CN103905358A - Improved type differential chaos shift keying DCSK confidentiality communication method - Google Patents

Abstract

The invention discloses a confidentiality communication method based on an improved type DCSK, and belongs to the technical field of signal transmission. In response to the confidentiality problem of the DCSK, after the improvement, information is scattered to two communication channels to be transmitted, a reference signal of the information in each channel is transmitted in the other channel, so that even the information in one channel is intercepted and captured in the transmission process, the original signal cannot be decoded, and the problem of low channel utilization rate is solved. Through the comparison of the original system bit error rate with the improved system bit error rate, the bit error rate of the improved type DCSK system is lower than the bit error rate of the traditional system in the data transmission process, and the channel utilization rate is much higher and confidentiality is much stronger. Through simulation it can be seen that the simulation result is consistent with the theoretical analysis, and confidentiality is greatly enhanced. Meanwhile, the improved type differential chaos shift keying DCSK confidentiality communication method is relatively low in complexity, easy for the project to be realized, and will has wide application prospect in the fields of images, military confidential information and the like.

Description

A kind of modified model differential Chaos Shift Keying DCSK secret communication method

Technical field

The present invention relates to data communication system, relate to more specifically the Development of Chaotic Secure Communication Method that uses modified model differential Chaos Shift Keying to transmit and receive data.

Background technology

Since nineteen ninety, chaotic communication and Chaotic Synchronous technology become a study hotspot of the world, home communications.The development of Control of Chaotic Synchronization theory, for chaos has been established theoretical foundation in the application of the communications field.Utilizing synchronous chaos to carry out secure communication is a current large focus of research in the world.Propose so far to communicate by letter and be mainly divided into the synchronous chaos developing: chaos is covered, chaotic parameter modulation, chaos shift keying and chaos spread spectrum.Chaos is covered and is belonged to chaos analog communication, and its excess-three generic is in chaotic digital communication.It is a kind of chaotic secret communication mode early proposing that chaos is covered, it is to utilize nonlinear kinetics Predicting Technique that the signal transmission of covering under chaotic signal is extracted, its realization depends on the synchronous realization degree of system, therefore high-quality communication service can't be provided, be only applicable to slow varying signal, can't well process fast changed signal and time varying signal.Chaotic parameter modulation be by send Information hiding in system parameters, this scheme key is the recovery extent of chaos system parameter, the demodulation of system parameters interference ratio is to external world more responsive, thereby has reduced communication efficiency.Chaos spread spectrum communication is exactly the pseudo random sequence that substitutes legacy communications system with chaos sequence, thereby adapts to the requirements at the higher level of people to future communications.Due to the Some features of chaotic signal itself, therefore the random performance of chaos spread spectrum sequence is good, and security performance is high, has good correlation properties, and useful number is many.The key of chaos spread spectrum communication is the selection of chaos spread spectrum sequence, is also an important aspect of at present chaotic communication being studied to the research of chaos sequence.Chaos shift keying is to have multiple chaos systems at transmitting terminal, according to the code value that will transmit, and the chaos system that gating is different.The chaotic signal that transmitted signal represents different chaos attractors by a section like this forms, and each chaos system of transmitting terminal has corresponding synchro system at receiving terminal.By each synchro system of signal driver receiving, reach synchronous situation according to each synchro system in a code-element period and judge the code value transmitting in this cycle.In chaotic digital communication system, chaos shift keying has very strong antijamming capability, and can effectively suppress multipath and disturb the impact on system, and it occupies an important position in communication plan, and numerous scholars think that it has good development prospect and using value.Chaos shift keying modulation technique has stronger anti-noise jamming and parameter mismatch ability, and power spectral density is lower, is therefore widely used in digital secret communication system.Parlitz etc. take the lead in having proposed chaos shift keying technology, have gone out chaos offset keying (CSK), chaos on-off keying (COOK), differential Chaos Shift Keying (DCSK), frequency modulation differential Chaos Shift Keying (FM-DCSK) etc. based on this derives from technology.Wherein CSK and COOK technology need to change according to the variation of signal to noise ratio the threshold judgement of system receiving terminal, cause the performance of system to reduce otherwise system has the higher error rate.For addressing this problem, G.Kolumban etc. have proposed again the differential Chaos Shift Keying (DCSK) based on non-coherent demodulation, and it has overcome CSK and COOK judging threshold and depend on the shortcoming of signal to noise ratio, does not need synchronously at receiving terminal simultaneously, simple in structure, but.The concrete intrinsic broadband properties of FM-DCSK, adopts and first chaotic signal is carried out to warbled method, thereby makes signal energy keep constant, but need to increase analog phase-locked look (APLL) and FM modulator at FM-DCSK transmitting terminal thus, makes circuit complicated.

