International Journal of Antennas and Propagation

Volume 2018, Article ID 6387317, 10 pages

https://doi.org/10.1155/2018/6387317

## Design and Performance Analysis of MISO-SRMR-DCSK System over Rayleigh Fading Channels

School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Correspondence should be addressed to Yi man Hao; moc.liamxof@namiy_oah

Received 30 January 2018; Accepted 14 May 2018; Published 13 August 2018

Academic Editor: Giuseppina Monti

Copyright © 2018 Gang Zhang et al. 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

The major drawback of the differential chaos shift keying (DCSK) system is that equal time and energy are spent on the reference and data signal. This paper presents the design and performance analysis of a short reference multifold rate DCSK (SRMR-DCSK) system to overcome the major drawback. The SRMR-DCSK system is proposed to enhance the data rate of the short reference differential chaos shift keying (SR-DCSK) system. By recycling each reference signal in SR-DCSK, the data slot carries N bits of data and by P times. As a result, compared with SR-DCSK, the proposed system has a higher data transmission rate and evaluates the energy efficiency with respect to the conventional DCSK system. To further improve the bit-error-rate (BER) performance over Rayleigh fading channels, the multiple-input single-output SRMR-DCSK (MISO-SRMR-DCSK) is also studied. The BER expression of the proposed system is derived based on Gaussian approximation (GA), and simulations in Rayleigh fading channels are performed. Simulation results show a perfect match with the analytical expression.

#### 1. Introduction

CHAOS signals are suitable for spread spectrum communications due to broadband and nonperiodic characteristics. In the past few decades, the coherent and noncoherent algorithms of various chaotic communication systems have been proposed [1–15]. Coherent detection requires synchronization of chaotic carriers, for example, chaos shift keying (CSK) [1]; therefore, its application is limited. In light of the shortcomings of coherent detection, differential chaos shift keying (DCSK) [2] becomes the most worthy consideration in the development of chaotic communication system. The reason is that the DCSK system can demodulate the transmitted information at the receiver without the chaotic carrier synchronization and channel state estimation. In addition, DCSK has better antimultipath fading capability than differential phase shift keying (DPSK) [3] and is more suitable for ultra-wideband transmission. However, the traditional DCSK system transmission efficiency is low, and low security limits its application. To overcome the shortcoming of traditional DCSK, researchers have proposed a number of improvements. For example, in [4], Herceg et al. introduce the correlation multidelay shift keying (CMDCK). In their proposal, the reference slot and the data slot that delays different chip times are subtracted to transmit the multibit information to improve the data rate. In [5], quadrature chaos-shift keying (QCSK), an orthogonal chaotic keying system, is proposed by Galias and Maggio through the Hilbert transformation to obtain two completely orthogonal chaotic sequences for the transmission of two consecutive time slots. This improvement of transmission rate is sacrificed at the expense of the cost of modulation. In [6], Kaddoum et al. propose the short reference DCSK (SR-DCSK) system, a work in which the length of the reference slot is shortened while the data slot remains unchanged. Moreover, Cai et al. propose M-ary DCSK [7] and differential DCSK [8], which are also aimed at improving the DCSK transmission rate. Kaddoum et al. [9] introduced a multicarrier DCSK system to improve the safety of the DCSK system, and [10] propose a new MC-DCSK system, where no RF delay line is required, while improving the spectrum utilization and reducing energy consumption. In [11], Xu et al. propose the code-shifted DCSK (CS-DCSK), which makes the Walsh code to distinguish between reference slot and data slot, thereby reducing the interference between the signal and improving the performance of BER. The extension of CS-DCSK is proposed in [12], in which N bits of information are transmitted in the same time slot, while using only a reference slot and obtaining a high transmission rate. In [13], high-efficiency DCSK (HE-DCSK) is studied and inspected. In this system, the data signal transmits 2 bits of data, where the 1-bit signal is demodulated by the reference slot of the previous frame. And it improves the utilization of the reference slot. In [14], reference-modulated DCSK (RM-DCSK) is introduced. RM-DCSK is to use the previous frame as the reference signal of the latter frame to improve the data transmission efficiency. The permutation DCSK (P-DCSK) proposed in [15] is to add the random permutation matrix in the traditional DCSK system to disrupt the sequence of chaotic signal samples, destroy the similarity between the reference signal and the information signal, and eliminate the possibility of detecting the bit rate from the square spectrum, thereby increasing the data security. However, P-DCSK does not improve the DCSK system data transmission rate.

In this work, we propose a novel DCSK modulation scheme based on the SR-DCSK system, named short reference multifold rate differential chaos shift keying (SRMR-DCSK). In this system, a data frame is composed of the reference slot and the data slot, and the data slot can transmit bits of data at a time. And the length of the reference slot is of the data slot, where is any integer that can be divisible by a spreading factor. This solution solves the problem that the DCSK reference slot does not transmit information. In order to improve the BER performance of the system over the Rayleigh fading channels, the multiple-input single-output SRMR-DCSK (MISO-SRMR-DCSK) is proposed. In the paper, we define as the number of transmit antennas and the number of receive antennas, where and . As a potential application, the MISO-SRMR-DCSK is considered and the BER formula is derived over the Rayleigh fading channel.

The rest of this paper is organized as follows: In Section 2, a description of the SISO-SRMR-DCSK transmitter scheme and demodulation structure is given, and the traditional DCSK system is described briefly. Moreover, the energy efficiency and data rate of SISO-SRMR-DCSK are analyzed and the energy efficiency is evaluated with respect to the conventional DCSK system. In Section 3, SISO-SRMR-DCSK is extended to MISO-SRMR-DCSK and analytical BER expression is explained. MISO-SRMR-DCSK, the extension of the SISO-SRMR-DCSK, is explained. The performance of the MISO-SRMR-DCSK system is derived in Gaussian approximation (GA). Section 4 simplifies the channel model between each antenna and the receiving antenna at the transmitter to a two-way Rayleigh fading channel. Further, it is assumed that the channel is slowly fading; that is, the channel is static in a one-bit period. If the gain of one channel is zero and the other gain is 1, it is the Gaussian channel. The simulation of the new system is compared with other systems in Section 4. And the conclusion is presented in Section 5.

#### 2. Noncoherent Chaos-Based Communication System

##### 2.1. DCSK System

In the modulation of the DCSK system, each bit represents the same length of two chaotic sequences in the frame. The first time slot transmits a chaotic sequence as the reference sequence, and the second one transmits the chaotic sequence of the modulated data as data sequence. If +1 is transmitted, the reference sequence is equal to the data sequence, and if −1 is transmitted, the reverse reference sequence is transmitted as a data sequence. The spreading factor in the DCSK system is defined as the number of chaotic samples used to spread each transmitted bit and is presented by , where is an integer. In addition, the bit period of the DCSK system is , where is the chip time and , and is a slot time, that is, half a bit of time. The bit interval at the output of the DCSK system modulator can be expressed as (1) below. where is the chaotic sequence of the reference signal, is the delay signal of , and represents any one of the chips in a frame. In order to demodulate the transmitted information, the received signal will be compared with its delay signal for the length of time () correlation calculation, and it is determined by the zero threshold in the receiver. The transmitter structure and receiver structure are given in Figures 1 and 2, respectively. In Figure 1, for every bit of information, the transmitter outputs a chaotic sequence of length followed by the same sequence multiplied by the information signal , where is the bit counter. In Figure 2, the received signal is multiplied by the received signal delayed by , . The product is then averaged over the spreading sequence length . In the DCSK system, half of the frame time is used to transmit the reference signal that does not carry any useful information; thus, the data transmission rate is reduced.