Likelihood-Based Demodulation in Multi-User Chaos Shift Keying Communication

Abstract

This paper deals with the theory of multi-user chaos shift keying communication systems in the coherent case and in particular with bit error performance under near optimal demodulation. The new approximated likelihood and near optimal demodulator is based on the statistical likelihood of the received signal and is a theoretical generalization of the conventional correlation demodulator involving autocorrelations of the spreading. Near optimal theoretical results beginning from an exact analysis are derived for the bit error rate of a typical user; there is emphasis on their structure in regard to separating the effects of channel noise and interference from other users, and in comparison with single-user results. The new demodulator is shown under particular assumptions to be a form of rake demodulator in the sense that it involves autocorrelation-like terms at various lags. The results are illustrated by theoretical calculations and numerical simulations which point out the enhanced performance of the near optimal demodulator relative to the correlation demodulator.

Recent theory and new applications in chaos communications

“…Earlier approaches, see [2], much advanced the topic by giving simple Gaussian approximation (SGA) to the distribution. But to improve on this, Lawrance [13], [6], introduced the conditional Gaussian approximation (CGA). This gave two useful equivalent expressions of the result as…”

“…However, there has also been criticism that the bit error performance of chaos-based systems is often inferior to that conventional sinusoidal systems. This point may be lessened by optimized coding and decoding which means not following the conventional approaches, but using statistically efficient ones, Lawrance [6]. Alternatively, as first pointed out by Kolumban [7] and continued by Kolumban [8] and Wang [9] in this session, the applications should be ones where the perceived criticisms are irrelevant, such as ultra wide-band radio, low data rate personal networks and optical laser systems.…”

Chaos Communication Performance: Theory and Computation

“…However, in [19] the likelihood was approximated by a multivariate Gaussian distribution and this led to a generalized correlation decoder which took the form l x This decoder is thus seen to take account of autocorrelation within the spreading, and to be the same as the correlation decoder if there is no autocorrelation within the spreading. The exact theory for its BER follows similarly to that of the correlation decoder at (38) and (39), and the result from [19] is ( )…”

Chaos Communication: An Overview of Exact, Optimum and Approximate Results Using Statistical Theory

“…They are illustrated by Figure 2 in that logistic spreading with its zero quadratic autocorrelations is better than Bernoulli-shift spreading with its geometric one-quarter quadratic autocorrelations. The corresponding SGA for the non-optimum correlation decoding in non-coherent CSK is Both (12) and (13) give statistical structure and simplicity to the computational results in Lau and Tse, 2003[9]; the additional terms in (13) indicate the loss in performance due the transmission of reference segments in place of their exact replication at the receiver. An exact BER result for correlation decoding in single-user non-coherent CSK is given in Lawrance and Ohama, 2003 [11] in terms of non-central F-distributions, and optimal likelihood-based decoding is has been developed by T. Papamarkou, Chaos, 2009 [1].…”

“…A correlation decoder could still be used but would not be as good in BER terms as a likelihood-based decoder, as will be seen. The likelihood decoder of the multi-user CSK system requires a careful analysis which significantly departs from that of the single-user case, Lawrance and Yao, 2008 [13], and leads to the generalized correlation decoder…”