Quantization method suitable for physical layer key extraction in atmospheric turbulence channel

Abstract

This invention relates to the field of communication security technology, and particularly to a quantization method for physical layer key extraction in atmospheric turbulence channels. The communicating parties first acquire direct time-domain observation sequences through atmospheric turbulence channel detection, and then perform fractional Fourier transform operations on the two sets of observation sequences, mapping them to different transform domains to obtain complex signals. Subsequently, an optimization function is constructed to traverse candidate fractional orders to determine the optimal transform order. The real part of the transform domain signal at this order is then extracted to construct a sum of real-valued features, which are quantized using a dual-threshold quantization algorithm to generate an initial key bit sequence. Based on the optimal transform domain features and quantization rules, the two communicating parties can generate a shared initial key that combines consistency and randomness, thereby achieving high efficiency and robustness in physical layer key extraction under atmospheric turbulence channels, providing a lightweight and highly secure key generation scheme for wireless communication systems.

Description

Technical Field

[0001] This invention relates to the field of communication security technology, and in particular to a quantization method for physical layer key extraction in atmospheric turbulence channels. Background Technology

[0002] With the rapid development of wireless communication technology, free-space optical communication has become a key technology in the field of wireless communication due to its advantages such as high bandwidth and resistance to electromagnetic interference. However, in the digital information age, the information transmitted in communication often involves sensitive content, making encryption protection of atmospheric optical channel transmission of significant practical importance. How to ensure information confidentiality and promote in-depth research on information security has become a key research direction in the field.

[0003] In turbulent atmospheric channels, wireless signal transmission is susceptible to random fluctuations in atmospheric refractive index, resulting in time- and space-varying channel responses. Traditional key distribution methods rely on computational complexity, leading to issues such as complex key management and weak resistance to quantum attacks. Physical layer key extraction technology leverages the reciprocity, time-varying nature, and uniqueness of the channel to generate shared keys, offering advantages such as no need for key distribution and resistance to eavesdropping.

[0004] However, in practical applications, atmospheric channels exhibit extremely low randomness in their extracted channel features due to strong time-domain correlation. To remove this correlation, traditional methods attempt to map the signal to the frequency domain using Fourier transform. For low-pass turbulent signals, the energy after transformation is mainly concentrated in the DC and low-frequency components, resulting in uneven feature distribution within the quantization interval. Existing methods have the following shortcomings in atmospheric turbulence scenarios: the time-domain to frequency-domain transformation has limited ability to characterize turbulent channel features, and it is difficult to balance key consistency and randomness; the quantization process is susceptible to noise interference, leading to significant differences in initial key bits between the two parties and high overhead for subsequent key negotiation. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and propose a quantization method for physical layer key extraction in atmospheric turbulence channels based on fractional Fourier transform. This method is applicable to wireless communication scenarios such as atmospheric laser communication that are susceptible to turbulence effects. Through the synergistic effect of adaptive optimization of the optimal fractional order and dual-threshold quantization strategy, it can effectively overcome the performance bottleneck of traditional methods in turbulence scenarios.

[0006] To achieve the above objectives, the present invention adopts the following specific technical solution:

[0007] The quantization method for physical layer key extraction in atmospheric turbulence channels provided by this invention includes the following steps:

[0008] S1. Channel sounding to obtain the direct observation sequence: Both parties in legitimate communication perform channel sounding operations through an atmospheric turbulence channel, sending sounding signals to each other and receiving sounding responses. The received sounding response signals are sampled and processed to obtain the time-domain direct observation sequence. and ;

[0009] S2. Fractional Fourier transform mapping the transform domain; for directly observed time-domain sequences. and Perform fractional Fourier transform operations on each domain to map from the time domain to the fractional Fourier transform domain, obtaining the corresponding complex signals in the transform domain. and ;

[0010] S3. Establish an optimization function to find the optimal fractional order; construct the optimization function. This is used to comprehensively quantize the combined performance of key consistency and randomness; it iterates through all candidate score orders. Calculate the corresponding Value; find the value through an optimization algorithm. The order in which the optimal value is obtained is called the optimal fractional order. This ensures that the characteristics of the complex signal in the transform domain at this order are best suited for generating a high-quality key.

[0011] S4. Extract and quantize the real part of the complex signal in the transform domain; For the complex signal in the transform domain... and Extract the real part separately and construct real feature quantities. and To eliminate interference from the imaginary part of complex signals and highlight real-number features that can be used for quantization; a dual-threshold quantization algorithm is used to quantize real-number features. and The process involves mapping continuous real-number features to discrete binary bits using two preset quantization thresholds, resulting in the initial key bit sequence for legitimate communication parties. and .

