盲信号分离中基于四阶累积量的源信号个数估计

研究了盲信号分离中源信号个数小于观测信号个数情况下源信号个数的估计方法.分别就带噪声和不带噪声两种情形进行了研究.对不带噪声的情形,给出源信号个数的以概率1正确的估计.对带噪声情形,通过构造适当的四阶累积量矩阵,将源信号个数的估计问题转化成为四阶累积量矩阵有效秩的估计问题,利用矩阵的SVD分解方法给出了源信号个数的估计.最后,利用计算机仿真将本文提出的估计方法与已有的估计方法进行了比较,并对实验结果进行了分析.

Estimation of source number using fourth-order cumulant in blind source separation

The estimation method of source number in blind source separation (BSS) is studied when the number of source signals is less than the number of observed signals.When there is not additive noise,an accurate estimation of source number can be given in probability 1.When there is additive noise,the estimation of source number can be obtained by constructing an appropriate fourth-order cumulant matrix,converting the estimation of source number into the estimation of the effective rank of the matrix and making the SVD decomposition of the matrix.Finally,the proposed estimation method is compared with available GDE estimation method by simulation,it is shown that when signal-noise ratio is greater than 5 dB,the former can estimate well the source number but the latter does not.