CN113328969B - Multi-beam directional modulation method and system based on MP-WFRFT and artificial noise - Google Patents

Multi-beam directional modulation method and system based on MP-WFRFT and artificial noise Download PDF

Info

Publication number
CN113328969B
CN113328969B CN202110623512.3A CN202110623512A CN113328969B CN 113328969 B CN113328969 B CN 113328969B CN 202110623512 A CN202110623512 A CN 202110623512A CN 113328969 B CN113328969 B CN 113328969B
Authority
CN
China
Prior art keywords
matrix
wfrft
symbol
vector
encryption
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202110623512.3A
Other languages
Chinese (zh)
Other versions
CN113328969A (en
Inventor
任清华
樊志凯
张广大
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Air Force Engineering University of PLA
Original Assignee
Air Force Engineering University of PLA
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Air Force Engineering University of PLA filed Critical Air Force Engineering University of PLA
Priority to CN202110623512.3A priority Critical patent/CN113328969B/en
Publication of CN113328969A publication Critical patent/CN113328969A/en
Application granted granted Critical
Publication of CN113328969B publication Critical patent/CN113328969B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/18—Phase-modulated carrier systems, i.e. using phase-shift keying
    • H04L27/20—Modulator circuits; Transmitter circuits
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0408—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas using two or more beams, i.e. beam diversity

Landscapes

  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Mobile Radio Communication Systems (AREA)

Abstract

The disclosure relates to a multi-beam directional modulation method and a multi-beam directional modulation system based on MP-WFRFT and artificial noise. The method comprises the following steps: modulating an input signal to obtain a symbol matrix; performing MP-WFRFT conversion on the symbol matrix to generate a first encryption matrix; carrying out artificial noise processing on the first encryption matrix to obtain a second encryption matrix; the second encryption matrix is transmitted to a receiving end through a channel by a direction modulation method; and the receiving end performs inverse MP-WFRFT conversion and decryption on the received signal vector to finish the demodulation process. The method and the device enhance the wireless physical security performance of each legal user in different specified spatial directions, and further improve the confidentiality.

