CN108684037B - OFDM (orthogonal frequency division multiplexing) safe transmission method combining subcarrier pairing and signal inversion - Google Patents

Abstract

The invention discloses an OFDM safe transmission method combining subcarrier pairing and signal inversion, which utilizes known channel state information to rearrange the serial numbers of each subcarrier, divides the subcarrier into two parts by taking a middle point as a boundary, and sets the first half part as a poor carrier and the second half part as a good carrier. And defining a pairing mapping relation between the poor channel and the good channel, respectively sending an inversion signal and a useful signal, and carrying out joint receiving by a receiving end. The average bit error rate of the system and a lower bound of the secrecy capacity of the system are deduced by using the theorem theory of order statistics, simulation verification is carried out, and a simulation result shows that the scheme realizes a good anti-eavesdropping effect, meets good safety transmission requirements, and has certain stability and practicability.

Description

OFDM (orthogonal frequency division multiplexing) safe transmission method combining subcarrier pairing and signal inversion

Technical Field

The invention belongs to the technical field of wireless communication physical layer security, and particularly relates to an OFDM (orthogonal frequency division multiplexing) security transmission strategy combining subcarrier pairing and signal inversion, which is suitable for various communication networks.

Background

The natural openness and broadcastability of wireless communication systems presents a significant challenge to the security of transmissions. In order to ensure the communication security, the traditional method is to use the security mechanism of a wired network for reference and realize security protection at the high level of a protocol, and the method assumes that an eavesdropper has limited computing capacity and cannot crack in a short time. However, with the development of high-speed computers, the traditional encryption mode is threatened. The Physical Layer Security (PLS) technology is produced as a security method for assisting an upper layer in the field of secure communication, and the method directly prevents an eavesdropper from intercepting useful information by using the physical layer attribute, namely the uniqueness of a wireless channel, as a guide of information theory security. Compared with the traditional upper layer security scheme, the physical layer security has the advantages of low system overhead, simple protocol stack and low complexity, and is therefore widely concerned.

Orthogonal Frequency Division Multiplexing (OFDM), as a suitable solution standard for many major wireless and wireline communication physical layers, is widely adopted by LTE and Wi-Fi systems today, as it can be extended to large bandwidth applications, and has high spectral efficiency and low data complexity, well meeting the 5G requirements. Therefore, it is a necessary trend that research on OFDM technology puts more and higher innovative requirements. The OFDM system has uniqueness, each carrier can be subjected to different fading, so that each carrier has different transmission capacity, based on the uniqueness, the throughput of the system can be improved through reasonable resource (carrier and power) distribution, the power consumption can be reduced, the resource utilization rate can be improved, channel characteristics of two communication parties can be influenced while the resources are distributed, and the essence that the physical layer safety can be implemented is the difference of the wireless communication channel characteristics, so that different resource distribution shows channel differences of different degrees to influence the safety of the system. However, the traditional resource allocation usually considers how to increase the capacity and reduce the bit error rate spread, and does not consider the secrecy capacity of the system too much. Therefore, it is necessary to consider a physical layer security technique under the OFDM system.

Different from the previous scheme, the research for improving the system performance through subcarrier selection and pairing is also multiple, and because of differences among subcarrier channels, each time a channel is realized, a channel with a poor transmission environment and a channel with a good transmission environment are presented, so that the subcarrier selection and pairing have certain research value. However, it can be seen that most subcarrier matching schemes are applied in a relay or multi-relay scenario, and carriers of two time slots are paired and combined, which is very similar to the multi-antenna selection. In simple single-hop transmission systems, similar schemes are rare. In fact, due to different carrier transmission environments, the better channel and the poorer channel can be jointly operated, and the safety performance of the system can be further improved under the condition of reducing the complexity of the system. In addition, in actual transmission, due to imperfect reciprocity of channels, certain reciprocity errors are necessarily brought, and most schemes do not consider the influence brought by the reciprocity errors.

Disclosure of Invention

The invention aims to provide an OFDM (orthogonal frequency division multiplexing) secure transmission strategy for combining subcarrier pairing and signal inversion, which is suitable for various transmission networks, in a simple classical eavesdropping single-antenna model. The method fully utilizes the uniqueness of the subcarrier, greatly increases the bit error rate of an eavesdropper, obtains better safety performance, and can still keep better system performance under the condition of existence of reciprocity errors.

