Journal of Computer Networks and Communications

Volume 2016, Article ID 5976282, 7 pages

http://dx.doi.org/10.1155/2016/5976282

## Design and Implementation of a Chaotic Scheme in Additive White Gaussian Noise Channel

Middle East College, Knowledge Oasis Muscat, PB No. 79, Al Rusayl, 124 Muscat, Oman

Received 30 January 2016; Accepted 3 May 2016

Academic Editor: Gianluigi Ferrari

Copyright © 2016 Nizar Al Bassam and Oday Jerew. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A new chaotic scheme named Flipped Chaotic On-Off Keying (FCOOK) is proposed for binary transmission. In FCOOK, the low correlation value between the stationary signal and its mirrored version is utilized. Transmitted signal for binary 1 is a chaotic segment added to its time flipped (mirrored) version within one bit duration, while in binary 0, no transmission takes place within the same bit duration. The proposed scheme is compared with the standard chaotic systems: Differential Chaos Shift Keying (DCSK) and Correlation Delay Shift Keying (CDSK). The Bit Error Rate (BER) of FCOOK is studied analytically based on Gaussian approximation method. Results show that the BER performance of FCOOK outperforms DCSK and CDSK in AWGN channel environment and with various levels. Additionally, FCOOK offers a double bit rate compared with the standard DCSK.

#### 1. Introduction

In recent years, chaotic signals become natural candidates for spreading narrow band information due to their wideband characteristic. Thus, using chaotic signals to encode information, the resulting signals are spread spectrum signals having larger bandwidths and lower power spectral densities. Chaotic signals enjoy all the benefits of spread spectrum signals such as a difficulty of uninformed detection, mitigation of multipath fading, and antijamming. Moreover, a large number of spreading waveforms can be produced easily as a consequence of the sensitive dependence upon initial conditions and parameters variations. This provides a low cost and simple means for spread spectrum communications [1].

A number of modulation and demodulation schemes have been proposed for digital chaos based communications [2–5]. In most proposed methods, the basic principle is to map the digital symbols to nonperiodic chaotic basic signals. For instance, Chaos Shift Keying (CSK) maps different symbols to different chaotic basic signals, which are produced from various dynamical systems. If synchronized copies of the chaotic basis signals are available at the receiver, detection can be conducted by evaluating synchronization error [6] or based on a conventional correlator type [7, 8]. This class of detection is known as a coherent detection. An enhanced technique to improve BER is suggested in [9]. If synchronized copies of the chaotic basis signal are not available at the receiver, detection has to be done by noncoherent detection as in noncoherent CSK and Chaotic On-Off Keying (COOK). Detection depends on estimation of transmitted signal energy. However, determining an optimum threshold between signal elements is the major drawback due to noise power contribution [6, 7] and the noise performance can be increased only by increasing the distance between signal elements. This requires the transmitter to consume more energy for each bit to increase the distance between signal elements and the receiver. Noise performance in coherent system is superior to the noncoherent systems. On the other hand, accuracy in synchronization is required to be achieved in coherent systems, which is difficult task [8].

Another widely used technique for modulation is known as differential coherent systems where Differential Chaos Shift Keying (DCSK) and Correlation Delay Shift Keying (CDSK) [10] are the basic schemes. Each information bit is transmitted by the generation of twin chaotic segments; first signal is called reference and the second, which is modulated by the information bit, is called information bearing signal. Information detection is performed by correlating reference with the information signal over last half of bit duration. Therefore, half of the average bit energy is wasted with respect to noncoherent systems. An enhancement technique is suggested by using single reference signal for multiple bits transmission [11]. A generalized Correlation Delay Shift Keying scheme is suggested in [12] by producing several delayed versions of a chaotic signal; selected version is modulated with the information bits. Although the system requires bank of transmitter, it can achieve similar performance compared to that of DCSK at reasonable range. Additionally, sending the reference signal and the information signal on the same time slot is discussed in [13–18]. Data rate and BER performance are increased, but schemes are complex and require additional synchronization circuits. Multicarrier modulation for DCSK (MC-DCSK) signal is explored in [13]. In spite of an efficient utilization of the transmitted energy, system implementation in (MC-DCSK) includes bank of narrow band modulator that needs a high degree of accuracy in the design to maintain subcarrier synchronization.

In this paper, we introduce new version of chaotic on-off scheme named (FCOOK). In FCOOK the stationary signal and its flipped version are added together within one bit duration to represent binary 1. for binary 0, no transmission takes place for the same bit duration. Based on the fact that the chaotic signal and its time flipped version are stationary, low cross correlation can be achieved [10]. This helps to design a new signal for the binary information transmission. The design allows the receiver to correlate each first half of incoming signal with the flipped version of the second half. Since both halves contain noncorrelated noise segments, this can be used to overcome the threshold shifting problem.

The remainder of this paper is organized as follows. Standard differentially coherent systems are described in Section 2. In Section 3, the transmitter and receiver models of FCOOK are described. Theoretical estimation of BER is derived in Section 4. Finally, simulation results are discussed in Section 5.

#### 2. Chaos Based Systems: Revisited

##### 2.1. DCSK

The transmitter structure of the DCSK is shown in Figure 1. Each information bit , where , is transmitted by sending two chaotic segments into successive identical time slots. Each slot is occupied by samples, where represent the spreading factor. First time slot contains a reference signal and second slot contains a delayed version of the reference signal multiplied by the information bit . Therefore, the th transmitted signal for a single bit can be written asHence, average bit energy , where is the variance operator and the expected value of .