CN114285707B - Frequency control array safety communication method based on chaos index modulation - Google Patents

Frequency control array safety communication method based on chaos index modulation Download PDF

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CN114285707B
CN114285707B CN202111609013.5A CN202111609013A CN114285707B CN 114285707 B CN114285707 B CN 114285707B CN 202111609013 A CN202111609013 A CN 202111609013A CN 114285707 B CN114285707 B CN 114285707B
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CN114285707A (en
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廖轶
曾光辉
申晨雨
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University of Electronic Science and Technology of China
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Abstract

The invention discloses a frequency control array safety communication method based on chaos index modulation, which is characterized in that the correlation between the weighting phase sets of each transmission signal of a frequency control array is as small as possible by establishing the relation between a chaos sequence and each array element weighting phase set of the frequency control array, so that the confidentiality of the invention can be improved to a certain extent. In addition, the invention determines the weighted amplitude and the weighted phase of the M+1th array element of the frequency control array according to the weighted phase and the frequency deviation index of the M array elements before the frequency control array and the user position, so that the user can receive the correct constellation diagram, the constellation diagram of an eavesdropper generates distortion, and the process is analytic calculation, thus the calculation complexity is lower than that of the traditional heuristic optimization algorithm.

Description

Frequency control array safety communication method based on chaos index modulation
Technical Field
The invention belongs to the field of directional modulation of multi-antenna arrays, and particularly relates to a frequency control array safety communication method based on chaos index modulation.
Background
In contrast to phased arrays, the frequency of transmission of each element in the frequency-controlled array is slightly offset from the initial element, so that the signal transmitted by the array is not only angle-dependent, but also distance-dependent. Therefore, the directional modulation technology based on the frequency control array can realize the safe communication of the angle dimension and the distance dimension at the same time.
However, most of the current directional modulation techniques based on the frequency control array use heuristic optimization algorithm to solve when calculating the weighting coefficient of each array element of the frequency control array, so the calculation complexity is relatively high. Furthermore, for a fixed target user, the weighting coefficient of each array element of the frequency control array is fixed, which has a certain defect in confidentiality.
Aiming at the problems, the invention introduces the chaotic sequence into the direction modulation based on the frequency control array for the first time and maps the chaotic sequence into the weighting coefficient of each array element of the frequency control array, so that the weighting coefficient of each array element of the frequency control array changes along with the chaotic sequence, thereby realizing more effective confidentiality, generating a correct constellation diagram at a target user and generating a distorted constellation diagram at an eavesdropper through simple numerical calculation, and realizing safe transmission of information.
Disclosure of Invention
In order to solve the problems that the current most of directional modulation methods based on the frequency control array use heuristic optimization algorithm to calculate the weighting coefficient of each array element of the frequency control array, so that the calculation complexity is high, and the weighting coefficient of each array element of the frequency control array is fixed for a fixed target user, so that certain defect exists in confidentiality. The invention provides a frequency control array safety communication method based on chaos index modulation, which specifically comprises the following steps:
s1, a chaotic signal generator generates a chaotic sequence.
S2, mapping the chaotic sequence generated in the S1 into a binary sequence by binary mapping.
S3, mapping the binary sequence generated in the step S2 into a weighted phase and frequency offset index of the frequency control array, so as to generate a transmitting signal except the last array element.
And S4, calculating the amplitude and the phase, and generating the weighted amplitude and the phase of the last array element of the frequency control array according to the result of the S3 and the position information of the target user, so as to generate the transmitting signal of the last array element.
And S5, the receiver receives the signals generated in the S3 and the S4 and performs phase weighting on the signals.
S6, dividing the signals processed in the S5 into multiple paths, respectively performing down-conversion and matched filtering.
And S7, summing the multipath signals processed in the step S6, and judging the signal transmitted by the sender through the summed signal.
(1) The transmitter of the invention is used for generating each array element (T 1 ,T 2 ,...,T M+1 ) The signal processing process of each part of the transmitted signal is as follows:
s1, a chaotic signal generator generates a chaotic sequence.
