最速下降与共轭梯度在数字波束形成中的研究

在自适应波束形成技术中，共轭梯度法是求解最优化问题的一种常用方法，最速下降法在不需要矩阵求逆的情况下，通过递推方式寻求加权矢量的最佳值。文中将最速下降法与共轭梯度法有机结合，构造出一种混合的优化算法。该方法在每次更新迭代过程中，采用负梯度下降搜索方向，最优自适应步长，既提高了共轭梯度算法的收敛速度，又解决了最速下降法在随相关矩阵特征值分散程度增加而下降缓慢的问题，具有收敛速度快，运算量低的特点。计算机仿真给出了五阵元均匀线阵的数字波束形成系统实例，分别从波束形成、误差收敛及最佳权值等方面与传统LMS 算法进行了比较分析，结果表明了该方法的可行性与有效性。

Research of steepest descent and conjugate gradient in digital beamforming

In the adaptive beamforming technology,the conjugate gradient method is a common method.The steepest descent method searchs the optimum weights by iterative method without matrix reverse.In this paper,a hybrid algorithm is proposed based on the the steepest descent method and the conjugate gradient method.In each iteration,by the negative conjugate gradient search direction and the optimum adaptive step this method raises the convergence rates of the conjugate gradient and solves the problem which the convergence rates get slower with the small eigenvalue spread of the correlation matrix.In conclusion,this paper has the features with quick convergence rate,low operation.The computer simulation shows the five ULA array elements digital beamforming example,analyzes the beamforming,error convergence and the optimum weight and so on by comparing with the traditional LMS algorithm.The results indicate this method is feasibility and validity.