CN107135060B - Artificial noise signal construction method and physical layer encryption method - Google Patents

Artificial noise signal construction method and physical layer encryption method Download PDF

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CN107135060B
CN107135060B CN201710153297.9A CN201710153297A CN107135060B CN 107135060 B CN107135060 B CN 107135060B CN 201710153297 A CN201710153297 A CN 201710153297A CN 107135060 B CN107135060 B CN 107135060B
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CN107135060A (en
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高宝建
黄士亚
景利
王少迪
胡云
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Northwestern University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/002—Countermeasures against attacks on cryptographic mechanisms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
    • H04L9/0618—Block ciphers, i.e. encrypting groups of characters of a plain text message using fixed encryption transformation
    • H04L9/0631—Substitution permutation network [SPN], i.e. cipher composed of a number of stages or rounds each involving linear and nonlinear transformations, e.g. AES algorithms

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Abstract

The invention provides an artificial noise signal construction method and a physical layer encryption method, which are characterized in that DFT conversion is firstly carried out on an artificial noise key sequence in a complex form, zero insertion is carried out, and then the DFT conversion and zero insertion are sequentially and respectively carried out
Figure DDA0001246275020000011
The point IDFT transformation generates discrete noise signals, so that the peak-to-average ratio of the noise signals is low, the bandwidth is slightly smaller than the signal bandwidth, and the power is controllable. And the modulated OFDM signal is superposed with the artificial noise signal to realize the encryption of data. The encryption process enables the noise signals and the OFDM signals to realize mutual overlapping interference and mutual protection of frequency spectrums in a radio frequency domain, destroys the orthogonality among original signal subcarriers, inhibits carrier leakage and resists spectrum analysis, thereby ensuring the safety of data and algorithm.

Description

Artificial noise signal construction method and physical layer encryption method
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to an artificial noise signal construction method and a physical layer encryption method.
Background
With the rapid development of wireless communication technology towards the direction of convergence and broadband, the security threats faced by the wireless communication technology are more complicated and diversified, and how to ensure the secure transmission of data while maintaining broadband and convergence is a serious and realistic problem.
To solve this problem, the idea of physical layer encryption has been proposed. Encryption is carried out on a physical layer, so that the algorithm complexity can be effectively reduced while the security is ensured; the flag information, the signaling information and the like can be protected; to a certain extent, the problem of the link layer encryption can be compensated. The existing physical layer encryption algorithm has the security analysis limited in the aspect of symbol operation, does not consider the problems of carrier leakage and spectrum leakage of a radio frequency domain, and a large number of algorithms are difficult to resist the spectrum analysis attack.
Disclosure of Invention
Aiming at the technical problems of poor safety, carrier leakage and incapability of resisting spectrum analysis attack in the conventional physical layer encryption method, the invention provides an artificial noise signal construction method and a physical layer encryption method, which are specifically realized by the following technical scheme:
a method of constructing an artificial noise signal, comprising the steps of:
firstly, mN/2bit information is generated in the counter working mode of AES encryption algorithm, and 2 bits of information controlled by regulating factor α are carried out on the informationmQAM constellation mapping to obtain N/2 complex symbol keys a1,a2,...,aN/2；
Wherein N represents the number of sub-carriers of the OFDM system in one period, and m represents 2mA QAM constellation mapping mode, wherein m is more than or equal to 2 and less than or equal to 8;
step two: for obtaining complex symbol key a1,a2,...,aN/2Performing N/2 point DFT conversion to obtain symbol sequence containing N/2 complex symbols, inserting 0 behind each symbol in the symbol sequence to obtain new noise symbol c1,c2,...,cN；
Step three: judging the new noise symbol c1,c2,...,cNWhether the following conditions are satisfied:
Figure BDA0001246275000000021
wherein k, h is 1,2, N/2 in formula (1)ν，l＝1，2，...2νV is a positive integer; if a new noise symbol c is generated1,c2,...,cNIf said condition is satisfied, the new noise symbol c is selected1,c2,...,cNRespectively do in turn
Figure BDA0001246275000000022
Point IDFT transform to generate artificial noise signal sCO(k) K is 1,2,. cndot.n; otherwise, repeating the first step and the second step until the artificial noise signal s is foundCO(k),k＝1,2,...,N。
The invention also provides a method for using the obtained artificial noise signal for physical layer encryption, which comprises the steps of superposition based on a discrete signal mode and superposition based on a continuous signal mode;
the superposition based on the discrete signal mode comprises the following steps:
the method comprises the following steps: the information to be encrypted is transformed into symbol information m after constellation mapping1,m2,...,mNPerforming IDFT on the symbol information to generate OFDM signal sOFDM(k) (ii) a Wherein k is 1,2,3.. N;
step two: OFDM signal s to be generated according to equation (2)OFDM(k) And said artificial noise signal sCO(k) Are superposed to generate an encrypted signal sCO-OFDM(k)：
sCO-OFDM(k)＝sOFDM(k)+sCO(k) (2)
Formula (2) wherein k is 1,2,3.
