OFDM transmission method and system based on two-dimensional chaotic mapping amplitude and phase encryption

Abstract

The present disclosure is about an OFDM transmission method and system based on two-dimensional chaotic mapping amplitude phase encryption. The method comprises the following steps: performing IFFT transformation on the modulated column vector after symbol mapping is completed to generate a frequency domain signal, and obtaining the column vector of the frequency domain signal; generating a first sequence and a second sequence through two-dimensional chaotic mapping, and using the first sequence and the second sequence to perform amplitude expansion and constellation rotation on the column vector of the frequency domain signal to generate an encrypted signal; after the encrypted signal is transmitted to the receiving end through the channel, the receiving end generates a decryption matrix according to the parameters of the two-dimensional chaotic mapping, and uses the decryption matrix to decrypt the encrypted signal; performing FFT transformation on the decrypted data to complete symbol demodulation. The present disclosure enhances the physical layer security performance of the OFDM transmission system.

Description

Technical Field

[0001] The present disclosure relates to the field of secure communication technology, and in particular to an OFDM transmission method and system based on two-dimensional chaotic mapping amplitude and phase encryption. Background Art

[0002] Orthogonal Frequency Division Multiplexing (OFDM) is a multi-carrier transmission (Multi Carrier Modulation, MCM) scheme that solves the problem of high receiver complexity of traditional single-carrier time-domain transmission technology. It can realize parallel transmission of high-speed serial data through frequency division multiplexing and has good resistance to multipath fading. It is an important modulation and demodulation technology commonly used in various wireless communication standards.

[0003] As we all know, the wireless channel is an open channel, and wireless transmission signals are subject to the risk of malicious eavesdropping and detection. At present, the research on OFDM transmission technology mainly focuses on aspects such as receiver processing algorithms, but there are still deficiencies in how to prevent eavesdropping activities by non-cooperative eavesdroppers and improve the physical layer security performance of OFDM systems. Therefore, it is necessary to improve one or more problems existing in the above-mentioned related technical solutions to enhance the physical layer security performance of OFDM systems.

[0004] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute the prior art known to ordinary technicians in the field. Summary of the invention

[0005] The purpose of the embodiments of the present disclosure is to provide an OFDM transmission method and system based on two-dimensional chaotic mapping amplitude and phase encryption to enhance the physical layer security of the OFDM system.

[0006] According to a first aspect of an embodiment of the present disclosure, an OFDM transmission method based on two-dimensional chaotic mapping amplitude phase encryption is provided, the method comprising the following steps:

[0007] Performing IFFT transformation on the modulation column vector after symbol mapping is completed to generate a frequency domain signal, and obtaining a column vector of the frequency domain signal;

[0008] Generate a first sequence and a second sequence through a two-dimensional chaotic map, and use the first sequence and the second sequence to perform amplitude expansion and constellation rotation on the column vector of the frequency domain signal to generate an encrypted signal;

[0009] After the encrypted signal is transmitted to the receiving end through the channel, the receiving end generates a decryption matrix according to the parameters of the two-dimensional chaotic map, and uses the decryption matrix to decrypt the encrypted signal;

[0010] Perform FFT transformation on the decrypted data to complete symbol demodulation.

[0011] In one embodiment of the present disclosure, the step of performing amplitude expansion and constellation rotation on the column vector of the frequency domain signal using the first sequence and the second sequence further includes the following steps:

[0012] Using the first sequence to extend and encrypt the amplitude of the modulation symbol, and using the second sequence to rotate and encrypt the phase of the modulation symbol, to generate an encryption matrix of the amplitude and phase of the modulation symbol;

[0013] The modulation column vector is encrypted according to the encryption matrix.

[0014] In one embodiment of the present disclosure, in the step of generating the encrypted matrix of the amplitude and phase of the frequency domain signal, the first sequence first obtains the amplitude expansion factor r by formula (1): n , and then generate the amplitude encryption matrix R of the frequency domain signal through formula (2);

[0015]

[0016] R = diag(r) (2);

[0017] Where u is the first sequence, r = (r 0 ,r 1 ,…,r N-1 ) T .

