Method for secure communication of multi-carrier ftn physical layer based on symbol-level time-varying compression

Abstract

This invention belongs to the field of wireless communication security technology, specifically relating to a secure communication method for the physical layer of a multi-carrier FTN physical layer based on symbol-level time-varying compression. First, a symbol-level time-varying compressed multi-carrier Super Nyquist (MFTN) transmission waveform design is performed. Then, the received MFTN signal with a variable time-varying time-domain compression factor (TDCF) is detected using a maximum a posteriori probability criterion based on optimal state selection. The received signal first undergoes time-frequency matched filtering and then enters the MFTN equalization module. The matched signal is then subjected to Turbo iterative equalization decoding based on MFTN to obtain the decoded output bits. This invention guarantees BER performance without increasing demodulation complexity, preventing eavesdroppers from detecting symbol intervals for demodulation and information acquisition, thereby achieving superior security performance.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication security technology, specifically relating to a multi-carrier FTN physical layer secure communication method based on symbol-level time-varying compression. Background Technology

[0002] With the rapid growth of communication data volume, security issues during data transmission have become increasingly prominent. Traditional upper-layer encryption algorithms rely on complex mathematical operations and high-strength key management, whose computational complexity and processing latency are insufficient to meet the performance requirements of future high-speed real-time communication such as 6G terahertz communication. Therefore, Physical Layer Security (PLS) technology leverages the randomness and unpredictability of the channel to ensure information security, freeing itself from the constraints of complex mathematical operations. It can provide near-instantaneous security guarantees for the real-time requirements of high-speed data transmission systems, demonstrating enormous application potential.

[0003] Traditional physical layer secure communication methods targeting eavesdroppers mainly include artificial noise generation, beamforming, and power allocation. While these technologies have played a crucial role in secure communication through advancements in multi-antenna technology and sophisticated power control strategies, they inevitably lead to low efficiency in the utilization of resources such as power, bandwidth, and antennas. Furthermore, their high implementation complexity and cost often fail to achieve the desired results, thus limiting the overall efficiency of the communication system. Due to the inherent self-interference characteristics of Super Nyquist (FTN) transmission technology, it has become a highly promising technology for ensuring communication security. However, most existing FTN transmission schemes have limitations: poor compatibility with the multi-carrier architectures used in mainstream communication systems, high modification costs, and their interference being limited to a single dimension in the time domain, making them easily estimated and suppressed by eavesdroppers. Compared to FTN, Multi-Carrier Super Nyquist (MFTN) technology compresses two-dimensional signals simultaneously in the time and frequency domains, improving spectral efficiency while maintaining bit error rate (BER) performance. This indicates the enormous potential of multi-carrier super Nyquist (MFTN) secure communication systems. It offers greater design freedom and signal structure advantages, making it an important candidate for physical layer security systems.

[0004] Most previous methods for secure multi-carrier communication focused on optimizing the security rate within the constraints of subcarrier and power allocation. These methods often sacrifice either the performance of the spectrum or the power, and fail to utilize the inherent characteristics of the two-dimensional transmission signal itself. Therefore, this invention provides a secure multi-carrier FTN physical layer communication method based on symbol-level time-varying compression. Building upon the above method, it introduces multi-carrier super Nyquist (MFTN) technology with time-frequency compression characteristics. The MFTN signal itself contains two-dimensional interference, and the rapid change in the compression factor reduces the risk of eavesdropping. Therefore, it can be designed as a secure communication system with high security performance. Summary of the Invention

[0005] The purpose of this invention is to provide a secure communication method for the physical layer of a multi-carrier FTN based on symbol-level time-varying compression. This method introduces strong interference by constructing a drift-based time-varying compression factor multi-carrier super-Nyquist MFTN architecture to confuse eavesdroppers, while the legitimate receiver can utilize time-varying mode prior information to suppress interference in the multi-carrier super-Nyquist MFTN signal. Based on this, a symbol-by-symbol maximum a posteriori probability (MAP) detection method based on an optimal state selection mechanism is designed, combined with Turbo iterative equalization decoding, ensuring BER performance without increasing demodulation complexity. This prevents eavesdroppers from detecting symbol intervals for demodulation and information acquisition, thereby achieving superior security performance.

