阅读说明：本技术 一种用于无线安全通信的物理层密钥生成方法 (Physical layer secret key generation method for wireless secure communication ) 是由 穆鹏程 郭子豪 王文杰 张渭乐 郑通兴 于 2021-08-27 设计创作，主要内容包括：本发明提供一种用于无线安全通信的物理层密钥生成方法,密钥由用户随机生成,使用本发明中的方法生成的密钥具有更大的密钥熵,更难以被窃听用户恶意分析；即使在信道衰落变化较慢的环境中,本发明依然能保证密钥的生成和更新速率本发明考虑通信双方采样非同步时接收端的采样信号中存在的采样时间偏差和载波相位偏差,在接收端对采样信号的采样时间偏差和载波相位偏差进行了补偿,使本发明中的物理层密钥生成方法在通信双方采样非同步的情况下也能正常使用。(The invention provides a physical layer key generation method for wireless secure communication, wherein keys are randomly generated by users, and the keys generated by the method have larger key entropy and are more difficult to be maliciously analyzed by eavesdropping users; even in an environment with slow channel fading variation, the method can still ensure the generation and update rate of the key, and the method considers the sampling time deviation and the carrier phase deviation existing in the sampling signals of the receiving end when the two communication parties sample asynchronously, compensates the sampling time deviation and the carrier phase deviation of the sampling signals at the receiving end, and enables the physical layer key generation method in the invention to be normally used under the condition that the two communication parties sample asynchronously.)

1. A method for physical layer key generation for wireless secure communications, comprising:

a user A receives a frequency domain pilot signal sent by a user B, and estimates the phase of a frequency domain legal channel according to the received frequency domain pilot signal;

a user A randomly generates an original key symbol;

the user A pre-distorts the original key symbol according to the estimated frequency domain legal channel phase to obtain a frequency domain transmission signal of the user A, and the user A performs multi-carrier modulation on the frequency domain transmission signal to obtain a physical layer key transmission signal and transmits the physical layer key transmission signal to the user B;

the user B samples and demodulates the physical layer key sending signal of the user A to obtain a frequency domain signal, and performs sampling time deviation and carrier phase deviation compensation on the frequency domain signal to obtain a synchronous symbol set;

the user B carries out channel decoding on the synchronous symbol set to obtain an estimated key sequence set;

the user B judges whether an effective estimated key sequence exists in the estimated key sequence set according to a preset rule; if the key sequence exists, the effective estimated key sequence is used as an effective key sequence, and a signal of successful generation of the physical layer key is sent to the user A; otherwise, user B sends a signal of failure of physical layer key generation to user A, and starts a new round of physical layer key generation.

2. The method for generating the physical layer key for the wireless secure communication according to claim 1, wherein the user a receives the frequency domain pilot signal sent by the user B, and estimates the phase of the frequency domain legal channel according to the received frequency domain pilot signal, specifically:

user A receives frequency domain pilot signal { S) sent by user B_pilot(k)|k＝0,1,...,N_sub-1} and represents the received frequency-domain pilot signal in the frequency domain as:

Y_A(k)＝S_pilot(k)H(k)+N_A(k),k＝0,1,...,N_sub-1；

estimating a frequency domain legal channel according to the following formula, and further obtaining the phase of the frequency domain legal channel

Wherein N is_subDenotes the total number of subcarriers used by the frequency-domain legal channel, { h (k) | k ═ 0,1_sub-1 represents a frequency domain legal channel,representing an additive complex white gaussian noise signal received by user a; | · | represents taking the amplitude, θ (-) represents taking the phase.

3. The method of claim 1, wherein the user a randomly generates an original key symbol, specifically: and the user A generates a random key sequence, adds a CRC sequence to the random key sequence, and then carries out channel coding and MPSK mapping to obtain an original key symbol.

