基于MM算法的脉冲串模糊函数设计方法

Pulse-Train Ambiguity Function Design Based on Majorization-Minimization

针对离散相位调制脉冲串信号的模糊函数优化问题,提出了一种基于MM算法的波形设计方法。MM算法是一种求解最优化问题的迭代算法,通过重复“构造辅助函数-求解辅助函数最优值”的过程,可以逐步逼近原问题的全局最优解。本文首先将脉冲串模糊函数设计问题建模为带约束四次型最优化问题,然后根据泰勒展开,给出了位于原函数上界的辅助函数的构造方法。其中,辅助函数的形式为带约束二次型最优化问题,可通过交替方向乘子法(ADMM)求解。最后通过计算机仿真说明了该方法的有效性。

To design discrete phase coded pulse train with low ISL ambiguity function,a waveform design method based on MM method is proposed.The MM algorithm is an iterative algorithm for solving the optimization problem.By repeating the process of constructing the auxiliary function and solving the optimal value of the auxiliary function,the global optimal solution of the original problem can be gradually approached.Firstly,the problem is established as a constrained quartic optimization problem.Then,the method of constructing the au-xiliary function which upperbounds the original target function through Taylor expansion is given.The form of the auxiliary function is constrained quadratic optimization problem which can be solved through ADMM algorithm.Finally,computer simulation results show the effectiveness of the method.