[0012] Furthermore, in step S1, the detection signal is selected as a pseudo-random sequence or a single-frequency signal. For the observation sequence of one end of a legitimate communication, For the observation sequence at the other end, The number of sampling points; the two sets of observation sequences originate from independent measurements of the same channel, have natural reciprocity, and also include random disturbances and noise interference introduced by atmospheric turbulence.

[0013] Furthermore, in step S2, the fractional Fourier transform formula is as follows:

[0014] ;

[0015] In the formula, Represents time-domain signal The fractional-domain complex signal obtained after fractional Fourier transform. For the generalized frequency coordinates in the fractional domain; The kernel function of the fractional Fourier transform determines the core characteristics of the transform. The input is a direct observation sequence in the time domain. Use time coordinates;

[0016] This fractional Fourier transform satisfies the principle of linear superposition, that is, for any time-domain signal... , Given constants a and b, we have:

[0017] ;

[0018] Transform kernel function It consists of a normalization factor and a phase modulation factor, and its specific form is as follows:

[0019] ;

[0020] In the formula, the normalization factor It is in complex form to ensure the energy conservation and invertibility of the fractional Fourier transform; when the transform order... When changing, Adjustments were made accordingly. The modulus and phase angle are adaptively varied to ensure the consistency of signal energy before and after transformation and to avoid energy distortion caused by phase rotation;

[0021] Phase modulation factor , The introduction of time-domain linear frequency modulation is equivalent to performing linear frequency modulation filtering on the time-domain signal; The introduction of frequency domain linear frequency modulation is equivalent to performing linear frequency modulation filtering on the frequency domain signal; The term embodies the time-frequency coupling characteristics and corresponds to the cross term in the time-frequency plane rotation, realizing the fusion representation of time-domain and frequency-domain features.

[0022] Furthermore, in step S3, the optimization function... The expression is:

[0023] ;

[0024] In the formula, Cross-correlation coefficient, used to measure the transformed characteristic sequences of two parties in legitimate communication. and The degree of consistency is calculated using the following formula:

[0025] ;

[0026] The closer the value is to 1, the better the consistency of the transform domain features between the two parties, and the lower the bit error rate after key generation.

[0027] The autocorrelation function is used to measure the autocorrelation of a sequence in the transform domain. The randomness of the sequence is such that the smaller the integral of the denominator with respect to the absolute value of the autocorrelation function, the faster the correlation of the sequence decays and the stronger the randomness; the range of the fractional order traversal is set. With fixed step size Iterate through all candidate orders, and for each candidate order... Calculate the corresponding optimization function value ;

[0028] Based on the discrete fractional Fourier transform matrix Time-domain sampled signal and Perform the transformation to obtain the discrete transform domain signal. and The calculation formula is as follows:

[0029] ;

[0030] in, for The elements of the discrete fractional Fourier transform matrix are given, where N is the number of sampling points. Consistency and randomness indices are calculated based on the transform domain signal, and the corresponding... The extreme value search algorithm is used to iterate through the obtained values. Analyze the sequence to find... The fractional order that yields the maximum value is the optimal fractional order. .

[0031] Furthermore, in step S4, the extraction and quantization of the real part of the transform domain signal is as follows:

[0032] Based on the optimal fractional order obtained in step S3 For complex signals in the transform domain and Real part extraction and double threshold quantization are performed to generate the initial key bit sequence;

[0033] First extract respectively and The real part is used to obtain the real eigenvalues:

[0034] ;

[0035] ;

[0036] in, This means extracting the real part of a complex number. Extracting the real part features eliminates the interference of the imaginary part of the complex signal and highlights the real number features that can be used for quantization.

[0037] Using a dual-gated quantization algorithm and Processing is performed based on the feature sequence. Two quantization thresholds are set for the mean and standard deviation. and , will be greater than The measured value is quantized to 1, which is less than The measured value is quantized to 0, and the value located at... and Feature sequence value removal between:

[0038] ;

[0039] ;

[0040] In the formula, The quantized bit value, The dynamic mean of the feature sequence. It is the standard deviation of the characteristic sequence. It is a quantization factor that uses double-threshold quantization to eliminate uncertain samples, thus obtaining the initial key bit sequence for legitimate communication between the two parties. and .