The chaotic signal generator generates a mapping function z (n+1) =u (0.5) according to the array element number M+1 of the linear frequency control array 2 -z 2 (n)) -0.5 generating a chaotic sequence of length 1000+l, wherein n represents an nth sample time of the chaotic sequence, z (n) represents a sample value of the chaotic sequence at the nth time, u represents a parameter of generating the chaotic sequence, n=0, 1,2,3,..]2.5 < u < 4, z (0) is [ -0.5,0.5]Is randomly generated, L is determined by the following formula
Figure BDA0003429461610000021
Wherein C (2M, M) represents the number of combinations of M mutually different elements from a set containing 2M elements,
Figure BDA0003429461610000022
representing a rounding down.
S2, mapping the chaotic sequence generated in the S1 into a binary sequence by binary mapping.
Binary mapping constructs a subsequence of the last L bits of data in the chaotic sequence (denoted as F 1 ) Mapping to binary sequences (denoted F 1 ') the mapping rules are as follows:
Figure BDA0003429461610000023
wherein fi Represents F 1 Data of the ith bit of f i ' represents F 1 The i-th bit data in' i=1, 2,..l.
S3, mapping the binary chaotic sequence generated in the step S2 into a weighted phase and frequency offset index of a frequency control array, thereby generating a transmitting signal except the last array element.
Phase mapping binary sequence F 1 ' convert to the corresponding decimal number by:
Figure BDA0003429461610000024
assuming a binary sequence of 1110, conversion to decimal 0 x 2 0 +1×2 1 +1×2 2 +1×2 3 ＝14。
Then, the decimal number D is mapped into weighted phases and frequency offset indexes of M array elements before the frequency control array, and the mapping rule is as follows:
first, decimal number D is mapped to sequence s= { D M ,d M-1 ,d M-2 ,...,d 1 }，d m E {0,1, 2..2M-1 }, m=1, 2,..m. Let d=c (D M ,M)+C(d M-1 ,M-1)+...+C(d 1 ,1)，d M Is satisfied with C (d) M M) is less than or equal to the maximum number of Dmax, D is D if D=0 M =m-1, and others d M-l L e {1,2,., M-1}, calculated by the following relationship:
Figure BDA0003429461610000031
here, d is given first m But there is no specific calculation method, and "d M Is satisfied with C (d) M The maximum number of M) is D M Is of the value of C (d) M M) is operated from the group consisting of d M In a collection of numbersSelecting a combination number of M different numbers, for example, C (3, 2) represents a combination number of 3 selected from 2 different numbers among 3 numbers, wherein the meaning is the same as that of C (2M, M) in S1; d, d m It is calculated by the following relationship. Here, given as an example of calculation S, assuming m=8, one can calculate
Figure BDA0003429461610000032
Suppose a 13-bit binary sequence F 1 ' 0010001001011, the corresponding decimal number d=1099, due to D 8 Is satisfied with C (d) 8 A maximum number of 8). Ltoreq.1099, d 8 =12, (because C (12, 8) =495, C (13, 8) =1287), since C (d) 7 ,7)≤D-C(d 8 ,8)＜C(d 7 +1, 7), so d 7 =11, similarly, d can be calculated 6 To d 1 Finally, s= {12,11,10,8,5,3,2,1}.
The positions of the elements in the random exchange S are obtained into a set W which can be used as a frequency offset index set of M array elements before the frequency control array.
Then, let the
Figure BDA0003429461610000033
wherein dm ∈S,γ m ∈Ψ＝{γ 1 ,γ 2 ,...,γ M }。
Finally, the positions of the elements in the psi are subjected to random exchange to obtain a weighted phase set omega= { phi of M array elements before the frequency control array 1 ,φ 2 ,...,φ M }。
Thus, the first M array elements T 1 ,T 2 ,...,T M The form of the transmitted signal can be written as
Figure BDA0003429461610000041
wherein ,
Figure BDA0003429461610000042
representing the weighting coefficient of the mth array element, f m ＝f 0 +Δf m Representing the transmission frequency of the mth array element, f 0 Representing the carrier frequency, Δf m ＝η m Δf, the frequency offset of the mth array element, η m E W, Δf is the fundamental frequency increment, +.>
Figure BDA0003429461610000043
Represents imaginary units, t represents time, +.>
Figure BDA0003429461610000044
Is a complex baseband signal, satisfy->
Figure BDA0003429461610000045
T represents waveform duration, (. Cndot. * Representing the conjugation operator.