[0006] The specific technical solution adopted by this invention is as follows: A Multi-Carrier FTN Physical Layer Secure Communication Method Based on Symbol-Level Time-Varying Compression The transmitter first constructs a two-dimensional compression architecture consisting of a symbol-level time-varying time-domain compression factor (TDCF) and a fixed frequency-domain compression factor. Based on the root-raised cosine shaping pulse, a multi-carrier super Nyquist MFTN baseband signal with non-uniform symbol spacing is generated. Two-dimensional interference combining controllable inter-symbol interference (ISI) and inter-carrier interference (ICI) is introduced through time-frequency dual compression. The transmitter and the legitimate receiver pre-share the time-varying mode of the time-domain compression factor (TDCF). After the legitimate receiver receives the signal transmitted through the additive white Gaussian noise (AWGN) channel, it first performs time-frequency matched filtering and sampling to extract the received symbols of each subcarrier. Then, it uses the BCJR algorithm based on optimal state selection to achieve time-domain controllable inter-symbol interference (ISI) suppression. Combined with serial interference elimination (SIC) reconstruction and cancellation of inter-carrier interference (ICI), it obtains preliminary symbol log-likelihood ratios (LLRs) soft information. Subsequently, the Turbo iterative equalization decoding process is initiated. The symbol posterior probability (APPs) output by the equalization module is deinterleaved and sent to the external code decoder. The decoder outputs external information based on the (7,5) convolutional code, which is then interleaved and fed back to the equalization module as a new first-order signal. The algorithm iterates through equalization and decoding operations until the iteration gain saturates or the maximum number of iterations is reached. Finally, it makes a decision on the optimized soft information and outputs reliable demodulated bits. Meanwhile, the eavesdropping end cannot obtain the prior information of the time-varying mode of the time-domain compression factor TDCF. It can only use non-T-orthogonal time interval sampling, and the received noise exhibits colored noise characteristics. It cannot perform optimal state screening and accurate interference suppression, and cannot effectively eliminate inter-symbol interference (ISI) and inter-carrier interference (ICI). The BER always hovers around 0.5, and it cannot obtain effective transmission information. Ultimately, the goal of achieving high-performance communication on the legitimate end and complete suppression of information on the eavesdropping end is achieved at the physical layer.

[0007] The multi-carrier FTN physical layer secure communication method based on symbol-level time-varying compression disclosed in this invention includes the following steps: Step 1: Design the symbol-level time-varying compressed multi-carrier super-Nyquist MFTN transmission waveform. The transmitter uses a variable compression factor to generate the signal; the signal generation method changes for each symbol to improve security. Consider the linear baseband modulation signal of the multi-carrier super-Nyquist MFTN system. Its expression is written as: ; in The average energy of the transmitted bandwidth signal; Let TDCF be the time-domain compression factor of the i-th signal, satisfying ; Let be the frequency domain compression factor, satisfying ; and These represent the subcarrier index and the time index, respectively. and These refer to the symbol spacing and subcarrier spacing in a multi-carrier super Nyquist MFTN system, respectively. The molding impulse response that satisfies T-orthogonality is: ,in Indicates complex conjugation; For allocation in the The first subcarrier Symbolic information; let The roll-off factor is The root-raised cosine pulse, at this time satisfies It can be seen that for each modulation symbol transmitted at a non-uniform time interval... Given a shaping pulse, the degree of interference caused by adjacent symbols to the current symbol varies.

[0008] Step 2: Perform signal detection on the received multi-carrier super Nyquist MFTN signal with a variable time-domain compression factor (TDCF) based on the maximum a posteriori probability criterion of optimal state selection. For a legitimate receiver, without loss of generality, considering the signal passing through an additive white Gaussian noise (AWGN) channel, the continuous-time response of the received signal in the cooperative link after being affected by AWGN is: ; in It is a Gaussian distribution with a variance of 0, i.e. ; Let be the channel coefficient between the transmitter and receiver, modeled as a linear time-invariant function; assume that the two ends of the legitimate link share a time-varying time-domain compression factor TDCF, and after matched filtering and sampling at the receiver, the th... The first subcarrier Each symbol is represented as: ; in: ; Due to time-domain compression factor and The function, The pulses are no longer orthogonal to each other. In this case, the orthogonality between different subcarriers is destroyed. The last two terms in the above equation represent the inter-symbol interference (ISI) caused by adjacent symbols to the current symbol and the inter-subcarrier interference (ICI) caused by adjacent frequency subcarriers to the current subcarrier, respectively. They are the result of time-frequency compression destroying orthogonality.

