针对未知稀疏信号的压缩自相关检测算法

Compressive Autocorrelation Detecting Algorithm for Unknown Sparse Signal

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。

Abstract： A compressive autocorrelation detection problem of unknown high bandwidth sparse signals. lized to acquire the signals at a sampling rate which algorithm is proposed for overcoming the detection Firstly, the compressive sensing technology is unuti- is far lower than Nyquist sampling rate. Then based on researching autocorrelation matrix theories of signal detection, a sparse coefficients compressive auto- correlation detection algorithm using statistical distribution is deduced through the restricted isometry property of the sensing matrix and the compressive samplings are dealt with directly. The connection is subsequently obtained between the decision threshold and the false alarm probability theoretically. More- over, the computational complexity of the algorithm is analyzed. Therefore, the method can improve the detection timeliness efficiently through few compressive samplings without reconstructing signal. Simula- tions show that the proposed algorithm still perform well in unknown signal detection with low signal-to- noise ratio.