改进相关矩阵估计的LMS牛顿算法分析与仿真

在LMS牛顿算法中权值的更新采用了输入信号矢量的相关矩阵估计，不同的估计方法对算法的性能影响很大，该文分析了一种改进相关矩阵估计的LMS牛顿算法，该算法通过对LMS牛顿算法中的相关矩阵采用改进的指数加权估计，大大提高了算法的性能，同时维持了适中的计算复杂度。此外，还比较了LMS牛顿算法与RLS算法，从原理上说明了它们的密切联系；指出算法改善性能的关键在于变步长特性，即步长随着时间增加而逐渐变小，使得算法既可以保持较快的收敛速度，又获得了较小的失调。算法在智能天线中的仿真结果表明，该算法具有比常规LMS牛顿算法更优的性能。

Analysis and Simulation of LMS Newton Algorithm Using Improved Estimate of Autocorrelation Matrix

In the LMS Newton algorithm the estimate of autocorrelation matrix of the input signal vector is used for updating the weight. Different estimating methods have notable influences on the algorithm. An LMS Newton algorithm using improved esitimate of the autocorrelation matrix is analyzed; it can give better performance than the conventional LMS Newton algorithm while maintaining comparative computational complexity. Furthermore, a comparison between LMS Newton algorithm and RLS algorithm is made, and the quite close relationship between them is demonstrated. The key factor in which the algorithm's improved performance lies is the variable step property, i.e. the step decreases over time, thus small misadjustment can be obtained while keeping rather faster convergence speed. The simulation results in smart antennas show that the proposed algorithm has expected performance.