In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:

an OFDM safety transmission strategy combining subcarrier pairing and signal inversion comprises the following steps:

(1) the sending end rearranges the serial numbers of all sub-carriers according to the known channel state information and the sequence from small to large of the square of the channel coefficient modulus value to obtain a new channel coefficient sequence of the sub-carriers, divides the new channel coefficient sequence into two parts by taking a middle point as a boundary, sets the first half part as a poor carrier and the second half part as a good carrier;

(2) copying a useful signal containing N/2 bits to be transmitted and carrying out inversion operation, sequentially placing the useful signal to be transmitted in a carrier wave with good back half part according to a reverse order mode for transmission, sequentially placing the inverted signal in a carrier wave with poor front half part for transmission, and jointly forming an original OFDM symbol with N bits;

(3) according to a certain pairing mapping relation, pairing and combining a good subcarrier and a poor subcarrier in a one-to-one correspondence manner;

(4) the receiving end carries out equalization processing on the received original OFDM symbol information, then the information in the two matched subcarriers is jointly received in sequence by adopting a maximum ratio combining mode to obtain the Kth subcarrier output signal-to-noise ratio gamma_{symbol_K}Wherein K ═ 1, 2.., N/2;

(5) in the case of power equalization, the average bit error rate p of the scheme under a classical interception model and a lower bound C of the system secret capacity are obtained by using the theorem of order statistics.

Further, in the step (1), the subcarrier sequence numbers (1, 2., N) are rearranged to obtain a new group of channel sequence numbers, where N is the number of subcarriers, and is implemented by the following steps:

1a) obtaining the channel state information of each transmission by using a channel state information feedback system;

1b) extracting channel coefficient [ h ] of each carrier wave₁,h₂,...,h_N]Calculating the square | h of each sub-carrier coefficient modulus value_i|²Wherein i is 1, 2.. times.n; according to | h_i|²Rearranging the sequence numbers of the subcarriers according to the sequence from small to large to obtain a group of channel coefficient sequences of new subcarriers with channel states from bad to good: [ h ] of₍₁₎,h₍₂₎,...,h_(N)]；

1c) The channel coefficient sequence of the new subcarrier is simply divided into two parts, and the second half part is a good carrier [ h_(N),h_(N-1),...,h_(N/2)]The first half being the differential carrier [ h ]₍₁₎,h₍₂₎,...,h_(N/2)]。

Further, in step (2), the original OFDM symbol is generated by:

2a) BPSK modulating useful signal to obtain modulated useful signal [ x₁,x₂,...,x_N/2]；

2b) The modulated useful signals are copied and rotated by 180 ℃ respectively, and the signals after rotation are defined as inversion signals [ x'₁,x′₂,...,x′_N/2]；

2c) The modulated useful signal and the inverted signal are combined to form an OFDM symbol to be transmitted.

Further, in step 2c), the modulated useful signal and the inverted signal are combined by the following method:

according to the pairing method in the step (3), the signal is subjected to channel coefficient sequence [ h ] of a new subcarrier₍₁₎,h₍₂₎,...,h_(N/2)]Are combined to obtain N bits [ x'₁,x′₂,...,x′_N/2,x_N/2,...,x₂,x₁]And arranging each bit according to the actual carrier position corresponding to the new subcarrier channel coefficient sequence in sequence to obtain the required transmission OFDM symbol.

Further, in the step (3), the defined mapping relationship specifically includes the following processes:

according to the mapping relation:

g＝N-k+1

pairing the kth subcarrier with the corresponding g subcarrier, where k is 1, 2.

Further, in the step (4), the output signal-to-noise ratio gamma of the Kth sub-carrier is obtained_{symbol_K}The specific method comprises the following steps:

4a) the equalization processing method is that the received signal y in each carrier channel is processed_iMultiplying the conjugate of the channel coefficient at the receiving end

4b) Adopting a maximum ratio combination mode to carry out combined receiving to obtain the output signal-to-noise ratio gamma of each pair of subcarriers_{symbol_K}

Wherein | h_(k)|²And | h_(g)|²The squares of the channel coefficient modulus values of the kth subcarrier and the g subcarrier, respectively, k being 1, 2., N/2, g being N/2, N/2+ 1., N; n is a radical of₀Noise for each branchAcoustic power spectral density, P₀Is the average power of each subcarrier, gamma₀Is the signal to noise ratio.

