CN114050958B - Probability forming method and system based on Lorenz hyperchaotic model - Google Patents
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Abstract
The invention discloses a probability forming method and a probability forming system based on a Lorenz hyperchaotic model, wherein the method comprises the following steps: generating a first constellation and a third information bit sequence based on the pseudorandom bit sequence; generating a second constellation diagram by utilizing a Lorenz hyperchaotic model based on a third information bit sequence, and superposing CAP-4 constellation points on the first constellation diagram and CAP-4 constellation points on the second constellation diagram to obtain SP-CAP-16 constellation points on a third constellation diagram; the probability of the constellation points in the second constellation diagram has different probability distributions according to different quadrants of the constellation points in the first constellation diagram; and modulating and demodulating the PS-CAP-16 constellation points on the third constellation diagram. The invention utilizes Lorenz hyper-chaotic model as redundancy, and adopts a superposition mode to obtain PS-CAP-16 constellation points, thereby not only having lower complexity, but also having better BER performance.
Description
Technical Field
The invention relates to the technical field of communication, in particular to a probability forming method and system based on a Lorenz hyperchaotic model.
Background
Due to the emergence of various communication technologies, the application, virtual reality, 4k video and the like of the fifth generation mobile communication technology (5G) are continuously developed, and the search for a modulation technology with low cost and high reliability is a key research method for communication development. The carrierless amplitude/phase (CAP) modulation has the advantages of better spectrum utilization rate, low complexity and the like, and the multidimensional CAP modulation technology not only improves the data transmission rate, but also provides a larger space for further development of CAP system throughput, user multiple access and other performances.
Probability Shaping (PS) is a digital signal processing technology which can ensure that the capacity of a communication system reaches the Shannon limit, different probabilities are distributed according to different energies of constellation points, the constellation points with large energy have small transmission probability, the constellation points with small energy have large transmission probability, and the method can reduce the nonlinear influence on signals.
The commonly used encrypted chaotic bit sequences are: a Logistic chaotic bit sequence, a Chen chaotic bit sequence, a Chua's circuit chaotic bit sequence, a Lorenz chaotic bit sequence, a hyperchaotic bit sequence and the like. The chaotic bit sequences are used for generating corresponding 0 bit sequence and 1 bit sequence, and joint coding is carried out on the chaotic bit sequences and randomly generated information bits, so that constellation points with different probabilities can be generated. However, the above method has problems of complexity, large average transmission energy, and poor BER performance.
Disclosure of Invention
The invention aims to provide a probability forming method and a probability forming system based on a Lorenz hyper-chaos model, so as to reduce complexity, reduce average transmission energy and improve BER performance.
In order to achieve the above object, the present invention provides a probabilistic modeling method based on a Lorenz hyperchaotic model, wherein the method comprises:
step S1: generating a first constellation and a third information bit sequence based on the pseudorandom bit sequence; the first constellation diagram is a uniformly distributed square constellation diagram; the square constellation diagram consists of CAP-4 constellation points;
step S2: generating a second constellation diagram by using a Lorenz hyperchaotic model based on the third information bit sequence, wherein the second constellation diagram is a rectangular constellation diagram which is unevenly distributed and consists of CAP-4 constellation points;
and step S3: superposing the CAP-4 constellation points on the first constellation diagram and the CAP-4 constellation points on the second constellation diagram to obtain SP-CAP-16 constellation points on a third constellation diagram; the probability of the constellation points in the second constellation diagram has different probability distribution according to different quadrants of the constellation points in the first constellation diagram; wherein SP represents probability forming, CAP represents carrierless amplitude/phase, 16 represents the number of constellation points;
and step S4: and modulating and demodulating PS-CAP-16 constellation points on the third constellation diagram.
Optionally, the generating the first constellation and the third information bit sequence based on the pseudorandom bit sequence specifically includes:
step S11: based on the pseudo-random bit sequence, the pseudo-random bit sequence is converted into three parallel rows of information bit sequences, namely a first information bit sequence P1, a second information bit sequence P2 and a third information bit sequence P3;
step S12: and directly mapping the first information bit sequence P1 and the second information bit sequence P2 according to a gray mapping rule to form CAP-4 constellation points in a first constellation diagram.
Optionally, the generating a second constellation diagram by using a Lorenz hyperchaotic model based on the third information bit sequence specifically includes:
step S21: constructing a Lorenz hyperchaotic model;
step S22: setting a time step, solving the Lorenz hyperchaotic model by adopting a Runge-Kutta method to generate 3 chaotic sequences x, y and z, and transforming the 3 chaotic sequences to obtain 3 chaotic bit sequences w1, w2 and w3;
step S23: and mapping the third information bit sequence and the 3 chaotic bit sequences w1, w2 and w3 together to obtain a CAP-4 constellation point in a second constellation diagram.