[0018] In one embodiment of the present disclosure, in the step of generating the encrypted matrix of the amplitude and phase of the frequency domain signal, the second sequence first obtains the phase rotation factor φ by formula (3): n , and then generate the phase encryption matrix Φ of the frequency domain signal through formula (4);

[0019]

[0020]

[0021] Among them, v is the second sequence.

[0022] In one embodiment of the present disclosure, in the step of encrypting the column vector of the frequency domain signal according to the encryption matrix, encryption is performed using formula (5);

[0023] X C=RΦX (5);

[0024] Wherein, X is the column vector of the frequency domain signal.

[0025] In one embodiment of the present disclosure, the decryption matrix and the encryption matrix are inverse matrices of each other.

[0026] In one embodiment of the present disclosure, in the step of generating a decryption matrix according to the parameters of the two-dimensional chaotic map and decrypting the encrypted signal using the decryption matrix, the decryption formula is:

[0027] X d =R -1 Φ -1 y (6);

[0028] Among them, y is the signal received by the receiving end;

[0029] R -1 is the amplitude decryption matrix of the frequency domain signal, and

[0030] Φ -1 is the phase decryption matrix of the frequency domain signal, and Φ -1 =Φ H .

[0031] In one embodiment of the present disclosure, the two-dimensional chaotic map is a Hénon chaotic map.

[0032] In one embodiment of the present disclosure, the modulation mode of the symbol mapping is PSK modulation, ASK modulation or QAM modulation.

[0033] According to a second aspect of an embodiment of the present disclosure, an OFDM transmission system based on two-dimensional chaotic mapping amplitude phase encryption is provided, the system comprising:

[0034] An IFFT transform unit, used for performing IFFT transform on the modulation column vector after symbol mapping is completed, generating a frequency domain signal, and obtaining a column vector of the frequency domain signal;

[0035] A chaotic mapping encryption unit, used to generate a first sequence and a second sequence through a two-dimensional chaotic mapping, and use the first sequence and the second sequence to perform amplitude expansion and constellation rotation on the column vector of the frequency domain signal to generate an encrypted signal;

[0036] A decryption unit, used to generate a decryption matrix according to the parameters of the two-dimensional chaotic map, and use the decryption matrix to decrypt the encrypted signal transmitted to the receiving end;

[0037] The FFT transform unit is used to perform FFT transform on the decrypted data to complete the demodulation process.

[0038] The technical solution provided by the present disclosure may have the following beneficial effects:

[0039] In the embodiment of the present disclosure, after the symbol mapping and serial-to-parallel conversion of the input signal are completed, the IFFT transformation is performed, and then the amplitude and phase encryption matrices are generated respectively using a two-dimensional chaotic sequence, so that the frequency domain signal obtained after the IFFT transformation is expanded in amplitude and controllably rotated in phase, and then a cyclic prefix is ​​added and transmitted to the receiving end. The receiving end uses the two-dimensional chaotic mapping parameters that are exactly the same as those of the transmitting end to generate the amplitude and phase decryption matrices respectively, and decrypt the encrypted signal. Finally, the decrypted signal is subjected to FFT transformation and the original transmitted signal is demodulated. Due to the initial value sensitivity of the two-dimensional chaotic sequence, the cooperative receiver and the transmitter have the same modulation parameters and chaos initialization parameters, and the eavesdropping party cannot correctly process the received signal even if there is a very small parameter deviation, thereby enhancing the physical layer security performance of the OFDM transmission system.

[0040] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The accompanying drawings herein are incorporated into the specification and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification are used to explain the principles of the present disclosure. Obviously, the accompanying drawings described below are only some embodiments of the present disclosure, and for ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without creative work.

