A Methodology for Bit Error Rate Prediction in Chaos-based Communication Systems

Abstract

This paper is devoted to the derivation of an exact analytical expression of the bit error rate for chaos-based DS-CDMA systems. For the studied transmission system, we suppose that synchronization is achieved perfectly, coherent reception is considered, and an Additive White Gaussian Noise channel (AWGN) is assumed. In the first part of the paper, performance of a mono-user system with different chaotic sequences is evaluated and compared in terms of the error probability. This comparison is realized thanks to the probability density function of the bit energy of a chaotic sequence. The bit error rate can be easily derived by numerical integration. In some particular cases, for certain chaotic sequences with known probability density function of bit energy, we propose an analytical expression of the bit error. In the second part of the paper, the performance of a chaos-based DS-CDMA system is evaluated in the multi-user case. A general conclusion is that probability density function of chaos bit energy, for a given spreading factor, can give a clear idea about how to choose a "good" chaotic sequence for improving the performance of the chaos-based CDMA system.Keywords Chaos-based DS-CDMA · Energy distribution · Bit error rate · Multi-user interference

Commutation Code Index DCSK Modulation Technique for High-Data-Rate Communication Systems

“…This is due to the fact that for longer spreading codes, both maps will tend to have similar crosscorrelation profiles and the variance of the bit energy spread by the chaotic map becomes negligble. Note that the impact of the chaotic map on the BER performance behavior is well studied in [15]. V. CONCLUSIONS In this brief, a new multi-level, non-coherent CCI-DCSK scheme where IM principle is used to increase energy and spectral efficiencies.…”

“…This performance improvement is a consequence of the decrement in the cross-signal interference caused by the proportionally increased orthogonality between the reference signal and its commutated replica. Furthermore, in order to show the influence of the chaotic maps on the CCI-DCSK performance, the BER of this latter is plotted using a piecewise linear (PWL) map [15] having a flat invariant probablity density distibution, as spreading code. As clearly witnessed, the BER performance of the CCI-DCSK scheme with either CPF or PWL is similar.…”

“…In this work, Chebyshev polynomial function (CPF) is employed for generating chaotic samples due to its excellent correlation properties and its ease of implementation in radio hardware platforms [15], [16]. The CPF map is defined as x i,k = 1 − 2x 2 i,k−1 .…”

Analysis and Design of an Energy Efficient Differential Coherent Chaos Based System in Additive White Gaussian Noise Environment

“…For small value of , an integration method is preferred. This is due to the fact that bit energy is not constant for each transmitted bit [16]. The rest of the analyses will be based on the following [4,5,12]:…”

Applying Estimation Techniques to Chaos-Based Digital Communications

“…Chaos has also been shown in connection to devices used in signal processing such as nonlinear adaptive filters and phase-locked loop networks (Endo & Chua, 1988;Harb & Harb, 2004;Monteiro et al, 2009;Tavazoei & Haeri, 2009). In particular, many recent works have described digital modulations using chaotic carriers (Kennedy & Kolumban, 2000;Kennedy, Setti & Rovatti, 2000;Kolumban et al, 1997;Kolumban, Kennedy & Chua, 1998;Lau & Tse, 2003) even though their performance proved below that of equivalent conventional systems under additive white gaussian noise channel (Kaddoum et al, 2009;Williams, 2001). This chapter's first aim is to compare these chaos-based modulations to their conventional counterparts via their discrete-time low-pass equivalent models.…”