The output signal of differential Chaos Shift Keying (DCSK) has intrinsic broadband properties and noiseproof feature, because it adopts non-coherent demodulation technology, needn't set up synchronously at transmitting-receiving two-end, and comparing legacy communications system has a lot of advantages.But its transmission rate is lower, and confidentiality is poor.

Summary of the invention

For above deficiency of the prior art, the object of the present invention is to provide one not only to ensure transmission rate but also improved fail safe, be difficult for being cracked, and error performance also increases, improved the modified model differential Chaos Shift Keying DCSK secret communication method of utilance., technical scheme of the present invention is as follows:

A kind of modified model differential Chaos Shift Keying DCSK secret communication method, it comprises the following steps:

101, adopt Logistic chaotic maps generator to produce two different chaotic signals at the transmitting terminal of chaos system and chaotic signal

and by chaotic signal

and chaotic signal

after spread spectrum coefficient M phase delay, obtain postponing chaotic signal respectively

with delay chaotic signal

102, by message to be sent

after serial/parallel conversion, be divided into sequence a and b that two-way speed reduces by half, then become two-way bipolar signal through level conversion

with

and by bipolar signal

with the delay chaotic signal obtaining in step 101 multiply each other and obtain signal transmission be placed in channel I and transmit, described bipolar signal

with the delay chaotic signal obtaining in step 101

multiply each other and obtain signal transmission

be placed in channel II and transmit, the output signal of described channel I is

the output signal of described channel II is

wherein channel I is in a symbol period T, front half period

transmission be reference signal, then half cycle transmission be signal transmission

half period before channel II transmission be reference signal, then half in cycle, transmission is signal

103, when the output signal of channel I in step 102

the output signal of channel II

be transferred to after the receiving terminal of chaos system, receiving terminal is decoded the signal receiving to revert to r1, n and r2, n;

104, by the signal r that in step 103, decoding recovers _{1, n}and r _{2, n}through the auto-correlation computation of correlator, the signal r receiving _{1, n}and r _{2, n}carry out related operation with the signal r (n+M) of time delay M position in spread spectrum coefficient M interval and draw y _{1, k}and y _{2, k};

105, by the signal y1 after auto-correlation computation in step 104, k and y2, k makes serial transmission into by parallel transmission, completes the transfer of data of secure communication.

Further, the expression formula of the Logistic chaotic maps generator in step 101 is

, wherein, x (n) is chaotic signal, μ is coefficient.

Further, in the time of μ=2.9 and μ=3.0, Logistic chaotic maps generator produces chaotic signal and chaotic signal

Further, in step 104, autocorrelative expression formula is

, wherein r (n) represents the signal receiving, r (n) comprises r _{1, n}and r _{2, n},, r (n+M) represent time delay the signal of M position, M is spread spectrum coefficient.

Advantage of the present invention and beneficial effect are as follows:

The present invention is directed to the shortcoming of prior art in chaos shift keying communication, proposed a kind of modified model DCSK

System, the output signal of differential Chaos Shift Keying (DCSK) has intrinsic broadband properties and antinoise spy

Property, because it adopts non-coherent demodulation technology, needn't set up synchronously at transmitting-receiving two-end, compare traditional communication

System has a lot of advantages.But its transmission rate is lower, and confidentiality is poor.For the problems referred to above, propose a kind of

Modified model DCSK secret signalling, has not only ensured transmission rate but also has improved fail safe, its guarantor

Close property is greatly strengthened, and be difficult for being cracked, and error performance also increases, and has improved profit

By rate.

