Analysis of Chaos-Based Code Tracking Using Chaotic Correlation Statistics

A new statistical method for examining correlation of chaos-based systems is presented and the proposed method is applied to the analysis of a chaos-based noncoherent tracking loop. The motivation behind this approach is the lack of accuracy in the treatment of chaos-based code tracking when conventional correlation analysis is used. The proposed method has it roots in the chaotic correlation statistics (CCS) of the chaotic spreading code. CCS can be used for chaotic as well as any other nonbinary spreading code. The accuracy of the proposed model is shown to be very high by means of comparison with simulation and implementation results. The distributions of two critical points on S-curve have been derived and shown to closely match the simulation results as well as hardware implementation results. This paper highlights the need for a statistical approach for accurate treatment of nonbinary spreading codes specifically chaos-based spreading codes.