利用随机矩阵理论的MDL信源数估计算法

MDL Algorithm for Source Enumeration Using Random Matrix Theory

  • 摘要: 针对阵元数较大,采样快拍数相对较少时传统信息论准则信源数估计方法性能下降的问题,提出一种基于随机矩阵理论的最小描述长度准则(minimum description length criterion, MDL)信源数估计算法。该算法基于传统的MDL准则,将随机矩阵理论中特征值分布的部分特性与观测数据的分布特性相结合,给出一种新的MDL准则,并利用该准则实现信源数的估计。仿真实验与理论分析表明该算法是一致估计,在采样快拍数相对较少时,无论阵元数大小,均有较高的检测概率,应用范围较广,而且算法的运算量与经典的MDL方法相当。

     

    Abstract: According to the problem that the traditional information theoretic criteria has a performance decline in the case of large number of array sensors but relatively small number of sample snapshots, a novel MDL algorithm for source enumeration based on random matrix theory is proposed. The method combines some features on the distribution of eigenvalues in random matrix theory with the density of the observed data to construct a new MDL criterion based on the traditional MDL criterion framework, and then it is used for source enumeration. Simulation results and theoretical analysis show that it is consistent. Regardless of the number of array sensors, it has a high detection probability in the case of small sample snapshots number. As a result, it has a wide range of applications. Furthermore, it has a comparable computational cost compared with the traditional MDL method.

     

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