Numerical algorithm for POCET optimal phase search

Usually a modern navigation satellite needs to combine multiple signal components at the same carrier frequency or even two/three adjacent frequencies into a constant-envelope signal before its high power amplifier. The phase-optimized constant-envelope transmission (POCET) technique can deal with any number of signal components and achieve the highest power efficiency. The existing numerical algorithms for POCET phase searching, however, have some problems such as large amount of computation, slow convergence rate, and possible failure of convergence when the initial point is far from the optimal solution or when higher accuracy is required. Aimed at the argumentation of optimized multiplexing for satellite navigation signals, this paper firstly introduces the augmented Lagrange multiplier method to ensure convergence with smaller termination error. Next, the inexact line search algorithm based on Armijo criterion is adopted instead of the exact line search for determination of search steps. Then, the characteristics and applicability of several search direction optimization algorithms are comparatively analyzed, such as the steepest descent method, the conjugate gradient method, and the quasi-Newton method (including the BFGS method and the symmetric rank 1 method). Finally, the high accuracy, low computational complexity, and strong convergence of the improved algorithm are validated by its application in the search of optimal phase-table and evaluation of combining loss of BDS B1 signals under different power allocation and phase constraints. The study provides a reference for the design and optimization of the navigation signal modulation.