Optionally, the CAP-4 constellation points on the first constellation diagram and the CAP-4 constellation points on the second constellation diagram are superimposed to obtain PS-CAP-16 constellation points on a third constellation diagram, where the specific formula is:
X CAP16 ＝α*X1 CAP4 +β*X2 CAP4
wherein, X1 CAP4 Representing CAP-4 constellation points, X2, on a first constellation diagram CAP4 Representing CAP-4 constellation points, X, on a second constellation diagram CAP16 Represents PS-CAP-16 constellation points on a three-constellation diagram, alpha and beta both represent weight coefficients, and alpha > beta.
Optionally, the probability of the constellation point in the second constellation map has different probability distributions according to different quadrants where the constellation point in the first constellation map is located, and specifically includes:
when the constellation point in the first constellation diagram is in a first quadrant, the probability of each constellation point in the second constellation diagram is 1/16,4/16,8/16,3/16 respectively; when the constellation point in the first constellation diagram is in a second quadrant, the probability of each constellation point in the second constellation diagram is 4/16,1/16,3/16,8/16 respectively; when the constellation point in the first constellation diagram is in a third quadrant, the probability of each constellation point in the second constellation diagram is 8/16,3/16,1/16,4/16 respectively; when the constellation point in the first constellation diagram is in the fourth quadrant, the probability of each constellation point in the second constellation diagram is 3/16,8/16,4/16,1/16 respectively.
Optionally, the modulating and demodulating the PS-CAP-16 constellation points on the third constellation diagram specifically includes:
step S41: forming and filtering the PS-CAP-16 constellation points on the third constellation diagram to obtain modulation signals;
step S42: sending the modulation signal to a channel by using a sending end for transmission;
step S43: receiving the modulation signal by using a receiving end;
step S44: performing matched filtering, down sampling and offline DSP signal processing on the received modulation signal to obtain a PS-CAP-16 constellation point with interference;
step S45: determining bit information of a CAP-4 constellation point on the first constellation diagram according to quadrant information of the PS-CAP-16 constellation point with interference; the bit information of the CAP-4 constellation point on the first constellation diagram comprises a fourth information bit sequence Q1 and a fifth information bit sequence Q2;
step S46: determining the CAP-4 constellation points on the second constellation diagram according to the PS-CAP-16 constellation points on the third constellation diagram and the CAP-4 constellation points on the first constellation diagram;
step S47: generating bit information of the CAP-4 constellation points on the second constellation diagram by utilizing a mapping rule table according to the quadrant information of the CAP-4 constellation points on the second constellation diagram, the corresponding quadrant information of the CAP-4 constellation points on the first constellation diagram and 3 chaotic bit sequences; the bit information of the CAP-4 constellation point on the second constellation diagram comprises a sixth information bit sequence Q3;
step S48: and performing parallel-to-serial conversion on the fourth information bit sequence Q1, the fifth information bit sequence Q2 and the sixth information bit sequence Q3 to obtain a converted pseudo-random bit sequence.
The invention also provides a probability modeling system based on the Lorenz hyperchaotic model, which comprises:
a first constellation determination module for generating a first constellation and a third information bit sequence based on the pseudorandom bit sequence; the first constellation diagram is a uniformly distributed square constellation diagram; the square constellation diagram consists of CAP-4 constellation points;
a second constellation determination module, configured to generate a second constellation based on the third information bit sequence by using a Lorenz hyperchaotic model, where the second constellation is a rectangular constellation that is unevenly distributed, and the rectangular constellation is composed of CAP-4 constellation points;
a superposition module, configured to superpose the CAP-4 constellation point on the first constellation diagram and the CAP-4 constellation point on the second constellation diagram, so as to obtain an SP-CAP-16 constellation point on a third constellation diagram; the probability of the constellation points in the second constellation diagram has different probability distribution according to different quadrants of the constellation points in the first constellation diagram; wherein SP represents probability forming, CAP represents carrierless amplitude/phase, 16 represents the number of constellation points;
and the modulation and demodulation module is used for modulating and demodulating the PS-CAP-16 constellation points on the third constellation diagram.
Optionally, the first constellation determination module specifically includes:
a serial-to-parallel conversion unit, configured to perform serial-to-parallel conversion on the pseudorandom bit sequence to obtain three parallel rows of information bit sequences, namely a first information bit sequence P1, a second information bit sequence P2, and a third information bit sequence P3;
and a mapping unit, configured to directly map the first information bit sequence P1 and the second information bit sequence P2 according to a gray mapping rule to form a CAP-4 constellation point in a first constellation diagram.
Optionally, the probability of the constellation point in the second constellation map has different probability distributions according to different quadrants where the constellation point in the first constellation map is located, which specifically includes:
when the constellation point in the first constellation diagram is in a first quadrant, the probability of each constellation point in the second constellation diagram is 1/16,4/16,8/16,3/16 respectively; when the constellation point in the first constellation diagram is in a second quadrant, the probability of each constellation point in the second constellation diagram is 4/16,1/16,3/16,8/16 respectively; when the constellation point in the first constellation diagram is in a third quadrant, the probability of each constellation point in the second constellation diagram is 8/16,3/16,1/16,4/16 respectively; when the constellation point in the first constellation diagram is in the fourth quadrant, the probability of each constellation point in the second constellation diagram is 3/16,8/16,4/16,1/16 respectively.