4. The method as claimed in claim 3, wherein the step of randomly generating the original key symbol by the user a includes:

step 1, generating a random key sequenceWherein N is_origRepresents the length of the random key sequence;

step 2, calculating a random key sequence b_origCRC sequence ofWherein N is_CRCIndicates the length of the CRC sequence; a CRC sequence b_CRCCombined into a random key sequence b_origEnd part to obtain original key sequenceWherein N is_keyRepresenting the length of the original key sequence, N_key＝N_orig+N_CRC；

Step 3, channel coding is carried out on the original key sequence b to obtain code wordsWherein N is_codeRepresents the length of the codeword;

step 4, mapping the code word c by using the binary Gary code MPSK to obtain an original key symbol { S_A(k)|k＝0,1,...,N_S-1 }; wherein MPSK represents M-order phase shift keying; n is a radical of_S＝N_code/N_mapRepresents the length of the original key symbol and satisfies N_S≤N_sub，N_subDenotes the total number of subcarriers used by the frequency domain legal channel, N_map＝log₂(M) representsThe number of binary bits corresponding to each constellation point in the constellation symbol set S.

5. The method for generating physical layer keys for wireless secure communication according to claim 4, wherein the determining whether there is a valid estimated key sequence in the set of estimated key sequences is specifically: and judging whether an estimated key sequence meeting CRC (cyclic redundancy check) check exists in the estimated key sequence set, if so, judging that an effective estimated key sequence exists in the estimated key sequence set.

6. The method of claim 1, wherein the user a pre-distorts an original key symbol according to the estimated frequency domain legal channel phase to obtain a frequency domain transmission signal of the user a, and specifically performs the following steps:

wherein the content of the first and second substances,estimated phase of user A for a frequency domain legal channel, { S_A(k)|k＝0,1,...,N_S-1 is the original key symbol, N_SDenotes the length of the original key symbol, { X_A(k)|k＝0,1,...,N_S-1 is the frequency domain transmission signal for user a.

7. The method for generating the physical layer key for the wireless secure communication according to claim 1, wherein the user B samples and demodulates the physical layer key signal sent by the user a to obtain a frequency domain signal, specifically:

the user B samples the physical layer key signal sent by the user A, and the signal obtained by sampling is subjected to FFT (fast Fourier transform) to obtain a frequency domain signal of the user BExpressed as:

wherein, { X_A(k)|k＝0,1,...,N_S-1 is the frequency domain transmit signal of user a, { h (k) | k ═ 0,1_S-1 represents a frequency domain legal channel,representing additive white Gaussian noise, N, received by user B_SRepresenting the length of the original key symbol.

8. The method for generating a physical layer key for wireless secure communication according to claim 7, wherein the frequency domain signal is compensated for sampling time offset and carrier phase offset to obtain a synchronization symbol set, and specifically:

setting search value of carrier phase deviationThe search value tau epsilon (-0.5,0.5) of the sampling time deviation is utilized to obtain the phase of the frequency domain signal of the user BCompensation is performed, and the phase of the signal after compensation { phi (k) | k ═ 0,1_S-1} is:

{ω(k)|k＝0,1,...,N_S-1 represents the subcarrier frequency of the legitimate channel; n is a radical of_SRepresents the length of the original key symbol;

the compensated signal phase { phi (k) | k ═ 0, 1., N is calculated as follows_S-1 mean square error between each phase in the MPSK constellation point and the phase of the nearest MPSK constellation point

Searching for mean square error in both phase and time dimensionsMinimum value δ of_minAnd will minimize the value delta_minCorresponding signal phase phi^min(k)|k＝0,1,...,N_S-1} amplitude of the frequency domain signal with user BCombine to obtain a sync symbol Y_B(k)|k＝0,1,...,N_S-1} and the formula is:

each synchronization symbol is corresponded to obtain M synchronization symbol samples, and a complete synchronization symbol sample set Y_BExpressed as:

wherein M represents the order of MSPK.