And S4, calculating the amplitude and the phase, and generating the weighted amplitude and the phase of the last array element of the frequency control array according to the result of the S3 and the position information of the target user, so as to generate the transmitting signal of the last array element.
Amplitude and phase calculations will be
Figure BDA0003429461610000046
Figure BDA0003429461610000047
Respectively used as the amplitude weighting and the phase weighting of the M+1th array element of the frequency control array, wherein
Figure BDA0003429461610000048
γ ii Representing the angle, Δf, in the constellation corresponding to the transmitted signal M+1 ＝η M+1 Δf represents the frequency offset of the M+1st array element, η M+1 Random integer set [0, 1. ], 2m+1]But are different from the elements in W. (r) D ,θ D ) Representing the location of the target user, where r D Representing the distance, θ, of the target user from the transmitter D The angle of the target user relative to the normal direction of the transmitter is represented, d represents the array element spacing of the frequency control array, and c represents the speed of light.
Then M+1th array element T M+1 The form of the transmitted signal can be written as
Figure BDA0003429461610000049
wherein ,
Figure BDA00034294616100000410
representing the weighting coefficient of the M+1th array element, f M+1 ＝f 0 +η M+1 Δf。
(2) The signal processing steps of the receiver of the invention are as follows:
and S5, the receiver receives the signals generated in the S3 and the S4 and performs phase weighting on the signals.
The received signal at the far field region arbitrary target point position (r, θ) can be written as:
Figure BDA0003429461610000051
wherein r represents the distance from the target point to the transmitter, θ represents the angle of the target point relative to the normal direction of the transmitter, r m ' approximately r- (m ' -1) dsin theta represents the distance from the m ' th array element to the target point, and r represents the 1 st array element T 1 The distance to the target point, d is the array element spacing, and c represents the speed of light.
Assume that
Figure BDA0003429461610000052
Is a narrowband signal>
Figure BDA0003429461610000053
The received signal may be rewritten as
Figure BDA0003429461610000054
Thus, the phase weighted signal is
Figure BDA0003429461610000055
S6, dividing the signal processed in the S5 into multiple paths (M+1 paths) to respectively perform down-conversion and matched filtering.
For the n 'th signal, n' =1, 2,..m+1, down-converting and matched filtering the output as
Figure BDA0003429461610000056
wherein
Figure BDA0003429461610000057
Representing a convolution operation.
Assume that
Figure BDA0003429461610000058
Satisfy the following orthogonal relationship
Figure BDA0003429461610000059
Where τ represents the delay and δ (·) represents the Kronecker delta function, i.e
Figure BDA0003429461610000061
The nth signal output signal can be rewritten as
Figure BDA0003429461610000062
And S7, summing the multipath signals processed in the step S6, and judging the signal transmitted by the sender through the summed signal. The summed signal is
Figure BDA0003429461610000063
The receiver then determines the transmitted signal by x.