Optionally, the modulation and demodulation module specifically includes:
the forming filtering unit is used for forming and filtering the PS-CAP-16 constellation points on the third constellation diagram to obtain a modulation signal;
the channel transmission unit is used for transmitting the modulation signal to a channel by using a transmitting end for transmission;
a receiving unit, configured to receive the modulated signal by using a receiving end;
the preprocessing unit is used for performing matched filtering, down sampling and offline DSP signal processing on the received modulation signal to obtain a PS-CAP-16 constellation point with interference;
a first bit information determining unit, configured to determine bit information of a PS-CAP-16 constellation point on the first constellation according to quadrant information where the constellation point is located; the bit information of the CAP-4 constellation point on the first constellation diagram comprises a fourth information bit sequence Q1 and a fifth information bit sequence Q2;
a constellation point determining unit, configured to determine a CAP-4 constellation point on the second constellation according to a PS-CAP-16 constellation point on the third constellation and a CAP-4 constellation point on the first constellation;
a second bit information determining unit, configured to generate bit information of the CAP-4 constellation point on the second constellation diagram by using a mapping rule table according to the quadrant information of the CAP-4 constellation point on the second constellation diagram, the corresponding quadrant information of the CAP-4 constellation point on the first constellation diagram, and the 3 chaotic bit sequences; the bit information of the CAP-4 constellation point on the second constellation diagram comprises a sixth information bit sequence Q3;
and a parallel-to-serial conversion unit, configured to perform parallel-to-serial conversion on the fourth information bit sequence Q1, the fifth information bit sequence Q2, and the sixth information bit sequence Q3 to obtain a converted pseudo-random bit sequence.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a Lorenz hyperchaotic model-based probability forming method and system, wherein a Lorenz chaotic model is applied to constellation probability forming to form PS-CAP-16 constellation points. The invention greatly reduces the complexity of forming the PS-CAP-16 constellation points by utilizing a superposition method, the probability of the superposed PS-CAP-16 constellation points is distributed according to the energy size, the distribution probability of large energy (far from the origin) is small, and the distribution probability of small energy (near to the origin) is large, so that the average transmission energy is reduced, and the maximum information rate is realized. In addition, the present invention has better BER performance compared to uniformly distributed CAP-16.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of a probability modeling method based on a Lorenz hyper-chaotic model according to the present invention;
FIG. 2 is a mapping diagram of the Lorenz hyper-chaotic model of the present invention;
FIG. 3 is a schematic diagram of the process of forming PS-CAP-16 constellation points by superposition according to the present invention;
FIG. 4 is a probability distribution diagram of the PS-CAP-16 of the present invention;
FIG. 5 is a constellation diagram of the probability distribution of the PS-CAP-16 of the present invention;
FIG. 6 is a graph of SNR-BER of the present invention;
FIG. 7 is a first structure diagram of a Lorenz hyper-chaotic model-based probabilistic modeling system of the present invention;
FIG. 8 is a second structural diagram of a probabilistic modeling system based on a Lorenz hyper-chaos model according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a probability forming method and a probability forming system based on a Lorenz hyper-chaos model, so as to reduce complexity, reduce average transmission energy and improve BER performance.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Example 1
As shown in fig. 1, the invention discloses a probability modeling method based on a Lorenz hyperchaotic model, which comprises the following steps:
step S1: generating a first constellation and a third information bit sequence based on the pseudo-random bit sequence; the first constellation diagram is a uniformly distributed square constellation diagram; the square constellation consists of CAP-4 constellation points.
Step S2: and generating a second constellation diagram by using a Lorenz hyperchaotic model based on a third information bit sequence, wherein the second constellation diagram is a rectangular constellation diagram which is unevenly distributed and consists of CAP-4 constellation points.
And step S3: and superposing the CAP-4 constellation points on the first constellation diagram and the CAP-4 constellation points on the second constellation diagram to obtain SP-CAP-16 constellation points on a third constellation diagram. The probability of the constellation points in the second constellation diagram has different probability distribution according to different quadrants of the constellation points in the first constellation diagram; wherein SP represents probability shaping, CAP represents carrierless amplitude/phase, and 16 represents the number of constellation points.
And step S4: and modulating and demodulating PS-CAP-16 constellation points on the third constellation diagram.
The individual steps are discussed in detail below:
step S1: generating a first constellation diagram and a third information bit sequence based on the pseudo-random bit sequence, specifically comprising:
step S11: based on the pseudo-random bit sequence, the pseudo-random bit sequence is converted into three parallel rows of information bit sequences, namely a first information bit sequence P1, a second information bit sequence P2 and a third information bit sequence P3.