9. The method as claimed in claim 8, wherein the user B performs channel decoding on the synchronization symbol set, specifically:

according to constellation point s_nCorresponding to N_mapIth bit b of binary bits_i(s_n) Equally dividing the constellation symbol set S into setsAndsoft information of the ith bit in the kth bit of the mth sync symbol sample is calculated as follows:

wherein M is 0,1, K, M-1, K is 0,1_S-1，i＝0,1,...,N_map-1，b_i(S_A(k) K bit S) representing the original key symbol_A(k) Corresponding to N_mapThe value of the ith bit in the binary bit,e represents the average power of MPSK constellation points, wherein E is the frequency domain equivalent noise power of the synchronization symbols;

and synthesizing soft information of all bits in all the synchronous symbol samples to obtain soft information of a synchronous symbol sample set, decoding according to the soft information of the synchronous symbol sample set, and outputting an estimated code sequence set.

Technical Field

The invention belongs to the field of wireless communication, and particularly relates to a physical layer secret key generation method for wireless secure communication.

Background

With the development of the wireless communication industry, communication security becomes an increasingly concerned issue. The openness of wireless channels and the broadcast characteristics of electromagnetic waves pose a serious threat to communication security, but researchers have noticed that wireless channels are a natural source of randomness, and the characteristics of short-time reciprocity, time-varying property, spatial uniqueness, etc. can be used for key extraction, thereby realizing "one-time pad" secure communication between two legitimate parties. In recent years, key extraction using wireless channel characteristics in the physical layer has become a research hotspot.

Wireless channel key extraction generally includes the following steps: channel acquisition, information quantization, key agreement, and security enhancement. Researchers have studied this from different directions and put forward corresponding solutions.

In 1996, an article entitled "Cryptographic Key agent for Mobile Radio" was published by am a. hassan in Digital Signal Processing, and proposed a scheme for obtaining an original Key by quantizing a phase difference between carriers. In 2000, an article entitled "Secure Information Transmission for Mobile Radio" published by IEEE Communications Letters by hash corporation was improved on the basis of the former, and a scheme for transmitting Information (key) by using a carrier phase difference was proposed. The two schemes have the advantages that the phase difference of the carrier wave is utilized to remove the influence of phase ambiguity; the disadvantage is that the influence caused by sampling non-synchronization of both sides of legal communication cannot be removed.

In 2012, Jalal Etesimi and Werner Henkel in First IEEE Conference on Communications in China: an article entitled "LDPC Code Construction for Wireless Physical-Layer Key Reconfiguration" was published in Communications and Security (CTS), and proposed the idea of using LDPC Code to perform Key negotiation for the first time in the article, and designed a specific scheme. In 2015, Oana Graur et al published an article entitled "quantification assays in LDPC Key Reconnation for Physical Layer Security" on Proceedings of 10th IEEE International ITG Conference on Systems, Communications and Coding-SCC 2015, which further developed accurate and approximate expressions for soft information computation based on the former. The two schemes introduce the channel coding and decoding technology into the key negotiation step, so that a new idea is provided for researchers, but the influence of sampling asynchronization of two legal communication parties is still not considered.

In practical communication systems, sampling asynchronism between communicating parties is ubiquitous and difficult to eliminate. Therefore, when designing a key extraction scheme based on a wireless channel, consideration must be given to the case where both parties of communication sample non-synchronization. Many existing wireless channel key extraction schemes quantize the channel parameters to the original key, which makes the key generation rate dependent on the channel variation speed. In an environment with slow channel change, the key generation rate of the schemes is low, and the performance of the key generation system is indirectly influenced.

Disclosure of Invention

The invention aims to provide a physical layer key generation method for wireless secure communication aiming at the sampling asynchronous problem and the key generation rate problem in the practical implementation process of the prior art, so that both communication parties can be normally used under the sampling asynchronous condition, and the key generation and updating rate is independent of the channel change speed.