The invention can make the correlation between the weighted phase sets of each transmitted signal of the frequency control array as small as possible by establishing the relation between the chaotic sequence and the weighted phase sets of each array element of the frequency control array, thereby improving the confidentiality of the invention to a certain extent. In addition, the invention determines the weighted amplitude and the weighted phase of the M+1th array element of the frequency control array according to the weighted phase and the frequency deviation index of the M array elements before the frequency control array and the user position, so that the user can receive the correct constellation diagram, the constellation diagram of an eavesdropper generates distortion, and the process is analytic calculation, thus the calculation complexity is lower than that of the traditional heuristic optimization algorithm.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
fig. 2 is a schematic structural diagram of a chaotic index modulation frequency control array transmitter;
fig. 3 is a schematic structural diagram of a chaotic index modulation frequency control array receiver;
fig. 4 is a graph of received signal amplitude versus spatial angle for r=50 km;
fig. 5 is a graph of the phase of the received signal versus the spatial angle when r=50 km;
fig. 6 is a graph of received signal amplitude versus spatial distance for θ=30°;
fig. 7 is a graph of the phase of the received signal versus the spatial distance when θ=30°;
fig. 8 is a constellation of received signals at a user location (30 °,50 km);
fig. 9 is a constellation of received signals at the eavesdropper 1 location (120 °,50 km);
fig. 10 is a constellation of received signals at the eavesdropper 2 location (30 °,70 km);
fig. 11 is a graph of error rate versus spatial angle for r=50 km;
fig. 12 is a graph of error rate versus spatial distance for θ=30°;
FIG. 13 is a graph showing the average bit error rate in three dimensions;
FIG. 14 is a top view of FIG. 13;
FIG. 15 is a graph of bit error rate versus signal to noise ratio;
FIG. 16 is a graph showing the relationship between bit error rate and array M;
FIG. 17 is a graph of bit error rate versus frequency increment Δf;
fig. 18 is a graph of genetic algorithm versus time in calculating the weight coefficients of a frequency controlled array according to the method of the present invention.
Detailed Description
The invention is explained in detail below with reference to the drawings and examples, and the technical solutions of the invention are clearly described. The examples selected herein are merely illustrative of the invention and are not intended to limit the invention.
(1) The structure of the transmitter of the invention is shown in FIG. 2, wherein T m Represents the m-th array element, f m The transmission frequency of the mth array element is represented, and θ represents the angle of the transmission signal deviating from the normal direction. As shown in fig. 1, the signal processing process of each part is as follows:
s1, a chaotic signal generator generates a chaotic sequence.
The chaotic signal generator generates a mapping function z (n+1) =u (0.5) according to the array element number M+1 of the linear frequency control array 2 -z 2 (n)) -0.5 generating a chaotic sequence of length 1000+l, wherein n represents an nth sample time of the chaotic sequence, z (n) represents a sample value of the chaotic sequence at the nth time, u represents a parameter of generating the chaotic sequence, n=0, 1,2,3,..]2.5 < u < 4, z (0) is [ -0.5,0.5]L is determined by:
Figure BDA0003429461610000071
wherein C (2M, M) represents M mutually exclusive elements from a set of 2M elementsThe number of combinations of the same element,
Figure BDA0003429461610000072
representing a rounding down.
S2, mapping the chaotic sequence generated in the S1 into a binary sequence by binary mapping.
Binary mapping constructs a subsequence of the last L bits of data in the chaotic sequence (denoted as F 1 ) Mapping to binary sequences (denoted F 1 ') the mapping rules are as follows:
Figure BDA0003429461610000081
wherein fi Represents F 1 Data of the ith bit of f i ' represents F 1 The i-th bit data in' i=1, 2.
S3, mapping the binary chaotic sequence generated in the step S2 into a weighted phase and frequency offset index of a frequency control array, thereby generating a transmitting signal except the last array element.
Phase mapping binary sequence F 1 ' conversion to the corresponding decimal number by
Figure BDA0003429461610000082
Then, the decimal number D is mapped into weighted phases of M array elements in front of the frequency control array, and the mapping rule is as follows:
first, decimal number D is mapped to sequence s= { D M ,d M-1 ,d M-2 ,...,d 1 }，d m E {0,1,2,., 2M-1}, the mapping rule is such that d=c (D M ,M)+C(d M-1 ,M-1)+...+C(d 1 ,1)，d M Is satisfied with C (d) M M) is less than or equal to the maximum number of Dmax, D is D if D=0 M =m-1, and others d M-l L e {1,2,., M-1}, calculated by the following relationship
Figure BDA0003429461610000083
The positions of the elements in the random exchange S can obtain a set W which can be used as a frequency offset index set of M array elements before the frequency control array.