Step S12: directly mapping the first information bit sequence P1 and the second information bit sequence P2 according to a gray mapping rule to form CAP-4 constellation points in a first constellation diagram; the coordinates of the generated information bit sequence [00,01,11,10] corresponding to the CAP4 constellation points are: (1/sqrt (3)) [1,1; -1,1; -1, -1;1, -1].
Step S2: based on the third information bit sequence, generating a second constellation diagram by using a Lorenz hyperchaotic model, which specifically comprises:
step S21: constructing a Lorenz hyperchaotic model, wherein the specific formula is as follows:
wherein a and b represent system parameters, c represents system state feedback variables, and the values of a, b and c are set to 10, 28 and 8/3, respectively; x, y and z each represent a system state variable, the initial values of x, y and z (x) 0 ，y 0 ，z 0 ) Set to (-1.6, -0.5, 21);
representing the derivatives of x, y and z, respectively.
Step S22: setting a time step, solving the Lorenz hyperchaotic model by adopting a Runge-Kutta (Runge-Kutta) method to generate 3 chaotic sequences x, y and z, and transforming the 3 chaotic sequences to obtain 3 chaotic bit sequences w1, w2 and w3; the 3 chaotic bit sequences are solution sequences with x, y and z as transformation, namely the 3 chaotic bit sequences are all 0,1 chaotic bit sequences. As shown in fig. 8, the chaotic bit sequence is also called a masking factor.
In the present invention, the specific rule for generating 0,1 chaotic bit sequence is as follows:
wherein w1, w2 and w3 respectively represent chaotic bit sequences, mod represents complementation, floor represents rounding down the decimal, and x, y and z all represent chaotic sequences. A map of the Lorenz hyper-chaotic model is shown in fig. 2.
Step S23: and mapping together based on the third information bit sequence and the 3 chaotic bit sequences w1, w2 and w3 to obtain a CAP-4 constellation point in a second constellation diagram. In this embodiment, the chaotic bit sequence and the third information bit sequence map CAP-4 constellation points with unequal probability distribution. The specific mapping rule is shown in table 1, and this mapping relationship also has a relationship with the quadrant where the square CAP4 constellation point is located, and the CAP-4 constellation point in the second constellation diagram is: (1/sqrt (10)) [3,1;3, -1; -3,1; -3, -1].
TABLE 1 constellation point mapping rule Table
And step S3: superposing the CAP-4 constellation points on the first constellation diagram and the CAP-4 constellation points on the second constellation diagram to obtain PS-CAP-16 constellation points on a third constellation diagram, wherein the specific formula is as follows:
X CAP16 ＝α*X1 CAP4 +β*X2 CAP4
wherein, X1 CAP4 Representing CAP-4 constellation points on a first constellation, X2 CAP4 Representing CAP-4 constellation points, X, on a second constellation diagram CAP16 Represents PS-CAP-16 constellation points on a three-constellation diagram, alpha and beta both represent weight coefficients, and alpha > beta.
In this embodiment, the constellation points of the two transmitting ends are normalized; in order to keep the superimposed constellation points within the respective quadrant according to the square constellation points, α > β. In the present invention, α =8 and β =2.5. The stacking process is shown in fig. 3; FIG. 4 is a schematic diagram of the probability distribution of PS-CAP-16 according to the present invention; FIG. 5 is a constellation diagram of the probability distribution of the PS-CAP-16 of the present invention.
The probability of the constellation point in the second constellation map has different probability distributions according to different quadrants where the constellation point in the first constellation map is located, and specifically includes:
when the constellation point in the first constellation diagram is in a first quadrant, the probability of each constellation point in the second constellation diagram is 1/16,4/16,8/16,3/16 respectively; when the constellation point in the first constellation diagram is in a second quadrant, the probability of each constellation point in the second constellation diagram is 4/16,1/16,3/16,8/16 respectively; when the constellation point in the first constellation diagram is in a third quadrant, the probability of each constellation point in the second constellation diagram is 8/16,3/16,1/16,4/16 respectively; when the constellation point in the first constellation diagram is in the fourth quadrant, the probability of each constellation point in the second constellation diagram is 3/16,8/16,4/16,1/16 respectively.
The probability distribution scheme of the invention is obtained by the constellation point mapping rule in table 1, and the specific constellation point distribution probability rule is shown in table 2 in detail.
TABLE 2 constellation Point distribution probability rules
In table 2, TX1 denotes a first constellation, and TX2 denotes a second constellation.
And step S4: modulating and demodulating the PS-CAP-16 constellation points on the third constellation diagram, which specifically comprises:
step S41: forming and filtering the PS-CAP-16 constellation points on the third constellation diagram to obtain modulation signals; specifically, the PS-CAP-16 constellation point on the third constellation is convolved with two mutually orthogonal filters and added to obtain a modulation signal.