[0041] The present invention can achieve the following technical effects:

[0042] This invention constructs a comprehensive optimization function that iterates through fractional orders to accurately determine the order that achieves the optimal balance between key consistency and randomness. This method ensures both a high degree of key matching between legitimate communication parties and high entropy unpredictability of the keys, resolving the contradiction that traditional methods struggle to balance these two aspects. Simultaneously, the fractional Fourier transform can flexibly map signals to the optimal transform domain, accurately characterizing the time-varying and space-varying features of atmospheric turbulence channels. Combined with a dual-threshold quantization mechanism to filter noise, it significantly enhances the method's resistance to turbulence interference and drastically reduces the key bit error rate. Furthermore, relying on the inherent reciprocity and randomness of atmospheric turbulence channels, this method eliminates the need for a complex key distribution and management system, ultimately forming a lightweight and highly secure physical layer key generation scheme. This effectively expands the application boundaries of physical layer security technologies in complex channel scenarios such as atmospheric laser communication and satellite communication. Attached Figure Description

[0043] Figure 1This is a flowchart illustrating the principle of generating the initial key for fractional Fourier transform quantization according to an embodiment of the present invention.

[0044] Figure 2 This is a schematic diagram of the fractional Fourier transform principle provided by an embodiment of the present invention;

[0045] Figure 3 This is a schematic diagram of the dual-gate quantization principle provided in an embodiment of the present invention. Detailed Implementation

[0046] In the following description, embodiments of the invention will be described with reference to the accompanying drawings. In the description below, the same modules are denoted by the same reference numerals. Where the same reference numerals are used, their names and functions are also the same. Therefore, their detailed description will not be repeated.

[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0048] This invention provides a quantization method for physical layer key extraction in atmospheric turbulence channels, specifically including the following steps:

[0049] S1. Channel probing yields direct observation sequences;

[0050] The two legitimate communicating parties, denoted as A and B, perform channel sounding operations through an atmospheric turbulence channel to obtain a direct time-domain observation sequence. and .

[0051] Both parties in legitimate communication perform channel sounding operations through an atmospheric turbulence channel, sending known sounding signals, such as pseudo-random sequences or single-frequency signals, to each other and receiving each other's sounding responses. They then sample and process the received signals to obtain a direct time-domain observation sequence. and .in, For the observation sequence at end A, For the observation sequence at end B, The number of sampling points; the two sets of observation sequences originate from independent measurements of the same channel and have natural reciprocity. They also contain random disturbances and noise interference introduced by atmospheric turbulence, which form the original data basis for subsequent key generation.

[0052] Figure 1The flowchart illustrates the principle of generating the initial key for fractional Fourier transform quantization. Terminals A and B perform channel sounding operations through an atmospheric turbulence channel to acquire the time-domain direct observation sequence. The operation is as follows: Terminal A sends a preset random sounding signal to Terminal B. This signal, after transmission through the atmospheric turbulence channel, is interfered with by random fluctuations in the turbulent refractive index. Terminal B receives the interfered sounding signal and processes it through the system sampling module to obtain the time-domain direct observation sequence for Terminal B. Similarly, terminal B sends the same random probe signal to terminal A. This signal is transmitted through the atmospheric turbulence channel and received by terminal A. Terminal A samples the signal using its sampling module to obtain its direct time-domain observation sequence. The above two sets of time-domain observation sequences and These independent measurements, originating from the same atmospheric turbulence channel, possess natural reciprocity and contain random disturbances and channel noise introduced by atmospheric turbulence, serving as the original data basis for subsequent key extraction.

[0053] S2. Fractional Fourier transform maps to the transform domain;

[0054] direct observation sequences in the time domain and Perform fractional Fourier transform operations on each signal to map it from the time domain to the fractional Fourier transform domain, obtaining the corresponding complex signal in the transform domain. and .

[0055] Combination Figure 1 The flowchart shows the two sets of time-domain observation sequences obtained in step S1. and Perform fractional Fourier transform operations on each signal to map the time-domain signal to the fractional Fourier transform domain, obtaining the corresponding complex signal in the transform domain. and Specifically, the core advantage of the fractional Fourier transform is that the order of the transform can be adjusted. This allows for flexible control of the signal representation emphasis between the time and frequency domains, thereby more accurately characterizing the time-varying and space-varying features of atmospheric turbulence channels; combined with Figure 2 As shown in the schematic diagram of the fractional Fourier transform principle, after inputting the directly observed time-domain sequence into the fractional Fourier transform module, the transform order is adjusted. Transform domain signals with different characteristics can be obtained: among which, non-optimal order , The corresponding transform domain signal waveform is chaotic and the energy distribution is scattered, making it difficult to effectively suppress atmospheric turbulence interference and extract stable signal features, which is not conducive to subsequent key generation; while the optimal fractional order The corresponding transform domain signal has a regular waveform, prominent features, and concentrated energy, which can effectively suppress interference from atmospheric turbulence, providing a better transform domain representation for subsequent optimal order optimization and key quantization; in this step, for and The fractional Fourier transform operations are all performed according to the preset order traversal range and step size to obtain the corresponding complex signals in the transform domain under different orders, providing data support for finding the optimal order.