[0009] For eavesdropping links, the signals received by the eavesdropper are represented using a signal model similar to that of a legitimate receiver: ; Among the noise It is a random variable that has the same properties as... Same distribution and variance This is the channel coefficient between the transmitter and the eavesdropper. Assume the eavesdropper has obtained the waveform of the transmitter pulse and uses a power spectral density estimation method to estimate the maximum bandwidth of the signal.

[0010] Step 3: The received signal first undergoes time-frequency matched filtering, and then enters the multi-carrier super-Nyquist (MFTN) equalization module. In the MFTN equalization module, an optimized BCJR algorithm is used to obtain the symbol log-likelihood ratio (LLRs) for each symbol. Based on the obtained LLRs, the soft-estimated signal is calculated. The estimated inter-carrier interference (ICI) signal is subtracted from the received signal, and the result is fed back to the multi-carrier super Nyquist (MFTN) equalization module. Given a set of subcarrier channel output observation sequences... and sending symbol sequences The original sequence is estimated by performing binary phase-shift keying (BPSK) modulation and using the symbol-by-symbol maximum a posteriori (MAP) probability criterion, as shown below. ; in This represents the estimated signal. All possible state pairs. set Divided into two subsets and , respectively corresponding to When the time domain pulse truncation length is At that time, the set The length is expressed as .to get The key point is to solve Under the premise of following the chain rule and Markov properties Decomposed into: ; in Indicates time state The forward metric, Indicates time state Backward metric. Indicates time Connection status and state Branching metric.

[0011] In the proposed multi-carrier super Nyquist MFTN system, the variation range of the time-domain compression factor TDCF is reduced to a finite interval, and its length is set to... Subsequently, based on the symbol sequence, selection... This converts the effective tap coefficients into a two-dimensional inter-code interference (ISI) tap matrix. Then, under noise-free conditions, the ideal output value of the channel is expressed as: ; in It is a matrix The elements. Using the mismatched Ungerboeck observation model here, the three-dimensional branch metric with a variable time-domain compressibility factor (TDCF) is represented as: ; in It is a sending symbol The prior probability, Represents the real part of a complex number. Indicates connection status and state noiseless output value .

[0012] To reduce detection complexity, the optimal permutation of the temporal compression factor TDCF used for branch metric calculation is selected at discrete time points n. For fixed-length variations in the temporal compression factor TDCF, the number of matrix rows remains constant. Using prior data from the transmitter, the legitimate receiver determines the start position of each frame and accesses the codebook containing variations of the temporal compression factor TDCF. The optimal branch metric is expressed as: ; Choose an appropriate value for the interference channel vector. Compared with current observations The combination of branch metric calculations is noteworthy. This is particularly important after the receiver performs frame start alignment, taking into account the time index. In numerical computation, it is restricted to integer values. Row indexes are obtained through modulo operations. To determine.

[0013] application The calculation results, and starting from the initial all-zero state, Performing a forward recursive operation is represented as: ; Similarly, Performing recursive operations backward from the given initial state is represented as follows: ; Finally, through calculation and The product of these yields the signed log-likelihood ratios (LLRs), which are: ; in ,and and None of them are zero; once the symbol log-likelihood ratios (LLRs) on all subcarriers are calculated, the estimated value of the transmitted symbol is... This can be expressed as: ; Based on prior knowledge of the inter-carrier interference (ICI) level, in serial interference cancellation (SIC), ICI estimation is performed using subcarrier-free subcarrier estimation. The estimation results for all symbols other than those used are expressed as follows: ; Then, the signal after inter-carrier interference (ICI) cancellation is represented as: ; Step 4: The matched signal undergoes Turbo iterative equalization decoding based on multi-carrier super Nyquist (MFTN) to obtain the decoded output bits. The process includes: the matched signal enters the equalization module, where the symbol posterior probabilities APPs are obtained. After deinterleaving, the signal enters the (7,5) convolutional code decoder. At this point, the estimated information sequence can be determined based on the symbol log-likelihood ratios (LLRs) obtained from the (7,5) convolutional code decoder. Assume that the symbol posterior probabilities APPs calculated by the equalizer, deinterleaver, external decoder, and interleaver are respectively... and During the initial calculation process, the receiver is known to... The prior probability was incorporated Calculation in progress; equalizer module calculation APPs are denoted as ; in This indicates the length of the observed data sequence; it is then obtained through deinterleaving. : ; Subsequently Unencoded data sent to an external decoder The sign-log likelihood ratio (LLRs) is calculated as follows: ; In addition, external decoders obtain It then makes a decision and outputs the decoded bits. .