Step S42: and sending the modulation signal to a channel by using a sending end for transmission.
Step S43: and receiving the modulation signal by using a receiving end.
Step S44: performing matched filtering, down sampling and offline DSP signal processing on the received modulation signal to obtain a PS-CAP-16 constellation point with interference; specifically, the received modulation signal is deconvoluted with an orthogonal filter, and then is subjected to down-sampling and off-line DSP signal processing to obtain an interfering PS-CAP-16 constellation point D i ＝(D ix ,D iy ) (ii) a Wherein D is i Represents the ith interfering PS-CAP-16 constellation point, D ix Representing the coordinates corresponding to the x-axis, D iy Representing coordinates corresponding to the y axis;
step S45: determining bit information of a CAP-4 constellation point on the first constellation diagram according to quadrant information of the PS-CAP-16 constellation point with interference; the bit information of the CAP-4 constellation point on the first constellation includes a fourth information bit sequence Q1 and a fifth information bit sequence Q2.
For example, if constellation point D i ＝(D ix ，D iy ) In (D) ix >0 and D iy >0, the quadrant in which it is located is the first quadrant, and according to the mapping relationship in table 1, we can demodulate that its bit information is: 00; similarly, when the constellation point is located in other boundaries, the bit information can be demodulated.
Step S46: determining the CAP-4 constellation points on the second constellation diagram according to the PS-CAP-16 constellation points on the third constellation diagram and the CAP-4 constellation points on the first constellation diagram, wherein the specific formula is as follows:
X2′ CAP4 ＝X′ CAP16 -α*X1′ CAP4
wherein, X2' CAP4 Representing CAP-4 constellation points, X 'on the second constellation diagram' CAP16 Represents PS-CAP-16 constellation points, X1 'on a third constellation diagram' CAP4 Representing the CAP-4 constellation points on the first constellation.
Step S47: generating bit information of the CAP-4 constellation points on the second constellation diagram by utilizing a mapping rule table according to the quadrant information of the CAP-4 constellation points on the second constellation diagram, the corresponding quadrant information of the CAP-4 constellation points on the first constellation diagram and 3 chaotic bit sequences; the bit information of the CAP-4 constellation point on the second constellation includes a sixth information bit sequence Q3.
Step S48: and performing parallel-to-serial conversion on the fourth information bit sequence Q1, the fifth information bit sequence Q2 and the sixth information bit sequence Q3 to obtain a converted pseudo-random bit sequence.
Because there may be other interferences such as noise during channel transmission, there may be errors in the obtained fourth information bit sequence Q1, the obtained fifth information bit sequence Q2, and the obtained sixth information bit sequence Q3 as compared with the first information bit sequence P1, the obtained second information bit sequence P2, and the obtained sixth information bit sequence P3, respectively, and there may be an error, and the transformed pseudo-random bit sequence may not be completely the same as the pseudo-random bit sequence before transformation, that is, there is an error.
As shown in FIG. 6, the BER performance of two kinds of CAP-16 under different SNR conditions is shown, and it can be seen that the probability modeling method provided by the invention has better BER performance compared with the uniformly distributed CAP-16.
The invention provides a probability forming method based on a Lorenz hyperchaotic model, which applies the Lorenz hyperchaotic model to constellation probability forming to form PS-CAP-16 constellation points. The invention greatly reduces the complexity of forming the PS-CAP-16 constellation points by utilizing a superposition method, the probability of the superposed PS-CAP-16 constellation points is distributed according to the energy size, the distribution probability of large energy (far from the origin) is small, and the distribution probability of small energy (near to the origin) is large, so that the average transmission energy is reduced, and the maximum information rate is realized. And also has better BER performance compared to uniformly distributed CAP-16.
Example 2
As shown in fig. 7-8, the present invention further provides a probabilistic modeling system based on the Lorenz hyperchaotic model, wherein the system comprises:
a first constellation determination module 701, configured to generate a first constellation and a third information bit sequence based on a pseudo-random bit sequence; the first constellation diagram is a uniformly distributed square constellation diagram; the square constellation consists of CAP-4 constellation points.
A second constellation diagram determining module 702, configured to generate a second constellation diagram by using a Lorenz hyperchaotic model based on the third information bit sequence, where the second constellation diagram is a rectangular constellation diagram that is unevenly distributed, and the rectangular constellation diagram is composed of CAP-4 constellation points.
A superposition module 703, configured to superpose the CAP-4 constellation point on the first constellation diagram and the CAP-4 constellation point on the second constellation diagram, so as to obtain an SP-CAP-16 constellation point on a third constellation diagram; the probability of the constellation points in the second constellation diagram has different probability distribution according to different quadrants of the constellation points in the first constellation diagram; wherein SP represents probability shaping, CAP represents carrierless amplitude/phase, and 16 represents the number of constellation points.
A modulation and demodulation module 704, configured to modulate and demodulate PS-CAP-16 constellation points on the third constellation diagram.