Description

Multi-beam directional modulation method and system based on MP-WFRFT and artificial noise
Technical Field
The present disclosure relates to the field of secure communication technologies, and in particular, to a multi-beam directional modulation method and system based on MP-WFRFT and artificial noise.
Background
Directional modulation is a technique for securing wireless communications at the physical layer by transmitting a standard signal constellation format to a signal receiver in a given direction while distorting the signal constellation in other directions.
In the related art, in order to achieve accurate implementation of constellation mapping of standard signals in a specific spatial direction, the rf front end is optimized, for example, the phase and amplitude of a radiation signal of the rf front end are changed. Then, the optimization method of the rf front end is generally complex, and there is a problem that the confidential information is easily intercepted by an eavesdropper when the eavesdropper approaches a legitimate user. Therefore, there is a need to improve one or more problems in the related art solutions to further enhance the wireless physical security performance of each legitimate user in different designated spatial directions, thereby improving the security.
It is to be noted that the information disclosed in the above background section is only for enhancement of understanding of the background of the present disclosure, and thus may include information that does not constitute prior art known to those of ordinary skill in the art.
Disclosure of Invention
The embodiment of the disclosure aims to provide a multi-beam directional modulation method and a multi-beam directional modulation system based on MP-WFRFT and artificial noise, so as to enhance the wireless physical safety performance of each legal user in different specified spatial directions and improve the confidentiality.
According to a first aspect of the embodiments of the present disclosure, there is provided a multi-beam directional modulation method based on MP-WFRFT and artificial noise, the method comprising the following steps:
modulating an input signal to obtain a symbol matrix;
performing MP-WFRFT conversion on the symbol matrix to generate a first encryption matrix;
carrying out artificial noise processing on the first encryption matrix to obtain a second encryption matrix;
the second encryption matrix is transmitted to a receiving end through a channel by a direction modulation method;
and the receiving end carries out inverse MP-WFRFT conversion decryption on the received signal vector to finish the demodulation process.
In an exemplary embodiment of the present disclosure, the size of the symbol matrix is K × L, where K is the number of legal user receivers, and L is the length of a symbol data stream in the symbol matrix.
In an exemplary embodiment of the disclosure, the first encryption matrix is generated after MP-WFRFT transformation is performed on the symbol matrix by using the following formula:
Figure BDA0003101049420000021
Figure BDA0003101049420000022
wherein Z is the first encryption matrix s k ＝[s k,1 ,…，s k,l ，…,s k，L ]Is a stream of symbol data transmitted independently to the receiving end of the kth said legitimate user,
Figure BDA0003101049420000023
respectively represent s k And ω is a weighting factor.
In an exemplary embodiment of the disclosure, the calculation formula of the weight factor ω is:
Figure BDA0003101049420000024
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003101049420000025
for modulation order, V = [ MV, NV =]Is a vector of parameters, and MV = [ m = 0 ,m 1 ,m 2 ,m 3 ]，NV＝[n 0 ,n 1 ,n 2 ,n 3 ]Are all integer vectors, i =0,1,2,3.
In an exemplary embodiment of the disclosure, a calculation formula of the second encryption matrix is:
Q＝[q 1 ,q 2 ,…,q l ,…,q L ]；
Figure BDA0003101049420000026
wherein Q is the second encryption matrix, P t Is the total transmit power, an
Figure BDA0003101049420000027
V d As a precoding matrix, t AN Is a pre-coded vector.
In an exemplary embodiment of the present disclosure, the V d The calculation formula of (2) is as follows:
Figure BDA0003101049420000028
wherein H H (θ d )V d ＝I K ，
Figure BDA0003101049420000031
In an exemplary embodiment of the disclosure, the received signal vector is decrypted using an inverse MP-WFRFT transform using the following formula:
Figure BDA0003101049420000032
Figure BDA0003101049420000033
wherein, y k For the received signal vector, n k Is composite Gaussian white noise n 'after inverse MP-WFRFT conversion' k ＝[n k,1 ,…,n k,l ,…,n k,L ]Is a complex additive white gaussian noise vector.
In an exemplary embodiment of the present disclosure, the MP-WFRFT is 4-WFRFT.
In an exemplary embodiment of the present disclosure, the modulation is a QPSK modulation.
According to a second aspect of the embodiments of the present disclosure, there is provided a multi-beam directional modulation system based on MP-WFRFT and artificial noise, the system comprising:
a WFRFT inverse transformation unit, configured to perform WFRFT inverse transformation on the modulated column vector after symbol mapping is completed to complete mixed carrier modulation, and obtain a column vector of the mixed carrier signal;
the chaotic mapping encryption unit is used for generating a first sequence and a second sequence through two-dimensional chaotic mapping, and performing amplitude expansion and constellation rotation on the column vector of the mixed carrier signal by utilizing the first sequence and the second sequence to generate an encrypted signal;
the decryption unit is used for generating a decryption matrix according to the parameters of the two-dimensional chaotic mapping and decrypting the encrypted signal transmitted to the receiving end by using the decryption matrix;
a WFRFT transform unit for performing WFRFT transform on the decrypted data to complete symbol demodulation.
The technical scheme provided by the disclosure can comprise the following beneficial effects:
in the embodiment of the disclosure, a first encryption matrix is generated after MP-WFRFT (multi-parameter weighted fractional Fourier transform) transformation is performed on a symbol matrix, so that the complex planar constellation distribution of confidential signals of legitimate users is changed, and a second encryption matrix obtained by performing artificial noise processing on the first encryption matrix increases artificial noise which cannot be eliminated, further confuses the distribution of the confidential signals, and enables the confidential signals transmitted to a legitimate user to be mixed in all the confidential signals, thereby improving the wireless physical security performance of each legitimate user in different specified spatial directions, and further improving the security by not correctly demodulating useful signals even if an eavesdropper is located near the legitimate user or at the same position as the legitimate user.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and together with the description, serve to explain the principles of the disclosure. It is apparent that the drawings in the following description are only some embodiments of the disclosure, and that other drawings may be derived from those drawings by a person of ordinary skill in the art without inventive effort.
Fig. 1 is a schematic diagram illustrating steps of a multi-beam directional modulation method based on MP-WFRFT and artificial noise in an exemplary embodiment of the disclosure;
fig. 2 shows a graph of bit error rate versus signal-to-noise ratio for each directional modulation method in an exemplary embodiment of the disclosure;
fig. 3 shows a graph of secret rate versus signal-to-noise ratio for each directional modulation method in an exemplary embodiment of the disclosure;
FIG. 4 is a graph showing bit error rate versus signal-to-noise ratio for a valid user direction estimate with errors for a radial port in an exemplary embodiment of the disclosure;
fig. 5 shows an anti-interception performance diagram of a multi-beam directional modulation method based on MP-WFRFT and artificial noise in an exemplary embodiment of the present disclosure;
fig. 6 shows a configuration diagram of a multi-beam directional modulation system based on MP-WFRFT and artificial noise in an exemplary embodiment of the present disclosure.
Detailed Description
Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.
Furthermore, the drawings are merely schematic illustrations of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and thus their repetitive description will be omitted. Some of the block diagrams shown in the figures are functional entities and do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in the form of software, or in one or more hardware modules or integrated circuits, or in different networks and/or processor devices and/or microcontroller devices.
In the present exemplary embodiment, first, a multi-beam directional modulation method based on MP-WFRFT and artificial noise is provided, and referring to fig. 1, the method may include the following steps:
step S101: modulating an input signal to obtain a symbol matrix;
step S102: performing MP-WFRFT conversion on the symbol matrix to generate a first encryption matrix;
step S103: carrying out artificial noise processing on the first encryption matrix to obtain a second encryption matrix;
step S104: the second encryption matrix is transmitted to a receiving end through a channel by a direction modulation method;
step S105: and the receiving end carries out inverse MP-WFRFT conversion decryption on the received signal vector to finish the demodulation process.
In the embodiment of the disclosure, the first encryption matrix generated after the MP-WFRFT conversion is performed on the symbol matrix changes the complex plane constellation distribution of the confidential signals of the legitimate users, and the second encryption matrix obtained by performing the artificial noise processing on the first encryption matrix increases the artificial noise which cannot be eliminated, further confuses the distribution of the confidential signals, and enables the confidential signals transmitted to a legitimate user to be mixed in all the confidential signals, thereby improving the wireless physical security performance of each legitimate user in different specified spatial directions, and even if an eavesdropper is located near the legitimate user or at the same position as the legitimate user, the useful signals cannot be correctly demodulated, thereby improving the security.
Hereinafter, each step of the above-described method in the present exemplary embodiment will be described in more detail.
In the present embodiment, vectors and matrices are represented herein by bold lower case letters and upper case letters, respectively. Symbol [ ·] H ,[·] T ,
Figure BDA0003101049420000051
[·] -1 Respectively representing complex conjugate transposition, transposition operation, moore-Penrose pseudo-inverse operation and inverse operation of the matrix. Symbol
Figure BDA0003101049420000052
| · | represents the matrix expectation operation and the matrix modulo operation. Symbol [. ]] + Is max {. The. F (α,V) (. And F) (-α,V) (. Cndot.) denotes 4-WFRFT and 4-IWFRFT, respectively. I is K And 0 M×N Expressed as an identity matrix of K × K size and a zero matrix of M × N size, respectively.
Figure BDA0003101049420000061
With mean m and variance σ 2 Complex gaussian distribution of (a).
In step S101, take the transmitting end as a linear antenna array with N array elements as an example, and set the number of legitimate users as K and satisfy K +1 but N. The input signal is QPS modulated to generate a symbol matrix S.
Specifically, in an embodiment, the size of the symbol matrix S is K × L, where K is the number of the receiving ends of the legal users, and L is the length of the symbol data stream in the symbol matrix, then
S＝[s 1 ，s 2 ，…,s k ，…s K ] T (1)
Wherein s is k ＝[s k，1 ，…，s k，l ,…,s k,L ]Is a symbol data stream with length L which is independently transmitted to the k legal user and satisfies
Figure BDA0003101049420000062
