Analytic Efficiency Optimal Constant-Envelope Multiplexing Technique for GNSS Signals

Past decades have witnessed the development of Global Navigation Satellite Systems ( GNSSs) and the progress of technology including navigation signal design techniques. Navigation signals are critical for boosting the performance of the whole navigation system, in which constant-envelope multiplexing ( CEM) is an important issue in navigation signal design supporting the optimal broadcast of signals. Despite some succesful CEM methods have sprung up in the last few years, there is still a lot of things to do in this research field. In general, methods with both flexible design freedoms and optimal multiplexing efficiency are welcome. Besides, the theoretical study of CEM needs to be strengthened, which might provide inspirations for finding better CEM methods. In this paper, we give theoretical analysis in CEM and deduce that the problem of multiplexing efficiency optimization is equivalent to a minimization of maximum problem and can be further transformed into a minimum circle-cover problem for three signal components. Then the analytic efficiency optimal constant-envelope multiplexing technique for three components is proposed, which ensures the optimality of multiplexing efficiency, and provides guidance to select the appropriate power and phase relationship among signal components. Concrete example and performance analysis of this technique are also given. Apart from this, we propose a method named modulation constellation compensation to eliminate direct current ( DC) component that might exist in the integrated signal sometimes. This technique helps to avoid the damage of DC component to signal tracking, while the multiplexing efficiency remains optimal and the power and phase relationship among signal components is unchanged.