As an optional implementation manner, the first constellation diagram determining module 701 of the present invention specifically includes:
and the serial-parallel conversion unit is used for converting the pseudo-random bit sequence into three parallel rows of information bit sequences which are a first information bit sequence P1, a second information bit sequence P2 and a third information bit sequence P3 respectively through serial-parallel conversion.
And a mapping unit, configured to directly map the first information bit sequence P1 and the second information bit sequence P2 according to a gray mapping rule to form a CAP-4 constellation point in a first constellation diagram.
As an optional implementation manner, the modem module 704 of the present invention specifically includes:
and the forming filtering unit is used for forming and filtering the PS-CAP-16 constellation points on the third constellation diagram to obtain a modulation signal.
And the channel transmission unit is used for transmitting the modulation signal to a channel by using the transmitting end for transmission.
A receiving unit, configured to receive the modulated signal by using a receiving end.
And the preprocessing unit is used for performing matched filtering, down sampling and offline DSP signal processing on the received modulation signal to obtain the PS-CAP-16 constellation points with interference.
A first bit information determining unit, configured to determine bit information of a PS-CAP-16 constellation point on the first constellation according to quadrant information where the constellation point is located; the bit information of the CAP-4 constellation point on the first constellation includes a fourth information bit sequence Q1 and a fifth information bit sequence Q2.
A constellation point determining unit, configured to determine a CAP-4 constellation point on the second constellation according to the PS-CAP-16 constellation point on the third constellation and the CAP-4 constellation point on the first constellation.
A second bit information determining unit, configured to generate bit information of the CAP-4 constellation point on the second constellation diagram by using a mapping rule table according to the quadrant information of the CAP-4 constellation point on the second constellation diagram, the corresponding quadrant information of the CAP-4 constellation point on the first constellation diagram, and the 3 chaotic bit sequences; the bit information of the CAP-4 constellation point on the second constellation includes a sixth information bit sequence Q3.
And a parallel-to-serial conversion unit, configured to perform parallel-to-serial conversion on the fourth information bit sequence Q1, the fifth information bit sequence Q2, and the sixth information bit sequence Q3 to obtain a converted pseudo-random bit sequence.
The same parts as those in embodiment 1 will not be described in detail.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (6)
1. A probability modeling method based on a Lorenz hyperchaotic model is characterized by comprising the following steps:
step S1: generating a first constellation and a third information bit sequence based on the pseudorandom bit sequence; the first constellation diagram is a uniformly distributed square constellation diagram; the square constellation diagram consists of CAP-4 constellation points;
the generating the first constellation diagram and the third information bit sequence based on the pseudorandom bit sequence specifically includes:
step S11: based on the pseudo-random bit sequence, performing series-parallel conversion to obtain three parallel rows of information bit sequences, wherein the three parallel rows of information bit sequences are a first information bit sequence P1, a second information bit sequence P2 and a third information bit sequence P3 respectively;
step S12: directly mapping the first information bit sequence P1 and the second information bit sequence P2 according to a gray mapping rule to form CAP-4 constellation points in a first constellation diagram; the coordinates of each generated row of information bit sequence [00,01,11,10] corresponding to the CAP4 constellation point in the first constellation diagram are: (1/sqrt (3)) [1,1; -1,1; -1, -1;1, -1];
step S2: generating a second constellation diagram by using a Lorenz hyperchaotic model based on the third information bit sequence, wherein the second constellation diagram is a rectangular constellation diagram which is unevenly distributed and consists of CAP-4 constellation points;
the generating a second constellation diagram by using a Lorenz hyperchaotic model based on the third information bit sequence specifically includes:
step S21: constructing a Lorenz hyperchaotic model, wherein the specific formula is as follows:
wherein,aandbare all indicative of a parameter of the system,ca feedback variable representing the state of the system,a、bandcare set to 10, 28 and 8/3, respectively;x、yandzare all representative of the state variables of the system,x、yandzinitial value of (A), (B)x 0 ，y 0 ，z 0 ) Set to (-1.6, -0.5, 21);
、/>
、/>
respectively representx、yAndza derivative of (a);
step S22: setting time step length, solving the Lorenz hyperchaotic model by adopting a Runge-Kutta method, and generating 3 chaotic sequenceso、pAndqand transforming the 3 chaotic sequences to obtain 3 chaotic bit sequences
、/>
And &>
(ii) a 3 chaotic bit sequences ofo、pAndqmaking a transformed solution sequence;
the specific rules for generating the chaotic bit sequence are as follows:
wherein,、/>and &>Respectively representing chaotic bit sequences, mod representing a remainder operation, floor representing rounding down on fractions,o、pandqall represent chaotic sequences;
step S23: based on the third information bit sequence and 3 chaotic bit sequences、/>And &>Mapping to obtain CAP-4 constellation points in a second constellation diagram according to unequal probability distribution so as to generate the second constellation diagram;
and step S3: superposing the CAP-4 constellation points on the first constellation diagram and the CAP-4 constellation points on the second constellation diagram to obtain SP-CAP-16 constellation points on a third constellation diagram; the probability of the constellation points in the second constellation diagram has different probability distribution according to different quadrants of the constellation points in the first constellation diagram; wherein SP represents probability forming, CAP represents carrierless amplitude/phase, 16 represents the number of constellation points;
the superposition of the CAP-4 constellation points on the first constellation diagram and the CAP-4 constellation points on the second constellation diagram has the following specific formula:
wherein,
represents a CAP-4 constellation point on a first constellation, and/or is present in a predetermined area of the first constellation>
Represents the CAP-4 constellation point on the second constellation, <' > v>
Represents a PS-CAP-16 constellation point on a third constellation diagram, and ` is `>
And &>
Are each represented by a weight factor, are>
；
And step S4: and modulating and demodulating PS-CAP-16 constellation points on the third constellation diagram.
