Hybrid nonlinear block encoded continuous phase frequency shift keying

Abstract

A block encoding approach is known to be an effective technique to increase the minimum Euclidean distance of continuous phase frequency shift keying (CPFSK) signals. R.H.-H. Yang et al. introduced rate-1/2 hybrid linear block encoded CPFSK to increase the Euclidean distance (see ISPACS, 2003). However, for a higher coding rate, namely rate-2/3, no useful hybrid linear encoder has been found. Two alternative hybrid nonlinear block encoders, viz., nonlinear/nonlinear and nonlinear/linear, are applied to CPFSK, to achieve larger inevitable merging intervals and prevent merging events with lower Euclidean distance. Numerical results are obtained for rate-1/2 and rate-2/3 nonlinear block encoding binary CPFSK modulation. We show that, for rate-1/2, both newly proposed hybrid approaches outperform conventional ones for the modulation indices of interest, that is, 0<h<0.25 and 0.75<h<0.85 for nonlinear/linear coded binary CPFSK, and 0.3<h<0.75 for rate-1/2 nonlinear/nonlinear coded binary CPFSK, respectively. Similar results are obtained for rate-2/3, with modulation index 0.65<h<0.7, for nonlinear/linear coded binary CPFSK, and the nonlinear/nonlinear coded binary CPFSK with 0<h<1; significant coding gains can be obtained and previous work is consistently outperformed.