Performance analysis of Differential Chaos Shift Keying over an AWGN channel Georges Kaddoum † , Pascal Charg´ e ‡ Daniel Roviras ⋆ and Dani` ele Fournier-Prunaret ‡ Abstract—In this paper, a study of the differential chaos shift keying for discrete time implementations is proposed. Then we analysed the performance of this modulation system. A new approach is considered to compute an exact bit error rate expression. The idea of this approach is to compute the probability density function of the chaotic bit energy and to integrate the bit error rate over all possible values of this probability density function. The formula of the bit error rate of the system is derived for mono user case under an Additive White Gaussian Noise channel. It is shown that this method can be easily applied for any kind of chaotic sequences in different environments. Computer simulations verify the accuracy of our approach to compute the performance of this chaos-based communication system. I. INTRODUCTION After the demonstration of the possibility to synchronize two chaotic systems [1], many researchers started to be inter- ested in the application of chaotic signal to communication systems. These signals applied in spread-spectrum commu- nications systems offer many advantages over traditional approaches. Chaotic signals are non-periodic, wide-band, and more difficult to predict or to reconstruct. Theses properties of chaotic signals make transmissions more difficult to be intercepted and then decoding of modulated data information is also less easy. Several chaos-based communication systems have been proposed and studied. Among theses systems, chaos shift keying (CSK) [2], Chaos-based DS-CDMA [3] and differ- ential chaos shift keying (DCSK) [4], [5], [6] systems are widely studied. In order to compute the performance for coherent systems like CSK and chaos-based DS-CDMA, the synchronisation of chaotic signals between the transmitter and receiver is assumed. Since the chaos synchronization proposed by Pecorra and Caroll is still practically impossi- ble to achieve in a noisy environment, the synchronisation assumption for chaos-based coherent systems can not be as- sumed. On the other hand, DCSK system represents a robust non-coherent scheme in which the exact knowledge of the chaotic signal at the receiver side is not required. In addition, the DSCK system is one of the most promising chaos-based communication schemes for a feasible implementation [7]. † G. Kaddoum is with Department of Telecommunication and Networks Engineering, IRIT/ENSEEIHT Laboratory, University of Toulouse, 2 rue Charles Camichel, France gkaddoum@enseeiht.fr ‡ P. Charg´ e and D. Fournier-Prunaret are with the Department of Electrical Engineering, LATTIS/INSA Laboratory, University of Toulouse, France pascal.charge@insa-toulouse.fr ⋆ D. Roviras with the Department of Telecommunication Engineering, LAETITIA Laboratory, CNAM Paris, France daniel.roviras@cnam.fr In DCSK system, the bit duration is divided into two equal slots. The first slot is the chaotic reference signal. Depending upon the symbol to be sent, the reference signal is either repeated or multiplied by the factor -1 and transmitted in the second slot. At the receiver, the signal is delayed by a half of bit duration and correlated with undelayed signal to estimate the transmitted bit information. The performance of coherent and non-coherent chaos- based digital communication systems under an additive white Gaussian noise (AWGN) environment has been widely stud- ied [8], [2]. In this paper we study the performance of mono- user DCSK system over and Additive White Gaussian Noise Channel (AWGN). In order to study the DCSK performance in the literature, a strong approximation is often used as in [4], [5], [6]. This approximation known as Gaussian approximation considers that the correlator output follows the approximate normal distribution. When the spreading factor is very large,this method gives rather good estimates of the BERs. But when the spreading factor is small, the Gaussian approximation method gives rather disappointing results. In fact, because of the non-periodic nature of chaotic signals, the transmitted bit energy after spreading by chaotic sequence varies from one bit to another. In [9], Lawrance et la developed an exact analytical expression of bit error rate (BER) for chaos based-communication system. In fact, there approach can gives accurate results but with an expensive computing charge. Since previously presented approach is not valid for small spreading factors or have a high computing charge, another accurate approach was recently developed to compute the exact BER performance for single and multi-user chaos- based DS-CDMA over an AWGN and multi-paths channels. The novelty of this paper is to extend the approach devel- oped in [10], [11], [12], [13] in order to give an accurate BER expression to non coherent chaos-based communication systems and especially when the spreading factor is low. For such system the noise variance increases proportionally with the spreading factor [5]. A high spreading factor can significantly degrade the performance of the DCSK system [5]. The optimal spreading factor is computed in [8]. Without any problem our approach can gives an accurate results compared to other approaches with a low computing charge. The idea is to compute the Probability Density Function (PDF) of the chaotic bit energy and to integrate BER over all possible values of this PDF. The shape of the PDF bit energy is a qualitative parameter concerning the expected BER performance. Section 2 presents the transmitter structure of DCSK ACTEA 2009 July 15-17, 2009 Zouk Mosbeh, Lebanon 978-1-4244-3834-1/09/$25.00 © 2009 IEEE 255