[0014] Meanwhile, the external decoder outputs based on the deinterleaver's output. Calculate the symbolic posterior probability APPs of the encoded data, denoted as: ; After interleaving, we obtain : , In subsequent iterations, It will be used in the balancing process The prior probability is calculated. The iterative process terminates and outputs the result after reaching the gain cap, thus ensuring an optimal balance between communication performance and computational complexity.

[0015] The technical effects achieved by this invention are as follows: 1. In this invention, by designing a time-frequency two-dimensional compression architecture that combines a symbol-level time-varying time-domain compression factor (TDCF) with a fixed frequency-domain compression factor, controllable inter-symbol interference and inter-carrier interference are introduced, improving the physical layer's security against eavesdropping. At the same time, by sharing the time-varying mode of the time-domain compression factor with legitimate transceivers, the legitimate transceivers can accurately grasp the signal interference characteristics and provide a priori basis for subsequent interference suppression. 2. In this invention, by employing the BCJR algorithm with optimal state selection combined with serial interference cancellation technology, the invention achieves precise hierarchical suppression of time-frequency two-dimensional interference and effectively reduces signal demodulation interference. 3. In this invention, by designing a Turbo iterative equalization decoding process and cyclically interacting with soft information, the reliability of symbol detection is optimized round by round, and the bit error rate of the legitimate link is brought close to that of the orthogonal multicarrier super Nyquist MFTN system without increasing demodulation complexity. 4. In this invention, through the dynamic design of time-varying compression factors, the effect of making it impossible for eavesdroppers to effectively estimate signal characteristics, maintaining the demodulation error rate at around 0.5, and completely suppressing the eavesdropper's ability to acquire information is achieved. Attached Figure Description

[0016] Figure 1 This is a system workflow block diagram for the present invention based on a multi-carrier super Nyquist (MFTN) secure communication scenario. Figure 2 This is a schematic diagram of the proposed multi-carrier super Nyquist MFTN signal generation method based on symbol-level variable compression of the present invention. Figure 3 This is a block diagram of the multi-carrier super Nyquist MFTN signal demodulation based on optimal state selection BCJR combined with serial interference cancellation SIC according to the present invention; Figure 4 This is a block diagram of the multi-carrier super Nyquist MFTN signal demodulation and Turbo equalization decoding of the present invention; Figure 5 This is a comparison of the bit error rate performance of cooperative links and non-cooperative links in Embodiment 1 of the present invention; Figure 6 This is a flowchart of the multi-carrier FTN physical layer secure communication method of the present invention; Figure 7 This is a flowchart illustrating the specific steps of step 3 of the present invention. Detailed Implementation

[0017] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.

[0018] like Figures 1-7 As shown, the specific implementation steps of the multi-carrier FTN physical layer secure communication method based on symbol-level time-varying compression are as follows: Figure 1 As shown, Step 1: Design the symbol-level time-varying compressed multi-carrier super Nyquist MFTN transmission waveform. Figure 2 This diagram illustrates the proposed multi-carrier super Nyquist MFTN signal generation method based on symbol-level variable compression. The transmitter uses a variable compression factor to generate the signal, changing the signal generation method for each symbol to enhance security. The time-domain compression factor is set. Within the range of [0.6, 0.8], and through uniformly distributed random generation, frequency domain compression factor Fixed at 0.75, roll-off factor Using a value of 0.3, employing binary phase shift keying (BPSK) modulation, and considering the linear baseband modulation signal of a multi-carrier super Nyquist MFTN system. Its expression can be written as: ; in The average energy of the transmitted bandwidth signal; For the first The time-domain compression factor TDCF of the signal satisfies ; and These represent the subcarrier index and the time index, respectively. and These refer to the symbol spacing and subcarrier spacing in a multi-carrier super Nyquist MFTN system, respectively. The molding impulse response that satisfies T-orthogonality is: ,in Indicates complex conjugation; For allocation in the The first subcarrier Symbolic information; assumption For a root-raised cosine pulse with a roll-off factor of 0.3, the following condition is met: It can be seen that for each modulation symbol transmitted at a non-uniform time interval... Given a shaping pulse, the degree of interference caused by adjacent symbols to the current symbol varies.

