基于特征函数和矩阵代数的卷积直扩信号分离

Convolutive Blind Separation of DSSS Based on Characteristic Function and Matrix-* algebraic

针对多个直接序列扩频信号在多径信道传输后的卷积盲分离问题,提出了一个基于特征函数和矩阵代数的卷积盲分离方法。首先利用多传感器的条件,构建生成信号模型,且证明此模型符合独立子空间分析的基本条件;接着通过引入独立子空间分析的定义,证明直扩信号源的特征函数的Hessian矩阵满足块对角化性质;然后利用矩阵代数中矩阵分解的方法,将多个矩阵的联合块对角化问题转化为求取某个矩阵代数的可交换代数的一般性矩阵问题。当这个一般性矩阵被对角化时,卷积盲分离问题求解简化为求取一组齐次线性方程组的一个随机解。理论分析还表明,当噪声信号为高斯白噪声且具有相同的能量时,算法对于噪声具有非常强的鲁棒性。最后通过计算机仿真和与现有算法的比较,验证了新算法的有效性和可靠性,且具有更好的分离性能和相对更少的约束条件。新算法的不足之处是所需传感器数目较多,但在大规模传感器条件下能满足要求。

A method based on characteristic function and matrxi-＊ algebraic is proposed to solve the convolutive blind separation of Direct sequence spread spectrum signals through the multi-path channels.First,the signals model under the condition of multiple sensors is built and proved to be consistent with the basis of the Independent subspace analysis.Then the concept of independent subspace analysis is introduced,also the Hessian of Characteristic functions of the DSSS signals are proved to be block diagonal.Finally the matrix decomposition theory of matrix-＊ algebraic is used to transform the joint block diagonalization of multiple matries into the problem of finding a generic matrix of the commutant algebra,which is correspond to the matrix-＊ algebraic formed by the Hessian of Characteristic functions of the observed signals.And the diagonalization of the generic matrix is proved to be equivalent with the Joint block diagnolization of some matrix-＊ algebraic.Then the original problem comes down to finding a random solution of a homogeneous linear equations.The theory analyze implies that the proposed algorithm is very robust if the sensor noise is gaussian and shares the same variance,whenever the noise is white or color.Computer simulation shows the validity and reliability of the algorithm in the condition of three DSSS signals.The result also demonstrates that the proposed algorithm has better performance and less constraints comparing with the exsiting algorithms.The only disadvantage is that there should be more sensors,but in the large sensor network,it can be easily satified.