In step S102, the symbol matrix S is subjected to MP-WFRFT conversion to generate a first encryption matrix. Specifically, in this embodiment, MP-WFRFT is 4-WFRFT. We use the transmitted data symbol vector s of the k-th legitimate user k A4-WFRFT protocol was performed for the example, namely:
Figure BDA0003101049420000063
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003101049420000064
respectively represents s k ω is a weight factor, and the corresponding weight factor is defined as:
Figure BDA0003101049420000065
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003101049420000066
is the modulation order, m a And n a By the self-contained parameter vector V = [ MV, NV ] in 4-WFRFT]A calculation is performed, in particular, the integer vector MV = [ m = [ ] 0 ,m 1 ,m 2 ,m 3 ]Integer vector NV = [ n = 0 ,n 1 ,n 2 ,n 3 ]，i＝0，1，2,3. The first encryption matrix Z generated by the symbol matrix S after 4-WFRFT operation is as follows:
Figure BDA0003101049420000067
wherein
Figure BDA0003101049420000068
Transpose the l row vector of the first encryption matrix Z for generating transmission data of N antenna elements of the multi-antenna linear array in the l symbol period in the subsequent step.
In step S103, performing artificial noise processing on the first encryption matrix Z to obtain a second encryption matrix Q:
Q＝[q 1 ，q 2 ，…，q l ，…，q L ] (5)
wherein q is l Is the transmitted signal vector in the l-th baseband symbol period, which can be written as:
Figure BDA0003101049420000071
P t is the total transmit power, beta d And beta e The power distribution coefficients of the transmitted information and the artificial noise are respectively satisfied
Figure BDA0003101049420000072
u represents the inserted complex artificial noise vector with the same symbol conversion rate as the baseband
Figure BDA0003101049420000073
V d And t AN Respectively representing a precoding matrix and a precoding vector, which are respectively designed to eliminate interference of the remaining legitimate users and artificial noise to the legitimate users in the specified direction. By designing V appropriately d And t AN The receiving end of the artificial legal user in the expected direction can obtain the required modulation signal, but the receiving end in the unexpected directionThe receiving end, i.e. the eavesdropper receiving end, can only obtain the modulated signal after the artificial interference. Thus, V d And t AN Should satisfy the following conditions:
Figure BDA0003101049420000074
wherein, theta d Indicating the azimuth of the legitimate user(s),
Figure BDA0003101049420000075
the normalized steering vector at any legitimate user receiving end of the direction can be expressed as:
Figure BDA0003101049420000076
Figure BDA0003101049420000077
in the formula (9), d is the distance between the antenna elements, λ is the transmission wavelength, and d = λ/2 is set, the total steering matrix including the steering vectors of K legitimate user receiving ends is:
Figure BDA0003101049420000078
therefore, the formula (7) can be obtained by the formulas (8), (9) and (10).
In one embodiment, to eliminate interference between multiple legitimate users, V d Complex conjugate transpose H designed as a total steering matrix H (θ d ) The Moore-Penrose inverse matrix of (1), i.e.:
Figure BDA0003101049420000079
formula (11) satisfies H H (θ d )V d ＝I K And
Figure BDA00031010494200000710
and t is AN Designing under SVD (Singular Value Decomposition) operation, and fitting matrix H H (θ d ) Performing an SVD operation can be expressed as:
H H (θ d )＝U∑V H (12)
since K < N, the matrix H H (θ d ) Has a null space, the right singular vector can continue to be decomposed into:
V＝[V (S) V (0) ] H (13)
wherein, V (S) Right singular vectors corresponding to non-zero singular values, and V (0) Then is H H (θ d ) Zero space vector of (2). Thus, a matrix based on H can be obtained H (θ d ) T of SVD AN ＝V (0) And t is AN Can satisfy
Figure BDA0003101049420000081
In step S104, the second encryption matrix Q is transmitted to the receiving end through a Line-of-Sight (LoS) channel by a directional modulation method.
The directional modulation method transmits a standard signal constellation format to the signal receiver in a specified direction while distorting the signal constellation in other directions.
After passing through the LoS channel in free space, the signal received by the kth LU in the l-th symbol period can be written as:
Figure BDA0003101049420000082
wherein
Figure BDA0003101049420000083
Is a mean of 0 and a variance of
Figure BDA0003101049420000084
Complex additive white gaussian noise.
In step S105, the receiving end performs inverse MP-WFRFT transform decryption on the received signal vector, thereby completing the demodulation process. In this embodiment, the inverse MP-WFRFT transform is an inverse 4-WFRFT transform.
After receiving all L signals, the signal received by the kth legal user constitutes a vector, which can be written as:
Figure BDA0003101049420000085
wherein, n' k ＝[n k，1 ，…，n k，l ，…，n k，L ]Is a complex additive white Gaussian noise vector and satisfies
Figure BDA0003101049420000086
Then, the received signal vector y with length L is processed k And (3) carrying out inverse 4-WFRFT conversion with parameters (-alpha, V) to obtain:
Figure BDA0003101049420000087
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003101049420000088
is composite white Gaussian noise processed by inverse WFRFT, and its distribution characteristics and n' k The same is true.
Therefore, it can be seen that the secret symbol vector s can be easily expressed by equation (16) for the k-th legitimate user k And (6) demodulating.
For a position at theta e To an eavesdropper of theta e Indicating the azimuth of the eavesdropper, the signal it receives in the l-th symbol period can be written as:
Figure BDA0003101049420000091
wherein the content of the first and second substances,
Figure BDA0003101049420000092
mean value of 0 and variance of
Figure BDA0003101049420000093
Complex additive white gaussian noise.
Specifically, when considering the k-th legal user of the eavesdropper, the eavesdropper does not know the parameters of the 4-WFRFT. After receiving all L signals, the received signal vector received by the eavesdropper can be written as:
Figure BDA0003101049420000094
wherein, n' e ＝[n e，1 ，…，n e，l ，…，n e，L ]Is a composite additive white Gaussian noise vector satisfying
Figure BDA0003101049420000095
Substituting the formula (2) into the formula (18) to obtain
Figure BDA0003101049420000096
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003101049420000097
it can be easily seen from equation (19) that the k-th received eavesdropped signal vector is composed of five components. The first component is the distorted signal of the kth legitimate user, the second component is the equivalent artificial noise caused by 4-WFRFT, the third component is the interference from the rest of the legitimate users, the fourth component is artificial noise, and the last component is additive white gaussian noise.
It is evident that since the 4-WFRFT operation changes the complex plane constellation distribution of the secret signal of the kth legitimate user, the added non-cancelable artifacts further confound the distribution of the secret signal, and the secret signal transmitted to the kth legitimate user is mixed in all secret signals, all of these operations making it impossible for an eavesdropper to correctly demodulate a useful signal even if not far away from the legitimate user or even at the same location.
The bit error rate, the secrecy rate, the robustness and the anti-interception performance of the scheme are analyzed:
1. error rate
Is provided with
Figure BDA0003101049420000101
Neglecting the path loss and normalizing the baseband modulation symbol, the signal-to-noise ratio r of the k-th legal user LU，k Can be written as:
Figure BDA0003101049420000102
due to conservation of energy before and after discrete Fourier transform, i.e. | ω 0 | 2 +|ω 1 | 2 +|ω 2 | 2 +|ω 3 | 2 =1, and since the change of the rotation split of the input sequence in the complex signal plane after 4-WFRFT transformation also causes interference to the eavesdropper receiving end, the influence factor is defined as
Figure BDA0003101049420000103
Figure BDA0003101049420000104
Therefore, as can be seen from equation (17), the average power of the confidential signal received by the eavesdropper is:
Figure BDA0003101049420000105
considering the case where the eavesdropper is very close to the kth legitimate user it eavesdrops on, i.e.
Figure BDA0003101049420000106
And assuming V =0, we can obtain:
Figure BDA0003101049420000107
according to the formula (21), the signal-to-noise ratio r of the eavesdropper EVE，k Can be expressed as:
Figure BDA0003101049420000108
since the QPS modulation is adopted in this embodiment, the theoretical error rate of the kth legitimate user and the corresponding eavesdropper in the additive white gaussian noise channel can be calculated as:
Figure BDA0003101049420000109
2. privacy rate
As can be seen from equation (14), the snr of the kth legitimate user can be defined as:
Figure BDA00031010494200001010
the achievable rate of the communication link from the transmitting end to the kth legitimate user can be written according to equation (24):
R LU，k ＝log 2 (1+SINR LU，k ) (26)
according to equation (18) and equation (20), the eavesdropper's signal-to-noise ratio can be defined as:
Figure BDA00031010494200001011
according to equation (27), the communication link reachable rate from the transmitting end to the eavesdropper can be written:
R EVE，k (θ e )＝log 2 (1+SINR EVE，k (θ e )) (28)
thus, a privacy rate is obtained:
Figure BDA0003101049420000111
3. robustness
In the foregoing analysis, we assume that all legitimate user locations are accurate. However, in an actual wireless communication scenario, whether using GPS technology or position estimation technology, there is some error in estimating the position information of the legitimate user receiver, namely:
Figure BDA0003101049420000112
wherein, delta theta d To estimate the angle error.
From equation (30), when there is an azimuth estimation error, H (θ) d ) Will be affected which will result in the normalized and zero forcing properties in equation (7) being affected.
4. Anti-blocking performance
Due to the 4-WFRFT operation, the signal has constellation rotation spread and the bit energy is evenly distributed. In this case, even if the eavesdropper knows that the transmitting end operates using the 4-WFRFT, the eavesdropper cannot demodulate a correct signal without knowing specific parameters. Meanwhile, artificial noise is utilized to further confuse the constellation distribution of the signals, and finally the anti-interference performance of the signals is improved.
5. Simulation result
FIG. 2 (a) depicts the present embodiment scheme (i.e., pro-DM) and the conventional scheme (i.e., con-DM) and the power allocation parameter β d The bit error rate BER of the artificial noise scheme (i.e., AN-DM) of (a-d) varies with the signal-to-noise ratio SNR (dB). As can be seen from fig. 3 (a): 1) When the error rate is less than 10 -2 Pro-DM is the same as AN-DM, requiring a SNR of about 0.5dB higher, in order to achieve the same bit error rate as Con-DM; 2) When eavesdroppingWhen the party is in the signal beam width, theoretical calculation and simulation results show that Pro-DM can ensure that the eavesdropping party can not eavesdrop the useful signal, and the bit error rate of the eavesdropping party of AN-DM is almost the same as that of the legal user.
FIG. 2 (b) shows the bit error rate performance of Pro-DM and AN-DM as a function of azimuth angle for the same signal-to-noise ratio. As can be seen from the figure: 1) The legal information beamwidth of Pro-DM is much narrower than AN-DM; 2) With Pro-DM, the bit error rate of the eavesdropper in each direction is almost 0.5, while with AN-DM the eavesdropper has almost the same bit error rate performance as the legitimate user. Thus, this again demonstrates that for Pro-DM, a useful signal cannot be decoded even if AN eavesdropper uses a highly sensitive signal receiver, as compared to AN-DM.
