Theoretical analysis and simulation of a code division multiple access system (cdma) for secure signal transmission in wideband channels

Abstract

Chaotic spreading sequences can increase secrecy and resistance to interception in signal transmission. Chaos-based CDMA systems have been well investigated in the case of flat fading and noise presence in the channel. However, these systems operating in wideband channels, characterized by the frequency selective fading and white Gaussian noise, have not been investigated to the level of understanding their practical applications. This paper presents a detailed mathematical model of a CDMA system based on chaotic spreading sequences. In a theoretical analysis, all signals are represented in the discrete time domain. Using the theory of discrete time stochastic processes, the probability of error expressions are derived in a closed form for a multi-user chaos based CDMA system. For the sake of comparison, the expressions for the probability of error are derived separately for narrowband and wideband channels. The application of the system interleaving technique is investigated in particular, which showed that this technique can substantially improve probability of error in the system.  The system is simulated and the findings of the simulation confirmed theoretically expected results. Possible improvements in the probability of bit error due to multipath channel nature, with and without interleavers, are quantified depending on the random delay and the number of users in the system. In the analyzed system, a simplified version of the wideband channel model, proposed for modern wideband wireless networks, is used.

Introduction

Over the past years, the demand for wireless communications has increased substantially due to advancements in mobile communication systems and networks. Following these increasing demands, modern communication systems require the ability to handle a large number of users to process and transmit wideband signals through complex frequency selective channels.

One of the techniques for transmission of multi-user signals is the Code Division Multiple Access (CDMA) technique which allows communications of multiple users in the same communication system. This is achieved in such a way that each user is assigned a unique code sequence, which is used at the receiver side to discover the information dedicated to that user. These systems belong to the group of communication systems for direct sequence spread spectrum systems. Traditionally, CDMA systems use binary orthogonal spreading codes.

In this paper, a mathematical model and simulation of a CDMA system based on the application of non-binary, precisely speaking, chaotic spreading sequences. In their nature, these sequences belong to random sequences with infinite periodicity, and due to that they are appropriate for applications in the systems that provide enhanced security against interception and secrecy in signal transmission.

Numerous papers are dedicated to the development of CDMA systems in flat fading channels. This paper presents the results of these systems analysis for the case when frequency selective fading is present in the channel. In addition, the paper investigates a possibility of using interleaving techniques to mitigate fading in a wideband channel with the frequency selective fading.

Basic structure of a CDMA communication system and its operation

In this paper, a CDMA system block schematic is ppresented and the function of all blocks is explained. Notation  to be used in the paper is introduced. Chaotic sequences are defined and explained in accordance with the method of their generation. A wideband channel with frequency selective fading is defined by its impulse response function.

Theoretical analysis of a CDMA system with flat fading in a narrowband channel

A narrowband channel and flat fading are defined. A mathematical analysis of the system is conducted by presenting the signal expressions at vital points in the transmitter and receiver. The expression of the signal at the output of the sequence correlator is derived. Then the expression for the probability of bit error is derived in a closed form and discussed from both the number of users and the spreading factor point of view.

Theoretical model of a CDMA sistem with frequency selective fading in a wideband channel

A wideband channel and frequency selective fading are defined. All signals in the system are presented in the discrete time domain. In order to use a finite length of chips, each chip is represented by identical samples. A mathematical analysis of a wideband CDMA system is conducted. The mathematical expressions of the signals at vital points in the transmitter and receiver are presented. The expression for probability of bit error is derived in a closed form. The principles of the transmitter and receiver operations with and without interleavers are separatelly analyzed.

Simulation model of the CDMA system and the  simulation results

The following system simulations are presented in this chapter: simulation of the system with a narrowband channel and flat fading;  simulation of the system with a wideband channel and frequency selectiive fading without interleaving and simulation of the system with a wideband channel and frequency selectiive fading with interleaving. It was shown that the probability of error curves obtained by the simulation follow the curves obtained by the theoretical analysis.

Conclusion

The basic aim of this research, the results of which are shown in this paper, is to investigate the properties of CDMA systems in the case when frequency selective fading is present in a wideband channel. The developed theoretical model of the system is presented and the expressions of the probability of error are derived in a closed form., The case when the block interleaving technique is applied in the system  is analysed in particular. The derived theoretical expressions for the probability of error show that it is possible to achieve significant improvement in the quality of signal transmission using this technique. Due to the random nature of chaotic sequences, the secrecy of information transmission is improved. For the same reason, the system's protection against interception is achieved. The modelled system is simulated in Matlab. The results of the simulation confirmed the results of the theoretical analysis.