Step three: for encrypted signal sCO-OFDM(k) Sequentially performing cyclic prefix adding, D/A conversion, intermediate frequency modulation and up-conversion processing, and sending the processed encrypted signal to a signal receiver;
step four: the signal receiver receives the encrypted signal and sequentially performs down-conversion, intermediate frequency demodulation, sampling and cyclic prefix removal processing on the encrypted signal to obtain an encrypted signal d interfered by channel noiseCO-OFDM(k)；
Step five: the signal receiving part receives the signal d according to the formula (3)CO-OFDM(k) Subtracting said discrete noise signal sCO(k) To obtain a signal dOFDM(k) And for the signal dOFDM(k) Performing DFT to obtain symbol information m1,m2,...,mN；
dOFDM(k)＝dCO-OFDM(k)-sCO(k) (3)
Formula (3) wherein k is 1,2,3.
The superposition based on the continuous signal mode comprises the following steps:
the method comprises the following steps: converting information to be encrypted into symbol information n after constellation mapping1,n2,...,nNFor said symbol information n1,n2,...,nNSequentially carrying out OFDM modulation and intermediate frequency modulation to obtain continuous OFDM signal sOFDM(T), wherein T is more than 0 and less than T, and T represents an OFDM modulation period and has the unit of s;
step two: for the artificial noise signal sCO(k) N adds a cyclic prefix with the same length as the OFDM signal, performs digital-to-analog conversion to obtain an analog signal, and performs intermediate frequency modulation on the analog signal with the same frequency as the signal to be encrypted to obtain a continuous noise signal sCO(T), wherein 0 < T < T;
step three: said continuous OFDM signal s according to formula (4)OFDM(t) and said continuous noise signal sCO(t) superimposing to generate an encrypted signal sCO-OFDM(t)；
sCO-OFDM(t)＝sOFDM(t)+sCO(T) (4), wherein 0 < T < T;
step four: for encrypted signal sCO-OFDM(t) after up-conversion modulation, sending the up-conversion modulated signal as a sending signal to a signal receiving party, and after receiving the sending signal, carrying out down-conversion modulation on the sending signal by the signal receiving party to obtain an encrypted signal d interfered by channel noiseCO-OFDM(t)；
Step five: the legitimate receiver of the signal follows the encrypted signal d according to equation (5)CO-subtracting said noise signal s in OFDM (t)CO(t) obtaining a signal dOFDM(t)；
dOFDM(t)＝dCO-OFDM(t)-sCO(T) (5), wherein 0 < T < T;
step six: signal receiving party to signal dOFDM(t) sequentially performing intermediate frequency demodulation, synchronization and sampling, and DFT conversion to obtain symbol information n1,n2,...,nN。
Compared with the prior art, the invention has the following technical effects:
1. the invention firstly carries out DFT conversion on the artificial noise key sequence in the complex form, and then carries out zero insertion and then respectively carries out the DFT conversion and the zero insertion in sequence
Figure BDA0001246275000000041
The point IDFT transformation generates discrete noise signals, so that the peak-to-average ratio of the noise signals is low, the bandwidth is slightly smaller than the signal bandwidth, and the power is controllable. And the data encryption is realized by superposing the modulated OFDM signal and the artificial noise signal. The encryption process enables the noise signals and the OFDM signals to realize mutual overlapping interference and mutual protection of frequency spectrums in a radio frequency domain, destroys the orthogonality among original signal subcarriers, inhibits carrier leakage and resists spectrum analysis, thereby ensuring the safety of data and algorithm.