Brief description of the drawings

Fig. 1 is the modulation principle figure of preferred embodiment of the present invention DCSK system;

The demodulation principle figure of Fig. 2 DCSK system;

Fig. 3 modified model DCSK modulation principle figure;

Fig. 4 modified model DCSK demodulation principle figure;

Fig. 5 modified model DCSK exchange sequence figure that receives information;

Fig. 6 tradition DCSK and the comparison of the modified model DCSK error rate;

The lower error rate of the different M values of Fig. 7 modified model DCSK;

Fig. 8 modified model DCSK difference

the lower error rate.

Embodiment

The invention will be further elaborated to provide the embodiment of an indefiniteness below in conjunction with accompanying drawing.

DCSK is the chaos shift keying secret signalling of current most study, system configuration is simple, the error rate is lower, antijamming capability is stronger, but there is in actual applications a problem: in a code-element period, the reference signal that transmitting terminal sends is identical with information signal or contrary, so channel security is lower, the information sending is easy to decode out signal transmission by analysis after being intercepted and captured, and the information that can only transmit 1bit in one-period cause channel utilization and transmission speed lower.For the privacy concerns of DCSK, through improving, make information dispersion two channel, and the reference signal of each road information is in another road transmission, even if a certain like this road information is intercepted and captured in transmitting procedure, also cannot decode primary signal, also solve the problem that channel utilization is low simultaneously.

1996, G.Kolumban proposed differential Chaos Shift Keying scheme (DCSK) and has solved CSK judging threshold and depend on the problem of signal to noise ratio.In DCSK scheme, the information exchange of each bit is crossed conversion, all formed by two sections of chaotic signals, first paragraph is " reference signal ", second segment carries useful information, in the time that being " 1 ", transmission information sends two sections of the same in-phase signals, and transmission information while being " 0 " transmitting terminal two segment signals anti-phase, after reference signal, be one section of anti-phase signal with it, what two segment signals were continuous sends.Receive after information signal and reference signal at receiving terminal, sent into correlation receiver, calculated the correlation properties of this two segment signal, carry out information recovery according to correlation properties positive and negative, correlation properties are greater than zero, and information signal is " 1 ", and correlation properties are less than zero information signal for " 0 ".The principles of modulation and demodulation of DCSK system

Figure is as Fig. 1, shown in 2.

Every bit information of DCSK system transmitting terminal is made up of the identical chaotic signal of two segment length, transmits reference signal the last period, and latter one section is transmitted information signal.First original binary signal is converted to bipolar signal through transducer, then in previous T/2, using M chaotic signal as sending with reference to signal, in a rear T/2, behind this M delayed reference signal M position, after modulating with bipolar signal, send.Wherein, if the signal sending is "+1 ", information signal is identical with reference signal; If the signal sending is " 1 ", information signal equals the reference signal after anti-phase so.Therefore, the output signal s of transmitting terminal (n) can be expressed as:

$s\left(n\right)\left\{\begin{array}{cc}x\left(n\right)& 1<n\&le;M\\ B\left(k\right)x(n-M)& M<n\&le;2M\end{array}---\left(1\right)\right.$

Wherein, x (n) is chaotic signal, and b (k) is bipolar signal, and M is spread spectrum coefficient.At receiving terminal, reference signal and information signal are carried out to related operation, the signal r (n) receiving is carried out to related operation with the signal r (n+M) of time delay M position in spread spectrum coefficient M interval.The output formula of correlator is:

$y\left(k\right)\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}r\left(n\right)r(n+M)---\left(2\right)$

Suppose that the signal receiving is r (n)=s (n)+ξ (n), wherein ξ (n) is interchannel noise.If receiver has been obtained synchronously, so, correlator is exported suc as formula shown in (3):

$\begin{array}{c}y\left(k\right)=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}r\left(n\right)r(n+M)\\ =\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\&lsqb;s\left(n\right)+\mathrm{\&xi;}\left(n\right)\&rsqb;\&lsqb;s(n+M)+\mathrm{\&xi;}(n+M)\&rsqb;\\ =b\left(k\right)\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}^2\left(n\right)\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\{x\left(n\right)\&lsqb;\mathrm{\&xi;}(n+M)+b\left(k\right)\mathrm{\&xi;}\left(n\right)\&rsqb;+\mathrm{\&xi;}\left(n\right)\mathrm{\&xi;}(n+M)\}\end{array}---\left(3\right)$