Then, let the
Figure BDA0003429461610000084
wherein dm ∈S,γ m ∈Ψ＝{γ 1 ,γ 2 ,...,γ M }。
Finally, the positions of elements in the psi are randomly exchanged to obtain a weighted phase set omega= { phi of M array elements in front of the frequency control array 1 ,φ 2 ,...,φ M }。
Thus, the first M array elements T 1 ,T 2 ,...,T M The form of the transmitted signal can be written as
Figure BDA0003429461610000091
wherein ,
Figure BDA0003429461610000092
representing the weighting coefficient of the mth array element, f m ＝f 0 +Δf m Representing the transmission frequency of the mth array element, f 0 Representing the carrier frequency, Δf m ＝η m Δf, the frequency offset of the mth array element, η m E W, Δf is the fundamental frequency increment, +.>
Figure BDA0003429461610000093
Represents imaginary units, t represents time, +.>
Figure BDA0003429461610000094
Is a complex baseband signal, satisfy->
Figure BDA0003429461610000095
T denotes the duration of the waveform and,(·) * representing the conjugation operator.
Note that as long as the initial values of the chaotic sequence are different, the weighted phase set Ω of each transmission signal is not the same, and thus variability of the weighting coefficients is achieved.
And S4, calculating the amplitude and the phase, and generating the weighted amplitude and the phase of the last array element of the frequency control array according to the result of the S3 and the position information of the target user, so as to generate the transmitting signal of the last array element.
Assume that the location of the target user is (r D ,θ D )，r D Represents distance position, theta D Represents the angular position, the received decision signal is in the form of
Figure BDA0003429461610000096
Wherein d represents the array element spacing of the frequency control array, c represents the light speed, f M+1 ＝f 0 +η M+1 Δf，η M+1 Random integer set [0, 1. ], 2m+1]But are different from the elements in W,
Figure BDA0003429461610000097
a weight coefficient representing the M+1th array element, A ii Represents amplitude weighting, phi ii Representing phase weighting. The following details calculate A ii And phi is equal to ii Is a value of (2).
Order the
Figure BDA0003429461610000098
Then formula (7) is rewritable as
Figure BDA0003429461610000099
The following derivation herein takes QPSK (quadrature phase shift keying ) as an example, assuming that the set of transmit information is: n= {00,01,10,11}, the corresponding signal form is g= { e jπ/4 ,e j3π/4 ,e -jπ/4 ,e -j3π/4 "asAfter the target user (r D ,θ D ) Form the correct constellation diagram, then equation (8) needs to be satisfied
Figure BDA00034294616100000910
wherein
Figure BDA0003429461610000101
According to Euler's formula
Figure BDA0003429461610000102
Figure BDA0003429461610000103
Bringing the formula (10) and the formula (11) into the formula (9) and obtaining the product by simple term shifting
Figure BDA0003429461610000104
Obtainable from (12)
Figure BDA0003429461610000105
Figure BDA0003429461610000106
Thus M+1th array element T M+1 The form of the transmitted signal can be written as
Figure BDA0003429461610000107
Note that in solving for a ii And phi is equal to ii The process of (2) is simple numerical calculation, so the complexityLower compared to heuristic optimization algorithms. In addition, since there are 4 elements in G, the weighting coefficient of the last element under each signal transmission condition can be obtained by solving equation (9) 4 times, and the above calculation process is still applicable compared with other modulation methods, except that the values of the elements in G and the number of the elements in G are different.
In the steps S1-S3, the weighted phases of the M array elements before the radio frequency control array are mapped by the chaotic sequence, so that the weighted phases of the radio frequency control array can be changed along with the change of the chaotic sequence, and the chaotic sequences with different initial values have great difference, namely the initial value sensitivity, so that the weights of the transmitted signals are ensured to be different. In step S4, the weighted amplitude and phase of the (m+1) th array element are calculated by the correct constellation diagram received by the target user position, so as to realize the secure communication of the frequency control array.
(2) The structure of the receiver of the present invention is shown in fig. 3, and the signal processing steps are as follows:
and S5, the receiver receives the signals generated in the S3 and the S4 and performs phase weighting on the signals.
The received signal at an arbitrary target point position (r, θ) in the far field region (the far field region is an antenna field region whose electromagnetic field distribution with angle is substantially independent of the antenna distance) can be written as
Figure BDA0003429461610000111
(15) The formula "≡" is because of the fact that at f 0 ＞＞Δf m Under the condition of (2), the secondary phase term can be omitted
Figure BDA0003429461610000112
Where r represents a distance position, θ represents an angular position, and can be considered as r under far field conditions m 'r- (M' -1) dsin θ represents the distance of the M 'th element to the target point, M' =1, 2.
