An Underwater Acoustic Orthogonal Frequency Division Multiplexing Secure Communication Method

Abstract

The present invention discloses an underwater acoustic orthogonal frequency division multiplexing secure communication method. The multiple transmit time reversal pre-filtering at the transmitter focuses the energy of the legitimate channel on the main path, shortening the channel of the cooperating party, while the eavesdropper still exhibits severe multipath characteristics. An orthogonal frequency division multiplexing signal with a short cyclic prefix smaller than the channel delay spread is transmitted, causing severe inter-symbol interference and inter-carrier interference to the eavesdropper. At the legitimate receiver, an interference cancellation-decision feedback equalizer is used to eliminate the residual interference of the cooperating party, improving the quality of the communication link of the cooperating party. Moreover, the secrecy capacity expression of the proposed method is given to evaluate the security performance of the system. The present invention is suitable for the underwater acoustic environment and has good performance in the long-delay frequency-selective underwater acoustic channel. When the location and channel information of the eavesdropper are both unknown, a considerable secrecy rate is obtained without the assistance of artificial noise.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater acoustic communication, and relates to an underwater acoustic orthogonal frequency division multiplexing secure communication method, in particular to an underwater acoustic orthogonal frequency division multiplexing secure communication method based on multi-transmission time reversal focusing. Background Art

[0002] The underwater acoustic channel is a wireless channel with sound waves as the medium, which has natural openness, and information transmission is easily eavesdropped or intercepted. Information security is an urgent problem to be solved in the field of underwater acoustic communication. Especially in fields related to national security such as military operations and marine security, ensuring the information security of underwater acoustic communication is extremely important. The traditional method is to encrypt in the upper layer protocol and then transmit the ciphertext in the underwater acoustic channel. With the development of computer technology, using encryption means in the upper layer protocol is not absolutely secure. Physical layer security is a technology to ensure information security without relying on upper layer protocol means. It utilizes the randomness and diversity of the channel and adopts signal processing means to achieve secure information transmission at the physical layer. While ensuring the robust communication of the cooperative receiver, even if the eavesdropper intercepts the signal, it cannot obtain useful information.

[0003] Wireless physical layer security technology usually realizes it through beamforming or transmitting artificial noise and interference. However, underwater eavesdropping nodes are usually silent, and it is difficult to obtain the channel information of the eavesdropping nodes, making it very difficult to achieve beamforming. On the other hand, underwater acoustic communication has limited resources. Transmitting artificial noise will waste precious resources and is also unfriendly to underwater organisms. Therefore, the underwater acoustic environment poses higher requirements for physical layer security technology. The eavesdropping risk it faces is usually completely unknown and blind. Technologies that perform signal processing at the transmitter using the information of the cooperative party are more suitable for the underwater acoustic scenario. On the other hand, orthogonal frequency division multiplexing (OFDM) has high spectral efficiency and can combat frequency selective fading channels, and is a commonly used technology in high-speed underwater acoustic communication. Protecting the transmission of OFDM is an important issue in physical layer security.

[0004] The literature [Furqan H M, Hamamreh J M, Arslan H. Enhancing physical layer security of OFDM systems using channel shortening[C] / / IEEE International Symposium on Personal. IEEE, 2017.] applies channel shortening technology at the transmitter of a single - transmit - single - receive system to reduce the length of the effective channel. The design of the channel shortening filter is based on the channel of the legitimate user, making the length of the legitimate channel equal to or less than the set cyclic prefix (CP), while the length of the eavesdropping channel is greater than the cyclic prefix length. At the eavesdropper, inter - symbol interference (ISI) and inter - carrier interference (ICI) are caused, the orthogonality is lost, and the overall performance at the eavesdropper deteriorates. However, the Z - transform (ZT) and MS - SNR channel shortening methods used also have an impact on the eavesdropping channel, and the interference is reduced accordingly. Chinese Patent Specification CN115278725A discloses a time - reversal filtering, power allocation, and artificial noise design method for enhancing the security performance of OFDM systems. This method performs time - reversal filtering at the transmitter and jointly optimizes the sub - carrier power allocation of the transmitter and the covariance matrix of the artificial noise with the goal of maximizing the system secrecy rate. Compared with the unoptimized system, the achievable secrecy rate is significantly improved. However, both power allocation and artificial noise in this method consume additional resources and are not suitable for application in the underwater acoustic environment. In addition, compared with a single - transmit system, time - reversal pre - filtering has more possibilities in a multi - transmit system. Summary of the Invention

[0005] Aiming at the above - mentioned prior art, the technical problem to be solved by the present invention is to provide an underwater acoustic orthogonal frequency - division multiplexing secure communication method based on multi - transmit time - reversal focusing, so as to achieve physical - layer - secure OFDM communication in an underwater acoustic environment with eavesdroppers.

