有关于单通道、多通道和恒模这三类常见谱稀疏信号的结构低秩矩阵恢复模型和求解算法,分析了这些模型的共同点和差异性,并对未来可能的研究方向进行了展望.

Spectral compressed sensing refers to the problem of recovering spectral-sparse signals and their continuous-valued frequency parameters from limited samples.It is an extension of the classical spectral analysis problem of signals and widely used in information technology fields such as array and radar signal processing and wireless communications.The classical methods for spectral compressed sensing and the convex relaxation methods of this century have limits in the scope of application,estimation accuracy or algorithm speed,which cannot satisfy the urgent demands for high accuracy and speed in technologies such as current 5G and future 6G wireless communications.Recently,a series of nonconvex optimization models based on structured low-rank matrices have been proposed.By characterizing the geometric structures of spectral sparse signals,the original highly non-convex optimization problem in the parameter domain is cast as a structured low-rank matrix recovery problem in the signal domain,which provides a novel solution for the spectral compressed sensing problem and brings a substantial improvement in the algorithm accuracy.In this paper,we systematically review the existing structured low-rank matrix recovery models and algorithms for three types of spectral sparse signals:single-channel,multichannel,and constant modulus,analyze commonalities and differences of these models;and point out possible future research directions.