CN105933104A - Multi-user difference chaotic communication system based on Walsh codes - Google Patents

Abstract

The invention provides a multi-user difference chaotic communication system based on Walsh codes, belonging to the field of communication systems. Through the construction of the data frame of a DCSK communication system, each frame includes N user data, each data frame distributes different Walsh codes to distinguish different users, in this way, each frame of signal carries N bit of user data. A transmitting end, by means of transmission reference, directly transmits the chaotic reference signals modulated by sign functions during the early half period of one frame period, and then transmits the data information of N users in parallel during the latter half period and distributes different orthogonal Walsh codes for each user. A receiving end demodulates the data information of each user by means of a correlated demodulation method and performs decision demodulation at the end, if the correlated demodulation result is greater than 0, the information signal determined for transmission is '+1', and if the correlated demodulation result is less than 0, the information signal determined for transmission is '-1'. The MU-DCSK is excellent in performance, so that the MU-DCSK is extensive in application prospects in the communication field.

Description

Multi-user's difference chaotic communication system based on Walsh code

Technical field

The present invention relates to data communication system, a kind of utilize chaos and communicating that Walsh code-phase combines Scheme, is a kind of new method improving system data transfer rate and security performance.

Background technology

Nonlinear science is the basic science of a research non-linear phenomena general character, is described as 20th century nature section " great revolution for the third time " learned.Chaos phenomenon is as a kind of motion specific in Kind of Nonlinear Dynamical System Form, is widely present in nature and human society, discloses in nature and human society and generally exists The unification of complexity, definitiveness and randomness, orderly and unordered unification.So-called chaos phenomenon, just Particular system produces, the most random, it is difficult to the random motion of prediction.

Chaotic communication is to utilize chaotic signal as carrier wave, replaces traditional sine wave carrier, will transmit signal It is hidden among chaotic carrier, at receiving terminal, utilizes the attribute of chaos or synchronizing characteristics to demodulate and transmitted Information.Chaotic signal has much special character, such as: aperiodicity, long-term unpredictability, similar In white noise wide spectrum characteristic, good from (mutually) correlation properties, Numerous and the equipment of generation simply etc., These character meet secret communication, spread spectrum (Spread Spectrum, SS) communication and multi-user communication system just System some particular/special requirement to signal.Therefore, chaos has tempting application in information security and the communications field Prospect and great practical value.Nearly two during the last ten years, and chaotic communication research achieves breakthrough, Multiple chaos communications is proposed.That is wherein updated by chaos offset keying and improved and grow up is mixed Ignorant keyed modulation systems is a kind of most chaotic digital communication method of research at present.

In chaos shift keying modulating system, the most typical two kinds of systems are respectively 1996 by Kolumban Et al. propose differential Chaos Shift Keying (differential chaos shift keying, DCSK) and 2000 Sushchik et al. proposes correlation delay keying (correlation delay shift keying, CDSK).DCSK Modulating system uses transmission-reference (Transmitted-Reference, T-R) pattern, each bit information of transmission Signal is made up of the chaotic signal that two segment length are identical, and first paragraph signal is reference signal, and second segment signal is used In carrying information signal.If the information sent is "+1 ", then send two segment signals identical, if sending letter Breath is "-1 ", then the signal carrying information is contrary with reference signal.Can not send out continuously to solve DCSK The number of delivering letters and the highest problem of efficiency of transmission, Sushchik in 2000 et al. proposes CDSK system, CDSK System be improved by instead of adder the switch in DCSK system so that the rate of information throughput is relative 1 times is improve in DCSK.But CDSK error rate of system is higher, cause the globality of CDSK system Can be good not as DCSK.

In consideration of it, the present invention is according to the deficiency of DCSK Yu CDSK, it is proposed that a kind of follow-on chaos key Prosecutor case multi-user based on Walsh code difference chaotic communication system (MU-DCSK).

Summary of the invention

The present invention is directed to prior art deficiency in the communication of multi-user's chaos shift keying, propose a kind of based on Walsh Multi-user's chaotic communication system of code.

The technical problem to be solved is: tied mutually with differential Chaos Shift Keying communication system by Walsh code Close；Multiple users send information simultaneously, improve system information transmissions speed；Study respectively at additive white gaussian Under noisy communication channel (additive white Gaussian noise channel, AWGN) and rayleigh fading channel, different The impact that the error performance of system is produced by user-user information signal and noise jamming.