2. The probability modeling method based on the Lorenz hyperchaotic model as claimed in claim 1, wherein the probability of the constellation points in the second constellation has different probability distributions according to the different quadrants where the constellation points in the first constellation are located, specifically comprising:
when the constellation point in the first constellation diagram is in a first quadrant, the probability of each constellation point in the second constellation diagram is 1/16,4/16,8/16,3/16 respectively; when the constellation point in the first constellation diagram is in a second quadrant, the probability of each constellation point in the second constellation diagram is 4/16,1/16,3/16,8/16 respectively; when the constellation point in the first constellation diagram is in a third quadrant, the probability of each constellation point in the second constellation diagram is 8/16,3/16,1/16,4/16 respectively; when the constellation point in the first constellation diagram is in the fourth quadrant, the probability of each constellation point in the second constellation diagram is 3/16,8/16,4/16,1/16 respectively.
3. The Lorenz hyper-chaotic model-based probability modeling method according to claim 1, wherein modulating and demodulating the PS-CAP-16 constellation points on the third constellation diagram specifically comprises:
step S41: forming and filtering the PS-CAP-16 constellation points on the third constellation diagram to obtain modulation signals;
step S42: sending the modulation signal to a channel by using a sending end for transmission;
step S43: receiving the modulation signal by using a receiving end;
step S44: performing matched filtering, down sampling and offline DSP signal processing on the received modulation signal to obtain a PS-CAP-16 constellation point with interference;
step S45: determining bit information of a CAP-4 constellation point on the first constellation diagram according to quadrant information of the PS-CAP-16 constellation point with interference; the bit information of the CAP-4 constellation point on the first constellation diagram comprises a fourth information bit sequence Q1 and a fifth information bit sequence Q2;
step S46: determining the CAP-4 constellation points on the second constellation diagram according to the PS-CAP-16 constellation points on the third constellation diagram and the CAP-4 constellation points on the first constellation diagram;
step S47: generating bit information of the CAP-4 constellation points on the second constellation diagram by utilizing a mapping rule table according to the quadrant information of the CAP-4 constellation points on the second constellation diagram, the corresponding quadrant information of the CAP-4 constellation points on the first constellation diagram and 3 chaotic bit sequences; the bit information of the CAP-4 constellation point on the second constellation diagram comprises a sixth information bit sequence Q3;
step S48: and performing parallel-to-serial conversion on the fourth information bit sequence Q1, the fifth information bit sequence Q2 and the sixth information bit sequence Q3 to obtain a converted pseudo-random bit sequence.