[0019] Step 2: Perform signal detection on the received multi-carrier super Nyquist MFTN signal with variable time-domain compression factor (TDCF) based on the maximum a posteriori probability criterion of optimal state selection. The overall demodulation block diagram of the receiver is shown below. Figure 3 As shown. For a legitimate receiver, without loss of generality, considering the signal passing through an additive white Gaussian noise (AWGN) channel, the continuous-time response of the received signal in the cooperative link after being affected by AWGN is: ; in It is a Gaussian distribution with a variance of 0, i.e. ; Let be the channel coefficient between the transmitter and receiver, which can be modeled as a linear time-invariant function. Set the time-domain compression length. Time-domain pulse truncation length Subcarrier truncation length The two ends of the legitimate link share the time-domain compression factor TDCF. After matched filtering and sampling at the receiving end, the first... The first subcarrier Each symbol is represented as: ; in: ; Due to the effect of the time-frequency compression factor The pulses are no longer orthogonal to each other. In this case, the orthogonality between different subcarriers is broken. Time-domain compression length This causes the time-domain compression factor TDCF to cycle with a period of 6 symbols, and the calculation is performed accordingly. This can be simplified to a sliding window accumulation. The third term in the above equation represents the inter-symbol interference (ISI) caused by adjacent symbols to the current symbol, when the time-domain pulse is truncated. hour The current symbol is only affected by interference from the seven symbols before and after it; the last term represents the inter-carrier interference (ICI) caused by adjacent frequency subcarriers to the current subcarrier, when the subcarrier truncation length... hour Only the interference of the three subcarriers to the left and right of the current subcarrier is retained, which are the result of time-frequency compression destroying orthogonality.

[0020] As for the eavesdropping link, the signal received by the eavesdropper can be represented in a way similar to the signal model of a legitimate receiver: ; Among the noise It is a random variable that has the same properties as... Same distribution and variance This is the channel coefficient between the transmitter and the eavesdropper. It is assumed that the eavesdropper has obtained the form of the transmitter pulse and uses a power spectral density estimation method to estimate the maximum bandwidth of the signal.

[0021] Step 3: The signal first undergoes time-frequency matched filtering and then enters the multi-carrier super-Nyquist (MFTN) equalization module. In the MFTN equalization module, the optimized BCJR algorithm is used to obtain the symbol log-likelihood ratio (LLRs) for each symbol. The BCJR algorithm is a bidirectional maximum a posteriori (MAP) decoding algorithm, also known as the Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm. Based on these symbol log-likelihood ratios (LLRs), the soft-estimated signal is calculated. The estimated inter-carrier interference (ICI) signal is subtracted from the received signal, and the result is fed back to the multi-carrier super Nyquist (MFTN) equalization module. Given a set of subcarrier channel output observation sequences... and sending symbol sequences The original sequence is estimated by performing binary phase-shift keying (BPSK) modulation and using the symbol-by-symbol maximum a posteriori (MAP) probability criterion, as shown below. ; in This represents the estimated signal. Any state pair Corresponding to All possible state pairs set Divided into two subsets and , respectively corresponding to When the pulse truncation length in the time domain At that time, the set The length is represented as 14. To obtain... The key point is to solve Under the premise of following the chain rule and Markov properties Decomposed into: ; in Indicates time state The forward metric, Indicates time state Backward metric. Indicates time Connection status and state Branching metric.

[0022] In the proposed multi-carrier super Nyquist MFTN system, the variation range of the time-domain compression factor TDCF is: Its length is 6. Then, based on the symbol sequence, we select... This transforms the effective tap coefficients into a two-dimensional inter-symbol interference (ISI) tap matrix. Then, under noise-free conditions, the ideal output value of the channel can be expressed as: ; in It is a matrix The elements. Using the mismatched Ungerboeck observation model here, the three-dimensional branch metric with a variable time-domain compressibility factor (TDCF) is represented as: ; in It is a sending symbol The prior probability in the first iteration The number of subsequent iterations is calculated by the external encoder and the interleaving module. get; yes elements, Represents the real part of a complex number. Indicates connection status and state noiseless output value .

[0023] To reduce detection complexity, discrete time points are selected. The optimal permutation of the temporal compression factor TDCF used for branch metric calculation is selected. For a fixed-length variation of the temporal compression factor TDCF, the number of matrix rows remains constant. Using prior data from the transmitter, a legitimate receiver can determine the start position of each frame and access the codebook containing the TDCF variant. The optimal branch metric is expressed as: ; Choose an appropriate value for the interference channel vector. Compared with current observations The combination of branch metric calculations is noteworthy. This is particularly important after the receiver performs frame start alignment, taking into account the time index. In numerical computation, it is restricted to integer values. Row indices can be obtained through modulo operations. To determine.