FIG. 3 (a) shows the privacy rate versus signal-to-noise ratio SNR for Pro-DM and AN-DM. As expected, when the eavesdropper is far from the legitimate user (e.g., θ) e =30 °), the secrecy rates of Pro-DM and AN-DM are almost the same. However, when the eavesdropper is also in the direction of the legitimate user (e.g., θ) e =60 °), the secret rate of the AN-DM system is 0, which means that the conventional AN-DM cannot obtain a positive secret rate when the locations of AN eavesdropper and a legitimate user are very close. In contrast, the Pro-DM privacy ratio is almost unchanged wherever the eavesdropper is located.
FIG. 3 (b) depicts the achievable rate for an eavesdropper of Pro-DM and a legitimate user as a function of SNR. As expected, regardless of how the parameters of the 4-WFRFT are changed, the reachable rate of the eavesdropper is always close to 0Bits/s/Hz, while the reachable rate of the legitimate user is always in a higher state.
FIG. 4 illustrates the bit error rate performance of Pro-DM versus SNR (dB) when the transmitting end estimates some error for the legitimate user direction. It is readily seen from the figure that at a given bit error rate condition (e.g., BER = 10) -3 ) When the azimuth estimation error is Δ θ d Is the same as an ideal state when the angle is 2 degrees; when the azimuth estimation error is delta theta d When the angle is =4 degrees, the signal-to-noise ratio is increased by about 1dB to achieve the same error rate as the ideal state; when the azimuth estimation error is delta theta d When =6 DEGAn increase of about 2dB in signal-to-noise ratio is required.
FIG. 5 shows the anti-blocking performance of Pro-DM. It is expected that the parameter mismatch of 4-WFRFT during the receiver demodulation process will lead to a drastic degradation of the error performance. In the case of V =0, if the error of the parameter α is greater than 0.1, the bit error rate performance of the eavesdropper becomes worse as the signal-to-noise ratio increases. In the case of V ≠ 0, if the error of the parameter α exceeds 2 × 10 -4 The bit error rate performance of the eavesdropper will become very poor. For the convenience of performance analysis, the parameters of the 4-WFRFT operation are set to fixed values in this embodiment, but in practical applications, all the parameters of the 4-WFRFT operation can be dynamically updated according to the proposed corresponding method, which means that the security of signal transmission will be better.
In summary, in order to improve the physical layer security performance of the signal transmission system, the present disclosure provides a multi-beam directional modulation method based on 4-WFRFT and artificial noise. The constellation distribution of the useful signal is first changed by using 4-WFRFT, and then irreversible artifacts are added to further confuse the distribution of the useful signal. The analysis and simulation results of the error rate, the privacy rate, the robustness and the anti-interception performance show that compared with the traditional multi-beam auxiliary directional modulation method, the directional modulation method provided by the disclosure has narrower information beam width, and can keep higher privacy rate when an eavesdropper is at any position.
It should be noted that although the steps of the methods of the present disclosure are depicted in the drawings in a particular order, this does not require or imply that the steps must be performed in this particular order or that all of the depicted steps must be performed to achieve desirable results. Additionally or alternatively, certain steps may be omitted, multiple steps combined into one step execution, and/or one step broken down into multiple step executions, etc. Additionally, it will also be readily appreciated that the steps may be performed synchronously or asynchronously, e.g., among multiple modules/processes/threads.
Further, in this exemplary embodiment, referring to fig. 6, this embodiment further provides a multi-beam directional modulation system based on MP-WFRFT and artificial noise, which includes a signal modulation module 100, an MP-WFRFT transformation module 200, a pre-coding module 300, a signal transmission module 400, and an inverse MP-WFRFT transformation module 500. The signal modulation module 100 is configured to modulate an input signal to obtain a symbol matrix. The MP-WFRFT transformation module 200 is configured to perform MP-WFRFT transformation on the symbol matrix to generate a first encryption matrix. The pre-coding module 300 is configured to perform artificial noise processing on the first encryption matrix to obtain a second encryption matrix. The signal transmission module 400 is configured to transmit the second encryption matrix to a receiving end through a channel by using a directional modulation method. And an inverse MP-WFRFT transform module 500, configured to perform inverse MP-WFRFT transform on the signal vector received by the receiving end and decrypt the signal vector to complete the demodulation process.
With regard to the system in the above embodiment, the specific manner in which each unit performs the operation has been described in detail in the embodiment related to the method, and will not be described in detail here.
It should be noted that although several units of the system for action execution are mentioned in the above detailed description, such a division is not mandatory. Indeed, the features and functions of two or more units described above may be embodied in one unit, in accordance with embodiments of the present disclosure. Conversely, the features and functions of one unit described above may be further divided into embodiments by a plurality of units. Some or all of the elements may be selected according to actual needs to achieve the objectives of the solution of the present disclosure. One of ordinary skill in the art can understand and implement it without inventive effort.
Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure disclosed herein. This application is intended to cover any variations, uses, or adaptations of the disclosure following, in general, the principles of the disclosure and including such departures from the present disclosure as come within known or customary practice within the art to which the disclosure pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.