The invention is realized by the following technical scheme:

a method of physical layer key generation for wireless secure communications, comprising:

a user A receives a frequency domain pilot signal sent by a user B, and estimates the phase of a frequency domain legal channel according to the received frequency domain pilot signal;

a user A randomly generates an original key symbol;

the user A pre-distorts the original key symbol according to the estimated frequency domain legal channel phase to obtain a frequency domain transmission signal of the user A, and the user A performs multi-carrier modulation on the frequency domain transmission signal to obtain a physical layer key transmission signal and transmits the physical layer key transmission signal to the user B;

the user B samples and demodulates the physical layer key sending signal of the user A to obtain a frequency domain signal, and performs sampling time deviation and carrier phase deviation compensation on the frequency domain signal to obtain a synchronous symbol set;

the user B carries out channel decoding on the synchronous symbol set to obtain an estimated key sequence set;

the user B judges whether an effective estimated key sequence exists in the estimated key sequence set according to a preset rule; if the key sequence exists, the effective estimated key sequence is used as an effective key sequence, and a signal of successful generation of the physical layer key is sent to the user A; otherwise, user B sends a signal of failure of physical layer key generation to user A, and starts a new round of physical layer key generation.

Preferably, the user a receives the frequency domain pilot signal sent by the user B, and estimates the phase of the frequency domain legal channel according to the received frequency domain pilot signal, specifically:

user A receives frequency domain pilot signal { S) sent by user B_pilot(k)|k＝0,1,...,N_sub-1} and represents the received frequency-domain pilot signal in the frequency domain as:

Y_A(k)＝S_pilot(k)H(k)+N_A(k),k＝0,1,...,N_sub-1；

estimating a frequency domain legal channel according to the following formula, and further obtaining the phase of the frequency domain legal channel

Wherein N is_subDenotes the total number of subcarriers used by the frequency-domain legal channel, { h (k) | k ═ 0,1_sub-1 represents a frequency domain legal channel,representing an additive complex white gaussian noise signal received by user a; | · | represents taking the amplitude, θ (-) represents taking the phase.

Preferably, the user a randomly generates an original key symbol, specifically: and the user A generates a random key sequence, adds a CRC sequence to the random key sequence, and then carries out channel coding and MPSK mapping to obtain an original key symbol.

Further, the randomly generating the original key symbol by the user a specifically includes:

step 1, generating a random key sequenceWherein N is_origRepresents the length of the random key sequence;

step 2, calculating a random key sequence b_origCRC sequence ofWherein N is_CRCIndicates the length of the CRC sequence; a CRC sequence b_CRCCombined into a random key sequence b_origEnd part to obtain original key sequenceWherein N is_keyRepresenting the length of the original key sequence, N_key＝N_orig+N_CRC；

Step 3, channel coding is carried out on the original key sequence b to obtain a code word c ═ (c)₀,c₁,...,c_Ncode-1) (ii) a Wherein N is_codeRepresents the length of the codeword;

step 4, mapping the code word c by using the binary Gary code MPSK to obtain an original key symbol { S_A(k)|k＝0,1,...,N_S-1 }; wherein MPSK represents M-order phase shift keying; n is a radical of_S＝N_code/N_mapRepresents the length of the original key symbol and satisfies N_S≤N_sub，N_subDenotes the total number of subcarriers used by the frequency domain legal channel, N_map＝log₂(M) represents the number of binary bits corresponding to each constellation point in the constellation symbol set S.

Preferably, the determining whether there is an effective estimated key sequence in the estimated key sequence set specifically includes: and judging whether an estimated key sequence meeting CRC (cyclic redundancy check) check exists in the estimated key sequence set, if so, judging that an effective estimated key sequence exists in the estimated key sequence set.

Preferably, the user a pre-distorts the original key symbol according to the estimated frequency domain legal channel phase to obtain a frequency domain transmission signal of the user a, specifically according to the following formula:

wherein the content of the first and second substances,estimated phase of user A for a frequency domain legal channel, { S_A(k)|k＝0,1,...,N_S-1 is the original key symbol, N_SDenotes the length of the original key symbol, { X_A(k)|k＝0,1,...,N_S-1 is the frequency domain transmission signal for user a.

Preferably, the user B samples and demodulates the physical layer key signal sent by the user a to obtain a frequency domain signal, specifically:

the user B samples the physical layer key signal sent by the user A, and the signal obtained by sampling is subjected to FFT (fast Fourier transform) to obtain a frequency domain signal of the user BExpressed as:

wherein, { X_A(k)|k＝0,1,...,N_S-1 is the frequency domain transmit signal of user a, { h (k) | k ═ 0,1_S-1 represents a frequency domain legal channel,representing additive white Gaussian noise, N, received by user B_SRepresenting the length of the original key symbol.