4. A probability modeling system based on a Lorenz hyperchaotic model is characterized by comprising:
a first constellation determination module for generating a first constellation and a third information bit sequence based on the pseudorandom bit sequence; the first constellation diagram is a uniformly distributed square constellation diagram; the square constellation diagram consists of CAP-4 constellation points;
the generating the first constellation diagram and the third information bit sequence based on the pseudorandom bit sequence specifically includes:
step S11: based on the pseudo-random bit sequence, performing series-parallel conversion to obtain three parallel rows of information bit sequences, wherein the three parallel rows of information bit sequences are a first information bit sequence P1, a second information bit sequence P2 and a third information bit sequence P3 respectively;
step S12: directly mapping the first information bit sequence P1 and the second information bit sequence P2 according to a gray mapping rule to form CAP-4 constellation points in a first constellation diagram; the coordinates of each generated information bit sequence [00,01,11,10] corresponding to the CAP4 constellation point in the first constellation diagram are: (1/sqrt (3)) [1,1; -1,1; -1, -1;1, -1];
a second constellation diagram determining module, configured to generate a second constellation diagram by using a Lorenz hyperchaotic model based on the third information bit sequence, where the second constellation diagram is a rectangular constellation diagram that is unevenly distributed, and the rectangular constellation diagram is composed of CAP-4 constellation points;
the generating a second constellation diagram by using a Lorenz hyperchaotic model based on the third information bit sequence specifically includes:
step S21: constructing a Lorenz hyperchaotic model, wherein the specific formula is as follows:
wherein,aandbare all indicative of a parameter of the system,ca feedback variable representing the state of the system,a、bandcare set to 10, 28 and 8/3, respectively;x、yandzare all representative of the state variables of the system,x、yandzinitial value of (A), (B)x 0 ，y 0 ，z 0 ) Set to (-1.6, -0.5, 21);
、
、/>
respectively representx、yAndza derivative of (a);
step S22: setting time step length, solving the Lorenz hyperchaotic model by adopting a Runge-Kutta method, and generating 3 chaotic sequenceso、pAndqand transforming the 3 chaotic sequences to obtain 3 chaotic bit sequences
、/>
And &>
(ii) a 3 chaotic bit sequences ofo、pAndqmaking a transformed solution sequence;
the specific rules for generating the chaotic bit sequence are as follows:
wherein,
、/>
and &>
Respectively representing chaotic bit sequences, mod representing a remainder operation, floor representing rounding down on fractions,o、pandqall represent chaotic sequences;
step S23: based on the third information bit sequence and 3 chaotic bit sequences
、/>
And &>
Mapping to obtain CAP-4 constellation points in a second constellation diagram according to unequal probability distribution so as to generate the second constellation diagram;
a superposition module, configured to superpose the CAP-4 constellation point on the first constellation diagram and the CAP-4 constellation point on the second constellation diagram, so as to obtain an SP-CAP-16 constellation point on a third constellation diagram; the probability of the constellation points in the second constellation diagram has different probability distribution according to different quadrants of the constellation points in the first constellation diagram; wherein SP represents probability forming, CAP represents carrierless amplitude/phase, 16 represents the number of constellation points;
the superposition of the CAP-4 constellation points on the first constellation diagram and the CAP-4 constellation points on the second constellation diagram has the following specific formula:
wherein,
represents a CAP-4 constellation point on a first constellation diagram, <' > is selected>
Represents the CAP-4 constellation point on the second constellation, <' > v>
Represents a PS-CAP-16 constellation point on a third constellation diagram, and ` is `>
And &>
Are each represented by a weight factor, are>
；
And the modulation and demodulation module is used for modulating and demodulating the PS-CAP-16 constellation points on the third constellation diagram.
5. The Lorenz hyperchaotic model-based probability modeling system as claimed in claim 4, wherein the probability of the constellation points in the second constellation has different probability distributions according to the different quadrants of the constellation points in the first constellation, specifically comprising:
when the constellation point in the first constellation diagram is in a first quadrant, the probability of each constellation point in the second constellation diagram is 1/16,4/16,8/16,3/16 respectively; when the constellation point in the first constellation diagram is in a second quadrant, the probability of each constellation point in the second constellation diagram is 4/16,1/16,3/16,8/16 respectively; when the constellation point in the first constellation diagram is in a third quadrant, the probability of each constellation point in the second constellation diagram is 8/16,3/16,1/16,4/16 respectively; when the constellation point in the first constellation diagram is in the fourth quadrant, the probability of each constellation point in the second constellation diagram is 3/16,8/16,4/16,1/16 respectively.
6. The Lorenz hyperchaotic model-based probability modeling system as claimed in claim 4, wherein the modem module specifically comprises:
the shaping filtering unit is used for carrying out shaping filtering on the PS-CAP-16 constellation points on the third constellation diagram to obtain a modulation signal;
the channel transmission unit is used for transmitting the modulation signal to a channel by using a transmitting end for transmission;
a receiving unit, configured to receive the modulated signal by using a receiving end;
the preprocessing unit is used for performing matched filtering, down sampling and offline DSP signal processing on the received modulation signal to obtain a PS-CAP-16 constellation point with interference;
a first bit information determining unit, configured to determine bit information of a PS-CAP-16 constellation point on the first constellation according to quadrant information where the constellation point is located; the bit information of the CAP-4 constellation point on the first constellation diagram comprises a fourth information bit sequence Q1 and a fifth information bit sequence Q2;
a constellation point determining unit, configured to determine a CAP-4 constellation point on the second constellation according to a PS-CAP-16 constellation point on the third constellation and a CAP-4 constellation point on the first constellation;
a second bit information determining unit, configured to generate bit information of the CAP-4 constellation point on the second constellation diagram by using a mapping rule table according to the quadrant information of the CAP-4 constellation point on the second constellation diagram, the corresponding quadrant information of the CAP-4 constellation point on the first constellation diagram, and the 3 chaotic bit sequences; the bit information of the CAP-4 constellation point on the second constellation diagram comprises a sixth information bit sequence Q3;
and a parallel-to-serial conversion unit, configured to perform parallel-to-serial conversion on the fourth information bit sequence Q1, the fifth information bit sequence Q2, and the sixth information bit sequence Q3 to obtain a converted pseudo-random bit sequence.
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