[0042] Figure 1 A schematic diagram showing the steps of an OFDM transmission method based on two-dimensional chaotic mapping amplitude phase encryption in an exemplary embodiment of the present disclosure is shown;

[0043] Figure 2 A block diagram showing a transmission method in an exemplary embodiment of the present disclosure;

[0044] Figure 3 The influence of the Hénon initial value on the chaotic sequence u in the exemplary embodiment of the present disclosure is shown;

[0045] Figure 4 The attractor of the Hénon map in the exemplary embodiment of the present disclosure is shown;

[0046] Figure 5 A bifurcation diagram of a Hénon map in an exemplary embodiment of the present disclosure is shown;

[0047] Figure 6 A diagram showing the anti-interception performance analysis in an exemplary embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0048] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that the disclosure will be more comprehensive and complete and to fully convey the concepts of the 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.

[0049] In addition, the accompanying drawings are only schematic illustrations of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the figures represent the same or similar parts, and their repeated description will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor devices and / or microcontroller devices.

[0050] In this example implementation, an OFDM transmission method based on two-dimensional chaotic mapping amplitude phase encryption is first provided. Figure 1 As shown in , the method may include the following steps:

[0051] Step S101: performing IFFT transformation on the modulation column vector after symbol mapping to generate a frequency domain signal, and obtaining a column vector of the frequency domain signal;

[0052] Step S102: Generate a first sequence and a second sequence through a two-dimensional chaotic map, and use the first sequence and the second sequence to perform amplitude expansion and constellation rotation on the column vector of the frequency domain signal to generate an encrypted signal;

[0053] Step S103: After the encrypted signal is transmitted to the receiving end through the channel, the receiving end generates a decryption matrix according to the parameters of the two-dimensional chaotic map, and uses the decryption matrix to decrypt the encrypted signal;

[0054] Step S104: Perform FFT transformation on the decrypted data to complete symbol demodulation.

[0055] In the embodiment of the present disclosure, after the symbol mapping and serial-to-parallel conversion of the input signal are completed, the IFFT transformation is performed, and then the amplitude and phase encryption matrices are generated respectively using a two-dimensional chaotic sequence, so that the frequency domain signal obtained after the IFFT transformation is expanded in amplitude and controllably rotated in phase, and then a cyclic prefix is ​​added and transmitted to the receiving end. The receiving end uses the two-dimensional chaotic mapping parameters that are exactly the same as those of the transmitting end to generate the amplitude and phase decryption matrices respectively, and decrypt the encrypted signal. Finally, the decrypted signal is subjected to FFT transformation and the original transmitted signal is demodulated. Due to the initial value sensitivity of the two-dimensional chaotic sequence, the cooperative receiver and the transmitter have the same modulation parameters and chaos initialization parameters, and the eavesdropping party cannot correctly process the received signal even if there is a very small parameter deviation, thereby enhancing the physical layer security performance of the OFDM transmission system.

[0056] Below, each step of the above method in this example implementation will be described in more detail.

[0057] In step S101, the modulation mode of symbol mapping may be PSK modulation, ASK modulation or QAM modulation.

[0058] Specifically, assuming that the modulation column vector after symbol mapping is x, first perform IFFT transformation on x to the frequency domain, which can be expressed as

[0059] X=F H x (7)

[0060] Where F is the normalized DFT matrix, which can be expressed as:

[0061]

[0062] In formula (8), W N =e -2πj / N .

[0063] Chaos reflects the inherent randomness of a certain system, which is extremely sensitive to initial values. A very small disturbance can produce a huge deviation, that is, the phenomenon of "a small error leads to a huge difference". In step S102, the two-dimensional chaotic map used in this example is the Hénon chaotic map, which is a typical two-dimensional chaotic map that can generate two sets of chaotic sequences at the same time, which is conducive to controlling multiple parameters of the system at the same time. Of course, the present disclosure does not limit this, and other chaotic maps can also be used in other examples.