Assume that
Figure BDA0003429461610000113
Is a narrowband signal, it can be considered +.>
Figure BDA0003429461610000114
Then the received signal formula (15) can be rewritten as +.>
Figure BDA0003429461610000115
The phase weighted signal is then
Figure BDA0003429461610000116
S6, dividing the signals processed in the S5 into multiple paths, respectively performing down-conversion and matched filtering.
Down-converting the n 'th signal (n' =1, 2.,. M+1) and matched filtering the output as
Figure BDA0003429461610000117
wherein
Figure BDA0003429461610000118
Representing a convolution operation.
Assume that
Figure BDA0003429461610000119
Satisfy the following equation
Figure BDA00034294616100001110
Where τ represents the delay and δ (·) represents the Kronecker delta function, i.e
Figure BDA0003429461610000121
The nth output signal may be rewritten as
Figure BDA0003429461610000122
And S7, summing the multipath (M+1 paths) signals processed in the step S6, and judging the signal transmitted by the sender through the summed signal.
The summed signal is
Figure BDA0003429461610000123
The receiver then determines the transmitted signal by x.
Examples
For experimental verification of frequency control array safety communication of chaos index modulation, the parameter settings are shown in the following table 1:
table 1 parameter setting table of example 1
Figure BDA0003429461610000124
Figure BDA0003429461610000131
Fig. 4-7 show graphs of amplitude and phase of a received signal versus spatial angle and spatial distance, and fig. 8-10 show signal constellations received at a target user location and an eavesdropper location, respectively, where fig. 4 is a graph of amplitude of a received signal versus spatial angle when r=50 km; fig. 5 is a graph of the phase of the received signal versus the spatial angle when r=50 km; fig. 6 is a graph of received signal amplitude versus spatial distance for θ=30°; fig. 7 is a graph of the phase of the received signal versus the spatial distance when θ=30°; fig. 8 is a constellation of received signals at a user location (30 °,50 km); fig. 9 is a constellation of received signals at the eavesdropper 1 location (120 °,50 km); fig. 10 is a constellation of received signals at the location of an eavesdropper 2 (30 °,70 km). It can be seen that the correct constellation is received only at the target user location, while the distorted constellation is received at the other locations.
Fig. 11-12 show the relationship between the bit error rate and the spatial angle and the spatial distance, fig. 13 shows the distribution of the average bit error rate of the randomly generated 1000-set chaotic sequences in the three-dimensional space, fig. 14 is a top view of fig. 13, and fig. 11 shows the relationship between the bit error rate and the spatial angle when r=50 km; fig. 12 is a graph of error rate versus spatial distance for θ=30°; FIG. 13 is a graph showing the average bit error rate in three dimensions; fig. 14 is a top view of fig. 13. Therefore, in the whole space, only the bit error rate of the target user is lower, and the bit error rates of other positions are higher, so that the invention is illustrated to realize the safety communication based on the frequency control array.
As shown in fig. 15, the relationship between the bit error rate and the signal to noise ratio of the target user location and the eavesdropper location is shown, so it can be seen that only the bit error rate of the target user location decreases with the increase of the signal to noise ratio, while the bit error rate of the eavesdropper location is basically unchanged with the increase of the signal to noise ratio, and the reason for this phenomenon is that the constellation diagram of the eavesdropper location is distorted.
Fig. 16 shows the relationship between the bit error rate of the target user position and the number M of the eavesdropper position, so that it can be seen that the bit error rate of the target user position does not change with the change of the number M of the array elements and remains a small value all the time, while the bit error rate of the eavesdropper position fluctuates with the change of the number M of the array elements and remains a large value all the time, because the weighted amplitude and phase of the mth array element are calculated by generating a correct constellation diagram at the target user position, and no matter what value M takes, the constellation diagram is not affected.
