An Approximation Method of the Continuous Phase Encoder in the Concatenated Coded GMSK System

In this paper, a reduced-complexity continuous-phase encoder (CPE) in the concatenated coded GMSK system, called linearly approximated CPE (LA-CPE) is presented. We show that the LA-CPE can be completely modeled as a trellis diagram with less state number than traditional CPE. Therefore, the benefit to use LA-CPE in concatenated GMSK systems is simple in design and convenient for performance analysis. As an example, serial concatenation of a convolutional code and a GMSK system is investigated. The results show that the performance of the concatenated approximated GMSK system with the LA-CPE is close to the performance of the concatenated exact GMSK system with the traditional CPE, which illuminates that LA-CPE is an effective approximation to traditional CPE. Moreover, the performance upper bound of a concatenated GMSK system with LA-CPE is easily derived in this paper while the traditional CPE is difficult to analyze the performance of concatenated GMSK system. The resulting bound is in accordance with the simulation results. Furthermore, this approach can readily be extended to the general CPM system.