Further, in the step (5), the specific method for obtaining the system average bit error rate p is as follows:

substituting x for | h_(k)|²Y instead of | h_(g)|²Then a received symbol x for each pair of subcarriers can be obtained_kError rate p_KComprises the following steps:

wherein f is_XY(x, y) is | h_(k)|²，|h_(g)|²The joint probability density function of (1), E]Meaning that the averaging function is taken, the Q function satisfies the following definition,

according to the theorem of order statistics, the method comprises the following steps:

the average bit error rate of the system is:

further, in the step (5), a specific method for obtaining a lower bound C of the system secret capacity is as follows:

defining an eavesdropping rate C of an eavesdropper_EThe formula:

wherein gamma is_E,K＝γ₀(max(|h_E,(k)|²,|h_E,(g)|²))，γ_E,KFor the received signal-to-noise ratio, | h, of the eavesdropper_E,(k)|²,|h_E,(g)|²Respectively eavesdropping the square of the modulus values of the coefficients of the two receiving channels of the kth symbol for an eavesdropper;

a lower bound C for the system's privacy capacity is:

wherein C is_DIndicates the receiving rate of a legitimate receiver]⁺Indicating the receiving rate C of the legitimate receiver_DLess than the eavesdropping rate C of an eavesdropper_EA lower bound C of the system privacy capacity is 0.

Compared with the prior art, the invention has the following characteristics:

1. the system model is simple and is suitable for various communication structure networks;

2. the theoretical values of the system average bit error rate and the secrecy rate under the scheme are deduced by combining the order statistics theorem;

3. the design scheme effectively utilizes the channel with poor performance to improve the system safety;

4. the OFDM subcarrier characteristics are fully utilized, and the average error rate performance of the system is effectively improved;

5. the performance change condition of the system under the imperfect reciprocity of the channel is fully analyzed, the tolerance to reciprocity errors is high, and the practicability of the scheme is further proved.

Drawings

FIG. 1 is a system model of the present invention;

FIG. 2 is a graph comparing the theoretical and simulated values of the bit error rate of the proposed scheme;

FIG. 3 is a graph of system safety capacity as a function of signal to noise ratio;

fig. 4 is a graph of system bit error rate as a function of reciprocity error variance.

Detailed Description

The invention is further described in detail below with reference to the drawings and examples, but the invention is not limited thereto.

Referring to fig. 1, the present invention is an OFDM secure transmission strategy combining subcarrier pairing and signal inversion, and the specific steps are as follows:

step 1, determining a rearranged subcarrier sequence.

1.1, obtaining the channel state information of each transmission by using a channel state information feedback system;

1.2 extracting the channel coefficient [ h ] of each carrier wave₁,h₂,...,h_N]Calculating the square | h of each sub-carrier coefficient modulus value_i|²Wherein i ═ 1, 2.., N. According to | h_i|²Rearranging the sequence numbers of the subcarriers according to the sequence from small to large to obtain a group of channel coefficient sequences of new subcarriers with channel states from bad to good: [ h ] of₍₁₎,h₍₂₎,...,h_(N)]；

1.3 simply divide the channel coefficient sequence of the new sub-carrier into two parts, the second half is the good carrier [ h_(N),h_(N-1),...,h_(N/2)]The first half being the differential carrier [ h ]₍₁₎,h₍₂₎,...,h_(N/2)]。

Step 2, determining OFDM symbol to be transmitted

2.1 BPSK-modulating the useful signal to obtain a modulated useful signal [ x₁,x₂,...,x_N/2]；

2.2 the modulated useful signals are copied and rotated by 180 ℃ respectively, and the signals after rotation are called inversion signals [ x'₁,x′₂,...,x′_N/2]；

2.3 combining the modulated useful signal and the reversal signal, according to the pairing mapping relation in the step 2, the signal is according to the new channel coefficient sequence [ h ] of the subcarrier₍₁₎,h₍₂₎,...,h_(N/2)]Are combined to obtain [ x'₁,x′₂,...,x′_N/2,x_N/2,...,x₂,x₁]And obtaining the OFDM symbol to be transmitted by each bit corresponding to the real position of each carrier.

And step 3, determining the pairing mapping relationship.

The worst channel and the best channel are paired and combined in sequence, namely the channel coefficients are h respectively_(k)And h_(g)And pairing corresponding subcarriers.

The pairing mapping relation is as follows:

g＝N-k+1

and pairing the kth subcarrier with the corresponding g subcarrier, wherein k is 1, 2.

