Design of High data Rate FM-QCSK Chaotic Communication System

The frequency modulated quadrature chaos shift keying FM-QCSK system is one of the most efficient systems in chaotic literature. One of the problems in this system is that half the bit duration is used for sending a chaotic reference signal which leads to increase the energy losses and reduces the data rate. In this paper, a novel scheme to enhance the performance of FM-QCSK system has been proposed. With the proposed scheme, FM-QCSK would be able to operate at higher data rates with reduced bit-error probability BER and energy consumption. The basic modification introduced by the proposed scheme is the use one reference chaotic chip to transmit multi information-bearing chips in both in-phase and quadrature-phase channels. The results showed that the proposed scheme have achieved more than 3 dB and 5 dB gains in SNR for AWGN and Rayleigh multipath fading channels respectively at BER=10 -3 over the conventional one. The results also showed that the optimum number information-bearing chip can be send per reference is 8. The theoretical expression of BER in AWGN channel has also been derived for the proposed scheme.


Introduction
With researching in the chaos-based communication systems, mo re and more methods are applied in this area and more and more modulation schemes are proposed. In which d ifferential chaotic shift key ing (DCSK) [1], using correlation to demodulate, was proposed to solve the problem of chaotic synchronization. These commun ication systems have the wide band characteristic of chaotic signal and advance in resisting multipath fading [2]. To enhance the noise performance of DCSK, FM-DCSK [3] scheme was proposed where frequency modulation is utilized to achieve constant energy per bit for the chaotic carrier. DCSK is a transmitted-reference signaling scheme. For each symbol period, the DCSK signal consists of a piece of chaotic waveform (called reference chip), fo llowed by its non-inverted or inverted copy (called in formation bearing chip), depending on the binary symbol ("0" o r "1") to be transmitted.
QCSK [4] (Quadrature Chaos Shift Keying) which can transmit 2 bits in a sample function was designed by Zbigniew Galais and Gian Maggio to improve the speed of chaos shift keying in 2001. Then in 2006, Yiwei Zhang devised FM-QCSK [5], wh ich enhanced the noise performance of QCSK by using frequency modulation, because it generates constant energy per bit and its frequency spectrum is wideband.
Several different methods have been proposed in the literature to increase the data rate in both DCSK and QCSK systems [6][7][8][9][10]. The simp lest options consist of scaling the informat ion and/or the reference parts of the signal like the work in [6][7][8]. More sophisticated approaches use mu lti-level signal constellations like QAM, M-ary phase shift keying o r mu lti-chaotic basis functions by dividing the symbol period into M-ary t ime slots [9] or by defining a set of orthogonal vectors [10]. All the previous works constrained; in principle, on increasing the space dimension of the chaotic carrier as a way to increase the data rate. However, there were no real concerns to the number of information-bearing chips which are referred to one reference. In this paper, an enhanced version of FM-QCSK scheme is proposed by using the idea of transmitting more than one informat ion-bearing chip for one reference chip and averaging the correlation results for both the in-phase and quadrature phase channels to improve the noise performance, reduce the energy consumption and to increase the data rate of FM-QCSK.

Background Theory
Z. Galias, and G. M . Maggio described in their article [4] that the orthogonal basis of chaotic functions[x(t ) and y(t)] can be easily generated through Hilbert transform and this chaotic sample functions over the interval[0,T] can be defined as follows: E b is the energy associated with chaotic signal x(t) and y(t) in a sample period[0,T]. Therefo re, the formu la can be defined as: The quadrature signal of x(t) is y(t) , so we can get the following equation: The corresponding to two typical versions of QCSK modulation, constellations distribution is shown in Figure 1, where dashed lines represent the decision boundaries respectively. In a FM-QCSK system, the chaotic reference chip c x (t) which is modulated by FM modulator is transmitted in the first half symbol period while the in formation chip m i (t) which is also modulated by FM is t ransmitted in the second half. The ith symbol of the modulated information signal m i (t) can be defined as follows: (4) Therefore, signals transmitted by FM-QCSK can be expressed in a symbol period T: ( ) In the above formula, a i and b i are the mapping coordinate of signal symbol in constellation. The combinations of a i and b i that denote the different symbols are shown in Table 1.

Enhanced FM-QCSK Modulation
The time slots of the original FM-QCSK signal are shown in the upper part of Figure 2. In this figure, R i denote the reference ch ips of the ith bit while a i and b i denote the information-bearing chips of the ith bit for the in-phase and quadrature-phase respectively. One o f the drawbacks of conventional FM-QCSK is that every information bit is transmitted by two chips (the reference and information-bearing chips). Hence, the bit rate (as well as the symbol rate) is halved and the transmitted energy per bit is doubled compared to the conventional binary modulation schemes where every samp le function represents one bit. A possible enhancement of the conventional FM-QCSK scheme is as follows: instead of transmitting only one information-bearing chip after one reference chip, N bits in each channel are transmitted using the same reference. Th is idea is first discussed in [6], but tested in DCSK system where there are no orthogonal chaotic carriers and symbol transmission is introduced as in FM-QCSK. The waveform of the enhanced FM-QCSK scheme is shown in the lower part of Figure 2, where T s denote the duration of one chip and E s is the energy carried by chip. Observe that in a block containing N+1chips for every chip, except the first one, carries information. The enhanced modulation scheme offers two advantages over the conventional one: firstly, the bit duration T is decreased fro m 2T s to ((N+1)/N)T s , i.e., the data rate is increased. Secondly, the transmitted energy per bit E b is reduced fro m 2E s to ((N+1)/N)E s (or equivalently energy per sy mbol is reduced fro m 4Es to 2((N+1)/N)E s . However, the enhanced system may also suffers from the drawbacks of increasing periodic component at frequency 1/T s and its harmonics as well as the increase in the system co mplexity (6) There are two observation signals of the mth symbol at the receiver for the in-phase and quadrature-phase channels. These are defined as: Note that ř m (t) and ř mI (t) signals are the same wh ile ř mQ (t) signal is ř m (t) signal after applying Hilbert transform. Figure 3 shows the implementation of the enhanced FM-QCSK modulator. First the chaos signal is applied to an FM modulator to get constant energy per bit. The enhanced modulator contains of a delay with N taps, the output of each tap is input to a QCSK modulator. The trans mission of each N symbols is preceded by a reference ch ip s0(t), after which the information-bearing chips sm(t) are transmitted. This is done by changing the switch positions at each Ts time instants.

Transmitter and Receiver Configurations
The block diagram of the demodulator contains N delay lines and correlator pairs as shown in Figure 4. The correlator pair outputs sampled at kTs, k=1, 2,…N constitute the elements of observation vectors for in-pahse and quadrature phase channels. They are denoted by z 1I , z 1Q , z 2I , z 2Q ..…z NI , z NQ in Figure 3 and their values are given in Table 2. The transmitted information is carried by the sign and relative orthogonality of the correlation between the reference and information-bearing chips. This informat ion is available for the mth symbol at the output of the mth correlator pair at (m+1)th sampling time instant as shown in Table 2. The estimated information is denoted by a vector Ď=(Ď 1 , Ď 2 …… Ď N ) and obtained from the output of symbol/bit converter.

Performance Evaluation in AWGN Channel
Based on the article by Yiwei Zhang, et al. [5], the BER of FM-QCSK is defined as follows: where T c is the chip duration o f d iscrete chaos signal. In [5], the term T/(2T c ) denoted as K, wh ich represent the number of chaotic samples in the reference signal. It is also shown in [5] that as K increase, the noise performance of QCSK is improved since it is a measure of the length of correlation interval. To get the BER of the enhanced FM-QCSK, we substitute the new values of b it duration ((N+1)/ N)T s and energy per bit ((N+1)/ N)E s in (9). In this way, the BER of enhanced FM-QCSK is:

Simulation Results
The chaotic spreading signal has generated by a discrete-time Hennon map : 3. The discrete signal is offset by -0.5 and scaled by 2 (to obtain zero mean) so that the signal range becomes[-1,1]. According to the article by Jiamin Pan and He Zhang [9], we define T c = 0.05 μs and T=4 μs. Subsequently, the FM modulator is defined as follows: In the above formu la, A c =1 V, f c =36 MHz, and K f =7.8 MHz/ V. Figure 5, shows the plot of BER versus E b /N 0 for conventional FM-QCSK (N=1) and the enhanced FM-QCSK for N=2, 4, 6, 8 and 10 in AW GN channel. The performance of BPSK (the best possible noise performance that can be achieved by any digital modulation scheme over AW GN) is also plotted for the purpose of perfo rmance co mparison. It can be seen in this figure that by increasing N, a significant improvement in the noise performance can be achieved. For example at BER=10 -3 , gains in SNR of 2 dB, 2.7 dB, 3.1 dB, 3.3 dB and 3.4 dB when N=2, 4, 6, 8 and 10 respectively have been obtained using enhanced FM-QCSK scheme over the conventional one. Actually, the reason behind the improvement in the BER using the proposed scheme is that the noise associated with the received signal would be averaged due to the division of the correlation to N t ime slots. However, above certain limit increasing N has little effect on the system noise performance, i.e. threshold effect can be observed. We noticed in our simu lations that this threshold occurs at N=8. However, the performance can be also relatively imp roved by increasing K (the length of correlation interval). Figure 6 shows the plot of BER versus E b /N 0 for conventional FM -QCSK (N=1) and the enhanced FM-QCSK for N=2, 4, 6, 8 and 10 in Rayleigh mult ipath fading channel. In this case we used in our simulat ions two paths; the second path delay was 75 ns with attenuation of -3 d B which represents the specification of mult ipath environ ment inside office buildings. It is obvious in this figure that the performance of FM-QCSK is improved as N increased too. For example at BER=10 -3 , gains in SNR of 3 dB, 4.6 dB, 5.2 dB, 5.6 and 5.8 d B when N=2, 4, 6, 8 and 10 respectively have been obtained. For N values greater than 8, a saturation region is reached such that no more than 0.1 d B imp rovement can be gained. As compared with BPSK, enhanced FM-QCSK offered superior performance starting fro m SNR=5 dB. For examp le at BER= 10 -3 , mo re than 10 d B gain in SNR can be gained by using enhanced FM-QCSK with N=8.

Conclusions
The increase of the data rate and the reduction in the energy consumption are important requirement for any modulation system. In FM-QCSK, these requirements can be optimized by making mu lti information-bearing chips associated with one reference chip. It has been shown by simulations in both AWGN and mult ipath fading channels that the performance of FM -QCSK system has been enhanced by introducing this optimizat ion criteria. Furthermore, the bit error rate has been also reduced. For instant, 3 d B and 5 d B gains in SNR for AW GN and Rayleigh multipath fading channels respectively at BER=10 -3 over the conventional one. The performance of the enhanced scheme is imp roved as the number of information bearing chips for one reference chip is increased up to a certain threshold ( N=8) after which the system co mplexity is increased without gaining considerable improvement. A theoretical expression of the error probability for the enhanced scheme has been derived and its plot versus SNR is very closed to the simu lation results. The possible future work can include analysing the effect of changing the correlation length on the system performance and hardware imp lementation of the proposed system.