The present invention solves the technical scheme of above-mentioned technical problem: mixed with difference with sign function by Walsh code Ignorant keying communication system combines, and transmitting terminal uses the mode of transmission reference, first before a frame period Half period directly transmits the chaos reference signal after being modulated by sign function, secondly, in second half of the cycle also Row transmits the data message of N number of user, and distributes different orthogonal Walsh codes for each user.Receiving terminal Correlation demodulation method is used to demodulate the data message of each user, first by the signal delay that receives half week Phase, secondly by the reception signal multiplication receiving signal and second half of the cycle of front half period, then adjust with user The Walsh code-phase distributing to different user time processed corresponding is taken advantage of, and finally makes decisions demodulation, if correlation demodulation Result more than zero, then judge that the information signal sent is "+1 ", if the result of correlation demodulation is less than zero, So judge that the information signal sent is as "-1 ".Result of determination is carried out different with the actual data message sent Or operation, count the data amount check of misjudgement, by the data amount check of misjudgement divided by the total data number sent, then The bit error rate of system can be tried to achieve.

Accompanying drawing explanation

Fig. 1 MU-DCSK of the present invention system sends block diagram；

Fig. 2 Rayleigh fading signal model；

Fig. 3 MU-DCSK of the present invention system receives block diagram；

Error rate of system performance map under Fig. 4 M=32 of the present invention rayleigh fading channel；

Error rate of system performance map under Fig. 5 M=128 of the present invention rayleigh fading channel；

Error rate of system performance map under Fig. 6 M=32AWGN of the present invention channel；

Error rate of system performance map under Fig. 7 M=128AWGN of the present invention channel；

Fig. 8 present system bit error rate changes performance map with spreading factor；

Detailed description of the invention

Below in conjunction with accompanying drawing and instantiation, the enforcement to the present invention is further described.

Fig. 1 show invention MU-DCSK system and sends block diagram, concrete steps: utilize Hadamard matrix Build 2ⁿRank Walsh code

$W_{2^n}=\left[\begin{array}{cc}{W}_{2^{(n-1)}}& W_{2^{(n-1)}}\\ W_{2^{(n-1)}}& -W_{2^{(n-1)}}\end{array}\right]---\left(1\right)$

Wherein:Each column all represents a Walsh code sequence, sequence length M=2ⁿ, and 2M For spreading factor, system one has N (N≤M) individual user.

Utilize Logistic to map and produce chaotic signal, then map generation chaos sequence x through sign function_i:

$\left\{\begin{array}{c}{y}_{i+1}=1-2y_i^2,\\ x_i=\mathrm{sgn}\left(y_i\right),\end{array}\right.y_i\∈(-1,1)---\left(2\right)$

(2) i=in formula (0,1,2 ... M), y_iIt is to be mapped the chaotic signal produced, x by Logistic_iIt is to reflect through sign function Chaos sequence after penetrating, x_i∈{+1,-1}.Chaos sequence E [x after sign function is modulated_i]=0, var[x_i]=1,E [*] represents average, and var [*] represents variance, and bit energy is constant.

The time simultaneously transmitting N-bit information is a frame period, and transmitting terminal uses the mode of transmission reference, First the front half period a frame period directly transmits chaos reference signal x after being modulated by sign function_i, Secondly, at the data message b of the N number of user of second half of the cycle parallel transmission_jx_i-M, and be that each user distributes not Same orthogonal Walsh code w_i,jIt is multiplied and sues for peace.The then transmission signal s of transmitting terminal_iSuch as formula (3):

$s_i=\left\{\begin{array}{cc}{x}_i& 0<i\&le;M\\ \underset{j=1}{\overset{N}{\&Sigma;}}{b}_j{w}_{i,j}{x}_{i-M}& (M+1)<i\&le;2M\end{array}\right.---\left(3\right)$

Can obtain and now transmit the bit energy of signal and be:

$E_b=e(\underset{i=1}{\overset{M}{\&Sigma;}}{x}_i^2+\underset{i=M+1}{\overset{2M}{\&Sigma;}}{\left(\underset{j=1}{\overset{N}{\&Sigma;}}{b}_j{w}_{i,j}{x}_i\right)}^2)=\frac{M(N+1)}{N}E\left(x_i^2\right)---\left(4\right)$

(3) b in formula_jFor jth road user data information, and b_j∈ {+1 ,-1}, w_i,jFor jth road user distribution

Walsh code.