In formula (3), Section 1 is useful signal, and Section 2 is that average is zero random noise.Can find out that y (k) is consistent with the polarity of bipolar signal b (k), therefore can demodulate primary signal,

$m\&prime;\left(k\right)\left\{\begin{array}{cc}1& y\left(k\right)>0\\ 0& y\left(k\right)>0\end{array}---\left(4\right)\right.$

This system changes into and will information dispersion to two channel, transmit from traditional single channel transmission means.In the DCSK scheme that G.Kolumban etc. propose, every bit information of system transmitting terminal is made up of the identical chaotic signal of two segment length, transmits reference signal the last period, and latter one section is transmitted information signal.After intercepting and capturing, by observing the frequency spectrum of signal transmission, be easy to find out rule, be easy to crack out raw information, be therefore difficult to good confidentiality.And every bit information can only transmit bit, information transfer efficiency is low.For above-mentioned situation, a kind of modified model DCSK system is proposed, its confidentiality is greatly strengthened, and be difficult for being cracked, and error performance also increases, and has improved utilance.

In conjunction with example, the concrete steps that the present invention realizes modified model DCSK secret signalling are:

Step 1:

Chaology starts to be applied in secure communication, and wherein with the most use is to utilize Logistic system to produce pseudo-random number sequence, and its theoretical foundation is the sensitiveness of Chaos dynamic system for initial value and parameter..But Logistic system is only only chaos in the time that initial value and parameter are got the value in some particular range, not to initial value and parameter are all chaos arbitrarily.Secondly, though Logistic system in chaos state, the randomness of the pseudo random sequence producing under different initial values and parameter also has very big difference.The present invention considers that the Logistic system expression formula with following form is:

$x_{n+1}=f\left(x_n\right)=1-{\mathrm{\&mu;x}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">n</figure-callout>}}^2$

While adopting different initial values, the chaotic signal difference of generation.Input signal

modulated, therefore the characteristic of modulating system is just transfused to signal and changes.For example, in the time that input signal becomes square wave by cosine wave, system has been not just a chaos system.Therefore,, for secret object, will keep the signal after modulation

chaotic characteristic.In this employing

two value produce two different chaotic signals.

Step 2:

In tradition DCSK transmission plan, reference signal and modulation signal are in same channel, and the information of transmission is easy to decode out signal transmission by analysis after being intercepted and captured.And modified model DCSK introduces a channel on original DCSK basis again.Can find out information from accompanying drawing 3 transmitting terminals

first become two-way bipolar signal through going here and there and changing

with then postpone latter two different chaotic signal from two-way through M respectively

with

signal multiplies each other to obtain

with, be put into respectively in two channels and transmit, make reference signal separately separate in different channels and transmit with modulation signal.Due to the special orthogonality of chaotic signal, the signal in two transmitting channels is orthogonal.In a code-element period T, demodulation mode sequence of information is reduced to as shown in Figure 2.Information is dispersed on two channels in transmitting procedure, and frequency spectrum greatly expanded, and confidentiality is strengthened greatly.Even if listener intercepts

or

sequence, also cannot be decoded, and like this, just can realize secure communication completely.Article two, channel output signal

with

respectively suc as formula (6) (7):

$\begin{array}{cc}{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_{1,n}=\underset{j=0}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\&lsqb;x_{1,n}\&CenterDot;R_{n-2\mathrm{jM}}+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">b</figure-callout>}}_{2,k}{x}_{2,n-M}\&CenterDot;R_{N-(2j+1)M}\&rsqb;& \&ForAll;j\&Element;N\end{array},---\left(6\right)$

${\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">s</figure-callout>}}_{2,n}=\begin{array}{cc}\underset{j=0}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\&lsqb;x_{2,n}\&CenterDot;R_{n-2\mathrm{jM}}+{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1,k}{x}_{1,n-M}\&CenterDot;R_{n-(2j+1)M}\&rsqb;& \&ForAll;j\&Element;N\end{array}----\left(7\right)$