[0064] The step of performing amplitude expansion and constellation rotation on the column vector of the frequency domain signal by using the first sequence and the second sequence in step S102 further includes the following steps:

[0065] Step S1021: using the first sequence to extend and encrypt the amplitude of the modulation symbol, and using the second sequence to rotate and encrypt the phase of the modulation symbol, to generate an encryption matrix of the amplitude and phase of the modulation symbol;

[0066] Step S1022: encrypt the modulated column vector according to the encryption matrix.

[0067] In a specific example, the Hénon two-dimensional chaotic map is used to generate the first sequence u=[u 0 ,u 1 ,…,u N-1 ] T and the second sequence v = [v 0 ,v 1 ,…,v N-1 ] T , which is used to perform amplitude expansion and constellation rotation on the column vector of the frequency domain signal after the serial-to-parallel transformation. The generation formula is as follows:

[0068]

[0069] v n+1 =bu n

[0070] In the above formula, when the parameter values ​​a=1.4 and b=0.3, chaotic phenomenon occurs.

[0071] Then, using the first sequence u=[u 0 ,u 1 ,…,u N-1 ] T and the second sequence v = [v 0 ,v 1 ,…,v N-1 ] T The amplitude and phase are expanded and encrypted respectively to obtain the encrypted matrices of the amplitude and phase of the frequency domain signal.

[0072] Specifically, the first sequence u first obtains the amplitude expansion factor r through formula (1): n In formula (1), max(|u|) means taking the absolute value of each element in the sequence u and then taking the maximum value. Then, the elements in formula (1) are converted into a diagonal matrix to obtain formula (2), which is used to expand and encrypt the amplitude information of the frequency domain signal and obtain the amplitude encryption matrix R. In formula (2), r = (r 0 ,r 1 ,…,r N-1 ) T To generate a column vector of elements using formula (1), diag(·) is a diagonal matrix operation.

[0073]

[0074] R = diag(r) (2).

[0075] The second sequence v first obtains the phase rotation factor φ through formula (3) n , and then use formula (4) to expand and encrypt the phase information of the frequency domain signal to obtain the phase encryption matrix Φ.

[0076]

[0077]

[0078] Finally, according to the amplitude encryption matrix R and phase encryption matrix Φ of the frequency domain signal, the column vector of the frequency domain signal is encrypted using formula (5) to obtain the encrypted signal X C , where X is the column vector of the frequency domain signal.

[0079] X C =RΦX (5);

[0080] In step S103, the encrypted signal X C After parallel-to-serial conversion and adding a cyclic prefix (CP), it is transmitted to the receiving end through the channel.

[0081] After removing the CP and converting the serial to parallel, the receiving end can be written as

[0082] y=X C +n (9)

[0083] Where n is a Gaussian white noise vector.

[0084] In addition, due to the cooperation between the receiver and the transmitter, the initial value of the Hénon two-dimensional chaotic sequence and the two-dimensional chaotic mapping parameters such as a and b can be accurately obtained, and then a decryption matrix is ​​generated according to the above parameters, and the encrypted signal is decrypted using the decryption matrix, wherein the decryption matrix and the encryption matrix are inverse matrices of each other.

[0085] The specific decryption formula is:

[0086] X d =R -1 Φ -1 y (6)

[0087] Among them, y is the signal received by the receiving end.

[0088] Furthermore, since the amplitude encryption matrix R is a real diagonal matrix, its amplitude inverse matrix, i.e., the amplitude decryption matrix formula is:

[0089]

[0090] The phase inverse matrix, i.e. the phase decryption matrix formula is:

[0091] Φ -1 =Φ H (11)

[0092] Then the decryption formula can be written as:

[0093]

[0094] In step S104, the decrypted data is subjected to FFT transformation, which can be expressed as

[0095]

[0096] Finally, parallel-to-serial conversion and symbol demapping are performed before decision processing.

[0097] The entire signal transmission process mentioned above can be referred to Figure 2 .

[0098] A computer simulation test was conducted on the above encrypted information to prove its encryption effect:

[0099] Experiment 1. Key sensitivity - initial value impact

[0100] Figure 3 The amplitude value change of the first sequence u generated by the Hénon two-dimensional chaotic map under different initial values. Obviously, in the sequence generation process, the amplitude values ​​of the first few chaotic sequences are relatively close, but as the number of iterations increases, the amplitude values ​​of the generated chaotic sequences change greatly and have less correlation.

[0101] Figure 4 and Figure 5 are the attractor and bifurcation diagram of the Hénon map, respectively. The parameter b is fixed to 0.3, u 0 and v 0 The initial value is (0,0), the value range of a is 0-1.4, when a=0.32, the sequence u enters period 2, when a=0.9, it enters period 4, and when a=1.4, the sequence u presents a full mapping.

[0102] Experiment 2. Analysis of key sensitivity and anti-interception performance

[0103] from Figure 6 As can be seen from the above, since the legitimate user can accurately obtain various parameters of the system, its system performance has a significant advantage over the eavesdropping user. Even if we assume that the receiver can obtain all information except the initial value of the Hénon two-dimensional chaotic map, and the initial value of the chaotic sequence obtained by the eavesdropper is only 1e different from the correct value, -10Although there is a difference of orders of magnitude, the interception performance of the eavesdropper is still very poor, and the bit error rate (BER) is always close to 0.5, which shows that the key sensitivity of the proposed algorithm is high and can meet the requirements of confidential communication.

[0104] In summary, the OFDM transmission method based on two-dimensional chaotic mapping amplitude and phase encryption provided by the present disclosure enhances the physical layer security performance of the OFDM transmission system.

[0105] It should be noted that, although the steps of the method in the present disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in this specific order, or that all the steps shown must be performed to achieve the desired results. Additionally or alternatively, some steps may be omitted, multiple steps may be combined into one step for execution, and / or one step may be decomposed into multiple steps for execution, etc. In addition, it is also easy to understand that these steps may be, for example, executed synchronously or asynchronously in multiple modules / processes / threads.

[0106] Furthermore, in this example implementation, an OFDM transmission system based on two-dimensional chaotic mapping amplitude phase encryption is also provided, which may include an IFFT transformation unit, a chaotic mapping encryption unit, a decryption unit, and an FFT transformation unit. Among them, the IFFT transformation unit is used to perform IFFT transformation on the modulation column vector after the symbol mapping is completed, generate a frequency domain signal, and obtain the column vector of the frequency domain signal. The chaotic mapping encryption unit is used to generate a first sequence and a second sequence through a two-dimensional chaotic mapping, and use the first sequence and the second sequence to perform amplitude expansion and constellation rotation on the column vector of the frequency domain signal to generate an encrypted signal. The decryption unit is used to generate a decryption matrix according to the parameters of the two-dimensional chaotic mapping, and use the decryption matrix to decrypt the encrypted signal transmitted to the receiving end. The FFT transformation unit is used to perform FFT transformation on the decrypted data, thereby completing the demodulation process.

[0107] Regarding the system in the above embodiment, the specific manner in which each unit performs operations has been described in detail in the embodiment of the method, and will not be elaborated here.

[0108] It should be noted that although several units of the system for action execution are mentioned in the above detailed description, this division is not mandatory. In fact, according to the embodiment of the present disclosure, the features and functions of two or more units described above can be concretized in one unit. Conversely, the features and functions of a unit described above can be further divided into multiple units for concretization. Some or all of the units can be selected according to actual needs to achieve the purpose of the disclosed solution. Those of ordinary skill in the art can understand and implement it without paying creative work.

[0109] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. This application is intended to cover any modification, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary techniques in the art that are not disclosed in the present disclosure. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present disclosure are indicated by the appended claims.

