IPC classes for russian patent Method of generating pseudorandom signal chaotic sequence. RU patent 2335842. (RU 2335842):
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FIELD: electrical engineering.
SUBSTANCE: proposed method incorporates generating chaotic sequence of pseudorandom signals by numeric integration of a non-linear set of differential equations with the dynamic chaos and the variable step of time count directly proportional to the depth of modulation and the control effect time function.
EFFECT: improved correlation characteristics of generated signals.
2 cl, 1 dwg, 1 tbl
The invention relates to the field of radio engineering, in particular to the formation of pseudo-random signals, and can be used in systems with slojnimi signals.
Known analogue of the proposed method lies in the fact that a pseudo-random sequence of pulses is formed by forming each pulse at the moment when the sawtooth is the result of integrating the DC voltage increases to a voltage threshold reset (A.S. USSR № 733093. The method of forming a pseudo-random sequence of pulses and a device for its implementation. - IPC2: NC 3/84. - Bull. No. 17, 05.05.80). The disadvantage of analogue is that the accuracy of controlling the dispersion of intervals between pulses depends on the accuracy of formation of the sawtooth voltage.
Also known analogue of the proposed method lies in the fact that chaotic oscillations are generated by the generator of chaotic oscillations, containing a resistor, the first and second findings of which are connected with the first pins respectively of the first and second capacitors (Patent RU № 2246790. The generator of chaotic oscillations. - IPC7: NV 29/00. - Bull. No. 5, 20.02.2005). The disadvantage of analogue is the lack of reproducibility of the statistical characteristics of the oscillations generated by the generator when switching from one the th sample to another.
The closest analogue is the way of generating a chaotic sequence of pseudorandom signals, which consists in transforming a random sequence of signals via numerical integration of the nonlinear system of differential equations with dynamical chaos in a chaotic sequence of pseudo-random signals with a constant time step count. (Dmitriev A.S., Panas A.I. Dynamical chaos: new media for communication systems. - M.: Publishing house of Physical and mathematical literature, 2002. - S). This analog adopted for the prototype.
The disadvantage of this method, taken as a prototype, is a relatively large time intervals correlation generated signals.
The main task, which is aimed by the invention is the reduction of time intervals correlation influencing the improvement of the correlation characteristics of the generated signals.
The technical result of the invention is to improve the correlation characteristics of the generated chaotic sequence of pseudo-random signals.
This technical result is achieved in that, in the known method of forming a pseudo-random signals, which consists in transforming a random sequence of signals posredstvennoj integration nonlinear systems of differential equations with dynamical chaos in a chaotic sequence of pseudo-random signals, according to the proposed technical solution,
chaotic sequence of pseudo-random signals form integration with variable step time count is directly proportional to the modulation depth and time function of the control action determined by the formula:
,
where ti- step time reference
i is the number of steps
Δt is a constant step,
m is the modulation depth fluctuations,
fitemporal function of the control action, for example, fi=sgn(Xi), where Xi- signal value;
the modulation depth charge within m∈(0,M], where M>1.
The drawing shows graphs of correlation functions of the signal Xiof the Lorenz system.
The essence of the proposed method of forming a pseudo-random signals is as follows.
Initially generated a random sequence of signals is converted into a chaotic sequence of pseudo-random signals through numerical integration of the nonlinear system of differential equations with dynamic chaos, such as the Lorenz system,
Xi+1=Xi+ti(-σXi+σYi),
Yi+1=Yi+ti(rXi-Yi-XiZi),
Zi+1=Zi+ti(-bZi+XiYi),
with ereminym step time reference directly proportional to the modulation depth and time function of the control action determined by the formula:
ti=Δt(1+mfi-1),
where Xi, Yi, Zi- pseudo-random signals;
i is the number of steps;
Δt - constant step;
m is the modulation depth of impact, m∈ (0,M], where M>1;
ti- step time reference;
fi-1- time function controlwhere
X*, Y*, Z* coordinates of the equilibrium points of the system;
and is a constant equal to 0.1, 0.5, 0.8;
X*=Y*=Z*=r-1.
An example of implementing the method of forming a chaotic sequence of pseudo-random signals.
Initially generated random sequence X0=8.86, Y0=8.97 and Z0=27 was converted by numerical integration of the Lorenz system with the parameters of equations σ=10, r=28 and b=8/3 with variable step time reference tidetermined by the formula
ti=Δt(1+mfi-1), where Δt=0.01, m∈(0,10].
The results of the evaluation of correlation functions R(ti/Δt) of chaotic signals shown in the figure, where the solid line is for m=10, dashed line for m=0.
The use of the proposed method obtained significant is ukrashenie time intervals correlation chaotic signal sequence, shown in the table.
Table.
The changes within time intervals of correlation |
And |
m |
|
|
|
|
|
0.1 |
2 |
0.82 0.9... |
0.83 0.9... |
0.79 0.92... |
0.82...1.15 |
0.28 2.02... |
|
5 |
0.73 0.75... |
0.72 0.75... |
0.72 0.74... |
0.58 0.73... |
0.2...0.82 |
|
10 |
0.57 0.61... |
0.58 0.61... |
0.55 0.62... |
0.43...at 0.57 |
0.18...0.5 |
0.5 |
2 |
0.64 0.75... |
0.64 0.72... |
0.63 0.69... |
0.56 0.77... |
0.21 0.87... |
|
5 |
0.43 0.46... |
0.43 0.47... |
0.4...0.45 |
0.33...at 0.43 |
0.12...at 0.43 |
|
10 |
0.28 0.33... |
0.32 0.34... |
0.3 0.33... |
0.27 0.31... |
0.08 0.28... |
0.8 |
2 |
0.53...at 0.58 |
0.52...at 0.57 |
0.48...at 0.57 |
0.41...at 0.58 |
0.18...0.6 |
|
5 |
0.28 0.31... |
0.28 0.29... |
0.25...0.3 |
0.21 0.28... |
0.08 0.25... |
|
10 |
0.13 0.15... |
0.15...at 0.16 |
0.14 0.15... |
0.15 0.17... |
0.05...at 0.18 |
Where,,,,- correlation values for the levels of 0.8, 0.6, 0.4, 0.2, 0.0 relative to the maximum value of correlation functions τ0without external influence.
1. The method of forming a chaotic sequence of pseudorandom signals, which consists in transforming a random sequence of signals via numerical integration of the nonlinear system of differential equations with dynamical chaos in a chaotic sequence of pseudo-random signals, characterized in that the chaotic sequence of pseudo-random signals form integration with variable step time count is directly proportional to the modulation depth and time function of the control action determined by the formula:
ti=Δt(l+mfi-1);
where ti- step time reference;
i is the number of steps;
Δt - constant step;
m is the modulation depth fluctuations;
fitemporal function of the control action, for example, fi=sgn(Xi),
where Xi- signal value.
2. The method according to claim 1, characterized in that the modulation depth charge within m∈(0,M], where M>1.
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