Wherein, with

chaotic signal,

with

be bipolar signal, Rn represents that length is the gate function of M, and M is spread spectrum coefficient, i.e. M bit chaotic signal modulation for each symbol.Pass after the speed of information rate and two paths of signals and final modulation between information rate is shown in (8), wherein rs, and rk and ri represent respectively channel speed, transformation rate and information rate.

rs=2Mrk=Mri(8)

In a symbol period T, (6) (7) can be reduced to (9) (10), wherein front half period

transmission be reference signal, then half

cycle transmission be the modulation signal on another road.If avoided a channel to be intercepted and captured, the problem that information will be cracked.

$s_{2,n}=x_{2,n}\&CenterDot;R_n+b_{1,k}{x}_{1,n-M}\&CenterDot;R_{n-M---\left(9\right)}$ $s_{1,n}=x_{1,n}\&CenterDot;R_n+b_{2,k}{x}_{2,n-M}\&CenterDot;R_{n-M}---\left(10\right)$

Step 3:

Accompanying drawing 4 can find out,

with

be transferred to after receiving terminal, front simultaneously get

with

front M position, after

get

with

rear M position and exchange channel, like this, recover again in the order of transmitting terminal multilated.Why take the mode of exchange to be intercepted and captured in transmitting procedure for fear of a certain road information, decode the weakness of primary signal, also solve the problem that channel utilization is low simultaneously.Signal after exchange is respectively, can find out from accompanying drawing 4,,, so just at receiving terminal, the order of upsetting before transmission is adjusted, respectively suc as formula (11) (12):

${\mathrm{<figure-callout\; id="3"\; label="r"\; filenames="HDA0000474913260000014.png,HDA0000474913260000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_{3,n}=\left\{\begin{array}{cc}{x}_{1,\mathrm{<figure-callout\; id="0"\; label="n"\; filenames="HDA0000474913260000014.png"\; state="\{\{state\}\}">n</figure-callout>}}& 0<t<T/2\\ {\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1,\mathrm{<figure-callout\; id="1"\; label="k\; X"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">k</figure-callout>}}{X}_{}{}_{1,n-M}& T/2<t<T\end{array}---\left(11\right)\right.$

$r_{4,n}=\{\begin{array}{cc}{x}_{2,\mathrm{<figure-callout\; id="0"\; label="n"\; filenames="HDA0000474913260000014.png"\; state="\{\{state\}\}">n</figure-callout>}}& 0<t<T/2\\ {\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">b</figure-callout>}}_{2,k}{x}_{2,n-M}& T/2<t<T\end{array}---\left(12\right)$

Step 4:

Readjust after order at receiving terminal, the signal of two-way carries out respectively auto-correlation computation, as shown in Figure 5.

Suppose that the two paths of signals of receiving at receiving terminal is r _{1, n}=s _{1, n}+ ξ _{1, n}, r _{2, n}=s _{2, n}+ ξ _{2, n}wherein ξ _{1, n}, ξ 2, n is expressed as additive white Gaussian noise (AWGN), and its average is 0, σ ₁ ²for ξ _{1, n}variance, σ ₂ ²for ξ _{2, n}variance.And as i ≠ j,

and ξ _{2, n}statistics is independent.The sequence after two-way merging is:

${\mathrm{<figure-callout\; id="3"\; label="r"\; filenames="HDA0000474913260000014.png,HDA0000474913260000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_{3,n}=\{\begin{array}{cc}{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_{1,\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">n</figure-callout>}}& 1<n\&le;\\ {\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">r</figure-callout>}}_{2,n}& M<n\&le;2M\end{array}---\left(13\right)$ $r_{4,n}=\{\begin{array}{cc}{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">r</figure-callout>}}_{2,\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">n</figure-callout>}}& 1<n\&le;\\ {\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_{1,n}& M<n\&le;2M\end{array}---\left(14\right)$

So, the output of first via correlator is suc as formula shown in (15):