[0006] To solve the above - mentioned technical problem, an underwater acoustic orthogonal frequency - division multiplexing secure communication method of the present invention includes:

[0007] Step 1: After each transmitting element obtains the channel impulse response from the cooperative receiver, select the path that arrives first among all paths, and synchronize the channel impulse responses (CIRs) of all transmitting elements at this moment. Select the intercept window length and intercept the CIR of each element. The CIR obtained after synchronization and interception of the r - th element is h r ′(t), h r ′(t) is then time - reversed and energy - normalized to obtain the response T r (t) of the time - reversal filter on the r - th element;

[0008] Step 2: Convolve the signals of each transmitting element with the corresponding filter responses respectively, and then all elements transmit the preprocessed signals simultaneously. Regard the equivalent channel from each transmitting element to the receiving end as the convolution of the actual channel experienced and the time-reversal filter response. Regard the overall multiple-input single-output channel at the receiving end as a single-input single-output channel in the time domain to obtain the equivalent legitimate channel Q ab (t) and the eavesdropping channel Q ae (t);

[0009] Step 3: Select the cyclic prefix length, and then establish a receiving signal model with inter-symbol interference and inter-carrier interference when the cyclic prefix is insufficient;

[0010] Step 4: Establish a block transmission interference model, and obtain the introduced additive interference according to the interference model;

[0011] Step 5: Transmit the legitimate channel information to the cooperating party in advance through the legitimate channel. The cooperating party's receiver demodulates the current block using an IC-DFE equalizer: first, use a zero-forcing equalizer to determine the information symbols of the current block; then, combine the decision results of the previous block, reconstruct the interference through the interference expression to obtain the feedback term, subtract the feedback term from the received signal, and then perform zero-forcing equalization. Finally, demodulate the transmitted information from the output of the second zero-forcing equalization.

[0012] Furthermore, the CIR h r ′(t) obtained after synchronization and truncation of the r-th element is:

[0013]

[0014] where h l,r is the amplitude coefficient of the l-th tap in the channel of the r-th element, τ l,r is its corresponding time delay, is the number of paths, δ(t) represents the unit impulse function, and the channel is stable within one probing-transmitting cycle.

[0015] Furthermore, the response T r (t) of the time-reversal filter on the r-th element is:

[0016]

[0017] Furthermore, the equivalent legitimate channel Q ab (t) and the eavesdropping channel Q ae (t) are specifically:

[0018]

[0019]

[0020] Furthermore, when the cyclic prefix established in step 3 is insufficient, the received signal model with inter-symbol interference and inter-carrier interference is specifically as follows:

[0021] The channel is divided into two parts: the paths arriving within the cyclic prefix and the paths arriving outside the cyclic prefix. The paths arriving within the cyclic prefix bring the desired signal, and the paths arriving outside the cyclic prefix bring the interference signal. Suppose an OFDM block has K subcarriers, and the receiver processes the blocks one by one. The received signal of the j-th transmission block is:

[0022]

[0023] Wherein, n j =[n j (0), n j (1), …, n j (K - 1)] T is the interference term containing inter-symbol interference and inter-carrier interference; y j =[y j (0), y j (1), …, y j (K - 1)] T , x j =[x j (0), x j (1), …, x j (K - 1)] T , e j =[e j (0), e j (1), …, e j (K - 1)] T are respectively the received time-domain signal, the transmitted time-domain signal, and the noise sequence on the baseband; W is the Fourier transform matrix, and D is a K×K diagonal matrix, and the elements on the diagonal are:

[0024]

[0025] Wherein, v is the length of the cyclic prefix, k represents the k-th subcarrier, and suppose the channel length is v + K + 1, and h l is the tap coefficient of the l-th path.

[0026] Furthermore, the additive interference is specifically:

[0027]

[0028] Wherein, n j represents the additive interference of the j-th transmission block, and H pre and H add are K×(v + K) matrices, satisfying:

[0029]

[0030] and represent the original CP - OFDM blocks of the (j - 1)-th transmission block and the j - th transmission block.

[0031] Furthermore, the feedback item is specifically:

[0032]

[0033] wherein, represents the feedback item of the j - th transmission block, W is the Fourier transform matrix, and is the CP - OFDM block reconstructed according to the decision result.

[0034] Furthermore, the output of the second zero - forcing equalization is:

[0035]

[0036] wherein, is the input of the second zero - forcing equalization of the j - th transmission block, satisfying:

[0037] Furthermore, after step 5, it also includes: calculating the system secrecy capacity for evaluating the secrecy performance of the system:

[0038]

[0039] wherein, N represents the number of primitive elements, β represents the total channel energy, σ 2 represents the noise power, when the cyclic prefix length v → 0, K represents the number of sub - carriers, g l represents the amplitude coefficient of the l - th tap in the equivalent channel of the eavesdropper after time reversal;

[0040] Compare the system secrecy capacity with the expected secrecy capacity standard to determine whether the secrecy performance is satisfied. If not, adjust the number of transmit array elements and the cyclic prefix length, and return to step 1.