Fig. 2 show the rayleigh fading channel of two independent pathways.Wherein α₁And α₂It is independent to meet Rayleigh The stochastic variable of distribution, τ is the time delay (τ ＜ ＜ 2M) between two paths.ζ_iMeeting average is zero, side Difference is N₀The additive white Gaussian noise of/2.Transmission signal is after rayleigh fading channel transmits, and receiving terminal receives Signal be:

r_i=α₁s_i+α₂s_i-τ+ζ_i (5)

Fig. 3 show MU-DCSK system and receives block diagram.Receiving terminal is first by the signal delay that receives half In the cycle, secondly front half period is received the reception signal multiplication of signal and second half of the cycle, then adjusts with user The Walsh code character distributing to different user time processed corresponding is multiplied, and finally makes decisions demodulation, then receiving terminal The output signal expression formula of middle correlator is:

$Z_j=\underset{i=M+1}{\overset{2M}{\&Sigma;}}{r}_i{r}_{i-M}{w}_{i,j}---\left(6\right)$

Utilize the orthogonality of Walsh codeAnd Chaotic Binary signalCan obtain:

$\begin{array}{c}{Z}_j=\underset{i=M+1}{\overset{2M}{\&Sigma;}}({\mathrm{\&alpha;}}_1\underset{k=1}{\overset{N}{\&Sigma;}}{b}_k{w}_{i,k}{x}_{i-M}+{\mathrm{\&alpha;}}_2\underset{k=1}{\overset{N}{\&Sigma;}}{b}_k{w}_{i,k}{x}_{i-M-\mathrm{\&tau;}}+{\mathrm{\&zeta;}}_i)({\mathrm{\&alpha;}}_1{x}_{i-M}+{\mathrm{\&alpha;}}_2{x}_{i-M-\mathrm{\&tau;}}+{\mathrm{\&zeta;}}_{i-M})w_{i,j}\\ =\underset{i=M+1}{\overset{2M}{\&Sigma;}}{\mathrm{\&alpha;}}_1^2{x}_{i-M}\left(\underset{k=1}{\overset{N}{\&Sigma;}}{b}_k{w}_{i,k}{x}_{i-M}\right)w_{i,j}+\underset{i=M+1}{\overset{2M}{\&Sigma;}}{\mathrm{\&alpha;}}_2^2{x}_{i-M-\mathrm{\&tau;}}\left(\underset{k=1}{\overset{N}{\&Sigma;}}{b}_k{w}_{i,k}{x}_{i-M-\mathrm{\&tau;}}\right)w_{i,j}\\ \mathrm{+2}{\mathrm{\&alpha;}}_1{\mathrm{\&alpha;}}_2\underset{i=M+1}{\overset{2M}{\&Sigma;}}{x}_{i-M-\mathrm{\&tau;}}\left(\underset{k=1}{\overset{N}{\&Sigma;}}{b}_k{w}_{i,k}{x}_{i-M}\right)w_{i,j}+\underset{i=M+1}{\overset{2M}{\&Sigma;}}({\mathrm{\&alpha;}}_1\underset{k=1}{\overset{N}{\&Sigma;}}{b}_k{w}_{i,k}{x}_{i-M}+{\mathrm{\&alpha;}}_2\underset{k=1}{\overset{N}{\&Sigma;}}{b}_k{w}_{i,k}{x}_{i-M-\mathrm{\&tau;}}){\mathrm{\&zeta;}}_{i-M}{w}_{i,j}\\ +\underset{i=M+1}{\overset{2M}{\&Sigma;}}({\mathrm{\&alpha;}}_1{x}_{i-M}+{\mathrm{\&alpha;}}_2{x}_{i-M-\mathrm{\&tau;}}){\mathrm{\&zeta;}}_i{w}_{i,j}+\underset{i=M+1}{\overset{2M}{\&Sigma;}}{\mathrm{\&zeta;}}_i{\mathrm{\&zeta;}}_{i-M}{w}_{i,j}\\ =A+B+C\end{array}---\left(7\right)$

