NATIONAL CONFERENCE ON NONLINEAR SYSTEMS & DYNAMICS 1 Performance of Differential Chaos Shift Keying over Multipath Fading Channels Soumyajit Mandal and Soumitro Banerjee Abstract—We analyze the performance of Differential Chaos Shift Key- ing (DCSK) over communication channels exhibiting multipath fading. Formulas are derived for the bit error rate (BER) performance in the single user case and compared with simulation results. Keywords—chaos, communication, fading, DCSK I. I NTRODUCTION HE inherently broadband nature of chaotic signals has made them promising for spread spectrum communication systems [1], [2], [3]. DCSK and other schemes have been pro- posed and their performance analyzed [4], [5], [6], [7], [8] for this application. In this paper, we extend DCSK performance analysis to a variety of communication channels encountered in practical systems. DCSK is a non-coherent method for transmitting binary in- formation using a chaotic signal. A reference chaotic waveform is transmitted during the first half of each data bit. If the bit is a ‘1’, is transmitted again during the second half. If the bit is a ‘0’, is transmitted. At the receiver, the signal is delayed by half a bit period and correlated with the undelayed signal to get the decision variable for producing the output data stream. The structure of a typical DCSK transmitter and receiver is shown in Fig. 1. T b 2 DELAY T b 2 DELAY CHAOTIC SOURCE DCSK OUT DATA SOURCE DCSK IN DECODER ACCUMULATOR CORRELATOR TRANSMITTER RECEIVER THRESHOLD OUT DATA Fig. 1. DCSK transmitter and receiver structures. Using chaotic signals for spreading introduces a non-zero variance in the transmitted energy per bit, which degrades the BER performance of DCSK. In [9], [10], FM was used to re- duce this variance. Alternatively, one can get constant bit en- ergy by using binary valued chaotic sequences for spreading. In this paper, we have used binary chaotic sequences obtained by quantizing the output of a wide variety of chaotic maps (iterated S. Mandal is with the Department of Electrical Engineering & Computer Sci- ence, Massachusetts Institute of Technology, Cambridge, USA S. Banerjee (Corresponding author) is with the Department of Electrical En- gineering, Indian Institute of Technology, Kharagpur - 721302, India, E-mail: soumitro@ee.iitkgp.ernet.in at the chip rate) for spreading. Binary chaotic sequences can be designed to have purely noise-like correlation properties and efficiently spread the spectrum of digital data [11]. This paper is organized as follows. Section II investigates DCSK performance in additive white Gaussian noise (AWGN) channels. Rayleigh fading channels are considered in Sec- tion III. Use of multipath diversity to improve performance is discussed in Section IV . Ricean fading channels are considered in Section V. Conclusions and suggestions for further work are presented in Section VI. II. AWGN CHANNELS In our case, the transmitted energy per bit is constant and the BER of DCSK in AWGN channels takes the form BER Q (1) where is the energy per bit, is the channel noise power spectral density, chips are transmitted per bit period and Q erfc . This type of BER expression is charac- teristic of the correlation despreading of transmitted reference signals like DCSK. The increasing effect of the noise cross- correlation in the decision variable causes the BER to increase as (the spreading factor) increases (Fig. 2). The BER val- ues predicted by (1) have also been verified against numerical simulations. Fig. 2. Theoretical DCSK performance in AWGN channels.