2. Compared with the existing encryption method, the encryption method of the invention has simple realization process, has small influence on the peak-to-average ratio, the bandwidth and the error rate of the original OFDM signal, and can meet the safety requirement of a high-speed wireless communication system.
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The embodiments of the invention will be explained and explained in further detail with reference to the figures and the detailed description.
FIG. 1 is a block diagram of an encryption process based on discrete signal mode superposition according to the present invention;
FIG. 2 is a block diagram of the decryption process based on the superposition of discrete signals according to the present invention;
FIG. 3 is a block diagram of an encryption process based on superposition of continuous signals according to the present invention;
FIG. 4 is a block diagram of the decryption process based on superposition of continuous signals according to the present invention;
FIG. 5 is a graph of the frequency spectrum of an artificial noise signal according to the present invention;
FIG. 6 is a spectrum diagram of an encrypted signal according to the present invention;
FIG. 7 is a graph comparing symbol error rates of legitimate and illegitimate recipients of encrypted signals according to the present invention;
FIG. 8 is a graph comparing the peak-to-average ratio of the encrypted signal to the OFDM signal according to the present invention;
fig. 9 is a schematic frequency spectrum diagram of an encrypted signal obtained when v is 1 and N is 32.
Detailed Description
Example 1
In this embodiment, a period T of OFDM modulation is 0.00008s, the number N of subcarriers in an OFDM system in one period is 128, ν is 3, and m is 2. Generating a corresponding artificial noise signal according to the following steps;
generating 128bit information in the counter working mode of AES encryption algorithm, performing 4QAM constellation mapping processed by a regulating factor α to generate 64 complex symbols a1,a2,...,a64；
Step two: for the obtained 64 complex symbols a1,a2,...,a64Performing 64-point DFT to obtain a symbol sequence containing 64 symbols, inserting 0 after each symbol in the symbol sequence to obtain a new noise symbol a1,0,a2,0,...,a640, which is denoted as c1,c2,...,c128；
Step three: judging the new noise symbol c1,c2,...,c128Whether the following conditions are satisfied:
Figure BDA0001246275000000061
formula (1) wherein k, h is 1,2,., 16, l is 1,2,. 8; if a new noise symbol c is generated1,c2,...,cNIf said condition is satisfied, the new noise symbol c is selected1,c2,...,cNRespectively do in turn
Figure BDA0001246275000000062
Point IDFT transform to generate artificial noise signal sCO(k) K is 1,2,. cndot.n; otherwise, repeating the first step and the second step until the artificial noise signal s is foundCO(k),k＝1,2,...,N。
The artificial noise signal s generated by the embodiment is judgedCO(k) N satisfies the formula 1,2For the artificial noise symbol c1,c2,...,c128Sequentially and respectively carrying out 16-point IDFT to generate a discrete noise signal sCO(k),k＝1,2,...,128。
Example 2
The present embodiment provides a method for applying an artificial noise signal to physical layer encryption, which, on the basis of embodiment 1, uses superposition based on a discrete signal mode, as shown in fig. 1, and specifically includes the following steps:
the method comprises the following steps: the information to be encrypted is transformed into symbol information m through constellation mapping and normalization processing1,m2,...,m128Performing IDFT on the symbol information to generate OFDM signal sOFDM(k) (wherein k ═ 1,2,3.. 128);
step two: OFDM signal s to be generated according to equation (2)OFDM(k) And said artificial noise signal sCO(k) Are superposed to generate an encrypted signal sCO-OFDM(k)：
sCO-OFDM(k)＝sOFDM(k)+sCO(k) (2)
Formula (2) wherein k is 1,2,3.., 128;
step three: for encrypted signal sCO-OFDM(k) Sequentially performing cyclic prefix adding, D/A conversion, intermediate frequency modulation and up-conversion processing, and sending the processed encrypted signal to a signal receiver;
step four: as shown in fig. 2, the signal receiver receives the encrypted signal and performs down-conversion, intermediate frequency demodulation, sampling and cyclic prefix removal processing on the encrypted signal in sequence to obtain an encrypted signal d interfered by channel noiseCO-OFDM(k)；
Step five: the signal receiving part receives the signal d according to the formula (3)CO-OFDM(k) Subtracting said discrete noise signal sCO(k) To obtain a signal dOFDM(k) And for the signal dOFDM(k) Performing DFT to obtain symbol information m1,m2,...,mN。