[0024] application The calculation results, and starting from the initial all-zero state, Performing a forward recursive operation can be represented as: ; Similarly, Performing recursive operations backward from the given initial state is represented as follows: ; Finally, through calculation and The product of these yields the signed log-likelihood ratios (LLRs), which are: ; in ,and and None of them are zero. Once the symbol log-likelihood ratios (LLRs) on all subcarriers are calculated, the estimated value of the transmitted symbol is... This can be expressed as: ; Based on prior knowledge of the inter-carrier interference (ICI) level, in serial interference cancellation (SIC), ICI estimation is performed using subcarrier-free subcarrier estimation. The estimation results for all symbols other than those used are expressed as follows: ; Then, the signal after inter-carrier interference (ICI) cancellation is represented as: ; Step 4: The matched signal undergoes Turbo iterative equalization decoding based on multi-carrier super Nyquist (MFTN) to obtain the decoded output bits. The process includes: the matched signal enters the equalization module, where the symbol posterior probabilities (APPs) are obtained. After deinterleaving, the signal enters an external (7,5) convolutional code decoder. At this point, the estimated information sequence can be determined based on the symbol log-likelihood ratios (LLRs) obtained from the (7,5) convolutional code decoder. Figure 4 The block diagram of the Turbo iterative equalization decoder receiver is shown. Let... and Let APPs represent the symbol posterior probabilities calculated by the equalizer, deinterleaver, external decoder, and interleaver, respectively. This represents the symbol log-likelihood ratio (LLRs) obtained from an external decoder.

[0025] During the initial calculation process, the receiver is known to... The prior probability was incorporated In the calculation, the encoding type is set to (7, 5) convolutional code, the encoding length is 512, and the equalizer module is used for calculation. The symbolic posterior probability APPs is denoted as ; Then, by de-interlacing it, we can obtain... : , Subsequently Unencoded data sent to an external decoder The sign-log likelihood ratio (LLRs) is calculated as follows: ; In addition, external decoders obtain It then makes a decision and outputs the decoded bits. .

[0026] Meanwhile, the external decoder outputs based on the deinterleaver's output. Calculate the symbolic posterior probability APPs of the encoded data, denoted as: ; After interleaving, we obtain : ; In subsequent iterations, It will be used in the balancing process The prior probability is calculated. The iterative process terminates and outputs the result after reaching the gain cap, thus ensuring an optimal balance between communication performance and computational complexity. Figure 5 This paper presents a comparison of bit error rate (BER) performance between cooperative and non-cooperative links. In this scenario, the pulse coefficients are normalized, and the Monte Carlo simulation is performed 80,000 times. The cooperative and non-cooperative communication links are compared under the assumption that the eavesdropper can estimate the time-frequency compression factor (TDCF). The TDCF is constrained within the range of [0.6, 0.8] and randomly generated using a uniform distribution. Furthermore, to benchmark the performance, Figure 5 It also showcased and BER comparison under various conditions. It can be observed that the BER of the scheme involved in this invention falls within the range defined by the compression factor, as shown by the shaded area in the figure. It is worth noting that, due to approximating adjacent subcarrier interference as noise and employing a non-ideal demodulation algorithm, the BER performance deviates from the theoretical prediction when the compression factor is 0.8. However, the resulting demodulation loss is still within a tolerable range. For a fixed time-domain compression factor TDCF, if the eavesdropper can accurately detect the compression factor, demodulation performance comparable to that of a legitimate receiver can be achieved. However, because the eavesdropper cannot sample the correct symbol positions, its BER performance hovers around 0.5. This indicates that the eavesdropper fails to obtain any useful information, thus demonstrating the superiority of the waveform design method proposed in this paper.

[0027] The above description is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained in this invention are implemented according to conventional methods in the art unless otherwise specified or limited.