$\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1,k={\mathrm{cor}}_M\left({\mathrm{<figure-callout\; id="3"\; label="r"\; filenames="HDA0000474913260000014.png,HDA0000474913260000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_{3,\mathrm{<figure-callout\; id="3"\; label="n\; r"\; filenames="HDA0000474913260000014.png,HDA0000474913260000021.png"\; state="\{\{state\}\}">n</figure-callout>}}{r}_{}{}_{3,n+M}\right)\\ =\underset{n=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="M\; r"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">M</figure-callout>}}{\mathrm{\&Sigma;}}}{r}_{}{}_{1,\mathrm{<figure-callout\; id="2"\; label="n\; r"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">n</figure-callout>}}{r}_{}{}_{2,n+M}\\ =\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}(x_{1,n}+{\mathrm{\&xi;}}_{1,n})({\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1,k}{x}_{1,n}+{\mathrm{\&xi;}}_{2,n+M})\\ ={\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1,k}\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_{1,\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}[x_{1,n}({\mathrm{\&xi;}}_{2,n+M}+{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1,k}{\mathrm{\&xi;}}_{1,n})+{\mathrm{\&xi;}}_{1,n}{\mathrm{\&xi;}}_{2,n+M}]\end{array}---\left(15\right)$

Formula (15) Section 1

required useful signal, Section 2

that average is zero random quantity, y _{1, k}and b _{1, k}polarity be consistent, can judge b _{1, k}shown in (16):

In like manner can derive (17) (18) two formulas:

${\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">y</figure-callout>}}_{2,k}={\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">b</figure-callout>}}_{2,k}\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_{2,\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}\&lsqb;x_{2,n}({\mathrm{\&xi;}}_{1,n+M}+{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">b</figure-callout>}}_{2,k}{\mathrm{\&xi;}}_{2,n})+{\mathrm{\&xi;}}_{2,n}{\mathrm{\&xi;}}_{1,n+M}\&rsqb;---\left(17\right)$ ${\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1,k}=\left\{\begin{array}{cc}1& {\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_{1,k}>0\\ 0& {\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_{1,k}<0\end{array}\right.---\left(16\right)$ ${\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">b</figure-callout>}}_{2,k}=\{\begin{array}{cc}1& {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">y</figure-callout>}}_{2,k}>0\\ 0& {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">y</figure-callout>}}_{2,k}<0\end{array}---\left(18\right)$

Step 5

Article two, channel recompile after auto-correlation, through parallel-serial conversion, rearrangement recovers data.As shown in Figure 5.

So far complete in steps.

The error performance of this modulation demodulation system and spread spectrum coefficient M and

in close relations.With the comparison of traditional modulation, analyze wherein P (0|1) probability of first channel, transmission ' 1 ' is judged as the error probability of ' 0 ', supposes b' _{1, K}=1, formula (15) becomes (19),

for the energy of signal within the T/2 time, on

Formula can be write as (20) formula:

$=,\begin{array}{c}{y}_k=\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_{1,\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}\&lsqb;x_{1,n}({\mathrm{\&xi;}}_{2,n+M}+{\mathrm{\&xi;}}_{1,N})+{\mathrm{\&xi;}}_{1,n+M}\&rsqb;\\ \underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_1^2+\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_{1,n}{\mathrm{\&xi;}}_{2,n+M}+\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_{1,n}{\mathrm{\&xi;}}_{1,n}+\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&xi;}}_{1,n}{\mathrm{\&xi;}}_{2,n+M}---\left(19\right)\\ =\frac{{\mathrm{<figure-callout\; id="2"\; label="E\; b"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">E</figure-callout>}}_b}{2}+\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_{1,n}{\mathrm{\&xi;}}_{2,n+M}+\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_{1,n}{\mathrm{\&xi;}}_{1,n}+\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&xi;}}_{1,n}{\mathrm{\&xi;}}_{2,n+M}<\end{array}$

$\mathrm{\&beta;}=\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_{1,n}{\mathrm{\&xi;}}_{2,n+M}+\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_{1,n}{\mathrm{\&xi;}}_{1,n}+\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&xi;}}_{1,n}{\mathrm{\&xi;}}_{2,n+M}<-\frac{E_b}{2}---\left(20\right)$

Formula (20) left side is a random process,

under (i, j) condition, x _i,n, ξ _i,nbetween statistics independent and

Average is 0, and under any i ≠ j condition, ξ _i,nand ξ _j,nto add up independently, σ ² ₁for ξ ₁side