dOFDM(k)＝dCO-OFDM(k)-sCO(k),k＝1,2,3,...,128 (3)
Example 3
On the basis of embodiment 1, this embodiment provides a superposition method based on a continuous signal mode, as shown in fig. 3, which specifically includes:
the method comprises the following steps: the information to be encrypted is transformed into symbol information n through constellation mapping and normalization processing1,n2,...,n128For the symbol information n1,n2,...,n128Sequentially carrying out OFDM modulation and intermediate frequency modulation to obtain continuous OFDM signal sOFDM(t), wherein 0 < t < 0.00008 s;
step two: for the artificial noise signal sCO(k) And k is 1, 2.. multidata, 128 adds a cyclic prefix with the same length as the OFDM signal, then performs digital-to-analog conversion to obtain an analog signal, and performs intermediate frequency modulation on the analog signal with the same frequency as the signal to be encrypted to obtain a continuous noise signal sCO(t), wherein 0 < t < 0.000s 0;
step three: said OFDM signal s is modulated according to equation (4)OFDM(t) and said artificial noise signal sCO(t) superimposing to generate an encrypted signal sCO-OFDM(t)；
sCO-OFDM(t)＝sOFDM(t)+sCO(t) (4)
Wherein t is more than 0 and less than 0.00008 s;
step four: for encrypted signal sCO-OFDM(t) after up-conversion modulation, sending the up-conversion modulated signal as a sending signal to a signal receiving party, and after receiving the sending signal, carrying out down-conversion modulation on the sending signal by the signal receiving party to obtain an encrypted signal d interfered by channel noiseCO-OFDM(t)；
Step five: as shown in fig. 4, the signal receiving side receives the encrypted signal d according to equation (5)CO-OFDM(t) subtracting said artificial noise signal sCO(t) obtaining a signal dOFDM(t)；
dOFDM(t)＝dCO-OFDM(t)-sCO(t) (5)
Wherein t is more than 0 and less than 0.00008 s;
step six: legal signal receiver pair signal dOFDM(t) sequentially performing intermediate frequency demodulation, synchronization and sampling, and DFT conversion to obtain symbol information n1,n2,...,n128。
The security analysis of the physical layer encryption method
The algorithm of the invention has a larger key space, and the subcarrier frequency of the artificial noise is a part of the subcarrier frequency of the original system. The artificial noise signal and the OFDM signal interfere with each other, they are superimposed at the same time from the time domain, and are difficult to separate from each other, and the simulation result such as the result of fig. 5 shows that the algorithm is safe from the time domain analysis. Therefore, the interference effect of the frequency domain analysis algorithm is emphasized, and the safety and the feasibility of the encryption method are mainly analyzed in the four aspects of subcarrier orthogonality, spectrum aliasing and carrier leakage, key space and system inherent performance.
(1) Subcarrier orthogonality analysis
One of the important characteristics of the OFDM system is that the subcarriers satisfy orthogonality, which ensures that the subcarriers 1/2 overlap, improving the utilization of the frequency band. For an illegal eavesdropper, if the encryption algorithm can destroy the orthogonality of the subcarriers of the original system, the original system cannot demodulate normally, so that the safety of the algorithm is ensured. The orthogonality between the subcarriers of the encrypted signal over a period is given below.
The artificial noise signal s is assumed to be disregarded for the intermediate frequency carrier and the cyclic prefixCO(t) can be expressed as:
Figure BDA0001246275000000091
wherein g isTFor the communication gating function, T is the OFDM period, l is 1,2νL, v are positive integers, the base band sBCO(t) is expressed as:
Figure BDA0001246275000000092
base band s of OFDM signalBOFDM(t) is expressed as:
Figure BDA0001246275000000093
in formula (8):
Figure BDA0001246275000000094
the baseband expression of the OFDM signal is written by a gate function, mkIs symbol information into which the encrypted information is transformed after constellation mapping,
Figure BDA0001246275000000095
is a fixed form expressed by a subcarrier of an OFDM baseband, k represents a few subcarriers, j represents operation
Figure BDA0001246275000000096
The encrypted signal baseband is represented as:
Figure BDA0001246275000000097
mu is the same as k in definition and is shown as the number one, and any one baseband subcarrier is selected
Figure BDA0001246275000000098
Multiplying and integrating the conjugate sum (4) as shown in formula (10), and if the obtained result is mμAnd if not, the orthogonality among the sub-carriers is destroyed.
