Analytical Transmission Model of POCET Technique for Compass B1 and B3 Signals

The Phase-Optimized Constant Envelope Transmission (POCET) technique was first proposed as a numerical algorithm that searches the minimum combining loss for any number of binary navigation signals. However, the optimum transmission solution of POCET is a phase look-up table and no analytical expression for the baseband signal can be obtained, which makes the compatibility and interference analysis difficult for transmitters and receivers. In this paper, a novel model that converts any phase look-up table into analytical expression for baseband generation is introduced. The inter-modulation products and useful signal components of an optimized transmission solution can be separated from this model, thus greatly simplifies the interference analysis. By using this technique, the symmetrical constraint of POCET optimization routine is proved to be unnecessary and even harmful by a convincing example that combines four codes with equal power. Then the analytical model is implemented to analyze the model of Compass. The UAltBOC modulation is a candidate proposed for Compass B1 band. The analytical solution of UAltBOC can be derived to characterize the inter-structure of useful signal components and inter-modulation components. DualQPSK is a novel modulation proposed to solve the backward compatibility problem on Compass B3 band. The DualQPSK modulation is modeled by POCET. The optimized look-up table is converted into analytical expression, which is proven exactly the same as DualQPSK. In this way, the DualQPSK is demonstrated as the optimum solution for Compass B3 band signals. In all, the proposed analytical model is a further development of the POCET technique, which makes the optimum transmission solution more clear for implementation and analysis. The Compass transmission schemes for B1 and B3 bands are demonstrated consistent with the POCET technique.