Poor, σ ² ₂for ξ ₂variance, N ₁, N ₂the noise average power spectrum density that is respectively two channels, therefore has

above formula left side average μ=E (β)=0, variance is:

$\begin{array}{c}{\mathrm{\&sigma;}}^2=\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_{1,\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">n</figure-callout>}}^2{\mathrm{\&sigma;}}_1^2+\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{x_{1,\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">n</figure-callout>}}^2\mathrm{\&sigma;}}_2^2+{\mathrm{\&sigma;}}_1^2{\mathrm{\&sigma;}}_2^{2}M\\ =\frac{1}{2}{E}_b{\mathrm{\&sigma;}}_1^2+\frac{1}{2}{E}_b{\mathrm{\&sigma;}}_2^2+{\mathrm{\&sigma;}}_1^2{\mathrm{\&sigma;}}_2^{2}M---\left(21\right)\\ =\frac{1}{4}{\mathrm{<figure-callout\; id="1"\; label="E\; b\; N"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">E</figure-callout>}}_b{N}_{}{}_1+\frac{1}{4}{\mathrm{<figure-callout\; id="2"\; label="E\; b\; N"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">E</figure-callout>}}_b{N}_{}{}_2+\frac{1}{4}{N}_1{N}_{2}M\end{array}$

In chaos system, chaotic signal x _i,nwith x _{i, n+M}between correlation along with the increase of M decays fast.Suppose that M is greater than correlated characteristic die-away time,, along with the increase of M, β is close to Gaussian Profile.So the BER formulas that improves DCSK system can be written as formula (22).Wherein erfc (x) is compensating error function, $\mathrm{erfc}\left(x\right)=\frac{2}{\sqrt{\mathrm{\&pi;}}}{\&Integral;}_x^{\&infin;}2\mathrm{xp}\left({-t}^2\right)\mathrm{dt}$

$\begin{array}{c}\mathrm{BER}=P(\mathrm{\&beta;}<-\frac{E_b}{2})\\ =\frac{1}{\sqrt{2\mathrm{\&pi;\&sigma;}}}{\&Integral;}_{-\&infin;}^{-\frac{E_b}{2}}{e}^{-\frac{{\mathrm{\&beta;}}^2}{{2\mathrm{\&sigma;}}^2}}\mathrm{d\&beta;}\\ =\frac{1}{2}\mathrm{erfc}\left(\frac{{\mathrm{<figure-callout\; id="2"\; label="E\; b"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">E</figure-callout>}}_b}{2\sqrt{2\mathrm{\&sigma;}}}\right)\\ =\frac{1}{2}\mathrm{erfc}\&lsqb;\frac{\sqrt{2}}{2}{(\frac{N_1}{E_b}+\frac{N_2}{E_b}+\frac{N_1}{E_b}\frac{N_2}{E_b}M)}^{\frac{1}{2}}\&rsqb;\end{array}---\left(22\right)$

Adopt Logistic to produce chaos sequence and carry out emulation, the initial value that is used for producing chaotic signal at each bit period is not identical, between the chaotic signal sample value that same initial value produces, have very strong correlation, and the chaotic signal sample value that different initial value produces is incoherent.Utilize this correlation and non-correlation just can realize the non-coherent demodulation of chaotic signal at receiving terminal.

Logistic sequence is worked as μ ₁=2.9, μ ₂2=3.0 can both produce chaotic signal.Make initial value x _{i, 1}=0.1, and make the chaotic signal that 50 iteration produce and as carrier wave, primary signal is modulated, as shown in (23) (24).

$x_{1,n}={\mathrm{\&mu;}}_1{x}_{1,n}(1-{\mathrm{<figure-callout\; id="1"\; label="x"\; filenames="HDA0000474913260000021.png"\; state="\{\{state\}\}">x</figure-callout>}}_{1,n}^2)---\left(23\right)$ $x_{2,n}={\mathrm{\&mu;}}_2{x}_{2,n}(1-{\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="HDA0000474913260000013.png,HDA0000474913260000014.png"\; state="\{\{state\}\}">x</figure-callout>}}_{2,n}^2)---\left(24\right)$

Simulation result and performance evaluation: simulation transmitting procedure in wireless channel, suppose that interchannel noise meets AWGN and distributes.