[0041] Advantages of the present invention: The present invention provides an OFDM communication method for achieving physical layer security in an underwater acoustic environment with eavesdroppers. When the channel state information of the legitimate channel is known, a method of multiple transmit time reversal focusing is adopted. The peaks of the time reversal channels of each array element are at the same moment and are superimposed, greatly improving the time reversal focusing effect. On this basis, an OFDM waveform is designed to transmit OFDM signals with variable short cyclic prefixes. The insufficient cyclic prefix will introduce ISI and ICI at the receiving end of the eavesdropper, while the legitimate receiving end uses an interference cancellation - decision feedback equalizer (IC - DFE) to eliminate this interference. This method utilizes the long delay characteristic of the underwater acoustic channel and can obtain good security performance and considerable secrecy rate without using any other resources.

[0042] The present invention combines the space - time focusing characteristics of time reversal and utilizes the multipath characteristics of the underwater acoustic channel to improve the security performance of the OFDM system. Aiming at the problem that the time compression ability of single - transmit time reversal filtering is insufficient, the present invention adopts a multiple - transmit time reversal focusing at the transmitting end, which can make the signals coherently add at the legitimate receiving end and improve the focusing effect. Aiming at the problem that there is still some interference at the legitimate receiving end after time reversal, the present invention adopts an interference cancellation decision feedback equalizer at the cooperative receiving end to improve the quality of the communication link of the cooperative party. Finally, the secrecy capacity expression of the proposed method is given to evaluate the security performance of the system. Compared with the existing wireless physical layer security technologies, the proposed method is more suitable for the underwater acoustic environment. Simulation results show that the present invention has good performance in the long - delay frequency - selective underwater acoustic channel. When the position and channel information of the eavesdropper are unknown, a considerable secrecy rate is obtained without the assistance of artificial noise. Brief Description of the Drawings

[0043] Figure 1 Schematic diagram of the equivalent channel after multiple - transmit time reversal pre - processing;

[0044] Figure 2 Schematic diagram of the interference superimposed on the current block, including inter - symbol interference and inter - carrier interference;

[0045] Figure 3 Three - party model for secure communication;

[0046] Figure 4 Processing flow chart of the transmitter;

[0047] Figure 5 Schematic diagram of time alignment and channel response truncation;

[0048] Figure 6 Structure diagram of the interference cancellation - decision feedback equalizer;

[0049] Figure 7(a) shows the legitimate channel after using time reversal focusing;

[0050] Figure 7(b) shows the wiretapping channel after anti-focusing during use;

[0051] Figure 8(a) shows the received constellation diagram when the cooperating party uses zero-forcing equalization;

[0052] Figure 8(b) shows the received constellation diagram when the cooperating party uses IC-DFE equalization;

[0053] Figure 8(c) shows the received constellation diagram when the wiretapper uses zero-forcing equalization;

[0054] Figure 9 are the bit error rate curves of the cooperating party and the wiretapper;

[0055] Figure 10 is the comparison of the secrecy rate curves when using different numbers of array elements;

[0056] Figure 11(a) shows the secrecy rate diagram over the entire simulation area with CP = 256 ms and ε = 0.5;

[0057] Figure 11(b) shows the secrecy rate diagram over the entire simulation area with CP = 120 ms and ε = 0.23;

[0058] Figure 11(c) shows the secrecy rate diagram over the entire simulation area with CP = 64 ms and ε = 0.125;

[0059] Figure 11(d) shows the secrecy rate diagram over the entire simulation area with CP = 40 ms and ε = 0.078. Detailed implementation manners

[0060] The present invention will be further described below in conjunction with the accompanying drawings of the specification and embodiments.

[0061] The object of the present invention is achieved as follows: Based on the cyclic prefix OFDM system, multi-transmit time-reversal pre-filtering is adopted at the transmitting end. A received signal model with interference is established, and an OFDM waveform with a short cyclic prefix is designed and transmitted. At the legitimate receiver, an IC-DFE equalizer is used for equalization. Finally, an analytical expression for the secrecy rate is derived to evaluate the performance. Specifically, it includes the following steps:

[0062] Symbol description: |·| represents the absolute value, represents convolution, x in lowercase bold represents a vector, a tilde on a lowercase bold letter represents the frequency-domain signal, H in uppercase bold represents a matrix, [e] + represents the larger number between 0 and e, and E{·} represents the mathematical expectation.