Step 4, obtaining the output signal-to-noise ratio of each pair of subcarriers

4.1 selecting any pair of subcarriers according to the pairing mapping relation in the step 2, wherein the information received by the two channels under the condition of equal power is as follows:

4.2, each path of signal is equalized at the receiving end, and the equalization is multiplied by the conjugate of the channel coefficient:

4.3 obtaining the output signal-to-noise ratio of each pair of subcarriers:

wherein, | h_(k)|²And | h_(g)|²The squares of the channel coefficient modulus values of the kth subcarrier and the g subcarrier, respectively, k being 1, 2., N/2, g being N/2, N/2+ 1., N; n is a radical of₀For the noise power spectral density, P, of each branch₀Is the average power of each subcarrier, gamma₀Is the signal to noise ratio.

Step 5, obtaining the average error rate of the system and a lower bound C of the secret capacity of the system

5.1 obtaining | h_(k)|²，|h_(g)|²Is a joint probability density function f_XY(x,y)

Selecting any pair of subcarriers according to the pairing mapping relation in the step 2, wherein the information received by the two channels under the condition of equal power is as follows: the transmission channel we use is a complex gaussian rayleigh channel, | h_i|²Compliance parameter of

Is distributed exponentially of (1), then | h_i|²(for ease of writing, replace by variable t, | h in the following_(k)|²And | h_(g)|²Respectively, x and y) and the distribution function at t > 0 are:

from the theorem of order statistics, we can find | h_(k)|²,|h_(g)|²The joint probability density distribution function of (a) is:

the theorem of the order statistics is as follows:

let the total X have a continuous distribution function F (X) with a distribution density f (X) (a < X < b), X₁,X₂,...,X_nIs a simple random sample of capacity n from the total X, X₍₁₎＜X₍₂₎＜...＜X_(n)Is composed of simple random samples X₁,X₂,...,X_nThe resulting order statistic, (X)_(i),X_(j)) (1. ltoreq. i < j. ltoreq. n) has a combined density of:

5.2 we can get the received symbol x for each pair of subcarriers_kThe bit error rate of (a) is:

wherein f is_XY(x, y) is | h_(k)|²，|h_(g)|²The joint probability density function of (1), E]Representing an averaging function, the Q function satisfies the following definition:

the average bit error rate of the system is:

5.3 because the eavesdropping end receiving situation can not be completely known, it is somewhat difficult to accurately solve the secrecy capacity of the system. Here, we assume that an eavesdropper has good eavesdropping capability, can know the channel where the OFDM symbol to be transmitted each time, but cannot distinguish which is the inverted signal and which is the useful signal, so he can only guess the channel where the useful information is transmitted with good signal quality. This is a comparatively strong eavesdropping capability for the eavesdropper under the scheme, and under the assumption that the eavesdropping rate C of the eavesdropper can be obtained_EThe following formula:

wherein gamma is_E,K＝γ₀(max(|h_E,(k)|²,|h_E,(g)|²))，γ_E,KFor the eavesdropperNoise ratio, | h_E,(k)|²,|h_E,(g)|²

The squares of the two received channel coefficient moduli of the k-th symbol are respectively overheard for the eavesdropper.

A lower bound C for the privacy capacity of the system is therefore:

wherein C is_DIndicates the receiving rate of a legitimate receiver]⁺Indicating the receiving rate C of the legitimate receiver_DLess than the eavesdropping rate C of an eavesdropper_EA lower bound C of the system privacy capacity is 0.

The advantages of the present invention can be further illustrated by the following simulation experiment results:

the performance of the proposed scheme is verified by simulation in the present invention. Our scheme considers an OFDM classical eavesdropping wireless network with N subcarriers. The system model is shown in fig. 1 and consists of a source node Alice, a receiving node Bob and a possible eavesdropping node Eve. Each node is equipped with a single antenna, in half duplex mode. The transmission process is based on OFDM modulation of N subcarriers, so that a legal channel and an eavesdropping channel are logically divided into orthogonal subcarriers h with flat fading respectively_ABAnd h_AE. By utilizing the reciprocity of the channel, according to the information feedback system, we assume that Alice is perfectly known about the channel state information. The channel modeling is a complex Gaussian Rayleigh channel, and the adopted baseband modulation mode is BPSK modulation.

Fig. 2 shows that under the condition of equal power, the theoretical value of the average bit error rate of the system and the variation of the Monte Carlo simulation value along with the signal-to-noise ratio are simulated, wherein the implementation represents the theoretical value, and the curve represents the simulation value. We can see that as the number of subcarriers increases, the deviation between the theoretical value and the simulated value tends to increase, but at N of 64, the deviation is still small, and the correctness of the theoretical derivation is well verified. Meanwhile, fig. 2 also shows a graph of the average bit error rate of the eavesdropper as a function of the signal-to-noise ratio. It can be seen that no matter gamma₀And how the number of subcarriers varies, the bit error rate of the eavesdropper is close to 0.5, which is equivalent to the case of a blind guess. The result effectively proves the interference effect of the scheme on the eavesdropper, and achieves good eavesdropping prevention effect.

