Performance of Improved FM-DeSK system Based on Differential-coding Method Weikai Xu 2
Liming Chen l 1. Inst. of Coding and Information Tech. Chongqing University of Post and Tech. Chongqing, 400065, China e-mail:
[email protected]
2. Dept.ofCommunication Engineering Xiamen University Fujian, 361005, China e-mail:
[email protected]
Abstract-In this paper a differential-coding method is applied to improved FM-DCSK transmitter to simplify the receiver configuration. Further based on our proposed scheme, a new error correction principle is presented to enhance the noise performance of the purposed system. The HER performance of the different FM-DCSK systems including proposed one is investigated over AWGN channels. Simulation results show that the proposed system using new error correction algorithm owns a comparable noise performance and much lower complexity and delay comparing improved systems.
I.
INTRODUCTION
Chaos-based communication theory applies a chaotic modulation scheme, which is different from the conventional modulation schemes in that a non-periodic chaotic signal is used as the carrier [1]. In 1992, a digital modulation using chaotic basis functions, which called chaos shift keying (CSK) was first introduced [2].In 1996, a robust noncoherent technique called differential chaos shift keying (DCSK)[3] was presented, and later optimized as frequencymodulated DCSK, namely, FM-DCSK [4]. After that, some literatures introduce an improved version of the DCSKlFMDCSK to overcome the drawback of themselves, and based on the schemes some sophisticated error correction principles were proposed [5, 6]. However these improvements introduced in DCSKlFMDCSK will increase the complexity of systems. Knowing this, our work is to focus on trading-off the complexity of implementation and their noise performance in these improved systems. It is found that performance of our scheme is comparable with improved one, but complexity of its receiver is much lower. The paper organized as follows: In Section II we give a scheme proposed so far in literature[5, 6] to improve the FMDCSK technique. Furthermore, we analyze its characteristics and make an improvement based on differential-coding method. In Section III we propose a proper error correction algorithm for our scheme. Section IV shows the noise
performance of different schemes by computer simulation. Finally, Section V summarizes the results of this work. II.
DIFFERENTIAL-CODING METHOD FOR THE IMPROVED
FM-DCSK MODULATION SCHEME The basic idea of the differential chaos shift keying (DCSK) modulation technique is that every information bit transmitted is represented by two chaotic sample functions. The first sample function serves as a reference while the second one carries the information. Bit "1" is sent by transmitting a reference signal provided by a chaos generator twice in succession, while for bit "0", the reference chaotic signal is transmitted, followed by an inverted copy of the same signal. The two sample functions are correlated at the receiver; a positive correlation indicates that bit "1" has been received, while a negative value indicates bit "0". Without considering the frequency modulation, the DCSK and FM-DCSK technique are almost the same. However, because the noise and multi-path performance of FM-DCSK system is superior, so here the paper just is attention to FM-DCSK system, and the simulation results given are also from FM-DCSK system. FM-DCSK The time slots of the original communications systems are shown in the upper part of Fig. 1. In this figure, R k denotes the reference signal of the k-th
, Es Fl\(l-DCSK
.. L~
==] 1 I R I A1-1
I
I
,
I I
A1
I
I
I I
===~ '_ Il!1P~oved FM-DCSK '
Figure 1. Typical time slots for the FM-DCSK systems(upper figure) and for the improved system(lower figure). One bit is transmitted every 2 Ts in the orginal system; N bits are transmitted every (N+ 1 )Ts in the improved system
This work is sponsored by the program of New Century Excellent Talents in Universities (NCET-04-0601), NSFC (No.60272005), as well as the Key Project of Science and Technology in Fujian Province of China (No.2006H0039).
978-1-4244-2064-3/08/$25.00 ©2008 IEEE
Lin Wang2
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information bit, while I k denotes the information-bearing part. The drawback of FM-DCSK compared to conventional modulation schemes results form the fact that every information bit is transmitted by two sample functions. Consequently, the bit rate is halved and the transmitted energy per bit is doubled compared to conventional binary modulation schemes where every sample function represents one bit [6]. A possible improvement of FM-DCSK technique is as follows: instead of transmitting only one information-bearing signal, N bits are transmitted using the same reference [6].
