Performance analysis and optimization, of multi-user differential chaos-shift keying communication systems

Bit-error rate (BER) performance of a generalized multi-user differential chaos-shift-keying (DCSK) digital communication system is analyzed and optimized in this paper using baseband models. The generalized version of DSCK involves use of multiple nonrepeating chaotic spreading segments and energy adjustments and allows considerable system optimization. Theoretical BER analysis of correlation decoders based on a mathematical two-stage exact conditional approach is given as the foundation of subsequent performance studies. The consequent fully theoretical BER result gives an odd-symmetric spreading map condition for the BER to be unaffected by the mix of transmitted bits. The basis of the theoretical result is used to improve on the traditional simple Gaussian approximation (SGA) approach to the calculation of BER; this is inaccurate because it does not recognise the chaotic dynamics of DCSK. To overcome this drawback, a dynamically improved Gaussian approximation (DIGA) is developed. The DIGA approach is compared with the SGA approach, with simulation results demonstrating its accuracy and efficiency, certainly for more than five to ten users. Not only does the DIGA approach provide a more accurate BER than the SGA approach, its simple form also makes optimization of the DCSK system practically possible. The BER lower bound for the multi-user DCSK system is deduced from the DIGA approach. It is shown how the parameters and structure of the multi-user DCSK communication system can be optimized to achieve this lower bound. The work gives an exact theoretical basis of DCSK and covers several aspects which have not been treated in earlier research or have been inexactly treated.