Figure BDA0001246275000000101
If μ ≠ 2νh, and
Figure BDA0001246275000000102
N/2ν,l＝1,2,3,...,2νthen, as demonstrated by equation (10), the following is true:
Figure BDA0001246275000000103
because of the fact that
Figure BDA0001246275000000104
So as to generate artificial noise signal c1,c2,...,cNSatisfies the condition of formula (11):
Figure BDA0001246275000000105
wherein k, h is 1,2ν,l＝1,2,...2ν
(11)
Then the frequency points other than the frequency point of the first term in equation (10) will never be equal to mμ. When N is 128 and ν is 3, it is easy to verify that the frequency points of the first term in the formula (10) are only 8 and account for only 6.25% of the total frequency points, and the condition of (11) is easy to satisfy, and has been judged to be satisfied when generating artificial noise signals, thereby proving that the encryption method provided by the present invention can effectively destroy the orthogonality among subcarriers, and proving the security of the encryption method of the present invention.
(2) Spectrum aliasing and carrier leakage analysis
The encrypted baseband signal represented by the formula (9) is subjected to fourier transform to obtain:
Figure BDA0001246275000000111
sa stands for Sa function, which is defined in communications.
The spectral density of any subcarrier frequency 2 π μ/T, μ ∈ {1, 2.., N } point can be calculated by equation (12) as follows:
Figure BDA0001246275000000112
we can readily see from formula (13) in conjunction with fig. 9:
1) at 2 pi 2νh/T,h＝1,2,...,N/2νAnd at the frequency point with even number, the frequency spectrum of the artificial noise signal and the frequency spectrum of the OFDM signal are not overlapped, and the artificial noise signal does not protect the information to be encrypted.However, when N is 128 and ν is 3, such frequency points only account for 6.25% of the total frequency points, and have little influence on the security of the whole data;
2) at 2 pi 2νh/T,h＝1,2,...,N/2νAt odd frequency points, the frequency spectrum of the corresponding OFDM signal interferes with the frequency spectrum of the point, and the frequency spectrums of the artificial noise signals are overlapped at the points with the density of
Figure BDA0001246275000000121
The artificial noise signals and the normal signals of the frequency points are mutually protected in the frequency domain;
3) at other frequency points, the OFDM signal frequency spectrum and the artificial noise signal frequency spectrum are seriously mixed, so that mutual interference and protection are realized, and carrier leakage cannot occur.
(3) Key space analysis
From example 1, it is readily apparent that AES encryption key O (2) of the method128) Space, symbol key space is O (4)64)＝O(2128) Therefore, it is difficult for an attacker to obtain the key by guessing; the second possible attack point of the attacker is the sum of 8 complex coefficients obtained by spectrum analysis in the second part of equation (13) when v is 3 and N is 8
Figure BDA0001246275000000122
However, since these 8 coefficients are the key symbols a1,a2,...,a64In a part of 64 symbols obtained after DFT transformation, an attacker must guess 64 key symbols to obtain a symbol key through the sum, so the complexity of obtaining the key symbols is at least O (4)64)＝O(2128) And is also very difficult.
(4) Influence on inherent performance of original system
Firstly, as the bandwidth of the artificial noise is slightly smaller than that of the original system, the encryption algorithm has no influence on the bandwidth of the original system, as shown in fig. 6, wherein the bandwidth of the artificial noise is 1587500Hz (9969500rad), and the bandwidth of the encrypted system is 1593750Hz (10008750 Hz); secondly, the influence on the peak-to-average power ratio of the system is small, as shown in FIG. 8; the influence on the error code performance of the original system is small, as shown in fig. 7; the only price paid is that the emission power of the original system is increased, and when the noise power is 1/4% of the original system power, the total power is increased by 30%.