[0063] Step 1: After each transmitting element obtains the channel impulse response from the cooperative receiver, select the path that arrives first among all paths, and synchronize the channel impulse responses (CIRs) of all transmitting elements at this moment. Select an appropriate truncation window length and truncate the CIR of each element. Let h l,r be the amplitude coefficient of the l-th tap in the channel of the r-th array element, and τ l,r be its corresponding time delay. There are a total of paths, and the channel is stable within one probing-transmitting cycle. δ(t) represents the unit impulse function. The CIR obtained after synchronization and truncation of the r-th element is h r ′(t)

[0064]

[0065] h r ′(t) is then time-reversed and energy-normalized to obtain the response of the time-reversal filter on the r-th element as

[0066]

[0067] Step 2: Convolve the signals of each transmitting element with the corresponding filter response respectively, and then all elements transmit the preprocessed signals simultaneously. Consider the equivalent channel from each transmitting element to the receiving end as the convolution of the actual channel experienced and the time-reversal filter response, and consider the overall multiple-input single-output channel at the receiving end as a single-input single-output channel in the time domain.

[0068] The equivalent channel at the final receiving end is as shown in the appendix Figure 1 . g r (t) is the CIR of the eavesdropper.

[0069] The legitimate channel Q ab (t) is:

[0070]

[0071] The eavesdropping channel Q ae (t) is:

[0072]

[0073] Step 3: Select an appropriate cyclic prefix length according to the delay spread of the legitimate channel and the OFDM symbol period. Then establish a received signal model with inter-symbol interference and inter-carrier interference when the cyclic prefix is insufficient. The channel is divided into two parts: the paths that arrive within the cyclic prefix and those outside the cyclic prefix. The paths that arrive within the cyclic prefix bring the desired signal, and those outside the prefix bring interference. Let an OFDM block have K subcarriers, and the received signal of the j-th transmission block can be expressed as:

[0074] wherein are the received signal, noise, and transmitted information symbol in the frequency domain, respectively. W is the Fourier transform matrix, D is a K×K diagonal matrix, v is the length of the cyclic prefix, k represents the k-th subcarrier, assuming the channel length is v+K+1, h l is the tap coefficient of the l-th path, and the elements on the diagonal are:

[0075]

[0076] n j =[n j (0), n j (1), …, n j (K-1)] T is the interference term containing inter-symbol interference and inter-carrier interference; y j =[y j (0), y j (1), …, y j (K-1)] T , x j =[x j (0), x j (1), …, x j (K-1)] T , e j =[e j (0), e j (1), …, e j (K-1)] T are the received time-domain signal, transmitted time-domain signal, and noise sequence in the baseband, respectively.

[0077] Step 4: Establish an interference model based on block transmission as Figure 2 shown. According to the interference model, the expression of the introduced additive interference can be obtained as:

[0078] wherein, H pre and H add are K×(v+K) matrices, which can be expressed as:

[0079]

[0080] and represent the original CP-OFDM blocks of the previous symbol and the current symbol.

[0081] Step 5: When the cooperative receiver demodulates the current block, it first determines the information symbol of the current block through a zero-forcing equalizer. Then, combined with the decision result of the previous block, the interference is reconstructed through the interference expression to obtain the feedback term Subtract the feedback term from the received signal. Then perform zero-forcing equalization, and finally demodulate the transmitted information from the output of the equalizer.

[0082] Among them, the output of the zero-forcing equalizer can be expressed as:

[0083]

[0084] Output of the IC-DFE equalizer can be expressed as:

[0085]

[0086] Step 6: Deduce the secrecy capacity expression of the proposed method, and evaluate the secrecy performance of the system by calculating the secrecy capacity of the system. The secrecy capacity obtained by this formula is the performance limit under ideal conditions, which can be compared with the expected secrecy capacity standard to see if the required secrecy performance is met. If not, the number of transmitting array elements and the cyclic prefix length can be adjusted, and then Steps 1-5 can be executed to achieve stronger secrecy performance.

[0087] Let the amplitude coefficient of the l-th tap in the channel that arrives at the r-th primitive of the cooperative party before time reversal be h l,r , and there are N primitives in total, and are the noise powers of the cooperative party and the eavesdropper respectively. The signal-to-interference-plus-noise ratio of the cooperative party is:

[0088] Let the amplitude coefficient of the l-th tap in the equivalent channel after time reversal of the eavesdropper be g l , and the proportion of the channel energy in the cyclic prefix in the channel after time reversal of the eavesdropper is The signal-to-interference-plus-noise ratio of the eavesdropper is:

[0089]

[0090] Assume that the cooperative party and the eavesdropper are in the same position, that is, the total channel energy β and the noise power σ 2 are the same:

[0091]

[0092] The secrecy capacity of the proposed method is:

[0093]

[0094] Secrecy capacity R E ≥0. The more array elements are used for time reversal, the better the focusing effect of the legitimate channel and the higher the secrecy rate. However, the more complex the system is and the more difficult it is to implement. Therefore, a trade-off is needed.

