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现代化的卫星导航信号要求在星上高功率放大器之前恒包络复用同频点甚至临近的双频点/三频点的多个导航信号分量。最优相位恒包络发射(POCET)技术能够恒包络复用任意路数信号且达到最高复用效率。已见诸报道的POCET最优相位搜索的数值算法存在计算量大、收敛速度慢、当迭代点远离最优解或要求提高计算精度时难以收敛到局部最优解等问题。针对导航信号最优恒包络复用论证的需求,首先在优化目标函数中引入增广拉格朗日乘子法以解决当终止误差减小无法收敛到局部最优解的问题;其次对于搜索步长的确定摈弃了已有的精确线搜索算法而采用基于Armijo准则的非精确线搜索算法,并比较研究了最速下降法、共轭梯度法、拟牛顿法(包括BFGS法和对称秩1法)等多种搜索方向优化算法的优缺点和适用性;最后通过对BDS B1频点不同功率分配下的最优相位搜索和合成损耗评估,验证了改进后算法的精度高、计算量小、收敛性强等优点,为导航信号调制复用方案的设计和优化提供参考。
Modern satellite navigation signals require constant envelope multiplexing of multiple navigation signal components at or near the dual-frequency / triple-frequency points in front of the high-power amplifiers on the satellite. The optimal phase constant envelope transmission (POCET) technique can constantly envelope any number of signals and achieve the highest multiplexing efficiency. It has been reported that the numerical algorithm of POCET optimal phase search has some problems such as large amount of calculation, slow convergence rate, difficulty of converging to local optimal solution when the iteration point is far away from the optimal solution or when it is required to improve the calculation accuracy. In order to meet the demand of the optimal constant envelope multiplexing of navigation signals, an augmented Lagrange multiplier method is introduced into the optimization objective function to solve the problem that the termination error can not converge to the local optimal solution. Secondly, The determination of the step length rejects the existing exact line search algorithm and adopts the non-precise line search algorithm based on the Armijo criterion, and compares the steepest descent method, the conjugate gradient method, the quasi-Newton method (including the BFGS method and the Symmetry Rank 1 method ), And so on. Finally, the optimal phase search and synthetic loss estimation under different power allocation of BDS B1 frequency points are given to verify the improved algorithm has high precision, small amount of computation, convergence Strong and other advantages, for the navigation signal modulation multiplexing program design and optimization provide a reference.