Claims (2)

1. A method of constructing an artificial noise signal, comprising the steps of:
firstly, mN/2bit information is generated in the counter working mode of AES encryption algorithm, and 2 bits of information controlled by regulating factor α are carried out on the informationmQAM constellation mapping to obtain N/2 complex symbol keys a1,a2,...,aN/2；
Wherein N represents the number of sub-carriers of the OFDM system in one period, and m represents 2mA QAM constellation mapping mode, wherein m is more than or equal to 2 and less than or equal to 8;
step two: for obtaining complex symbol key a1,a2,...,aN/2Performing N/2 point DFT conversion to obtain symbol sequence containing N/2 complex symbols, inserting 0 behind each symbol in the symbol sequence to obtain new noise symbol c1,c2,...,cN；
Step three: judging the new noise symbol c1,c2,...,cNWhether the following conditions are satisfied:
Figure FDA0002222138290000011
wherein k, h is 1,2, N/2 in formula (1)ν,l＝1,2,...2νV is a positive integer; if a new noise symbol c is generated1,c2,...,cNIf said condition is satisfied, the new noise symbol c is selected1,c2,...,cNRespectively do in turn
Figure FDA0002222138290000012
Point IDFT transform to generate artificial noise signal sCO(k) K is 1,2,. cndot.n; otherwise, repeating the first step and the second stepUntil the artificial noise signal s is foundCO(k),k＝1,2,...,N。
2. A method of using the artificial noise signal of claim 1 for physical layer encryption, comprising superposition based on a discrete signal mode and superposition based on a continuous signal mode;
the superposition based on the discrete signal mode comprises the following steps:
the method comprises the following steps: the information to be encrypted is transformed into symbol information m after constellation mapping1,m2,...,mNPerforming IDFT on the symbol information to generate OFDM signal sOFDM(k) (ii) a Wherein k is 1,2,3.. N;
step two: OFDM signal s to be generated according to equation (2)OFDM(k) And said artificial noise signal sCO(k) Are superposed to generate an encrypted signal sCO-OFDM(k)：
sCO-OFDM(k)＝sOFDM(k)+sCO(k) (2)
Formula (2) wherein k is 1,2,3.
Step three: for encrypted signal sCO-OFDM(k) Sequentially performing cyclic prefix adding, D/A conversion, intermediate frequency modulation and up-conversion processing, and sending the processed encrypted signal to a signal receiver;
step four: the signal receiver receives the encrypted signal and sequentially performs down-conversion, intermediate frequency demodulation, sampling and cyclic prefix removal processing on the encrypted signal to obtain an encrypted signal d interfered by channel noiseCO-OFDM(k)；
Step five: the signal receiving part receives the signal d according to the formula (3)CO-OFDM(k) Subtracting said artificial noise signal sCO(k) To obtain a signal dOFDM(k) And for the signal dOFDM(k) Performing DFT to obtain symbol information m1,m2,...,mN；
dOFDM(k)＝dCO-OFDM(k)-sCO(k) (3)
Formula (3) wherein k is 1,2,3.
The superposition based on the continuous signal mode comprises the following steps:
the method comprises the following steps: converting information to be encrypted into symbol information n after constellation mapping1,n2,...,nNFor said symbol information n1,n2,...,nNSequentially carrying out OFDM modulation and intermediate frequency modulation to obtain continuous OFDM signal sOFDM(T), wherein T is more than 0 and less than T, and T represents an OFDM modulation period and has the unit of s;
step two: for the artificial noise signal sCO(k) And adding a cyclic prefix with the same length as the OFDM signal, performing digital-to-analog conversion to obtain an analog signal, and performing intermediate frequency modulation on the analog signal with the same frequency as the signal to be encrypted to obtain a continuous noise signal sCO(T), wherein 0 < T < T;
step three: said continuous OFDM signal s according to formula (4)OFDM(t) and said continuous noise signal sCO(t) superimposing to generate an encrypted signal sCO-OFDM(t)；
sCO-OFDM(t)＝sOFDM(t)+sCO(T) (4), wherein 0 < T < T;
step four: for encrypted signal sCO-OFDM(t) after up-conversion modulation, sending the up-conversion modulated signal as a sending signal to a signal receiving party, and after receiving the sending signal, carrying out down-conversion modulation on the sending signal by the signal receiving party to obtain an encrypted signal d interfered by channel noiseCO-OFDM(t)；
Step five: the legitimate receiver of the signal follows the encrypted signal d according to equation (5)CO-OFDM(t) subtracting said noise signal sCO(t) obtaining a signal dOFDM(t)；
dOFDM(t)＝dCO-OFDM(t)-sCO(T) (5), wherein 0 < T < T;
step six: signal receiving party to signal dOFDM(t) sequentially performing intermediate frequency demodulation, synchronization and sampling, and DFT conversion to obtain symbol information n1,n2,...,nN。
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