Fig. 17 shows the error rate versus frequency increment Δf for the target user position versus the eavesdropper position, from which it can be seen that when Δf=0 kHz, the error rate at (30 °,50 km) is the same as that at (30 °,70 km), since when Δf=0 kHz the frequency control array degenerates into a phased array whose transmitted signal is independent of spatial distance, so the error rate at (30 °,50 km) is the same as that at (30 °,70 km), whereas at Δf+.0khz the error rate is lower for only the target user position and higher for the eavesdropper position, this phenomenon arises because the weighted amplitude and phase of the M-th element are calculated with the target user position yielding the correct constellation, and therefore the constellation is unaffected regardless of what Δf takes.
In this case, a typical genetic algorithm is used as a representative for comparison with the method of the present invention, but since the computational complexity of the genetic algorithm is not resolved, fig. 18 shows a graph of average time when calculating the weighting coefficient of the frequency control array 100 times under the same condition, and the coordinate axes are logarithmic, so that it can be seen that the present invention has advantages in terms of computational complexity over the genetic algorithm.
The embodiments described above are only some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

Claims (1)

1. The frequency control array safety communication method based on chaos index modulation is characterized by comprising the following steps:
s1) generating a chaotic sequence by adopting a chaotic signal generator;
s2) mapping the chaotic sequence generated in the step S1) into a binary sequence by utilizing binary mapping;
s3) mapping the binary sequence generated in the step S2) into a weighted phase and frequency offset index of the frequency control array by utilizing phase mapping, thereby generating a transmitting signal except the last array element;
s4) calculating the weighted amplitude and the phase of the last array element of the frequency control array according to the result of the step S3) and the position information of the target user by adopting the amplitude and the phase, so as to generate a transmitting signal of the last array element;
s5) receiving the transmitting signals generated in the step S3) and the step S4) by adopting a receiver, and carrying out phase weighting on the transmitting signals;
s6) dividing the signal processed in the step S5) into multiple paths, respectively performing down-conversion and matched filtering;
s7) summing the multipath signals processed in the step S6) and judging the signal transmitted by the sender through the summed signal;
wherein, the step S1) specifically includes:
the chaotic signal generator generates a mapping function z (n+1) =u (0.5) according to the array element number M+1 of the linear frequency control array 2 -z 2 (n)) -0.5 generating a chaotic sequence of length 1000+l, wherein n represents an nth sample time of the chaotic sequence, z (n) represents a sample value of the chaotic sequence at the nth time, u represents a parameter of generating the chaotic sequence, n=0, 1,2,3,..]2.5 < u < 4, z (0) is [ -0.5,0.5]L is determined by:
Figure FDA0004151433330000011
wherein C (2M, M) represents the number of combinations of M mutually different elements from a set containing 2M elements,
Figure FDA0004151433330000012
representing a downward rounding;
the step S2) specifically includes:
binary mapping is used for forming a subsequence F consisting of last L bits of data in the chaotic sequence 1 Mapping into binary sequence F 1 ' the mapping rule is as follows:
Figure FDA0004151433330000013
wherein fi Represents F 1 Data of the ith bit of f i ' represents F 1 Data in bit i, i=1, 2, ·l;
the step S3) specifically includes:
phase mapping binary sequence F 1 ' conversion to the corresponding decimal number by
Figure FDA0004151433330000021
Then, the decimal number D is mapped into weighted phases of M array elements in front of the frequency control array, and the mapping rule is as follows:
first, decimal number D is mapped to sequence s= { D M ,d M-1 ,d M-2 ,...,d 1 }，d m E {0,1,2,., 2M-1}, the mapping rule is such that d=c (D M ,M)+C(d M-1 ,M-1)+...+C(d 1 ,1)，d M Is satisfied with C (d) M M) is less than or equal to the maximum number of Dmax, D is D if D=0 M =m-1, and others d M-l L e {1,2,., M-1}, calculated by the following relationship
Figure FDA0004151433330000022
/>