Further, the frequency domain signal is subjected to sampling time deviation and carrier phase deviation compensation to obtain a synchronization symbol set, which specifically comprises:

setting search value of carrier phase deviationThe search value tau epsilon (-0.5,0.5) of the sampling time deviation is utilized to obtain the phase of the frequency domain signal of the user BCompensation is performed, and the phase of the signal after compensation { phi (k) | k ═ 0,1_S-1} is:

{ω(k)|k＝0,1,...,N_S-1 represents the subcarrier frequency of the legitimate channel; n is a radical of_SRepresents the length of the original key symbol;

the compensated signal phase { phi (k) | k ═ 0, 1., N is calculated as follows_S-1 mean square error between each phase in the MPSK constellation point and the phase of the nearest MPSK constellation point

Searching for mean square error in both phase and time dimensionsMinimum value δ of_minAnd will minimize the value delta_minCorresponding signal phase phi^min(k)|k＝0,1,...,N_S-1} amplitude of the frequency domain signal with user BCombine to obtain a sync symbol Y_B(k)|k＝0,1,...,N_S-1} and the formula is:

each synchronization symbol is corresponded to obtain M synchronization symbol samples, and a complete synchronization symbol sample set Y_BExpressed as:

wherein M represents the order of MSPK.

Further, the user B performs channel decoding on the synchronization symbol set, specifically:

according to constellation point s_nCorresponding to N_mapIth bit b of binary bits_i(s_n) Equally dividing the constellation symbol set S into setsAndsoft information of the ith bit in the kth bit of the mth sync symbol sample is calculated as follows:

wherein M is 0,1, K, M-1, K is 0,1_S-1，i＝0,1,...,N_map-1，b_i(S_A(k) K bit S) representing the original key symbol_A(k) Corresponding to N_mapThe value of the ith bit in the binary bit,frequency domain for synchronization symbols, etcEffective noise power, E represents the average power of MPSK constellation points;

and synthesizing soft information of all bits in all the synchronous symbol samples to obtain soft information of a synchronous symbol sample set, decoding according to the soft information of the synchronous symbol sample set, and outputting an estimated code sequence set.

Compared with the prior art, the invention has the following beneficial technical effects:

compared with a method for directly acquiring the key from the channel state information, the key generated by using the method has larger key entropy and is more difficult to be analyzed maliciously by eavesdropping users; the invention can still ensure the generation and update rate of the secret key even in the environment with slow channel fading variation. The invention uses the predistortion phase technique to ensure that only the appointed legal user receives the correct physical layer key signal, thereby ensuring the safety of the physical layer key generation method in the invention. The invention uses the channel coding technology to correct the possible errors of the physical layer key signal in the transmission process, thereby ensuring the reliability of the physical layer key generation method in the invention. The invention considers the sampling time deviation and the carrier phase deviation existing in the sampling signals of the receiving end when the two communication parties sample the asynchronous signals, and compensates the sampling time deviation and the carrier phase deviation of the sampling signals at the receiving end, so that the physical layer key generation method can be normally used under the condition that the two communication parties sample the asynchronous signals.

Drawings

FIG. 1 is a schematic diagram of a wireless secure communication channel model;

FIG. 2 shows the frame error rate of the legal user Bob and the eavesdropping user Eve;

FIG. 3 shows the agreement ratio between the estimated key sequence and the original key sequence satisfying the check equation;

FIG. 4 eavesdrops the bit error rate of the Eve decoding output key sequence of the user compared with the original key sequence;

FIG. 5 illustrates the impact of carrier frequency offset on system performance;

Detailed Description

The present invention will now be described in further detail with reference to specific examples, which are intended to be illustrative, but not limiting, of the invention.