Claims

1. An OFDM transmission method based on two-dimensional chaotic mapping amplitude and phase encryption, It is characterized in that The following steps are involved: Performing IFFT transformation on the modulation column vector after symbol mapping is completed to generate a frequency domain signal, and obtaining a column vector of the frequency domain signal, wherein the modulation mode of the symbol mapping is PSK modulation, ASK modulation or QAM modulation; Generate a first sequence and a second sequence through a two-dimensional chaotic map, and use the first sequence and the second sequence to perform amplitude expansion and constellation rotation on the column vector of the frequency domain signal to generate an encrypted signal; After the encrypted signal is transmitted to the receiving end through the channel, the receiving end generates a decryption matrix according to the parameters of the two-dimensional chaotic map, and uses the decryption matrix to decrypt the encrypted signal; Perform FFT transformation on the decrypted data to complete symbol demodulation; The step of performing amplitude expansion and constellation rotation on the column vector of the frequency domain signal by using the first sequence and the second sequence further includes the following steps: Using the first sequence to expand and encrypt the amplitude of the frequency domain signal, and using the second sequence to rotate and encrypt the phase of the frequency domain signal, to generate an encrypted matrix of the amplitude and phase of the frequency domain signal; The column vector of the frequency domain signal is encrypted according to the encryption matrix.

2. The transmission method according to claim 1, It is characterized in that In the step of generating the encryption matrix for the amplitude and phase of the frequency-domain signal, the first sequence first obtains the amplitude expansion factor through Equation (1) , and then generates the amplitude encryption matrix of the frequency-domain signal through Equation (2) ; （1）； （2）； in, For the first sequence, .

3. The transmission method according to claim 2, It is characterized in that In the step of generating the encrypted matrix of the amplitude and phase of the frequency domain signal, the second sequence first obtains the phase rotation factor by formula (3): , and then generate the phase encryption matrix of the frequency domain signal through formula (4) ; （3）； （4）； in, For the second sequence.

4. The transmission method according to claim 3, It is characterized in that In the step of encrypting the column vector of the frequency domain signal according to the encryption matrix, encryption is performed using formula (5); （5）； in, X is the column vector of the frequency domain signal.

5. The transmission method according to claim 4, It is characterized in that The decryption matrix and the encryption matrix are inverse matrices of each other.

6. The transmission method according to claim 5, It is characterized in that In the step of generating a decryption matrix according to the parameters of the two-dimensional chaotic map and decrypting the encrypted signal using the decryption matrix, the decryption formula is: （6）； in, is the signal received by the receiving end; is the amplitude decryption matrix of the frequency-domain signal, and is the phase decryption matrix of the frequency domain signal, and .

7. The transmission method according to claim 1, It is characterized in that The two-dimensional chaotic map is a Hénon chaotic map.

8. An OFDM transmission system based on two-dimensional chaotic mapping amplitude and phase encryption, It is characterized in that include: An IFFT transform unit, used for performing IFFT transform on the modulation column vector after symbol mapping is completed, generating a frequency domain signal, and obtaining a column vector of the frequency domain signal, wherein the modulation mode of the symbol mapping is PSK modulation, ASK modulation or QAM modulation; A chaotic mapping encryption unit, used to generate a first sequence and a second sequence through a two-dimensional chaotic mapping, and use the first sequence and the second sequence to perform amplitude expansion and constellation rotation on the column vector of the frequency domain signal to generate an encrypted signal; A decryption unit, used to generate a decryption matrix according to the parameters of the two-dimensional chaotic map, and use the decryption matrix to decrypt the encrypted signal transmitted to the receiving end; An FFT transform unit is used to perform FFT transform on the decrypted data to complete the demodulation process; The process of performing amplitude expansion and constellation rotation on the column vector of the frequency domain signal by using the first sequence and the second sequence includes: Using the first sequence to expand and encrypt the amplitude of the frequency domain signal, and using the second sequence to rotate and encrypt the phase of the frequency domain signal, to generate an encrypted matrix of the amplitude and phase of the frequency domain signal; The column vector of the frequency domain signal is encrypted according to the encryption matrix.

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