Here we put a differential-coding method on the front of the transmitter. The differential-coding method is showed in the Fig. 3, used in conventional binary DPSK [8] (1)
Where the symbol EB represents modulo-2 addition and the over bar denotes complement. In Fig. 3 the encoded message was obtained by using Equation (1). In other words, the present code bit Ci,k is 1 if the information bit Ii,k and the prior coded bit Ci,k-l are the same, otherwise, Ci,k is O.
A possible configuration of the improved FM-DCSK transmitter and receiver is shown in Fig. 2[6]. The transmission of each N bits is preceded by a reference signal Ri(=Ii,o), after which the information-bearing signals are transmitted. This is done by changing the switch position in Fig. 2(a) in each Ts time instants. A delay network with N taps is applied in the transmitter configuration. In the receiver configuration, the information-bearings correlated with the first reference signal needs a delay network with N taps too showed in Fig. 2(b). As we know, the more delay implementation in the receiver, the harder to do the synchronization work and the higher complexity the receiver will be.
0
1
2
3
4
Information Ii,k: Differential-code 1 Ci,k:
1
0
0
1
1
0
1
1
k:
The waveforms that can be observed in the improved FM-DCSK communication systems are shown in the lower part of fig. 1, where Ts denotes the duration of one sample function while Es is the energy of a sample function. Every sample function carries information except the first one.
Figure 3.
Differential encoding (here i denotes the i-th frame information,N=4 )
As we know, before using the differential-coding method, the information is carried by the correlation between the reference signal and information-bearing one, after that the information is mapped between adjacent sample signals. So demodulation of the proposed modulation scheme can be easily performed by the demodulator which is used in the original FM-DCSK systems [4]. The configuration in Fig. 4 offers a simple receiver circuit solution for the improved scheme. R(t) 0 - - , - - - - - - - - - - _ _ _ _ .
R(t)
set)
~
~ I
I
Differe 1-1_C--:i
---~ll
.=....2
ntialcode
x)------+--u
set) ~
I
I
C
~
i-----:i..::....3- - - - - - - - - - J o - - t XI
(a): transmitter with pre-coding
(a): translnitter configuration --~-
{~] ~ -T----~---
~i~ ~
(b): normal FM-DCSK receiver
Decision circuit
Figure 4. improved FM-DCSK transmitter and receiver configurations with di fferential-codi ng.
III. (b): receiver configuration
Figure 2.
Improved FM-DCSK transmitter and receiver configurations.
A NEW ERROR CORRECTION ALGORITHM FOR
IMPROVED SCHEME WITH DIFFERENTIAL-CODING
In the original and improved FM-DCSK receivers, the decision is made by determining the correlations between the information-bearing signals and the reference. However, note that additional information can be gained from the correlations between every pair of signals is evaluated at the
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receiver and this extra information is used to improve the noise performance. Recently, at least three ways to exploit the additional correlations in the improved DCSK: Improved DCSK with noise reduction by averaging [5]; Improved DCSK with non-redundant "error correction" using the shortest path algorithm and improved DCSK with nonredundant "error correction" using the spanning tree algorithm [6, 7]. A receiver configuration with error correction capability can be implemented as follows. Instead of correlating information-bearing signals with the reference, we correlate it with all ofthe received signals as shown in Fig. 5.
fi,l
f'N~ 1,
Figure 6. The error correction and decision in receiver is done using a graph. The graph vertices ri.kare the received signals, while its edges Vi,k denote the value of the correlation. The graph has N+ 1 vertices and N+ 1 edges.
(j\i\f2
/)1,
------\~3) fi,3
Figure 5. The emor correction and decision in the receiver is done using a graph. The graph vertices are the received signals, while its edges represent the correlations between them. The graph has N+ 1 vertices and (N+ 1 )N/2 edges
(for example the broken line between 2 and 3 in Fig. 6) to reevaluate. The broken line in Fig. 6 like a weak part in a circle chain, the correlation can be re-estimated through the direction of arrowhead. If the number of negative value of the correlation (except the weak part) in the circle is an even number, that is to say the two signals, the two ends of the broken line, are probably the same, so we can redecide the information about the "weak part" is bit "1 ", otherwise is bit "0". The steps of the new error correction are as follows:
In Figure 5 each vertex of the graph represents a received signal, Le., vertexj represents riJ. The edges of the graph are the correlations between the received signals. The graph has N+ 1 vertices and (N+ 1)N/2 edges. The redundancy carried by the improved FM-DCSK signal can be exploited through some sophisticated algorithm [ 7] based on each correlation (edge) in Fig. 5 calculated. If the length of a frame is N+ 1, the schemes need to do (N+ 1)N/2 correlations, and the algorithm also will introduce high complexity. Similarly, we make use of the property between the adjacent signals based on our proposed scheme to improve the noise performance of the system. To model this process we use the graph shown in Fig. 6. In the transmitter shown in Fig. 4 the information between information-bearing signals and the reference is mapped between adjacent received signals. Here in Fig. 6 the edges between adjacent vertices are built to form a cycle, and before the decision, the N + 1 values of the correlation between adjacent signals are calculated. Every received signal is corrupted by noise. Obviously, the smaller the absolute value of correlation, the higher probability of a wrong decision. Thus we choose the smallest absolute value
•
Each reference signal is followed by N informationbearing signals, Le., instead of individual bits, N-bit symbols are transmitted in one block.
•
The differential-coding is put on the front of the transmitter, so the information is mapped between the adjacent signals.
•
The value of the correlations between adjacent of received signals are calculated (including the correlation between the reference signal and the last information-bearing one).
•
Consider the smallest absolute value as a weak part in the circle chain. Other values are considered right decisions.
•
We judge whether the number of negative correlations in the circle (except the "weak part") is even or odd. If the number is even, we decide the information about the "weak part" is bit "1", otherwise is bit "0".
IV.
PERFORMANCE EVALUATION
In order to determine the BER performance of the different FM-DCSK systems, several simulations have been performed in AWGN channels. The results of these simulations are summarized in Fig. 7.
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v.
CONCLUSION
In this paper, we make an enhancement for improved FM-DCSK to simplify its receiver configuration through differential-coding method. Meanwhile a new error correction algorithm has been presented in purposed system. Through simulation we can find that the noise performance of improved FM-DCSK based on differential-coding method is further enhanced if our error correction algorithm is introduced, and comparing with improved FM-DCSK using the shortest path algorithm, our proposed system owns a comparable noise performance and much lower complexity. ACKNOWLEDGMENT
The authors would like to thank Xin Min for their help on simulation sincerely.
14 EblNo(dB)
Figure 7. Noise perfonnance of normal FM-DCSK(solid curve with '*'marks), the improved system(N=4,solid curve with '+' marks), the improved system with differential-coding(N=4,solid curve with' 0' marks), the improved system with the new error correction algorithm based on differential-coding (N=4 solid curve with' 0' marks), the improved system with shortest path algorithm (N=4, solid curve with' 0' marks)
Solid curve with '*' marks shows the noise perforn1ance of the original FM-DCSK system. The noise performance of the improved system for N=4 is given by solid curve with '+' marks. Note that the energy per bit has been reduced from 2 Es to 5E/4 and using the technique about 2.04dB improvement can be achieved at the BER of 10-5• As shown above, in order to simplify the receiver of the improved system, the differential-coding method is put on the front of the transmitter. The solid curve with 'D' n1arks represents for the performance of this system. Comparing with the solid curve with '+' marks, we can find that the noise performances of the two systems are almost the saIne. The noise performance of improved system is further improved if differential-coding method is combined with our error correction algorithm as shown in Fig. 7. Solid curves with' (>' marks and' 0' marks show the noise performances of the improved system with our algorithm and the shortest path algorithm respectively. Note that the performances of latter vs. former systems save about 0.7dB at the BER of 10-5, but obviously our algorithm applied in the improved FMDCSK with differential-coding shows much lower complexity.
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