The overall thought of the scheme of the invention is as follows: a certain legal communication user generates a random key and carries out LDPC coding, and then utilizes the estimated legal channel phase to pre-distort a key signal and then sends the key signal; and another legal communication user performs LDPC decoding on the received signal to recover a complete and effective secret key. The wireless channel key extraction scheme can be normally used even when two communication parties sample non-synchronization, and the key generation and update rate does not depend on the channel change speed.

As shown in fig. 1, the wireless secure communication scenario considered by the present invention includes a pair of legitimate communication users Alice (for a) and Bob (for B), and an eavesdropping user Eve. The three users all use OFDM to carry out multi-carrier modulation, the system has N sub-carriers in total, and the users use N of the N sub-carriers_subOne subcarrier communicates, {0,1,.. multidot.n_sub-1 represents the index of the used sub-carrier,

under the quasi-static fading channel environment, the length of a channel is set to be L, L is less than N, and the time domain channel from a user Bob to a user Alice is set to be { h_BA(n) | n ═ 0,1,.., L-1}, and the time-domain channel from user Alice to user Bob is { h }_AB(n) | n ═ 0,1,., L-1 }. In TDD mode, h can be considered according to reciprocity principle of wireless channel_AB(n)＝h_BA(N) ═ h (N), the corresponding frequency domain channel is { h (k) | k ═ 0,1,.., N-1}, and the frequency domain legal channel used in the present invention is { h (k) | k ═ 0,1,.., N-1}_sub-1}. Setting a time domain channel from Alice to Eve as h_AE(n) | n ═ 0, 1.., L-1}, and the corresponding frequency domain channel is { H |, L-1}, where_AE(k) I k is 0,1,., N-1, and the corresponding frequency-domain eavesdropping channel is H_AE(k)|k＝0,1,...,N_sub-1}. The present invention assumes that the frequency domain eavesdropping channel is independent of the frequency domain legal channel.

The invention relates to a physical layer key generation method for wireless secure communication, which specifically comprises the following steps:

step 1, a user Bob sends a frequency domain pilot signal { S ] to a user Alice_pilot(k)|k＝0,1,...,N_sub-1 }; wherein, N is 0,1_sub-1 represents the index of the sub-carriers used by the frequency domain legal channel, and the corresponding set of sub-carrier frequencies is { ω (k) | k ═ 0,1_sub-1}，N_subRepresenting the total number of subcarriers used by the frequency domain legal channel;

step 2, the user Alice estimates a frequency domain legal channel, pre-distorts an original key symbol according to the estimated phase of the frequency domain legal channel to obtain a frequency domain sending signal of the user Alice, and transmits the frequency domain sending signal after multi-carrier modulation, and the method comprises the following steps:

step 2.1, estimating the phase of the legal channel of the frequency domainThe method specifically comprises the following steps:

after the user Alice samples the received frequency-domain pilot signal, considering the effects of channel and noise, the received signal is represented in the frequency domain as:

Y_A(k)＝S_pilot(k)H(k)+N_A(k),k＝0,1,...,N_sub-1；

whereinRepresenting an additive complex white gaussian noise signal;

estimating a frequency domain legal channel by using a known frequency domain pilot signal according to the following formula, and further obtaining the phase of the frequency domain legal channel

Wherein, { Y_A(k)|k＝0,1,...,N_sub-1 represents the frequency domain received signal of user Alice; | DEG | represents taking amplitude, and theta (-) represents taking phase; j defaults to an imaginary symbol;

step 2.2, generating an original key symbol, comprising the steps of:

step 2.2.1, generating a random key sequenceWherein N is_origRepresents the length of the random key sequence;

step 2.2.2, calculate the random key sequence b_origCRC sequence ofWherein N is_CRCIndicates the length of the CRC sequence; a CRC sequence b_CRCCombined into a random key sequence b_origEnd part to obtain original key sequenceWherein N is_keyIndicating the length of the original key sequence after the addition of the CRC sequence;

step 2.2.3, channel coding is carried out on the original key sequence b to obtain code wordsWherein N is_codeIndicating the length of code word obtained by channel coding, the code rate R being N_key/N_code；