$\begin{array}{c}A={\mathrm{\&alpha;}}_1^2{b}_j\underset{i=M+1}{\overset{2M}{\&Sigma;}}{x}_{i-M}^2{w}_{i,j}^2+{\mathrm{\&alpha;}}_2^2{b}_j\underset{i=M+1}{\overset{2M}{\&Sigma;}}{x}_{i-M-\mathrm{\&tau;}}^2{w}_{i,j}^2+2{\mathrm{\&alpha;}}_1{\mathrm{\&alpha;}}_2\underset{i=M+1}{\overset{2M}{\&Sigma;}}{x}_{i-M}\left(\underset{k=1}{\overset{N}{\&Sigma;}}{b}_k{w}_{i,k}{x}_{i-M-\mathrm{\&tau;}}\right)w_{i,j}\\ +\underset{i=M+1}{\overset{2M}{\&Sigma;}}{\mathrm{\&alpha;}}_1^2{x}_{i-M}\left(\underset{k=1,k\&NotEqual;j}{\overset{N}{\&Sigma;}}{b}_k{w}_{i,k}{x}_{i-M}\right)w_{i,j}+\underset{i=M+1}{\overset{2M}{\&Sigma;}}{\mathrm{\&alpha;}}_2^2{x}_{i-M-\mathrm{\&tau;}}\left(\underset{k=1,k\&NotEqual;j}{\overset{N}{\&Sigma;}}{b}_k{w}_{i,k}{x}_{i-M-\mathrm{\&tau;}}\right)w_{i,j}\end{array}---\left(8\right)$

$B=\underset{i=M+1}{\overset{2M}{\&Sigma;}}({\mathrm{\&alpha;}}_1\underset{k=1}{\overset{N}{\&Sigma;}}{b}_k{w}_{i,k}{x}_{i-M}+{\mathrm{\&alpha;}}_2\underset{k=1}{\overset{N}{\&Sigma;}}{b}_k{w}_{i,k}{x}_{i-M-\mathrm{\&tau;}}){\mathrm{\&zeta;}}_{i-M}{w}_{i,j}+\underset{i=M+1}{\overset{2M}{\&Sigma;}}({\mathrm{\&alpha;}}_1{x}_{i-M}+{\mathrm{\&alpha;}}_2{x}_{i-M-\mathrm{\&tau;}}){\mathrm{\&zeta;}}_i{w}_{i,j}---\left(9\right)$

$C=\underset{i=M+1}{\overset{2M}{\&Sigma;}}{\mathrm{\&zeta;}}_i{\mathrm{\&zeta;}}_{i-M}{w}_{i,j}---\left(10\right)$

(8) in formula, Section 1 and Section 2 are useful item, and other are multi-user interference item, and (9) formula and (10) formula are Noise jamming.Due to Logistic map autocorrelation sidelobe be zero, in (8) formula, Section 3 goes to zero, again by Orthogonal property in Walsh code, it is to avoid the rear binomial of (8) formulas forms stronger DC component, and this is greatly Reduce other users interference, improve error performance.Then, demodulation is i.e. realized according to following judgement:

$b_j=\left\{\begin{array}{cc}-1,& Z_j<0\\ +1,& Z_j\&GreaterEqual;0\end{array}\right.---\left(11\right)$

According to central limit theorem, correlator output Z_jIt is approximately Gauss distribution.In order to try to achieve MU-DCSK Error rate of system formula, need to solve Z_jAverage and variance.The statistical property of known Chaotic map sequence After Walsh code is modulated, still keep constant.It is below the some properties about Walsh code: for length For Walsh code w different for M_i,jAnd w_i,k, work as j=1 ... N, k=1 ... N, and during j ≠ k, E[w_i,jw_i,k]=E [w_i,j]=E [w_i,k]=0, var [w_i,jw_i,k]=var [w_i,j]=var [w_i,k]=1.

Without loss of generality, if jth user send information b_j=+1, utilize above character to obtain

$\begin{array}{c}E\&lsqb;Z_j\&rsqb;=E\&lsqb;A\&rsqb;+E\&lsqb;B\&rsqb;+E\&lsqb;C\&rsqb;\\ =E\&lsqb;{\mathrm{\&alpha;}}_1^2{b}_j\underset{i=M+1}{\overset{2M}{\&Sigma;}}{x}_{i-M}^2{w}_{i,j}^2+{\mathrm{\&alpha;}}_2^2{b}_j\underset{i=M+1}{\overset{2M}{\&Sigma;}}{x}_{i-M-\mathrm{\&tau;}}^2{w}_{i,j}^2\&rsqb;\\ =({\mathrm{\&alpha;}}_1^2+{\mathrm{\&alpha;}}_2^2)\frac{{\mathrm{NE}}_b}{(N+1)}\end{array}---\left(12\right)$

var[Z_j]=var [A]+var [B] var [C]+2cov [A, B]+2cov [A, C]+2cov [B, C] (13)

Wherein cov [X, Y] represents the covariance of X and Y.