Claims (5)

1. A multi-beam directional modulation method based on MP-WFRFT and artificial noise is characterized by comprising the following steps:
modulating an input signal to obtain a symbol matrix, wherein the size of the symbol matrix is K multiplied by L, K is the number of legal user receiving ends, and L is the length of a symbol data stream in the symbol matrix;
performing MP-WFRFT conversion on the symbol matrix to generate a first encryption matrix, and performing MP-WFRFT conversion on the symbol matrix by using the following formula to generate the first encryption matrix:
Figure FDA0003905827880000011
Figure FDA0003905827880000012
wherein, F (α，V) Represents 4-WFRFT, Z is the first encryption matrix, s k ＝[s k，1 ，…，s k，l ，…，s k，L ]Is a symbol data stream that is transmitted independently to the receiving end of the kth said legitimate user,
Figure FDA0003905827880000013
Figure FDA0003905827880000014
respectively represents s k One to three order discrete Fourier transform, omega 0 、ω 1 、ω 2 And ω 3 Is a weight factor, where ω i The calculation formula of (2) is as follows:
Figure FDA0003905827880000015
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003905827880000016
for modulation order, V = [ MV, NV =]Is a vector of parameters, and MV = [ m = 0 ，m 1 ，m 2 ，m 3 ]，NV＝[n 0 ，n 1 ，n 2 ，n 3 ]Are all integer vectors, i =0,1,2,3;
and carrying out artificial noise processing on the first encryption matrix to obtain a second encryption matrix, wherein the calculation formula of the second encryption matrix is as follows:
Q＝[q 1 ，q 2 ，…，q l ，…，q L ]，
Figure FDA0003905827880000017
wherein Q is the second encryption matrix, P t Is the total transmit power, an
Figure FDA0003905827880000018
V d As a precoding matrix, t AN For the precoding vector, u is the inserted complex artificial noise vector at the same rate as the baseband symbol conversion,
Figure FDA0003905827880000019
transpose the l row vector of the first encryption matrix Z;
the second encryption matrix is transmitted to a receiving end through a channel by a direction modulation method;
and the receiving end performs inverse MP-WFRFT conversion and decryption on the received signal vector to finish the demodulation process.
2. The multi-beam directional modulation method of claim 1, characterized in that V d The calculation formula of (c) is:
Figure FDA0003905827880000026
wherein H H (θ d )V d ＝I K ，
Figure FDA0003905827880000021
θ d Indicating the azimuth angle of the legitimate user,
Figure FDA0003905827880000022
represent
Figure FDA0003905827880000023
Normalized steering vector at the receiving end of any legal user of direction, I K Expressed as an identity matrix of K size, H (θ) d ) A total steering matrix representing steering vectors for K legitimate user receivers,
Figure FDA0003905827880000027
complex conjugate transpose H representing the total steering matrix H (θ d ) Moore-Penrose inverse matrix of (g).
3. The multi-beam directional modulation method of claim 1, wherein the received signal vector is decrypted using an inverse MP-WFRFT transform using the following equation:
Figure FDA0003905827880000024
Figure FDA0003905827880000025
wherein, F (-α，V) Representation 4-IWFRFT, y k For the received signal vector, n k Is composite Gaussian white noise n 'after inverse MP-WFRFT conversion' k ＝[n k，1 ，…，n k，l ，…，n k，L ]As a complex additive white Gaussian noise vector。
4. The multi-beam directional modulation method of claim 1, wherein the modulation is a QPSK modulation.
5. A multi-beam directional modulation system based on MP-WFRFT and artificial noise, comprising:
the system comprises a signal modulation module, a symbol matrix and a symbol decoding module, wherein the signal modulation module is used for modulating an input signal to obtain the symbol matrix, and the size of the symbol matrix is K multiplied by L, wherein K is the number of legal user receiving ends, and L is the length of a symbol data stream in the symbol matrix;
the MP-WFRFT conversion module is used for performing MP-WFRFT conversion on the symbol matrix to generate a first encryption matrix, and performing MP-WFRFT conversion on the symbol matrix to generate a first encryption matrix by using the following formula:
Figure FDA0003905827880000031
Figure FDA0003905827880000032
wherein, F (α，V) Representing 4-WFRFT, Z being said first encryption matrix, s k ＝[s k，1 ，…，s k，l ，…，s k，L ]Is a symbol data stream that is transmitted independently to the receiving end of the kth said legitimate user,
Figure FDA0003905827880000033
Figure FDA0003905827880000034
respectively represent s k One to three order discrete Fourier transform, omega 0 、ω 1 、ω 2 And ω 3 Is a weight factor, where ω i The calculation formula of (2) is as follows:
Figure FDA0003905827880000035
wherein the content of the first and second substances,
Figure FDA0003905827880000036
for modulation order, V = [ MV, NV =]Is a vector of parameters, and MV = [ m ] 0 ，m 1 ，m 2 ，m 3 ]，NV＝[n 0 ，n 1 ，n 2 ，n 3 ]Are all integer vectors, i =0,1,2,3;
the pre-coding module is configured to perform artificial noise processing on the first encryption matrix to obtain a second encryption matrix, where a calculation formula of the second encryption matrix is as follows:
Q＝[q 1 ，q 2 ，…，q l ，…，q L ]，
Figure FDA0003905827880000037
wherein Q is the second encryption matrix, P t Is the total transmit power, an
Figure FDA0003905827880000038
V d As a precoding matrix, t AN For the precoding vector, u is the inserted complex artificial noise vector at the same rate as the baseband symbol conversion,
Figure FDA0003905827880000039
transpose the 1 st row vector of the first encryption matrix Z;
the signal transmission module is used for transmitting the second encryption matrix to a receiving end through a channel by a direction modulation method;
and the inverse MP-WFRFT conversion module is used for performing inverse MP-WFRFT conversion on the signal vector received by the receiving end and decrypting the signal vector to complete the demodulation process.
CN202110623512.3A 2021-06-04 2021-06-04 Multi-beam directional modulation method and system based on MP-WFRFT and artificial noise Active CN113328969B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110623512.3A CN113328969B (en) 2021-06-04 2021-06-04 Multi-beam directional modulation method and system based on MP-WFRFT and artificial noise