[0095] The following gives an embodiment in combination with specific parameters:

[0096] The secure communication model is as follows. Figure 3 As shown in the figure, the transmitter Alice desires to communicate securely with the legitimate receiver Bob, while the node Eve eavesdrops on their communication. Among them, the transmitter Alice has N transmitting transducers, while the legitimate receiver Bob and the eavesdropper Eve are equipped with a single receiving hydrophone. The channels from Alice to Bob and Eve are both multiple-input single-output (MISO) channels, and the channels among all participants are frequency-selective fading channels. Define h ab and h ae as the legitimate channel between Alice and Bob and the eavesdropping channel between Alice and Eve. Bob broadcasts pilots regularly so that Alice can estimate the channel h ba from Bob to Alice, satisfying the channel reciprocity h ab = h ba . The signal processing flow of the transmitter is as follows. Figure 4 The symbol period of OFDM is T d = K / B, where K is the number of subcarriers and the system bandwidth is B. The transmitted information symbol of the j-th block is X j = [X j (0), X j (1), …, X j (K - 1)] T . After serial-to-parallel conversion and inverse fast Fourier transform (IFFT), it is transformed into the information symbol x j = [x j (0), x j (1), …, x j (K - 1)] T . The transmitter uses the special key V agreed upon between nodes Alice and Bob to change the current CP length. The cyclic prefix length is a part of the signal length T cp = εT d , where ε ∈ [0, ε up , and ε up is determined by the known legitimate channel information. After inserting the CP, the transmitted time-domain signal with cyclic prefix is obtained. Then, it is up-converted to obtain the passband signal

[0097] After each transmitting element obtains the channel impulse response from the cooperative receiver, the path that arrives first among all paths is selected, and the channel impulse responses (CIRs) of all transmitting elements are synchronized at this moment. Select an appropriate truncation window length to truncate the CIR of each element, as shown in Figure 5 . Let h l,r be the amplitude coefficient of the l-th tap in the channel of the r-th element, and τ l,r be its corresponding time delay. There are a total of paths, and the channel is stable within a sounding - transmitting period. The CIR h r ′(t) obtained after the r - th primitive synchronization and interception is as follows:

[0098]

[0099] h r ′(t) is further subjected to time reversal and energy normalization to obtain the response of the time - reversal filter on the r - th primitive as:

[0100]

[0101] The signals of each transmitting primitive are respectively convolved with the corresponding filter responses, and all array elements simultaneously transmit the pre - processed signals. g r (t) is the CIR of the eavesdropper. The channel Q ab (t) of the legitimate receiver is as follows:

[0102]

[0103] The eavesdropping channel Q ae (t) is as follows:

[0104]

[0105] After the received signal at the receiver undergoes down - conversion and down - sampling, the received baseband signal is obtained. The baseband signal is divided into two parts: the desired signal and interference. The desired signal is contributed by the paths arriving within the cyclic prefix, and the interference comes from the paths arriving outside the cyclic prefix. The received signal of the j - th transmission block can be expressed as:

[0106]

[0107] where are the received signal, noise, and transmitted information symbol in the frequency domain respectively. W is the Fourier transform matrix. D is a K×K diagonal matrix, v is the length of the cyclic prefix, k represents the k - th sub - carrier, assuming the channel length is v + K + 1, h l is the tap coefficient of the l - th path, and the elements on the diagonal are:

[0108]

[0109] n j =[n j (0), n j (1), …, n j (K - 1)] T is the interference term containing inter - symbol interference and inter - carrier interference; y j =[y j (0), yj (1),…,y j (K - 1)] T ,e j =[e j (0),e j (1),…,e j (K - 1)] T are the received time - domain signals on the baseband and Gaussian noise signals respectively. Considering the assumption of block transmission, only the inter - symbol interference brought by the previous symbol and the inter - carrier interference generated by the current symbol are considered, and the channel length is set to v + K + 1. At this time, the schematic diagram of the superposition of ISI and ICI on the current transmission block is as Figure 2 shown, represents the ISI brought by the previous symbol, and y ICI∈xj (i) represents the ICI brought by the current symbol. They can be expressed as

[0110]

[0111]

[0112] The interference term can be obtained from the matrix representation of convolution as

[0113]

[0114] Among them, H pre and H add are K×(v + K) matrices, which can be expressed as:

[0115]

[0116] and represent the original CP - OFDM blocks of the (j - 1) - th and j - th transmission blocks.

[0117] The output of the zero - forcing equalizer (ZF) is:

[0118]

[0119] At this time, at the eavesdropper, the interference term will affect the equalization result, and using the zero - forcing equalizer will obtain extremely poor and unacceptable equalization results. For the cooperative party, due to the time - reversal space - time focusing characteristic, most of the channel energy is on the main path within the cyclic prefix. However, there is also a small amount of residue, and the IC - DFE equalizer can be used to eliminate the residual interference of the cooperative party. The cooperative party can also transmit information relatively accurately when only using the zero - forcing equalization. Suppose H pre and H add are known to the cooperative party, and the structure of the IC - DFE equalizer is as Figure 6As shown. The received signal is first zero-forcing equalized to obtain and then decision-making is performed to obtain which is the noise-free estimated value of Then, through IFFT and adding CP, the CP-OFDM block reconstructed from the first decision result is obtained Combined with the decision result of the previous block, the feedback term calculated by the interference model is

[0120]

[0121] Then the feedback term is subtracted from the received signal. The input for the second zero-forcing equalization of the j-th transmission block is:

[0122]

[0123] The output of the IC-DFE equalizer is:

[0124]

[0125] At the cooperative receiver, the signal-to-interference-plus-noise ratio (SINR) on each subcarrier is:

[0126]

[0127] Assume that the eavesdropper also achieves perfect time synchronization and correctly removes the cyclic prefix, although this is very difficult. The eavesdropper only uses a zero-forcing equalizer, and the SINR on each subcarrier at the eavesdropper is:

[0128]

[0129] The d in the above formula k and are calculated from the parameters of the eavesdropping channel. The average channel capacities of the legitimate communication link Alice - Bob and the eavesdropping link Alice - Eve can be calculated by the following formula

[0130]

[0131] The secrecy capacity of the system is calculated as

[0132]

[0133] Finally, the secrecy capacity of the proposed method is derived to evaluate the system performance. The secrecy capacity obtained by this formula is the performance limit under ideal conditions. In practical applications, the system secrecy capacity can be pre-calculated by this formula with the set parameters and compared with the expected secrecy capacity standard to adjust the parameters. Assume that there is perfect synchronization between the transmitter and the receiver, the transmitted information symbols are independent of each other, and have unit average power. The additive background noise is Gaussian white noise. Let the amplitude coefficient of the l-th tap in the channel that arrives at the cooperative party before the r-th basis element of the cooperative party be h l,r , and there are N basis elements in total. The interference brought by the paths outside the cyclic prefix is completely suppressed, and other paths within the cyclic prefix are ignored. The total energy of the original channel is It will focus entirely on the main path of the channel after time reversal. Since the scale of the array is much smaller than the distance from the transmitter to the receiver, it can be assumed that the losses of each array element to the receiver are the same, and the channel energies are approximately equal, that is The total energy of the legitimate channel is And The equal sign holds when all terms are the same. And are the noise powers of the cooperative party and the eavesdropper respectively. The signal-to-interference-plus-noise ratio of the cooperative party is derived as:

[0134]

[0135] Let the amplitude coefficient of the l-th tap in the equivalent channel after time reversal of the eavesdropper be g l , and the proportion of the channel energy within the cyclic prefix after time reversal of the eavesdropper is The interference term is

[0136]

[0137]

[0138]

[0139] The signal-to-interference-plus-noise ratio of the eavesdropper is:

[0140] Assume that the cooperative party and the eavesdropper are in the same position, that is, the total channel energy β and the noise power σ 2 are the same:

[0141]

[0142] The secrecy capacity of the proposed method is:

[0143]

[0144] Where When v → 0, R EReach the performance limit. The secrecy rate R E ≥0, and the larger the number of array elements N used for time reversal, the larger the proportion of paths outside the cyclic prefix of the eavesdropping channel, and the higher the secrecy rate.

[0145] The following is a simulation performance analysis in conjunction with the accompanying drawings. The present invention conducts digital simulation based on a time-invariant underwater acoustic multipath channel. The channel used in the simulation is generated by the ray acoustics software Bellhop. The sound source has 8 transmitting elements, which are deployed at a depth interval of 20 m centered on 200 m, and the transmitting end has a total power constraint. The legitimate receiver Bob is selected at the position (10 km, 3900 m). The positions of the eavesdroppers are selected in the form of a grid, and the simulated area is a depth of 0 - 4000 m and a distance of 0 - 250 km. The step size of the grid is (100 m, 5 km), so a total of 41 * 51 (2091) channel samples are obtained. Here we select (10 km, 3700 m) as the representative of the eavesdropper for analysis, and the equivalent channels of the cooperating party Bob and the eavesdropping party Eve are as shown in the accompanying Figure 7(a) and 7(b) figures. Assuming that the time is synchronized at the maximum path, it can be seen that the legitimate channel focuses on the peak path, and the focusing effect improves with the increase in the number of array elements used. The eavesdropping channel shows strong multipath characteristics, and the multipath effect becomes more severe with the increase in the number of array elements.