Fig. 3 shows the variation of the secrecy rate of the system with the signal-to-noise ratio when the eavesdropper has a better eavesdropping capability, and shows the variation of the secrecy rate with different numbers of subcarriers. As the number of subcarriers increases, we can see that the safety capacity of the system does not change much at low signal-to-noise ratios. The increase in security capacity is more pronounced at higher signal-to-noise ratios.

We introduce channel reciprocity errors into our proposed solution model for modeling analysis as follows:

the errors (RFRE) due to different transmit/receive rf circuit gains all satisfy the following distribution:

E＝Ae^φ

wherein A and φ each satisfy a mean value of μ_RFVariance is

Lognormal distribution and normal distribution.

The errors brought by the transmitting end and the receiving end are respectively:

the asymmetric time offset will cause a certain phase rotation error (TSRE) and affect the channel reciprocity property, and is distributed as follows:

Φ(n)＝exp(-j2πnΔd/N)

where Δ d can be understood as the timing deviation across the transmit ends, with the mean value μ_TSVariance is

N is the subcarrier number.

The error (FSRE) due to frequency offset due to local oscillator mismatch and the like is shown as follows:

Γ(m)＝exp(-j2π(m(N+N_cp)+N_cp)Δε/N)

where m is the OFDM symbol number, N_cpIs the cyclic prefix length, and Δ ε is the frequency offset. Since the FSRE mainly comes from time domain phase rotation and inter-carrier interference, and our strategy is implemented by using a modulus value, the influence caused by the phase rotation is well reduced. In addition, each independent subcarrier channel is adopted, so that the influence caused by interference between OFDM carriers is not considered, and the FSRE is not discussed more.

So the modeling of the downlink channel in our proposed solution model is as follows:

wherein: h_ULIn order to be the uplink channel, the base station,

to estimate the channel in the downlink with these reciprocity error factors taken into account, Λ (n) ═ E_tΦ(n)。

Fig. 4 shows the variation curve of the average bit error rate of the system with the error variance under different types of reciprocity errors. Simulation results show that the TSRE has little influence on the average bit error rate of the proposed scheme no matter how large the error variance value is; meanwhile, the RFRE does not have a great influence on the system average bit error rate of the scheme. The simulation result of fig. 4 shows that the proposed scheme can tolerate a certain error under the condition of imperfect reciprocity of channels, and further proves the stability and practicability of the performance of the proposed scheme.

Claims (6)

1. An OFDM safe transmission method combining subcarrier pairing and signal inversion is characterized by comprising the following steps:

(1) the sending end rearranges the serial numbers of all sub-carriers according to the known channel state information and the sequence from small to large of the square of the channel coefficient modulus value to obtain a new channel coefficient sequence of the sub-carriers, divides the new channel coefficient sequence into two parts by taking a middle point as a boundary, sets the first half part as a poor carrier and the second half part as a good carrier;

(2) copying a useful signal containing N/2 bits to be transmitted and carrying out inversion operation, sequentially placing the useful signal to be transmitted in a carrier wave with good back half part according to a reverse order mode for transmission, sequentially placing the inverted signal in a carrier wave with poor front half part for transmission, and jointly forming an original OFDM symbol with N bits; wherein N is the number of subcarriers;

(3) according to a certain pairing mapping relation, pairing and combining a good subcarrier and a poor subcarrier in a one-to-one correspondence manner;

the defined mapping relation comprises the following specific processes:

according to the mapping relation:

g＝N-k+1

pairing the kth subcarrier with the corresponding g subcarrier, wherein k is 1, 2.

(4) The receiving end carries out equalization processing on the received original OFDM symbol information, then the information in the two matched subcarriers is jointly received in sequence by adopting a maximum ratio combining mode to obtain the Kth subcarrier output signal-to-noise ratio gamma_{symbol_K}Wherein K ═ 1, 2.., N/2;

(5) in the case of power averaging, the average bit error rate p under the classical eavesdropping model and a lower bound C of the system secret capacity are obtained by using the theorem of order statistics.