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110623512.3A CN113328969B (en) 2021-06-04 2021-06-04 Multi-beam directional modulation method and system based on MP-WFRFT and artificial noise

Publications (2)

Publication Number Publication Date
CN113328969A CN113328969A (en) 2021-08-31
CN113328969B true CN113328969B (en) 2022-12-09

Family

ID=77419842

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110623512.3A Active CN113328969B (en) 2021-06-04 2021-06-04 Multi-beam directional modulation method and system based on MP-WFRFT and artificial noise

Country Status (1)

Country Link
CN (1) CN113328969B (en)

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110365374A (en) * 2019-06-26 2019-10-22 西北大学 The accurate radio transmitting method of safety based on the modulation of more phased array directions

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105187339B (en) * 2014-06-06 2018-12-07 华为技术有限公司 A kind of compensation method of doubly selective channel, system and relevant apparatus
CN109150368A (en) * 2018-06-22 2019-01-04 达新宇 A kind of anti-parameter scanning communication means of satellite based on ML-WFRFT and AN auxiliary
CN112583574B (en) * 2020-12-04 2023-01-20 中国人民解放军空军工程大学 WFRFT transmission method and system based on two-dimensional chaotic mapping amplitude phase encryption

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110365374A (en) * 2019-06-26 2019-10-22 西北大学 The accurate radio transmitting method of safety based on the modulation of more phased array directions

Also Published As

Publication number Publication date
CN113328969A (en) 2021-08-31

Similar Documents

Publication Publication Date Title
Shu et al. Secure and precise wireless transmission for random-subcarrier-selection-based directional modulation transmit antenna array
Fu et al. Robust secure beamforming design for two-user downlink MISO rate-splitting systems
CN106850021B (en) Method and device for realizing wireless communication physical layer safety based on polarization precoding
JP2004032679A (en) Communication apparatus and communication system
WO2004073226A1 (en) Transmitter apparatus and radio communication method
CN108366026B (en) Physical layer safety transmission method of artificial noise based on constellation rotation
Wei et al. Secure directional modulation with few-bit phase shifters: Optimal and iterative-closed-form designs
Wu et al. Performance analysis of secret precoding-aided spatial modulation with finite-alphabet signaling
JP2006230025A (en) Communication apparatus and communication method
Althunibat et al. Enhancing spatial modulation system performance through signal space diversity
Luo et al. Polarization filtering based physical-layer secure transmission scheme for dual-polarized satellite communication
Kalantari et al. Secure M-PSK communication via directional modulation
CN110290548A (en) A kind of secrecy rate calculations method of the collaboration space modulating system based on man made noise
Hafez et al. Secure multiple-users transmission using multi-path directional modulation
Krivochiza et al. Computationally and energy efficient symbol-level precoding communications demonstrator
Harper et al. MIMO wireless secure communication using data-carrying artificial noise
You et al. Spatial and directional modulation with scrambling
Helmy et al. On the robustness of spatial modulation to I/Q imbalance
CN113328969B (en) Multi-beam directional modulation method and system based on MP-WFRFT and artificial noise
US10862547B2 (en) MIMO-OFDM-based cooperative communication system for interference mitigation between cells in heterogeneous network and cooperative communication method using the same
Tubail et al. Physical Layer Security in Downlink of Cell-Free Massive MIMO With Imperfect CSI
Wu et al. Polarization shift keying for wireless communication
CN111224702A (en) Minimum regularization transmitting power beam forming method based on Lagrange multiplier
Song Achievable secrecy rate of artificial fast-fading techniques and secret-key assisted design for MIMO wiretap channels with multiantenna passive eavesdropper
Krunz et al. Secure Linear Precoding in Overloaded MU-MIMO Wireless Networks

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant