CN106357363A - Chaotic mapping method suitable for code division multiple access spread spectrum communication and application of chaotic mapping method - Google Patents

Abstract

The invention discloses a chaotic mapping method suitable for code division multiple access spread spectrum communication and application of the chaotic mapping method. The chaotic mapping method includes: using ICMIC (iterative chaotic mapping with infinite collapses) mapping as input of improved Logistic mapping to build a new chaotic mapping model L-I-OSCM; specifically, using an iteration value of the ICMIC mapping as an input value of the improved Logistic mapping and an iteration value of the improved Logistic mapping as an input value of the ICMIC mapping. The chaotic mapping method is higher in attractor complexity and sensitivity to initial conditions. The application refers to using a chaotic sequence generated the chaotic mapping method as a spreading code to be applied to a visible light communication to realize multiple access of a user.

Description

A Chaotic Mapping Method Applicable to Code Division Multiple Access Spread Spectrum Communication and Its Application

technical field

The present invention relates to the field of spread spectrum communication, and more specifically relates to a chaotic mapping method suitable for a code division multiple access spread spectrum communication system and its application.

Background technique

Spread spectrum communication is widely used in high security communication of national defense and civil communication systems. Common spread spectrum sequences include m-sequence, Gold sequence and other sequences, which are generated by multi-stage shift registers or other delay elements through linear feedback, have ideal autocorrelation characteristics, correlation functions are periodic, and cross-correlation functions have large peaks . However, the number of PN codes with relatively good correlation characteristics is extremely limited. In a large-capacity communication system, the number of these sequences cannot meet the system capacity requirements, and the anti-interception is also poor, easy to be seen through, and the confidentiality is not strong, such as " Xiao Wei, Research on Chaotic Spread Spectrum and Wireless Channel Parameter Estimation Technology in CDMA Communication [D], Master's Degree Thesis, Xi'an, Xi'an University of Technology, 2007 "Technology published in the paper.

As a nonlinear dynamic system, the chaotic system has high pseudo-random characteristics, but it is deterministic, and it is highly sensitive to the initial state. If the chaotic sequence generated by the chaotic system is used as the spread spectrum communication The spread spectrum sequence will greatly improve the anti-interception performance of spread spectrum communication, and realize secure communication with good performance. Moreover, due to the high pseudo-randomness of the chaotic sequence, the chaotic sequence will never repeat.

At present, many scholars are studying the use of chaotic sequences as spreading codes to replace Gold sequences and m sequences used in spread-spectrum communication systems, such as the papers " Zimmer.Rodger E, Peterson.Roger L, Broth.David E , Introduction to Spread Spectrum Communications[M],NewYork,Prentice-Hall, 1995 ”, and “ S.Shanmugam,H.Leung,A novel M-ary chaotic spread spectrum communication scheme for DSRC system in ITS [C],Los Angeles , IEEE Vehicular Technology Conference Fall, Sept 2004, 803-807 "Disclosed technical content.

Papers " B.Ghobad.H, M.Clare.D, A chaotic direct-sequence spread-spectrum communication system[J], IEEE Trans.Communication 42, 1524～1527 " and " C.Vladeanu, I.Banica, SEAssad, Periodic chaotic spreading sequences with better correlation properties than conventional sequences-BER performances analysis [C], Iasi, Roamnia, International symposium on signals, circuits ans.systems, 2: 2003 " on the use of one-dimensional chaotic maps generated for direct sequences The possibility of spread spectrum codes in spread spectrum communication systems is proved, and by applying Gold sequences, m sequences and chaotic sequences to asynchronous communication systems for simulation, the analysis results show that chaotic sequences used in spread spectrum communication systems have traditional spread codes Incomparable advantages can effectively reduce the bit error rate of the system.

However, due to the simple mapping structure of the traditional chaotic mapping method, it is easy for malicious users to obtain key parameters through methods such as chaotic synchronization, which threatens its security performance.

Contents of the invention

In order to overcome the deficiencies of the above-mentioned prior art, the present invention proposes a chaotic mapping method suitable for code division multiple access spread spectrum communication systems based on the requirements of spread spectrum communication, which is a method with higher attractor complexity and higher initial Value Sensitive Chaotic Mapping Methods.

Another object of the present invention is to propose an application of a chaotic mapping method, using the chaotic sequence as a spreading code and applying it to a visible light communication system to realize multiple access for users.

In order to solve the problems of the technologies described above, the technical solution of the present invention is:

A chaotic mapping method suitable for code division multiple access spread spectrum communication, using ICMIC mapping as the input of the improved Logistic mapping, constructing a new chaotic mapping model L-I-OSCM; specifically, the iterative value of ICMIC mapping each time As the input value of the improved Logistic mapping, and the iteration value of the improved Logistic mapping is used as the input value of the ICMIC mapping.

Preferably, the chaotic mapping model L-I-OSCM is defined as:

Among them, f(x) is the LI-OSCM mapping function, x is the sequence value, a and b are parameter constants, n is the number of iterations, x _n is the value of the nth iteration, and the initial value x ₀ ∈ [-1,0 )∪(0,1], the value range of x _n+1 is [-1,0)∪(0,1], P is the number of oversampling.

An application of a chaotic mapping method, using a chaotic mapping model L-I-OSCM to generate a chaotic sequence, and using the chaotic sequence as a spreading code, is applied to a visible light communication system to realize multiple access for users.

Compared with prior art, the beneficial effect of the present invention is:

The invention proposes a chaotic mapping method suitable for a code division multiple access spread spectrum communication system, which is a novel chaotic mapping method: L-I-OSCM mapping. The mapping scheme is based on the improved logistic mapping and ICMIC mapping methods, and a new chaotic mapping method is designed, which can increase the complexity of the chaotic sequence attractor, improve the sensitivity of the initial value, increase the complexity of the probability density distribution, and further improve the spread spectrum communication. security.

Description of drawings

Figure 1 is a comparison of attractors between L-I-OSCM mapping and improved Logistic mapping.

Figure 2 is a comparison chart of initial value sensitivity between L-I-OSCM mapping and improved Logistic mapping.

Figure 3 is a distribution diagram of L-I-OSCM mapping sequence.

Fig. 4 is a characteristic diagram of L-I-OSCM mapping.

Figure 5 is a comparison chart of the probability distribution function of the L-I-OSCM mapping and the improved Logistic mapping.

Fig. 6 is a flow chart of code division multiple access for visible light communication based on chaotic sequences.

Fig. 7 is an analysis and comparison diagram of the bit error rate of different chaotic sequences as spreading codes.

detailed description

The present invention will be further described below in conjunction with the accompanying drawings, but the embodiments of the present invention are not limited thereto.

The focus of the invention is to improve the characteristics of the new chaotic sequence, making it more suitable for spread spectrum communication systems.

The invention proposes to use the ICMIC mapping as the input of the improved Logistic mapping to construct a new form of chaotic mapping. This design is equivalent to using the iterative value of the ICMIC map as the input value of the improved Logistic map each time, and the iterative value of the improved Logistic map is used as the input value of the ICMIC map. In addition, on the basis of constructing the map, each value is oversampled, such as the paper " H. Zhang, J. Guo, H. Wang, and R. Ding, Oversampled Chaotic Map Binary Sequences: Definition [C], Performance and Realization, IEEE Asiapacific conference on circuit and system.Tianjin, 2000, 618～621. "The description of the oversampling technology, the value of each iteration is brought into the function for oversampling processing, so that the value of the new mapping control parameter The range is very wide, which not only increases the difficulty of parameter estimation of the chaotic system, but also increases the number of spread spectrum sequences generated by changing the value of the parameters.

The definition of the L-I-OSCM mapping of the present invention's design is:

Among them, f(x) is the LI-OSCM mapping function, x is the sequence value, a and b are parameter constants, n is the number of iterations, and x _n is the value of the nth iteration. The initial value x ₀ ∈[-1,0)∪(0,1], the value range of x _n+1 is [-1,0)∪(0,1], and P is the number of oversampling.

The performance of each basic feature of the L-I-OSCM mapping is analyzed through MATLAB simulation. In the following, the parameter a of the new mapping takes a value of 2, and the value of b takes a value of 2.

(1) Attractor

The trajectory of chaotic motion in phase space is usually called "attractor", which is the performance of the stability of a system. Published by the paper " H.Zhang, J.Guo, H.Wang, and R.Ding, Oversampled Chaotic MapBinarySequences: Definition[C], Performance and Realization, IEEE Asiapacific conference on circuit and system. Tianjin, 2000, 618～621. " The structure and complexity of the attractor determine the dynamic characteristics of the chaotic system.

Fig. 1(a) is the L-I-OSCM map attractor graph proposed in this embodiment, which is compared with the attractor graph of the improved Logistic chaotic map (Fig. 1(b)). It can be seen from Figure 1 that the L-I-OSCM mapping attractor structure proposed in this embodiment is more complex, the phase space distribution is more scattered and messy, and the difference between adjacent iteration values is larger without any regularity, effectively reducing the It eliminates the possibility of deciphering the sequence through means such as phase space inversion, and is more suitable for secure communication systems.

(2) Initial value sensitivity

Initial value sensitivity is an important feature of chaotic mapping. It refers to assigning two initial values with a small difference to the chaotic system. They separated and became two completely different trajectories.

It can be seen from Fig. 2(a) that the difference between the initial values is only 10 ^-7 . After 4 iterations of the LI-OSCM chaotic map proposed in this paper, the trajectories separated. The improved Logistic map (as shown in Fig. 2(b) ) will go through 22 iterations before the trajectories separate. It shows that the chaotic map proposed in this paper has strong sensitivity to the initial value, and its performance is better than that of the improved Logistic map. This feature is not only conducive to generating a more considerable number of chaotic spread spectrum sequences, but also provides a reliable guarantee for chaotic security communication.

(3) Traversal

The ergodicity is also called the ergodicity of each state. By selecting a certain initial value, after multiple iterations, and observing the distribution of sequence values, the ergodicity of the chaotic sequence can be analyzed. From the technical achievements published in the paper " Xue Hua, Zhao Hengbin, Simulation Analysis of Strange Attractors of Several Kinds of Chaotic Systems [J]. Journal of Binzhou University, 26(6), 2010, 66～70", we can see that ergodicity is the randomness of chaotic sequence Performance. The better the ergodicity and randomness of the chaotic sequence, the lower the probability of being deciphered in the chaotic communication. As shown in Figure 3, the initial value is 0.3600, and 1500 iterations are performed on the mapping in this paper. As long as the number of iterations is large enough, the mapping in this embodiment can traverse all values in the range of [-1, 1] to form a nearly uniform class. randomly distributed.

(4) Correlation analysis

According to the technical results published in the paper " VCDSundersingh and Z.Wu, Frequency Domain Processing Based Chaos Communication for Cognitive Radio[M].Department of Electrical Engineering, Wright State University, 2010. " It can be seen that the correlation characteristics of chaos are an important factor to measure the quality of chaotic sequences. According to the standard, the chaotic sequence has extremely high autocorrelation and low cross-correlation, which is an important basis for the application of the chaotic sequence as a spread spectrum sequence in spread spectrum communication. The autocorrelation and cross-correlation functions of chaotic sequences are defined as:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Among them, x _1i and x _2i represent chaotic sequences with different initial values, Represents the mean of the chaotic sequence.

Fig. 4 is a characteristic map of normalized autocorrelation and cross-correlation mapped in this embodiment. It can be seen from the figure that the autocorrelation function of the chaotic sequence generated by the mapping in this embodiment is similar to the unit shock response function and has good autocorrelation characteristics. The value of the cross-correlation function of two chaotic sequences obtained by taking two values whose initial value differs by 10 ^-7 is close to zero.

(5) Probability distribution function

Using the method of least squares, an approximate probability distribution function of the chaotic map can be found. Figure 5 (Figure 5(a) is the probability distribution function of the L-I-OSCM mapping, and Figure 5(b) is the probability distribution function of the improved Logistic mapping) shows that the change range of the probability distribution function curve L-I-OSCM mapping is greater than that of the improved Logistic mapping , that is, the corresponding chaotic sequence can provide higher system security.

Furthermore, the new chaotic mapping model L-I-OSCM mapping method is used to generate a chaotic sequence, and the chaotic sequence is used as a spreading code and applied to the visible light communication system. The system block diagram is shown in Figure 6. With the help of the good autocorrelation characteristics of the chaotic sequence, the user's multiple access can be realized.

The parameters used in the simulation experiment are shown in the table below:

Table 1 Simulation parameter list

In this embodiment, the bit error rate of the system using three different chaotic sequences as spreading codes is compared, and the chaotic sequences are: improved Logistics mapping, ICMIC mapping and L-I-OSCM mapping.

It can be seen from Figure 7 that when the signal-to-noise ratio is 8dB, the bit error rates of the system using three different chaotic sequences as spreading codes in the VLC system (visible light communication system) are: improved Logistics mapping 10 ^-2.9 , ICMIC mapping 10 ^-2.8 and LI-OSCM mapping 10 ^-3.6 , obviously, compared with the improved Logistics mapping and ICMIC mapping, the LI-OSCM mapping proposed in this embodiment can provide a 2dB gain for the system. Therefore, using the chaotic sequence generated by LI-OSCM mapping as the spreading code can provide better system performance.

Based on the requirement of spread spectrum communication, the present invention proposes a chaotic mapping method suitable for code division multiple access spread spectrum communication system, which is a new type of chaotic mapping method: L-I-OSCM mapping. The mapping scheme is based on the improved logistic mapping and ICMIC mapping methods, and a new chaotic mapping method is designed, which can increase the complexity of the chaotic sequence attractor, improve the sensitivity of the initial value, increase the complexity of the probability density distribution, and further improve the spread spectrum communication. security.

The manual introduces the current technical background, analyzes the defects of traditional chaotic sequences as spreading codes, introduces the construction method of new chaotic maps in detail, and analyzes etc. compared and analyzed the performance improvement of L-I-OSCM mapping compared with traditional chaotic mapping. Finally, the new chaotic mapping model L-I-OSCM mapping method was used to generate a chaotic sequence, and the chaotic sequence was used as a spreading code to apply to the visible light communication system. The improvement of the system performance by the new chaotic sequence is analyzed.

The above descriptions are only examples of the present invention, and are not intended to limit the present invention. Various suitable modifications and variations are possible in the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims (3)

1. a kind of chaotic maps method being applied to CDMA bandspread communication is it is characterised in that map icmic as improvement The input of type logistic mapping, constructs a kind of new chaotic maps model l-i-oscm；Specifically every time icmic is mapped The input value that maps as modified model logistic of iterative value, and the iterative value conduct of modified model logistic mapping The input value of icmic mapping.

2. the chaotic maps method according to claim is it is characterised in that definition chaotic maps model l-i-oscm is:

Wherein, f (x) is l-i-oscm mapping function, and x is sequential value, and a, b are constants, and n is iterationses, x_nFor n-th Iteration value, initial value x₀∈ [- 1,0) and ∪ (0,1], x_n+1Span be [- 1,0) ∪ (0,1], p is over-sampling number of times.

3. the application of a kind of chaotic maps method described in claim 1 or 2 is it is characterised in that adopt chaotic maps model l- I-oscm produces chaos sequence, using this chaos sequence as spreading code, is applied to visible light communication system, to realize the many of user Location accesses.