2. The OFDM secure transmission method combining subcarrier pairing and signal inversion according to claim 1, wherein in step (1), the subcarrier sequence numbers (1, 2.., N) are rearranged to obtain a new set of channel sequence numbers, where N is the number of subcarriers, and the method is implemented by the following steps:

1a) obtaining the channel state information of each transmission by using a channel state information feedback system;

1b) extracting channel coefficient [ h ] of each carrier wave₁,h₂,...,h_N]Calculating the square | h of each sub-carrier coefficient modulus value_i|²Wherein i is 1, 2.. times.n; according to | h_i|²Rearranging the sequence numbers of the subcarriers according to the sequence from small to large to obtain a group of channel coefficient sequences of new subcarriers with channel states from bad to good: [ h ] of₍₁₎,h₍₂₎,...,h_(N)]；

1c) The channel coefficient sequence of the new subcarrier is simply divided into two parts, and the second half part is a good carrier [ h_(N),h_(N-1),...,h_(N/2+1)]The first half being the differential carrier [ h ]₍₁₎,h₍₂₎,...,h_(N/2)]。

3. The OFDM secure transmission method combining subcarrier pairing and signal inversion according to claim 1, wherein in step (2), the original OFDM symbol is generated by:

2a) BPSK modulating useful signal to obtain modulated useful signal [ x₁,x₂,...,x_N/2]；

2b) The modulated useful signals are copied and rotated by 180 ℃ respectively, and the signals after rotation are defined as inversion signals [ x'₁,x'₂,...,x'_N/2]；

2c) Combining the modulated useful signal and the reversal signal to form an OFDM symbol to be transmitted;

the combination of the modulated useful signal and the inverted signal is realized by the following method:

according to the pairing method in the step (3), the signal is subjected to channel coefficient sequence [ h ] of a new subcarrier₍₁₎,h₍₂₎,...,h_(N/2)]Are combined to obtain N bits [ x'₁,x'₂,...,x'_N/2,x_N/2,...,x₂,x₁]Wherein each bit is true according to new sub-carrier channel coefficient sequenceAnd arranging the actual carrier positions to obtain the required transmission OFDM symbols.

4. The OFDM secure transmission method combining subcarrier pairing and signal inversion as claimed in claim 1, wherein in step (4), the output SNR γ of the Kth subcarrier is obtained_{symbol_K}The specific method comprises the following steps:

4a) the equalization processing method is that the received signal y in each carrier channel is processed_iMultiplying the conjugate of the channel coefficient at the receiving end

Wherein i is 1, 2.., N;

4b) adopting a maximum ratio combination mode to carry out combined receiving to obtain the output signal-to-noise ratio gamma of each pair of subcarriers_{symbol_K}

Wherein, | h_(k)|²And | h_(g)|²The squares of the channel coefficient modulus values of the kth subcarrier and the g subcarrier, respectively, k being 1, 2., N/2, g being N/2+1, N/2+ 2., N; n is a radical of₀For the noise power spectral density, P, of each branch₀Is the average power of each subcarrier, gamma₀Is the signal to noise ratio.

5. The OFDM secure transmission method combining subcarrier pairing and signal inversion according to claim 4, wherein in step (5), the specific method for obtaining the system average bit error rate p comprises:

substituting x for | h_(k)|²Y instead of | h_(g)|²Then a received symbol x for each pair of subcarriers can be obtained_kError rate p_KComprises the following steps:

wherein f is_XY(x, y) is | h_(k)|²，|h_(g)|²The joint probability density function of (1), E]Meaning that the averaging function is taken, the Q function satisfies the following definition,

according to the theorem of order statistics, the method comprises the following steps:

the average bit error rate of the system is:

6. the OFDM secure transmission method combining subcarrier pairing and signal inversion as claimed in claim 1, wherein in step (5), the specific method for obtaining a lower bound C of the system secret capacity is:

defining an eavesdropping rate C of an eavesdropper_EThe formula:

wherein gamma is_E,K＝γ₀(max(|h_E,(k)|²,|h_E,(g)|²))，γ_E,KFor the received signal-to-noise ratio, | h, of the eavesdropper_E,(k)|²,|h_E,(g)|²Squaring, gamma, of the modulus values of the coefficients of two reception channels, respectively of the kth and the g-th symbol, for eavesdropping by an eavesdropper₀Is the signal-to-noise ratio;

a lower bound C for the system's privacy capacity is:

wherein C is_DIndicates the receiving rate of a legitimate receiver]⁺Indicating the receiving rate C of the legitimate receiver_DLess than the eavesdropping rate C of an eavesdropper_EA lower bound C of the system privacy capacity is 0.

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