$\mathrm{var}\&lsqb;A\&rsqb;=\mathrm{var}\&lsqb;{\mathrm{\&alpha;}}_1^2{b}_j\underset{i=M+1}{\overset{2M}{\&Sigma;}}{x}_{i-M}^2{w}_{i,j}^2+{\mathrm{\&alpha;}}_2^2{b}_j\underset{i=M+1}{\overset{2M}{\&Sigma;}}{x}_{i-M-\mathrm{\&tau;}}^2{w}_{i,j}^2\&rsqb;=0---\left(14\right)$

$\begin{array}{c}var\&lsqb;B\&rsqb;=var\&lsqb;\underset{i=M+1}{\overset{2M}{\&Sigma;}}({\mathrm{\&alpha;}}_1\underset{k=1}{\overset{N}{\&Sigma;}}{b}_k{w}_{i,k}{x}_{i-M}+{\mathrm{\&alpha;}}_2\underset{k=1}{\overset{N}{\&Sigma;}}{b}_k{w}_{i,k}{x}_{i-M-\mathrm{\&tau;}}){\mathrm{\&zeta;}}_{i-M}{w}_{i,j}+\underset{i=M+1}{\overset{2M}{\&Sigma;}}({\mathrm{\&alpha;}}_1{x}_{i-M}+{\mathrm{\&alpha;}}_2{x}_{i-M-\mathrm{\&tau;}}){\mathrm{\&zeta;}}_i{w}_{i,j}\&rsqb;\\ =({\mathrm{\&alpha;}}_1^2+{\mathrm{\&alpha;}}_2^2)MN\frac{{\mathrm{NE}}_b}{M(N+1)}\frac{N_0}{2}+({\mathrm{\&alpha;}}_1^2+{\mathrm{\&alpha;}}_2^2)M\frac{{\mathrm{NE}}_b}{M(N+1)}\frac{N_0}{2}\\ =({\mathrm{\&alpha;}}_1^2+{\mathrm{\&alpha;}}_2^2)\frac{{\mathrm{NE}}_b{N}_0}{2}\end{array}---\left(15\right)$

$\mathrm{var}\&lsqb;C\&rsqb;=\mathrm{var}\&lsqb;\underset{i=M+1}{\overset{2M}{\&Sigma;}}{\mathrm{\&xi;}}_i{\mathrm{\&xi;}}_{i-M}{w}_{i,j}\&rsqb;=\frac{M}{4}{N}_0^2---\left(16\right)$

May certify that, cov [A, B]=cov [A, C]=cov [B, C]=0, therefore, the output variance of correlator is:

$\mathrm{var}\&lsqb;Z_j\&rsqb;=\frac{({\mathrm{\&alpha;}}_1^2+{\mathrm{\&alpha;}}_2^2)N}{2}{E}_b{N}_0+\frac{M}{4}{N}_0^2---\left(17\right)$

Then the system bit error rate under rayleigh fading channel is:

$\begin{array}{c}BER({\mathrm{\&alpha;}}_1,{\mathrm{\&alpha;}}_2)=\frac{1}{2}\mathrm{Pr}ob(Z_i<0|Z_i=+1)+\frac{1}{2}\mathrm{Pr}ob(Z_i>0|Z_i=-1)\\ =\frac{1}{2}erfc\left(\frac{|E\&lsqb;Z_j\&rsqb;|}{\sqrt{2\mathrm{var}\&lsqb;Z_j\&rsqb;}}\right)\\ =\frac{1}{2}erfc{(\frac{{(N+1)}^2}{N({\mathrm{\&alpha;}}_1^2+{\mathrm{\&alpha;}}_2^2)}{\left(\frac{E_b}{N_0}\right)}^{-1}+\frac{M{(N+1)}^2}{2N^2{({\mathrm{\&alpha;}}_1^2+{\mathrm{\&alpha;}}_2^2)}^2}{\left(\frac{E_b}{N_0}\right)}^{-2})}^{-\frac{1}{2}}\end{array}---\left(18\right)$

