Signal sparsity is directly related to the determination of sampling rate and the construction of measurement matrix in compressive sensing.However,the sparsity order is often unknown or time-varying.In this context,investigating blind sparsity order estimation (SOE) techniques is an open research issue.To address this,asymptotic random matrix spectrum analysis theory was used to derive the asymptotic eigenvalue probability distribution function (AEPDF) of the measured signal's covariance matrix.Then,the paper used the relation between the measurement energy and AEPDF to further deduce the corresponding relation between the sparsity order,compressive rate,SNR and the measured signal energy.Subsequently,based on this relation,a technique to estimate the sparsity order using the measured signal energy was proposed.Simulation resuits show that the proposed algorithm can gain higher estimation performance with lower computational complexity compared with the existing algorithm.And the estimation accuracy can be enhanced by increasing the sampling overhead.%压缩感知理论中,信号稀疏度直接关系到采样速率的设定以及观测矩阵的构造,而该先验信息往往受限.针对这一问题,本文从大维随机矩阵谱分析理论出发,分析了采样协方差矩阵的极限特征值概率分布特征,并结合其与观测信号能量的关系推导得到观测信号能量与压缩率、稀疏度和信噪比之间的对应关系,提出一种基于观测信号能量的稀疏度估计算法.相对于已有算法,该算法计算复杂度较低,且估计精度较好,并可通过增加采样开销进一步提升稀疏度估计精度,仿真实验验证了本文算法的有效性.
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