Claims

1. A method for secure communication of multi-carrier FTN physical layer based on symbol-level time-varying compression, characterized in that: The transmitter first constructs a two-dimensional compression architecture with a symbol-level time-varying time-domain compression factor TDCF and a fixed frequency-domain compression factor. Based on the root raised cosine shaping pulse, a multi-carrier super Nyquist MFTN baseband signal with non-uniform symbol spacing is generated. Two-dimensional interference combining controllable inter-symbol interference (ISI) and inter-carrier interference (ICI) is introduced through time-frequency dual compression. The transmitter and the legitimate receiver share the time-varying mode of the time-domain compression factor TDCF in advance. After the legitimate receiver receives the signal transmitted through the additive white Gaussian noise (AWGN) channel, it first performs time-frequency matched filtering and sampling to extract the received symbols of each subcarrier. Then, it completes time-domain controllable inter-symbol interference (ISI) suppression through the optimal state selection (BCJR) algorithm. Combined with serial interference elimination (SIC) reconstruction and cancellation of inter-carrier interference (ICI), it obtains preliminary symbol log-likelihood ratio (LLRs) soft information. Subsequently, the Turbo iterative equalization and decoding process is initiated. The symbol posterior probabilities (APPs) output by the equalization module are deinterleaved and sent to the external code decoder. The decoder outputs external information based on a (7,5) convolutional code with a constraint length K=3, a code rate of 1 / 2, and a generator polynomial of 111 / 101. This information is then interleaved and fed back to the equalization module as a new prior probability. The equalization and decoding operations are repeatedly iterated until the iterative gain saturates or the maximum number of iterations is reached. Finally, the optimized soft information is judged, and the demodulated bits are output. Ultimately, the goal of physical layer secure transmission, which achieves high-performance communication at the legitimate end and complete suppression of information at the eavesdropping end, is realized.

2. The multi-carrier FTN physical layer secure communication method based on symbol-level time-varying compression according to claim 1, characterized in that: Specifically, the following steps are included: Step 1: Design the symbol-level time-varying compressed multi-carrier super Nyquist MFTN transmission waveform; Step 2: Perform signal detection on the received multi-carrier super Nyquist MFTN signal with variable time-domain compression factor TDCF based on the maximum a posteriori probability criterion of optimal state selection; Step 3: The received signal first undergoes time-frequency matched filtering, and then enters the multi-carrier super Nyquist (MFTN) equalization module; Step 4: Perform Turbo iterative equalization decoding on the matched signal based on multi-carrier super Nyquist MFTN and obtain the decoded output bits.

3. The multi-carrier FTN physical layer secure communication method based on symbol-level time-varying compression according to claim 2, characterized in that: In step 1, specifically: The transmitter uses a variable time-domain compression factor (TDCF) to generate the signal, considering the linear baseband modulation signal of a multi-carrier super Nyquist (MFTN) system. Its expression is written as: ； in The average energy of the transmitted bandwidth signal; Let TDCF be the time-domain compression factor of the i-th signal, satisfying ; Let be the frequency domain compression factor, satisfying ; and These represent the subcarrier index and the time index, respectively. and These refer to the symbol spacing and subcarrier spacing in a multi-carrier super Nyquist MFTN system, respectively. The molding impulse response that satisfies T-orthogonality is: ,in Indicates complex conjugation; For allocation in the The first subcarrier Symbolic information; let The roll-off factor is The root-raised cosine pulse, at this time satisfies .

4. The multi-carrier FTN physical layer secure communication method based on symbol-level time-varying compression according to claim 2, characterized in that: In step 2, specifically: For a legitimate receiver, considering the signal passes through an additive white Gaussian noise (AWGN) channel, the continuous-time response of the received signal in the cooperative link after being affected by AWGN is: ； in It is a Gaussian distribution with a variance of 0, i.e. ; Let be the channel coefficient between the transmitter and receiver, modeled as a linear time-invariant function; assume that the two ends of the legitimate link share a time-varying time-domain compression factor TDCF, and after matched filtering and sampling at the receiver, the th... The first subcarrier Each symbol is represented as: ； in: ； Due to time-domain compression factor and The function, The pulses are no longer orthogonal to each other, and the orthogonality between different subcarriers is broken; The last two terms in the above equation represent the inter-symbol interference (ISI) caused by adjacent symbols to the current symbol and the inter-subcarrier interference (ICI) caused by adjacent frequency subcarriers to the current subcarrier, respectively. They are the result of time-frequency compression destroying orthogonality. For eavesdropping links, the signals received by the eavesdropper are represented using a signal model similar to that of a legitimate receiver: ； Among the noise It is a random variable that has the same properties as... Same distribution and variance It is the channel coefficient between the transmitter and the eavesdropper.

5. The multi-carrier FTN physical layer secure communication method based on symbol-level time-varying compression according to claim 2, characterized in that: In step 3, specifically: In the multi-carrier super Nyquist (MFTN) equalization module, an optimized BCJR algorithm is used to obtain the symbol log-likelihood ratio (LLRs) for each symbol; based on the obtained LLRs, the soft-estimated signal is calculated. And input it into the inter-carrier interference (ICI) signal generation module; The estimated inter-carrier interference (ICI) signal is subtracted from the received signal, and the result is fed back to the multi-carrier super Nyquist (MFTN) equalization module. Given a set of subcarrier channel output observation sequences and sending symbol sequences The original sequence is estimated by performing binary phase-shift keying (BPSK) modulation and using the symbol-by-symbol maximum a posteriori (MAP) probability criterion, as shown below. ； in Represents the estimated signal; all possible state pairs set Divided into two subsets and , respectively corresponding to When the pulse truncation length in the time domain is At that time, the set The length is expressed as ; to get The key point is to solve ; Under the premise of adhering to the chain rule and Markov properties Decomposed into: ； in Indicates time state The forward metric, Indicates time state Backward metric; Indicates time Connection status and state Branching metric.

6. The multi-carrier FTN physical layer secure communication method based on symbol-level time-varying compression according to claim 5, characterized in that: In the proposed multi-carrier super Nyquist MFTN system, the variation range of the time-domain compression factor TDCF is reduced to a finite interval, and its length is set to... ; Subsequently, based on the symbol sequence, selection This converts the effective tap coefficients into a two-dimensional inter-code interference (ISI) tap matrix. Then, under noise-free conditions, the ideal output value of the channel is expressed as: ； in It is a matrix The elements; using the mismatched Ungerboeck observation model here, the three-dimensional branch metric with a variable time-domain compressibility factor TDCF is represented as: ； in It is a sending symbol The prior probability, Represents the real part of a complex number. Indicates connection status and state noiseless output value .

7. The multi-carrier FTN physical layer secure communication method based on symbol-level time-varying compression according to claim 6, characterized in that: The optimal permutation of the temporal compression factor TDCF for branch metric calculation is selected at discrete time point n; the number of matrix rows remains unchanged for a fixed-length variation of the temporal compression factor TDCF; using prior data from the transmitter, the legitimate receiver determines the start position of each frame and accesses the codebook containing the TDCF variant; the optimal branch metric is expressed as: 。 8. The multi-carrier FTN physical layer secure communication method based on symbol-level time-varying compression according to claim 7, characterized in that: Choose an appropriate value for the interference channel vector. Compared with current observations Combining this with branch metric calculation is noteworthy; After the receiver performs frame start alignment, the time index is taken into account. In numerical computation, it is restricted to integer values. Row indexes are obtained through modulo operations. To determine; application The calculation results, and starting from the initial all-zero state, Performing a forward recursive operation is represented as: ； Similarly, Performing recursive operations backward from the given initial state is represented as follows: ； Finally, through calculation and The product of these yields the signed log-likelihood ratios (LLRs), which are: ； in ,and and None of them are zero; once the symbol log-likelihood ratios (LLRs) on all subcarriers are calculated, the estimated value of the transmitted symbol is... This can be expressed as: ； Based on prior knowledge of the inter-carrier interference (ICI) level, in serial interference cancellation (SIC), ICI estimation is performed using subcarrier-free subcarrier estimation. The estimation results for all symbols other than those used are expressed as follows: ； Then, the signal after inter-carrier interference (ICI) cancellation is represented as: 。 9. The multi-carrier FTN physical layer secure communication method based on symbol-level time-varying compression according to claim 8, characterized in that: In step 4, specifically: The matched signal enters the equalization module, where the symbol posterior probability (APPs) is obtained. After deinterleaving, the signal enters the (7,5) convolutional code decoder. At this point, the estimated information sequence is determined based on the symbol log-likelihood ratio (LLRs) obtained from the (7,5) convolutional code decoder. It is assumed that the APPs calculated by the equalizer, deinterleaver, external decoder, and interleaver are respectively... and ; During the initial calculation process, the receiver is known to... The prior probability was incorporated Calculation in progress; equalizer module calculation APPs are denoted as ； in This indicates the length of the observed data sequence; it is then obtained through deinterleaving. : ； Subsequently Unencoded data sent to an external decoder The sign-log likelihood ratio (LLRs) is calculated as follows: ； In addition, external decoders obtain It then makes a decision and outputs the decoded bits. .

10. The multi-carrier FTN physical layer secure communication method based on symbol-level time-varying compression according to claim 9, characterized in that: Meanwhile, the external decoder outputs based on the deinterleaver's output. Calculate the symbolic posterior probability APPs of the encoded data, denoted as: ； After interleaving, we obtain : ， In subsequent iterations, It will be used in the balancing process The prior probability; The iterative process terminates and outputs the result once the gain limit is reached, thus ensuring an optimal balance between communication performance and computational complexity.

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