Robust synchronization for asynchronous multi-user chaos-based DS-CDMA
Introduction
Within the past decade, several research efforts have addressed the use of chaotic signals in digital communications. Chaotic signals can offer very attractive properties such as the security of transmission and low probability of interception [1]. In addition, the improvement of the system performance when chaotic sequences are applied instead of conventional binary codes for spreading spectrum motivates the developments of chaos-based DS-CDMA transmission techniques [1], [2]. The major problem of chaos based DS-CDMA systems remains the synchronization of the received chaotic signal with the local chaotic signal generated in the receiver despread information. The intensive work of Pecora and Carroll in synchronization field [3] has opened the way for chaotic transmission systems implementation [4], [5], [6], [7]. For classical DS-CDMA using binary pseudo-noise (PN) codes, an other synchronization method has been proposed in the literature [8], [9], [10], [11]. The synchronization problem is solved via a two-step approach: An acquisition search is first activated in order to align the local sequence to the received sequence within an uncertainty of a half time chip duration [8]. The time uncertainty, which is basically determined by the transmission time of the transmitter and the propagation delay, can be much longer than a chip duration. As initial acquisition is usually achieved by a search through all possible phases (delays) of the sequence, a larger timing uncertainty means a larger search area. Moreover, in many cases, initial code acquisition must be accomplished in low signal-to-noise-ratio (SNR) environments and in presence of jammers. The acquisition procedure is possible when the spreading sequence exhibits some kind of periodicity. Given the initial acquisition, code tracking takes place and is usually accomplished by a delay lock loop (DLL). The tracking loop keeps on operating during whole communication period. If the channel changes abruptly, the DLL lose track of the correct timing and initial acquisition will be re-performed [8]. Sometimes, we perform initial code acquisition periodically no matter whether the tracking loop loses track or not.
This classical synchronization technique has been applied for chaos-based DS-CDMA systems in [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22]. In [13], [14] the authors have studied the performance of the acquisition process when a Markov chaotic sequence is used as a spreading code for DS-CDMA. They have shown in [13] that the Markov code outperforms the independent and identically distributed code in acquisition and bit error rate (BER) frameworks. The authors have shown in [12] that the Bernoulli and tailed shift map give a better performance in the acquisition phase than Gold sequences. Noise perturbations have not been included in [12], [16], [18], [22] in order to study the effects of the multi-user interferences on the acquisition process. However, the presence of noise is inevitable for any real communication system and we have included it in the study of the system performance. In most cases, when evaluating the sequence synchronization of chaos-based DS-CDMA systems only code acquisition is analyzed [12], [13], [14], [15], [16], [18], [19], [20], [21], [22].
Jovic et al. presented in [23] a new method for achieving and maintaining synchronization for synchronous multi-user chaos-based DS-CDMA. This method called code aided synchronization (CAS) is proposed and evaluated in the presence of additive white Gaussian noise (AWGN) and multi-user interferences. Code acquisition and tracking phases are studied and analyzed in [23]. The synchronization system proposed in [23] uses a single pseudo-random binary sequence as pilot signal to achieve and maintain the synchronization. The use of a binary periodic pilot signal (PPS) for chaos-based DS-CDMA synchronization system in [23] is to show that robust synchronization of a chaos-based DS-CDMA system is possible. They also show in [23] that in terms of code acquisition, the binary pilot signal outperforms the logistic and Bernoulli chaotic maps. The authors have proposed in their paper a multi-user chaos based DS-CDMA system with a synchronization unit to achieve and maintain fine synchronization of chaotic sequences.
In many papers, chaos-based communication systems are mainly studied for showing the attractive properties of chaotic sequences in the spreading spectrum framework [24], [25], [26], [27]. A lower attention is put on the implementation techniques. In order to implement practical chaos-based DS-CDMA systems, it is necessary to develop robust synchronization techniques which are able to work in low SNR environment. In our paper we have focused our attention on such robust synchronization.
In our paper we are interested in the synchronization system proposed in [23]. We proposed here two synchronization systems. The first system is the extension of the synchronous CAS method of [23] to an asynchronous multi-user case. In this system, a PN signal will be used for synchronization purpose, like in [23], as an additive periodic pilot sequence. This synchronization procedure is called asynchronous CAS with additive pilot sequence (ACAS-A).
In the second system, the PN code is used also for the synchronization purpose but instead of being an additive sequence as in ACAS-A and in [23], we have used it as a multiplicative one. This synchronization procedure is called asynchronous CAS with multiplicative pilot sequence (ACAS-M). This second approach outperforms the ACAS-A in terms of synchronization and BER performances.
In our paper we have focused on the first synchronization phase (acquisition) of the chaotic sequence. The mathematical model of the code tracking loop is presented for the chaos-based DS-CDMA system in [23].
The paper is organized as follows. In Section 2 we have first presented chaos-based DS-CDMA system with the synchronization unit. First of all, the initial synchronization is presented and analyzed in terms of probability of detection () and probability of false alarm (). Simulation results together with some conclusive remarks are then given. In Section 3 the chaotic communication system with the ACAS-M unit is presented. Then, the synchronization performance is shown in Section 3.3, simulation results and comparisons with the ACAS-A system are provided. The final section reports some conclusive remarks.
Section snippets
Chaotic generator
Throughout the paper, a Chebyshev polynomial function of order 2 is chosen as chaotic generator:The choice of this map is related to its simplicity for generating chaotic sequences. Moreover, it is shown in [23], [28], [29] that it allows better performances than many other maps for chaos-based DS-CDMA systems. Chaotic sequences are normalized such that their mean values are all zero and their mean squared values are unity, i.e., and .
Transmitter structure
The studied system is a DS-CDMA
Chaos-based DS-CDMA system with a multiplicative pilots signal (ACAS-M)
For this system we have focused also our study in the first synchronization phase (acquisition) of the chaotic sequence. A PPS sequence will be also used for synchronization purposes but instead of being an additive sequence as in [23] or in our first system, we have used it as a multiplicative sequence [32]. This new acquisition procedure has several advantages. First of all, in this procedure the PPS sequence acts no more as a noise for the chaotic spreaded signal like our first
Conclusion
In this paper we have presented two systems in order to achieve synchronization for chaos-based DS-CDMA system. In order to compare and to evaluate the additive PPS degradation for synchronization process in asynchronous multi-user. We extend synchronization method of [23] applied for the synchronous multi-user case to asynchronous multi-user case (ACAS-A) in the first chaos-based-DS-CDMA system. The synchronization performance of the chaotic communication system is evaluated in presence of
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