The positions of elements in the random exchange S can obtain a set W which can be used as a frequency offset index set of M array elements before a frequency control array;
then, let the
Figure FDA0004151433330000023
wherein dm ∈S,γ m ∈Ψ＝{γ 1 ,γ 2 ,...,γ M }；
Finally, the positions of elements in the psi are randomly exchanged to obtain a weighted phase set omega= { phi of M array elements in front of the frequency control array 1 ,φ 2 ,...,φ M }；
Thus, the first M array elements T 1 ,T 2 ,...,T M The form of the transmitted signal can be written as
Figure FDA0004151433330000024
wherein ,
Figure FDA0004151433330000025
representing the weighting coefficient of the mth array element, f m ＝f 0 +Δf m Representing the transmission frequency of the mth array element, f 0 Representing the carrier frequency, Δf m ＝η m Δf, the frequency offset of the mth array element, η m E, W, af is the fundamental frequency increment,
Figure FDA0004151433330000026
represents imaginary units, t represents time, +.>
Figure FDA0004151433330000027
Is a complex baseband signal, satisfy->
Figure FDA0004151433330000028
T represents waveform duration, (. Cndot. * Representing a conjugation operator;
as long as the initial values of the chaotic sequence are different, the weighted phase set omega of each transmitted signal is not the same, so that the variability of the weighted coefficient is realized;
the step S4) specifically includes:
assume that the location of the target user is (r D ,θ D )，r D Represents distance position, theta D Represents the angular position, the received decision signal is in the form of
Figure FDA0004151433330000031
Wherein d represents the array element spacing of the linear frequency control array, c represents the light speed, f M+1 ＝f 0 +η M+1 Δf，η M+1 Random integer set [0, 1. ], 2m+1]But are different from the elements in W,
Figure FDA0004151433330000032
a weight coefficient representing the M+1th array element, A ii Represents amplitude weighting, phi ii Representing phase weighting, a is calculated in detail below ii And phi is equal to ii Is the value of (1):
order the
Figure FDA0004151433330000033
Then formula (7) is rewritable as
Figure FDA0004151433330000034
When the modulation mode is quadrature phase shift keying QPSK, the set of sending information is set as follows: n= {00,01,10,11}, the corresponding signal form is g= { e jπ/4 ,e j3π/4 ,e -jv/4 ,e -j3π/4 To be in the target user (r) D ,θ D ) Form the correct constellation diagram, then equation (8) needs to be satisfied
Figure FDA0004151433330000035
wherein
Figure FDA0004151433330000036
According to Euler's formula
Figure FDA0004151433330000037
/>
Figure FDA0004151433330000038
Bringing the formula (10) and the formula (11) into the formula (9) and obtaining the product by simple term shifting
Figure FDA0004151433330000039
Obtainable from (12)
Figure FDA0004151433330000041
Figure FDA0004151433330000042
Thus M+1th array element T M+1 The form of the transmitted signal can be written as
Figure FDA0004151433330000043
Because of 4 elements in G, the weighting coefficient of the last array element under each signal sending condition can be obtained by solving the formula (9) for 4 times;
the step S5) specifically includes:
the received signal at the far field region arbitrary target point position (r, θ) can be written as
Figure FDA0004151433330000044
At f 0 ＞＞Δf m Under the condition of (a) and (b),
Figure FDA0004151433330000045
wherein r represents a distance position, θ represents an angular position, and r is considered under far field conditions m′ R- (M ' -1) dsin θ represents the distance of the M ' th element to the target point, M ' =1, 2,., m+1;
assume that
Figure FDA0004151433330000049
Is a narrowband signal, consider->
Figure FDA0004151433330000046
Then receiveIs rewritten as signal x (t)
Figure FDA0004151433330000047
The phase weighted signal is then
Figure FDA0004151433330000048
The step S6) specifically includes:
for any nth 'signal, n' =1, 2,..m+1 down-converted and matched filtered output is
Figure FDA0004151433330000051
wherein
Figure FDA0004151433330000052
Representing a convolution operation;
assume that
Figure FDA0004151433330000053
Satisfy the following equation
Figure FDA0004151433330000054
Where τ represents the delay and δ (·) represents the Kronecker delta function, i.e
Figure FDA0004151433330000055
The nth output signal is rewritten as
Figure FDA0004151433330000056
The step S7) specifically includes:
the signal after summing the multiple signals is
Figure FDA0004151433330000057
The receiver then determines the transmitted signal by x.
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