[0146] The underwater acoustic OFDM system carried has 1024 subcarriers. The communication from Alice to Bob is a medium-range underwater acoustic communication with a distance of 10.8 km. The frequency band can be set to 8 - 14 kHz, the system bandwidth is 6 kHz, the modulation method is QPSK, and the length of an OFDM signal is 170.7 ms. To control the variable, the cyclic prefix length is set to 240 (40 ms, ε = 0.2344) and remains unchanged. At this time, the paths arriving within 40 ms at the eavesdropping side are protected. When using eight array elements for time reversal and without adding noise, the constellation diagrams of the cooperating party and the eavesdropping party are as shown in the accompanying Figure 8(a)-8(c) figures. It can be seen that the interference term is small at Bob, and the received constellation diagram can be correctly decoded. At Eve, the constellation diagram is completely disrupted due to the introduction of the interference term. Based on Figure 8(a) above, the constellation diagram obtained by applying the IC-DFE equalizer at Bob is shown in Figure 8(b). At this time, the bit error rate at Bob is reduced to 0, and the distribution of constellation points is very concentrated, indicating that the IC-DFE equalizer minimizes the interference on the subcarriers. By introducing the noise term and Monte Carlo with different information symbols, the bit error rate curves of the cooperating party and the eavesdropping party are obtained as shown in the accompanying Figure 9As shown. As can be seen from the figure, the eavesdropper cannot decode correctly under large interference, and the bit error rate is very high, close to 0.5. The performance of the partner using 8-element time inversion is much better than that of single-element time inversion. The bit error rate performance is less than 10-3 when the 8-element time inversion is used, and the symbol error rate performance is less than 10-5 after IC-DFE. Thus, under the condition that the partner can decode correctly, the effect of the non-cooperative party being unable to decode correctly is achieved. The two channels selected above can represent the performance of the legitimate receiver and the eavesdropper when this method is used, which verifies the effectiveness of the proposed method.

[0147] Next, the confidentiality rate of this method is analyzed. The confidentiality rate is calculated by two methods: the confidentiality rate expression derived by the present invention and the numerical simulation method, as shown in the attached figure. Figure 10 As shown. It can be seen from the figure that as the number of array elements increases, the time-reversal focusing effect is better, which makes the decoding effect before feedback better, and thus the equalization effect of IC-DFE is better. When using 8-element time reversal, the simulation curve approaches the analytical curve. From the expression of the confidentiality rate, it can be seen that as the number of array elements increases, the energy on the main path will increase N times, increasing the confidentiality capacity of the system. However, the increase in the number of array elements comes at the expense of increased system complexity, so it is necessary to choose according to the actual situation and the required confidentiality capacity. It has been proved above that the analytical expression of the confidentiality rate is consistent with the simulation results when enough array elements are used. The following is an analysis of the confidentiality capacity in the entire area based on the analytical expression of the confidentiality rate, and the propagation loss is taken into account. At this time, the frequency band is reduced to 2-4khz, the OFDM symbol period is 512ms, 8 array elements are used for time reversal, and the noise is set to -80dBm in the entire area. Select different cyclic prefix lengths to calculate the confidentiality capacity in the entire simulation area as shown Figure 11(a)-11(d) As shown. It can be seen from the figure that as the CP length decreases, the confidentiality capacity increases and the bright area becomes larger. As shown in Figure 11(a), when the CP length is 256ms, the confidentiality capacity of some areas is very low. In Figures 11(b), 11(c), and 11(d), the ratio of the cyclic prefix length to the symbol period is within the set interval [0, 0.25], and the confidentiality capacity of most areas is above 6bps. The partner is marked with "+" in the figure, and its channel capacity is 7.28bps. It is the darkest point in the figure, while the confidentiality capacity in other locations is at a high level. The above results show that this method can obtain considerable confidentiality capacity in the entire area.

