Abstract
A multiuser communication scheme which is a hybrid of Walsh code with DCSK and CDSK is proposed to improve low data transmission rate of Differential Chaos Shift Keying (DCSK), poor bit error ratio (BER) performance of Correlation Delay Shift Keying (CDSK), and disadvantage of orthogonality in traditional multiuser DCSK. It not only overcomes the disadvantages of DCSK and CDSK, but also has better performance than CDSK and higher transmission data rate than DCSK. It has been proved that the novel multiuser CDSK-DCSK has better properties than traditional Multiple Input Multiple Output-Differential Chaos Shift Keying (MIMO-DCSK) and Modified-Differential Chaos Shift Keying (M-DCSK). Also the multiuser interference is greatly suppressed due to the orthogonality of Walsh code.
1. Introduction
Spread spectrum technology is used in communication system to bear low data rate information by using spread spectrum sequence due to its broad bandwidth characteristics. The technology has advantages such as high security, anti-interference, and antimultipath fading and being easy to be realized in code division multiple access (CDMA) [1]. In recent years, chaotic spread spectrum communication system has been deeply researched in spread spectrum technology [2]. It is different from the traditional spread spectrum technology since the carriers are high speed chaotic signals which are generated by different chaotic maps. Chaotic signal has the advantages of high bandwidth, being nonperiodic, being difficult to predict, and good autocorrelation and cross correlation features [3].
According to the way of demodulation, chaotic communication system is divided into two types: the coherent and the noncoherent demodulation [4]. Coherent demodulation needs the receiver to reconstruct chaotic signal, which means that the security and noise immunity are better than noncoherent demodulation. But it is difficult to realize chaotic synchronization. The security in noncoherent demodulation is worse than in coherent demodulation, but it is easy to implement and the cost of hardware is much lower. In the existing noncoherent systems, reference signal is used for dispreading in most of the receivers [5–10]. Differential Chaos Shift Keying (DCSK) has disadvantages of low data rate [11]. In Correlation Delay Shift Keying (CDSK), the data rate is 2 times that of DCSK [12], but the BER performance is worse than DCSK [13]. Much attention has been attracted since the concept of multiple access DCSK has been proposed [14]. In [15], different interval between transmit signal and carrier is used to distinguish different users. But the orthogonality is poor when using the smaller spread factor.
A combination of multiuser CDSK-DCSK with Walsh coded scheme is proposed in this paper. It can not only overcome the disadvantages of DCSK and CDSK, which means that the BER is better than CDSK and the data rate is higher than DCSK, but also suppress multiuser interference well, due to the orthogonality of Walsh code.
2. Novel Multiuser CDSK-DCSK System
The novel multiuser CDSK-DCSK scheme is shown in Figure 1, where the system has users totally, and the th user is discussed for special purpose.
Chaotic signal is generated by the logistic map firstly. Then, chaotic sequence is generated after the symbolic function mapping as follows:where is chaotic signal, is symbolic function, and is chaotic sequence of the th user.
The transmitter is illustrated in Figure 2. A pair of bit is modulated and transmitted in a frame, where . In the th frame, and are transmitted in the first slot, where is the time delay of and . In the second and third slots, and are multiplied with chaotic sequence and the assigned Walsh code, respectively. Transmitting signal of th user is shown in where is the spread factor. and are Walsh code of th user.
From Figure 1 and (2), the total transmitting signal is easy to be obtained. The received signal after transmission is shown as follows:where is assumed as Additive White Gaussian Noise (AWGN) and is the total number of users.
Figure 3 shows the receiver’s structure. Walsh code is multiplied with and or . The Walsh code in the th receiver must agree with the one of the th transmitter. After correlation demodulation the original signal is obtained and is shown in
In order to simplify the output, can be divided into three parts , , and as follows:
The chaotic sequence has the following properties [16]:(1)Chaotic sequence generated by the same map but with different initial value is noncorrelated.(2)The chaotic sequence is the same as impulse function after normalized autocorrelation.
Besides, due to the orthogonal property of Walsh code such as , , and , in (5) is the only useful signal and the rest of (5), (6), and (7) are interference. The first item is the cross correlation of chaotic sequence and the second item equals 0. can be demodulated according to the following rules:
Similarly, the decision rules for are
3. Performance Analysis
By central limit theorem, the correlation output approximately obeys the normal distribution. The mean and variance of are required to get the system’s BER. Features of chaotic sequence and Walsh code are presented in [17].(1)For different chaotic sequences and generated by the same map, and , when .(2)For different Walsh codes and , where and , when , .(3)Correlation among chaotic sequences, AWGN and Walsh codes, is 0.(4)For (4), .
Suppose the th user’s first bit in th frame is “”:where represents the mean of . Considerwhere represents variance and is noise power density.
So the variance of iswhere represents covariance.
Similarly, when , the mean and variance of are
The system’s bit error ratio (BER) iswhere is the error function, , and is bit energy, .
From (14), with a certain value of and , there exists to realize the best system performance. Suppose . It is easy to obtain after differentiating :
Suppose that ; the equation of is as follows:
By (16), for certain , under different , is different. For example, suppose dB; when and , is 13.33 and 26.66, respectively.
4. Simulation Comparisons
Figure 4 shows that the smaller the value of , the stronger the influence on BER by . It is obvious that the intervals between different curves under the same in are significantly larger than that of . With increasing, BER gets smaller and the system’s performance gets better.
Figure 5 shows that selecting an appropriate has great impact on the system’s performance. On one hand, there exists an optimum to achieve the best BER. If is increased continuously, the system’s performance gets worse. On the other hand, the transmission efficiency is too low if is too large.
Figure 6 displays that multiuser interference increases with the users’ total number increasing, so the system’s performance gets worse. Under different , the BER gradually tends to be constant and unrelated with .
It can be seen from Figure 7 that the performance of multiuser CDSK-DCSK is slightly inferior to MIMO-DCSK [11] when is low. But the proposed system’s data rate is 2 times that of MIMO-DCSK. When dB, the proposed system’s performance is much better than that of MIMO-DCSK. Compared with M-DCSK proposed in [9], in low , there is not much difference between multiuser CDSK-DCSK and M-DCSK. But when dB, the proposed system’s BER is improved one-order magnitude.
5. Conclusion
The excellent autocorrelation and cross correlation characteristics of chaotic signal are used in traditional multiuser DCSK system [15] to distinguish different users. When the spread factor is small, the orthogonality between different chaotic signals is poor. A hybrid CDSK-DCSK combined with Walsh code system is proposed in this paper to realize the multiuser transmission. The signal is transmitted in pairs, so transmitting rate is 2 times the traditional ones. Interference between different users can be reduced due to the application of Walsh code. Also, the simulation results show that, under the same circumstances, the performance of multiuser CDSK-DCSK system is much better than that of M-DCSK and MIMO-DCSK, especially when is larger than 16 dB and 10 dB, respectively.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgments
This research is supported by the National Natural Science Foundation of China (Grants nos. 61371164, 61071196, and 61102131), the Program for New Century Excellent Talents in University (Grant no. NCET-10-0927), the Project of Key Laboratory of Signal and Information Processing of Chongqing (Grant no. CSTC2009CA2003), the Chongqing Distinguished Youth Foundation (Grant no. CSTC2011jjjq40002), the Natural Science Foundation of Chongqing (Grants nos. CSTC2010BB2398, CSTC2010BB2409, CSTC2010BB2411, and CSTC2012JJA40008), and the Research Project of Chongqing Educational Commission (Grants KJ120525 and KJ130524).