Wherein, erfc is compensating error function,

Orderγ_b=γ₁+γ₂, then formula (18) can abbreviation be:

$BER\left({\mathrm{\&gamma;}}_b\right)=\frac{1}{2}erfc{(\frac{{(N+1)}^2}{N}{\left({\mathrm{\&gamma;}}_b\right)}^{-1}+\frac{M{(N+1)}^2}{2N^2}{\left({\mathrm{\&gamma;}}_b\right)}^{-2})}^{-\frac{1}{2}}---\left(19\right)$

Due to α₁And α₂Independence and Rayleigh distributed, order So γ₁And γ₂Obey following card side to be distributed:

$f\left(\mathrm{\&gamma;}\right)=\frac{1}{\stackrel{\&OverBar;}{\mathrm{\&gamma;}}}{e}^{-\frac{\mathrm{\&gamma;}}{\stackrel{\&OverBar;}{\mathrm{\&gamma;}}}},\mathrm{\&gamma;}\&GreaterEqual;0---\left(20\right)$

Then γ_b=γ₁+γ₂Distribution below obeying:

$f\left({\mathrm{\&gamma;}}_b\right)=\left\{\begin{array}{cc}\frac{{\mathrm{\&gamma;}}_b}{{\stackrel{\&OverBar;}{{\mathrm{\&gamma;}}_1}}^2}{e}^{-\frac{{\mathrm{\&gamma;}}_b}{\stackrel{\&OverBar;}{{\mathrm{\&gamma;}}_1}}},& E\&lsqb;{\mathrm{\&alpha;}}_1^2\&rsqb;=E\&lsqb;{\mathrm{\&alpha;}}_2^2\&rsqb;\\ \frac{1}{\stackrel{\&OverBar;}{{\mathrm{\&gamma;}}_1}-\stackrel{\&OverBar;}{{\mathrm{\&gamma;}}_2}}(e^{-\frac{{\mathrm{\&gamma;}}_b}{\stackrel{\&OverBar;}{{\mathrm{\&gamma;}}_1}}}-e^{-\frac{{\mathrm{\&gamma;}}_b}{\stackrel{\&OverBar;}{{\mathrm{\&gamma;}}_2}}}),& E\&lsqb;{\mathrm{\&alpha;}}_1^2\&rsqb;\&NotEqual;E\&lsqb;{\mathrm{\&alpha;}}_2^2\&rsqb;\end{array}\right.---\left(21\right)$

According to formula (19) and (21), the bit error rate that can obtain jth user is:

$BER={\&Integral;}_0^{\mathrm{\&infin;}}BER\left({\mathrm{\&gamma;}}_b\right)f\left({\mathrm{\&gamma;}}_b\right){\mathrm{d\&gamma;}}_b---\left(22\right)$

Work as α₁=1, α₂When=0, MU-DCSK BER formulas under awgn channel can be obtained:

${\mathrm{BER}}_{AWGN}=\frac{1}{2}erfc{(\frac{{(N+1)}^2}{N}{\left(\frac{E_b}{N_0}\right)}^{-1}+\frac{M{(N+1)}^2}{2N^2}{\left(\frac{E_b}{N_0}\right)}^{-2})}^{-\frac{1}{2}}---\left(23\right)$

Working as N=1, formula (23) is the BER formulas of FM-DCSK system.

Observation type (23) can obtain, affect BER because have N, M and E_b/N₀.As M and E_b/N₀It is fixing During value, certainly exist an optimum N value so that BER is minimum, i.e. systematic function is optimal.

Order:Y is obtained about N derivation:

$y^{\&prime;}=(1-\frac{1}{N^2}){\left(\frac{E_b}{N_0}\right)}^{-1}-M(1+\frac{1}{N})\frac{1}{N^2}{\left(\frac{E_b}{N_0}\right)}^{-2}---\left(24\right)$

Obtaining optimum N extreme value is:

$N_{opt}=\frac{1}{2}+\frac{1}{2}\sqrt{1+4M{\left(\frac{E_b}{N_0}\right)}^{-1}}---\left(25\right)$

(19) formula is had to understand, when M is the biggest, E_b/N₀The least, then corresponding N_optThe biggest；Otherwise, when M gets over Little, E_b/N₀Long-range, N_optThe least, its limit tends to 1., make E_b/N₀=10dB, M=32 and M=128 Time, N_optIt is respectively 1.37 and 2.01.