Step 2.2.4, using binary Gary code MPSK to map code word c to obtain original key symbol { S_A(k)|k＝0,1,...,N_S-1 }; wherein MPSK represents M-order phase shift keying, and constellation symbol set S ═ S₀,s₁,...,s_M-1}；N_S＝N_code/N_mapRepresents the length of the original key symbol and satisfies N_S≤N_sub，N_map＝log₂(M) representing the number of binary bits corresponding to each constellation point in the constellation symbol set S;

step 2.3, using the estimated phase of the user Alice in step 2.1 to the legal channel of the frequency domainFor the original key symbol S in step 2.2_A(k)|k＝0,1,...,N_S-1} performing phase pre-phasingDistortion is carried out to obtain a frequency domain transmission signal { X of the user Alice_A(k)|k＝0,1,...,N_S-1}, as shown in detail below:

step 2.4, sending a signal X from the frequency domain of the user Alice_A(k) And carrying out multi-carrier modulation to obtain a physical layer secret key signal of the user Alice, and sending the signal to the user Bob.

Step 3, the user Bob samples and demodulates the physical layer secret key signal sent by the user Alice to obtain a frequency domain signalThe frequency domain signal is subjected to sampling time deviation and carrier phase deviation compensation to obtain a synchronous symbol Y_B(k)|k＝0,1,...,N_S-1} sum frequency domain equivalent noise powerThe method comprises the following steps:

step 3.1, the user Bob samples the received signal (i.e. the physical layer secret key signal sent by the user Alice), and the sampled signal is transformed by FFT to obtain a frequency domain signal of the user Bob, which is expressed as:

whereinRepresenting an additive complex white gaussian noise signal.

Setting search value of carrier phase deviationThe search value tau epsilon (-0.5,0.5) of the sampling time deviation is used for calculating the phase of the frequency domain signal of the user BobCompensation is performed, and the phase of the signal after compensation { phi (k) | k ═ 0,1_S-1} is represented by:

the compensated signal phase { phi (k) | k ═ 0, 1., N is calculated as follows_S-1 mean square error between each phase in the MPSK constellation point and the phase of the nearest MPSK constellation point

Searching for mean square error in both phase and time dimensionsMinimum value δ of_minAnd will minimize the value delta_minCorresponding signal phase phi^min(k)|k＝0,1,...,N_S-1} with amplitude of received signalCombine to obtain a sync symbol Y_B(k)|k＝0,1,...,N_S-1, expressed as:

step 3.2, considering the influence of phase ambiguity in the synchronization process, each synchronization symbol corresponds to M synchronization symbol samples and complete synchronization symbol samplesSet Y_BExpressed as:

wherein M represents the order of MPSK;

step 4, the user Bob sets the synchronization symbol Y_BAnd judging whether the estimated code sequence output by the channel decoding is effective or not, comprising the following steps:

step 4.1, calculating soft informationM is 0,1, K, M-1; wherein the content of the first and second substances,n corresponding to k bit of representing m-th synchronous symbol_mapSoft information of one binary bit: according to constellation point s_nCorresponding to N_mapIth bit b of binary bits_i(s_n) By dividing the constellation symbol set S into setsAndsoft information of the ith bit in the kth bit of the mth sync symbol sample is calculated as follows:

wherein M is 0,1, K, M-1, K is 0,1_S-1，i＝0,1,...,N_map-1，b_i(S_A(k) K bit S) representing the original key symbol_A(k) To pairCorresponding to N_mapThe value of the ith bit in the binary bit,representing the frequency domain equivalent noise of the synchronization symbol, and E representing the average power of the MPSK constellation points;

synthesizing soft information of all bits in all synchronous symbol samples to obtain soft information L of synchronous symbol sample set_m，m＝0,1,K,M-1；

Step 4.2, the decoder bases on the soft information L^mM is 0,1, K, M-1, decoding and outputting the estimated key sequence setM is 0,1, K, M-1; the estimated key sequence in the set of estimated key sequences represents the original key sequence in step 2.2.2(ii) an estimate of (d);

step 4.3, judging whether an effective estimated key sequence exists in the estimated key sequence set: estimating the presence of an estimated key sequence in a set of cipher sequencesIf the CRC check is satisfied, the estimated key sequence is considered to be valid, namely an effective estimated key sequence exists in the estimated key sequence set, otherwise, an effective estimated key sequence does not exist in the estimated key sequence set.