Accompanying drawing 6 has shown the comparison of the error rate between traditional DCSK and modified model DCSK, and wherein that solid line is traditional DCSK, dotted line be modified model DCSK.Can find out that modified model DCSK improves a lot than traditional DCSK.The error performance of DCSK system before and after relatively improving under same spread coefficient M, when known signal to noise ratio is lower, two error rate of systems are more or less the same, and work as E _b/ N ₀while being greater than 7.5dB, the difference of the error rate starts to increase, and the modified model DCSK error rate is lower than traditional DCSK.At identical E _b/ N ₀under, improve DCSK than low 1～2 order of magnitude of traditional DCSK error rate; Under identical BER, signal to noise ratio is also different, works as BER=10-3, when M=10, improves DCSK and has approximately improved 6dB than traditional DCSK.

DCSK system error performance and M have much relations.Accompanying drawing 7 is that M is respectively the emulation of 10,20,30,40,50 o'clock modified model DCSK system error performances.Also increase when M increases system BER, error performance is also poorer thereupon.

Accompanying drawing 8 is under different signal to noise ratios, the relation between M and BER.As can be seen from the figure, under identical M, the larger BER of signal to noise ratio is lower.

Totally it seems, improved DCSK systematic function is obviously better than legacy system, in the error performance of transfer of data and confidentiality, is all greatly improved.

These embodiment are interpreted as being only not used in and limiting the scope of the invention for the present invention is described above.After having read the content of record of the present invention, technical staff can make various changes or modifications the present invention, and these equivalences change and modification falls into the inventive method claim limited range equally.

Claims (3)

1. a modified model differential Chaos Shift Keying DCSK secret communication method, is characterized in that, comprises the following steps:

101, adopt Logistic chaotic maps generator to produce two different chaotic signals at the transmitting terminal of chaos system

and chaotic signal

and by chaotic signal

and chaotic signal

after spread spectrum coefficient M phase delay, obtain postponing chaotic signal respectively

with delay chaotic signal

102, by message to be sent

after serial/parallel conversion, be divided into sequence a and b that two-way speed reduces by half, then become two-way bipolar signal through level conversion

with and by bipolar signal

with the delay chaotic signal obtaining in step 101

multiply each other and obtain signal transmission

be placed in channel I and transmit, described bipolar signal

with the delay chaotic signal obtaining in step 101

multiply each other and obtain signal transmission be placed in channel II and transmit, the output signal of described channel I is

the output signal of described channel II is

wherein channel I is in a symbol period T, front half period

transmission be reference signal, then half

cycle transmission be signal transmission

half period before channel II

transmission be reference signal, then half

cycle transmission be signal

103, when the output signal of channel I in step 102

the output signal of channel II

be transferred to after the receiving terminal of chaos system, receiving terminal is decoded the signal receiving to revert to r1, n and r2, n;

104, by the signal r that in step 103, decoding recovers _{1, n}and r _{2, n}through the auto-correlation computation of correlator, the signal r receiving _{1, n}and r _{2, n}carry out related operation with the signal r (n+M) of time delay M position in spread spectrum coefficient M interval and draw y _{1, k}and y _{2, k};

105, by the signal y1 after auto-correlation computation in step 104, k and y2, k makes serial transmission into by parallel transmission, completes the transfer of data of secure communication.

2. modified model differential Chaos Shift Keying DCSK secret communication method according to claim 1, is characterized in that, the expression formula of the Logistic chaotic maps generator in step 101 is

wherein, x (n) is chaotic signal, and μ is coefficient, when μ=2.9 He

μ=3.0 o'clock Logistic chaotic maps generator produces chaotic signal and chaotic signal

3. modified model differential Chaos Shift Keying DCSK secret communication method according to claim 1, is characterized in that, in step 104, autocorrelative expression formula is

wherein r (n) represents the signal receiving, and r (n) comprises r _{1, n}and r _{2, n},, r (n+M) represent time delay the signal of M position, M is spread spectrum coefficient.

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