Claims

1. An underwater acoustic orthogonal frequency division multiplexing secure communication method, characterized in that, it includes: Step 1: After each transmitting element obtains the channel impulse response from the cooperative receiver, select the path that arrives first among all paths, and synchronize the channel impulse responses (CIRs) of all transmitting elements at this moment. Select the length of the truncation window and truncate the CIR of each element. The CIR obtained after synchronization and truncation of the r-th element is h r ′(t), h r ′(t) is then time-reversed and energy-normalized to obtain the response T r (t) of the time-reversal filter on the r-th element; Step 2: Convolve the signals of each transmitting element with the corresponding filter response respectively, and then all the array elements transmit the preprocessed signals simultaneously. Consider the equivalent channel from each transmitting element to the receiving end as the convolution of the actual channel experienced and the time-reversal filter response, and consider the overall multiple-input single-output channel at the receiving end as a single-input single-output channel in the time domain to obtain the equivalent legitimate channel Q ab (t) and the eavesdropping channel Q ae (t); Step 3: Select the cyclic prefix length, and then establish a received signal model with inter-symbol interference and inter-carrier interference when the cyclic prefix is insufficient; Step 4: Establish a block transmission interference model, and obtain the introduced additive interference according to the interference model; Step 5: The legitimate channel information is transmitted to the cooperation party in advance through the legitimate channel. The cooperation party receiver uses an IC-DFE equalizer to demodulate the current block: first, the information symbols of the current block are determined by a zero-forcing equalizer; then, combined with the decision result of the previous block, the interference is reconstructed through the interference expression to obtain a feedback term, and the feedback term is subtracted from the received signal, and then zero-forcing equalization is performed. Finally, the information transmitted is demodulated from the output of the second zero-forcing equalization.

2. The underwater acoustic orthogonal frequency division multiplexing secure communication method according to claim 1, characterized in that: The CIR h r ′(t) obtained after synchronizing and intercepting the r-th primitive element is as follows: where h l,r is the amplitude coefficient of the l-th tap in the channel of the r-th array element, τ l,r is its corresponding time delay, is the number of paths, δ(t) represents the unit impulse function, and the channel is stable within one sounding-transmission period.

3. The underwater acoustic orthogonal frequency division multiplexing secure communication method according to claim 2, characterized in that: Response T of the time reversal filter on the r-th primitive r (t) is as follows:

4. The underwater acoustic orthogonal frequency division multiplexing secure communication method according to claim 3, characterized in that: Equivalent legitimate channel Q ab (t) and eavesdropping channel Q ae (t) Specifically:

5. The underwater acoustic orthogonal frequency division multiplexing secure communication method according to claim 1, characterized in that: The specific establishment of the received signal model with inter-symbol interference and inter-carrier interference when the cyclic prefix is insufficient in Step 3 is as follows: The channel is divided into two parts: the path arriving within the cyclic prefix and the path arriving outside the cyclic prefix. The path arriving within the cyclic prefix brings the desired signal, and the path arriving outside the cyclic prefix brings the interference signal. Suppose an OFDM block has K subcarriers, and the receiver processes block by block. The received signal of the jth transmission block is: wherein, n j = [n j (0), n j (1),..., n j (K - 1)] T is an interference term including inter - symbol interference and inter - carrier interference; y j = [y j (0), y j (1),..., y j (K - 1)] T , x j = [x j (0), x j (1),..., x j (K - 1)] T , e j = [e j (0), e j (1),..., e j (K - 1)] T are respectively the received time - domain signal, the transmitted time - domain signal and the noise sequence on the baseband; W is the Fourier transform matrix, D is a K×K diagonal matrix, and the elements on the diagonal are: where v is the length of the cyclic prefix, k represents the k-th subcarrier, and assuming the channel length is v + K + 1, h l is the tap coefficient of the l-th path.

6. The underwater acoustic orthogonal frequency division multiplexing secure communication method according to claim 5, characterized in that: The specific additive interference is: where n j represents the additive interference of the j-th transport block, H pre and H add are matrices of K×(v+K) and satisfy: and represent the original CP - OFDM blocks of the (j - 1)-th transport block and the j-th transport block.

7. The underwater acoustic orthogonal frequency division multiplexing secure communication method according to claim 6, characterized in that: The specific feedback term is: Among them, represents the feedback item of the j-th transport block, W is the Fourier transform matrix, and is the CP-OFDM block reconstructed according to the decision result.

8. The underwater acoustic orthogonal frequency division multiplexing secure communication method according to claim 7, characterized in that: The output of the second zero-forcing equalization is: Among them, is the input of the second zero-forcing equalization for the j-th transport block, satisfying:

9. The underwater acoustic orthogonal frequency division multiplexing secure communication method according to claim 1, characterized in that: After Step 5, it further includes: calculating the system secrecy capacity for evaluating the secrecy performance of the system: where N represents the number of basis elements, β represents the total channel energy, and σ 2 represents the noise power, when the cyclic prefix length v → 0, K represents the number of subcarriers, and g l represents the amplitude coefficient of the l-th tap in the equivalent channel after time reversal at the eavesdropper; Comparing the system secrecy capacity with the expected secrecy capacity standard to determine whether the secrecy performance is satisfied. If not, adjust the number of transmitting array elements and the cyclic prefix length, and return to Step 1.

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