In simulation, the condition of asynchronous communication between users is considered, and sampling time offset, carrier phase offset and carrier frequency offset are properly introduced, and specific parameter settings are shown in table 1. Wherein T is_sRepresenting the sampling time interval and Δ ω representing the subcarrier frequency interval of the OFDM system.

Table 1 simulation parameter set-up of the invention

CRC	Channel coding	Code rate	Code length
				‘16’	LDPC	1/2	672
Total number of subcarriers	Using the number of sub-carriers	Constellation diagram	Channel length
				1024	336	QPSK	32
Phase offset of carrier wave	Time offset of sampling	Carrier frequency offset	Synchronization accuracy
				(-π,π)	(-0.5,0.5)	(-0.1,0.1)	400×100

Note: the sampling time bias is normalized by taking a sampling time interval as a standard;

the carrier frequency offset is normalized by taking the subcarrier frequency interval of the OFDM system as a standard;

two dimensions of the synchronization precision correspond to phase and time, respectively.

Fig. 2 shows the frame error rate performance of the legitimate user Bob and the eavesdropping user Eve in recovering the key. The graph shows that when the signal-to-noise ratio is less than 4dB, the frame error rate of two users is 1, the frame error rate of a legal user Bob is rapidly reduced along with the increase of the signal-to-noise ratio, and the frame error rate reaches 10 at about 14.5dB^-3And the frame error rate of the eavesdropping user Eve is always 1, that is, the eavesdropping user Eve cannot acquire a completely correct key of one frame all the time. This result demonstrates the security of the keys generated by the present invention.

Fig. 3 shows the coincidence rate of the decoded output estimation key sequence satisfying the CRC check with the original key sequence. The results in the figure show that when the output estimated key sequence satisfies the CRC check, the consistency ratio with the original key sequence is maintained at 100% (when the signal-to-noise ratio is less than 4dB, the decoded output estimated key sequence which does not satisfy the CRC check is set to 0 by default in order to maintain the integrity of the simulation result, and the process does not affect the above result). The result proves the reliability of the output estimation key sequence validity judgment standard.

Fig. 4 shows the bit inconsistency rate of the eavesdropping user Eve compared to the key sequence of the legitimate user Alice. The figure shows that when the eavesdropping user Eve directly uses the decoded sequence as the key sequence, the bit inconsistency rate of the key sequence of the eavesdropping user Eve compared with the original key sequence of the legal user Alice is always kept about 0.5 under different signal-to-noise ratios, i.e. the eavesdropping effect of the eavesdropping user Eve is equivalent to the random guessing effect. This result further demonstrates the safety of the present invention.

Fig. 5 illustrates the effect of crystal frequency offset on the performance of the system of the present invention. The figure shows that when a legitimate user Bob acts at 10^-3When the frame error rate is the standard, the frequency offset of the crystal oscillator with 0.1 times of subcarrier frequency interval brings less than 1dB of influence compared with the frequency offset without frequency offset. No matter whether the frequency offset of the crystal oscillator exists or not, the frame error rate of the eavesdropping user Eve is always 1. The results demonstrate that the present invention is in the presence of crystal oscillator frequency offsetThe situation is still valid.

In conclusion, the invention can ensure the security of key sharing between legal users. In addition, compared with the key acquired from the channel in the existing scheme, the key is randomly generated by a legal user, has larger key entropy and is more difficult to be maliciously analyzed by an eavesdropping user; the invention can still ensure the generation and update rate of the key even in the environment with slow channel fading.

The simulation result proves the safety of the invention (when the interception channel is independent of the legal channel, the interception user can not obtain the effective key) and the excellence of the performance (under the asynchronous condition, the frame error rate of the key frames of the legal communication parties can be reduced to 10 when the signal-to-noise ratio is about 15dB^-3)。