随机测量条件下的循环自相关函数无网格估计

利用循环平稳特性对通信信号进行参数估计是一种常用的处理方法。由于通信信号在循环频率域具有稀疏特性，可以利用随机测量有效降低采样处理的数据量，减轻硬件负荷，并基于压缩采样值进行信号参数估计。然而，在稀疏建模时通常将连续的信号参数空间划分为有限数量的均匀网格，引起基不匹配问题，使得信号在某个假定的离散变换基(傅里叶基、小波基等)下并不稀疏，从而严重影响信号参数估计精确度。为解决这个问题，本文利用原子范数描述循环频率域的连续性和稀疏性，提出一种随机测量条件下的高精确度循环自相关函数无网格估计方法。仿真实验表明，这种无网格估计方法能够有效降低循环自相关函数的估计误差。

Gridless cyclic autocorrelation estimation for random measurements

A common method for parameter estimation is adopting the inherent cyclostationary properties which vary periodically in the communication signals. Since the communication signals exhibit sparsity at the cycle frequency domain, the random measurements can be utilized to reduce the number of samples and lighten the burden of sampling hardware, and then the parameter estimation can be completed based on the compressive samples. However, in this kind of sparse modeling, it is inevitable that the continuous parameter space is discretized into a finite set of grid points, which will lead to basis mismatch. The signals cannot be expressed sparsely under an assumed finite dictionary, e.g. Fourier basis and DFT basis, therefore the parameter estimation accuracy is seriously affected by basis mismatch. In this paper, a gridless CA reconstruction which can locate the nonzero cyclic frequencies on an infinitely dense grid is proposed by utilizing the atomic norm to describe the continuity and sparsity of the cycle frequency domain. Numerical results demonstrate that the proposed method can reduce the mean square error of estimation effectively.