Statistical Aspects of Chaotic Maps With Negative Dependence in a Communications Setting

Circuits Syst Signal Process

2008

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.

Section: Markov-approximated Likelihood Demodulationmentioning

confidence: 68%

Section: Comparisons Of Correlation and Near Optimal Likelihood Demodmentioning

confidence: 99%

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

Circuits Syst Signal Process

2008

“…as first derived in Lawrance and Balakrishna, 2001 [10]. While this result is seriously inaccurate, partly shown by its incorrect limiting form as SNR o f , the roles of kurtosis and quadratic autocorrelation of the spreading are revealed.…”

Section: Single-user Csk: Exact and Approximate Bit Error Ratementioning

confidence: 86%

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

2010

Chaotic Systems

This paper overviews exact, optimum and approximate decoding and performance results for antipodal chaos shift-keying (CSK) in which a bit is transmitted by modulating a chaotic segment and decoded by use of the corresponding unmodulated reference segment. Both single-and multiple-user versions with both known-and transmitted-reference segments are considered, the so-called coherent and non-coherent cases. There are three main themes to the paper (i) the use of statistical likelihood theory for deriving optimum or improved decoders, (ii) the availability of mathematically exact theory for BER performance of decoders, (iii) qualitative statistical insights provided by simple Gaussian approximations to BER.

“…In [16] an SGA expression was derived specifically for the BER of singleuser CSK taking into account its non-constant bit energy; in [15] and also in related earlier work, [25], [26], many complex SGA expressions for the BERs of multi-user CSK were given. The aim here is to gain theoretical intuition from generalization and mathematical conciseness in the statistical aspects of SGA results, rather than to advocate their practical use.…”

Section: Csk Demodulation Schemementioning

confidence: 99%

“…This means that (39) can be regarded as a function two dependent random variables, bit energy T l l x x and the multi-user variable l Ψ , also from (16). The unconditional BER is thus the average of Q over the bit energy and the multi-user variable.…”

mentioning

confidence: 99%

Chaos Communication Performance: Theory and Computation

Kaddoum

Circuits Syst Signal Process

Chargé³

et al. 2010

In this paper new and existing approaches are developed to compute the bit error rate for chaos-based communication systems. The multi-user coherent antipodal chaos shift keying system is studied and evaluated in its coherent form, in the sense of perfect synchronization between transmitted and received chaotic sequences. Transmission is through an additive white Gaussian noise channel. Four methods are interrelated in the paper, three approximate ones and an exact one. The least accurate but most well known is based on simple Gaussian approximation; this is generalized to better reveal its structure. Two accurate and computationally efficient approximate methods are based on conditional Gaussian approximation and the statistical distribution of the typically non-constant bit energy. The most insightful but computationally expensive one is based on exact theory and rests on explicit mathematical results for particular chaotic maps used to spread binary messages. Both upper and lower bounds to the bit error rate are suggested. The relative advantages of the different approaches are illustrated with plots of bit error rate against signal to noise ratio.