基于子空间方法的最小二乘常模算法的研究

The study of the LSCM algorithm based on subspace

本文提出了两种基于子空间方法的常模算法,称为SUB_LSCMA和LSCMA_PASTd。SUB_LSCMA先采用奇异值分解(SVD)获得紧缩近似投影子空间(PASTd)算法的初值,用PASTd算法来计算信号子空间,并对该信号子空间作施密特正交化,将最小二乘常模算法(LSCMA)的权系数投影到正交的信号子空间上,目的是减轻噪声子空间干扰的影响,但复杂度比已有的基于直接对接收信号自相关矩阵做特征值分解(ED)的LSCM_SUB算法[6]复杂度低。LSCMA_PASTd在SUB_LSCMA的基础上作了进一步改进,采用改进的PASTd算法来计算信号子空间,该信号子空间具有正交性,并且对初值的选取不敏感,能运用于实际的多径衰落信道中。仿真结果表明这两种算法的收敛速度、跟踪性能和误码性能和LSCM_SUB算法基本相同,但是复杂度比LSCM_SUB算法低。

This paper proposes two subspace based CM algorithms, SUB LSCMA and LSCMA_PASTd. In SUB_LSCMA, the singular value decomposition （SVD） is employed to obtain the initial value of Projection Approximate Subspace Tracking with deflation （PASTd） algorithm. A Schmidt Reorthonormalization procedure is employed to obtain the orthonormal signal subspace, and then the weight vector of least-square constant modulus algorithm （LSCMA） is projected into the orthonormal signal subspace in order to reduce the influence of noise subspace. In addition, the computational complexity of the proposed SUB_LSCMA is lower than that of LSCMA-SUB which is based on the eigenvalue decomposition （ED） of the received signal autocorrelation matrix. The proposed LSCMA PASTd makes further improvements on the basis of SUB_LSCMA. An improved Projection Approximate Subspace Tracking with deflation （PASTd） algorithm is used here to calculate the orthonormal signal subspace. It is not sensitive to the selection of the initial value and can be applied to the practical multipath fading channel. Simulation results show that the performance of the proposed SUB_LSCMA and LSCMA_PASTd is similar to LSCMA-SUB on convergence rate, tracking ability and BER performance, but with much lower computational complexity.