针对未知稀疏信号的压缩自相关检测算法

针对未知的宽频带稀疏信号检测问题，提出了一种直接基于非重构采样值 的压缩自相关检测算法。首先利用压缩感知技术以远低于奈奎斯特采样速率获取信号，在自 相关矩阵检测信号理论的基础上，利用压缩感知中传感矩阵的严格等距特性，推导出基于统 计分布的信号稀疏系数自相关检测算法，从理论上给出了判决门限的选取和虚警概率之间的 关系，并进行了算法复杂度分析。由于无需重构原始信号，该算法直接利用少量的压缩测量 值进行检测，可以有效地提高检测过程的时效性。仿真表明在较低的信噪比时，该算法对未 知信号仍有良好的检测性能。

Compressive Autocorrelation Detecting Algorithm for Unknown Sparse Signal

A compressive autocorrelation detection al gorithm is proposed for overcoming the detection problem of unknown high bandwid th sparse signals. Firstly, the compressive sensing technology is unutilized to acquire the signals at a sampling rate which is far lower than Nyquist samplin g rate. Then based on researching autocorrelation matrix theories of signal dete ction, a sparse coefficients compressive autocorrelation detection algorithm usi ng statistical distribution is deduced through the restricted is ometry property of the sensing matrix and the compressive samplings are dealt wi th d irectly. The connection is subsequently obtained between the decision threshold and the f alse a larm probability theoretically. Moreover, the computational complexity of the algori thm is analyzed. Therefore, the method can improve the dete ction timeliness efficiently through few compressive samplings without reconstruct ing signal. Simulations show t hat the proposed algorithm still perform well in unknown signal detection with l ow signal to noise ratio.