Utilize emulation experiment that the theoretical derivation of inventive algorithm is verified, discuss respectively and believe in Rayleigh fading The error performance of system under road and under awgn channel.

1. the performance evaluation under rayleigh fading channel

In order to analyze MA-DCSK system error performance under rayleigh fading channel, according to formula (22), discuss Two kinds of different path gain situations, it may be assumed that

Situation one: two paths has identical average energy gain, it may be assumed that

$E\&lsqb;{\mathrm{\&alpha;}}_1^2\&rsqb;=E\&lsqb;{\mathrm{\&alpha;}}_2^2\&rsqb;=1/2---\left(26\right)$

The average energy gain difference 10dB of situation two: two paths, that is:

$E\&lsqb;{\mathrm{\&alpha;}}_1^2\&rsqb;=1/11,E\&lsqb;{\mathrm{\&alpha;}}_1^2\&rsqb;=10/11---\left(27\right)$

In the case of being respectively M=32 and M=128 shown in Fig. 4 and Fig. 5, MU-DCSK system auspicious Error performance figure under profit fading channel.As seen from the figure, along with the increase of M, system error performance is disliked Change；Along with the increase of number of users N, MU-DCSK becomes more preferable on the contrary.Its reason is MU-DCSK System uses Walsh code to distinguish different user, eliminates the interference between user, only has noise in system Interference, so can greatly reduce the bit error rate of system.

Performance evaluation under 2.AWGN channel

Fig. 6 and Fig. 7 is respectively error rate of system with signal to noise ratio change curve: knowable to figure, by formula (23) The MU-DCSK bit error rate derived matches with Computer Simulation Monte Carlo.Number of users N mono-timing, BER is along with E_b/N₀Monotone decreasing.When spreading factor is the biggest, the curve interval between different number users reduces.

Fig. 8 is E_b/N₀=15dB, the bit error rate is with spreading factor change curve.As seen from the figure, during M ＜ 100, Numerical simulation and Monto Carlo emulation is the most identical, and the main cause producing this phenomenon is: when M relatively Hour, the incomplete Gaussian distributed of defeated variable of correlator.Secondly, under different user number N, system BER is increasing trend with the increase of M, and gradually tends to definite value.But there is cross point between different user number, This is owing to, in formula (23), the increase of M, the impact on different user number is different, i.e. N is the least, action effect The most obvious.

Claims (3)

1. multi-user's chaotic communication system based on Walsh code, its step is, will The Frame of DCSK communication system is transformed, and makes each frame comprise N number of user data, often The Walsh code differentiation different user that the distribution of individual Frame is different, the every frame signal so sent is taken Band Nbit user data.Transmitting terminal uses the mode of transmission reference, first a frame period Front half period directly transmit and mix reference signal after being modulated by sign function, secondly, The data message of the N number of user of second half of the cycle parallel transmission, and distribute different for each user Orthogonal Walsh code.Receiving terminal uses correlation demodulation method to demodulate the data message of each user, First the signal delay half period that will receive, secondly front half period is received signal with after The reception signal multiplication of half period, then it is corresponding to distribute to different user with user when modulating Walsh code character is multiplied, and finally makes decisions demodulation, if the result of correlation demodulation is more than zero, then Judge the information signal sent for "+1 ", if closing the result of demodulation less than zero, then judge The information signal sent is "-1 ".Result of determination is carried out XOR with the actual data message sent Operation, counts the data amount check of misjudgement, by the data amount check of misjudgement divided by the total data sent Number, then can try to achieve the bit error rate of system.

Communication plan the most according to claim 1, it is characterised in that the every frame of the program is believed Number carry Nbit user data, be strict orthogonal relation between each user data, eliminate Inter-user interference, and each frame data only comprise a reference signal.

Method of estimation the most according to claim 1, it is characterised in that permissible from accompanying drawing 3 Finding out, receiving terminal demodulation method uses correlation demodulation method, and the method uses simple delay to be correlated with , method is simple, it is achieved easily and circuit is simple, and hardware cost is low.