基于F-范数的变换域通信系统同步参数估计算法

An Estimation Algorithm of Basis Functions Synchronous Parameters of Transform Domain Communication Systems Based on Frobenius Norm

在异步条件下应用特征值分解算法估计变换域通信系统基函数时,分段得到的特征向量存在模糊现象,此时将造成系统接收性能的下降。为了解决此问题,提出了基函数周期序列的同步算法。详细分析估计基函数的特征值分解算法,推导接收数据的采样延时与其自协方差矩阵特征值的关系式,得到同步参数的最大似然估计方法,依据范数的等价性原理,进一步将最大似然估计中的最大特征值求解问题转化为F-范数的求解以降低算法复杂度。仿真结果表明:相比最大特征值算法,采用F-范数的估计算法性能一致,但计算时间明显减少,算法的估计精度与接收信噪比成正比。异步条件下当估计的基函数存在模糊时,系统接收性能在同步之后能得到较好的改善。

When the eigenvalue decomposition（EVD）algorithm is used to estimate the basic function for transform domain communication systems（TDCS）under the asynchronous condition,the eigenvector got by the algorithm is fuzzy,thus degrading the system performance.A synchronous method of basis function is proposed to solve this problem.Based on a detailed study of the EVD algorithm,the relational expres-sion of the data sampling delay and the eigenvalue of self-covariance matrix is deduced,and then a maxi-mum likelihood（ML）estimation algorithm of the synchronization parameter is obtained.According to the norm-equivalence theorem,the frobenius norm is introduced in the problem of finding the largest eigenval-ue in ML estimation algorithm,so the algorithm complexity is reduced.The simulation results show that the frobenius norm-based algorithm has the same performance as the largest eigenvalue-based algorithm but it only requires a less calculating time,and its estimation accuracy is in direct proportion to the signal-to-noise ratio（SNR）.When the estimated basic function remains fuzzy under the asynchronous condition,the reception performance of the system can be improved by the use of basic function after synchronization.