[0056] The formula for the fractional Fourier transform is:

[0057] ; (1)

[0058] In the formula, Represents time-domain signal The fractional-domain complex signal obtained after fractional Fourier transform. For the generalized frequency coordinates in the fractional domain; The kernel function of the fractional Fourier transform determines the core characteristics of the transform. The input is a direct observation sequence in the time domain. The time coordinate is used; this transformation satisfies the principle of linear superposition, that is, for any time-domain signal... , Given constants a and b, we have:

[0059] ; (2)

[0060] Transform kernel function It consists of two parts: a normalization factor and a phase modulation factor, and its specific form is as follows:

[0061] ; (3)

[0062] In the formula, the normalization factor It is in complex form to ensure the energy conservation and invertibility of the fractional Fourier transform; when the transform order... When changing, Adjustments were made accordingly. The modulus and phase angle are adaptively varied to ensure the consistency of signal energy before and after transformation and to avoid energy distortion caused by phase rotation;

[0063] Phase modulation factor The quadratic phase structure is the core feature that distinguishes the fractional Fourier transform from the traditional Fourier transform; among which, The introduction of time-domain linear frequency modulation is equivalent to performing linear frequency modulation filtering on the time-domain signal; The introduction of frequency domain linear frequency modulation is equivalent to performing linear frequency modulation filtering on the frequency domain signal; The term embodies the time-frequency coupling characteristics and corresponds to the cross term in the time-frequency plane rotation, realizing the fusion representation of time-domain and frequency-domain features.

[0064] S3. Establish an optimization function to find the optimal fractional order;

[0065] Combination Figure 1 process and Figure 2 The principle of fractional Fourier transform is used, and this step is the core of the invention. By constructing a comprehensive optimization function, all candidate fractional orders in step S2 are traversed to determine the optimal fractional order. To ensure that subsequently generated keys simultaneously satisfy both high consistency and high randomness, the following is a detailed explanation:

[0066] Constructing the optimization function This is used to comprehensively quantize the combined performance of key consistency and randomness; it iterates through all candidate score orders. Calculate the corresponding Value; find the value through an optimization algorithm. The order in which the optimal value is obtained is called the optimal fractional order. This ensures that the characteristics of the transform domain signal at this order are best suited for generating a high-quality key.

[0067] Constructing the optimization function: Defining the comprehensive performance optimization function Its expression is:

[0068] ; (4)

[0069] In the formula, Cross-correlation coefficient, used to measure the characteristic sequences after transformation of ends A and B. and The degree of consistency is calculated using the following formula:

[0070] ; (5)

[0071] The closer the value is to 1, the better the consistency of the transform domain features between the two parties, and the lower the bit error rate after key generation. The autocorrelation function is used to measure the autocorrelation of a sequence in the transform domain. The randomness of the sequence is such that the smaller the integral of the denominator with respect to the absolute value of the autocorrelation function, the faster the correlation of the sequence decays and the stronger the randomness; the range of the fractional order traversal is set. With fixed step size Iterate through all candidate orders, and for each candidate order... Calculate the corresponding optimization function value .

[0072] Determining the optimal order through traversal: Traverse all candidate fractional orders one by one according to the preset order traversal range and step size. And through the extreme value search algorithm, for all candidate orders corresponding to Filter the values ​​to find those that make The order in which the maximum value is obtained is the optimal fractional order. As shown in Figure 2, this optimal order... The corresponding transform domain signal features are optimal, which can suppress atmospheric turbulence interference to the greatest extent and provide stable signal features for subsequent quantization steps.

[0073] Based on the discrete fractional Fourier transform matrix Time-domain sampled signal and Perform the transformation to obtain the discrete transform domain signal. and The calculation formula is as follows:

[0074] ; (6)

[0075] in, for The elements of the discrete fractional Fourier transform matrix are given, where N is the number of sampling points. Consistency and randomness indices are calculated based on the transform domain signal, and the corresponding... The extreme value search algorithm is used to iterate through the obtained values. Analyze the sequence to find... The fractional order that yields the maximum value is the optimal fractional order. .

[0076] S4. Extract and quantize the real part of the transform domain signal;

[0077] Extracting the real part of the transform domain signal and quantizing it; processing the complex signal in the transform domain. and Extract the real part separately and construct real feature quantities. and This method eliminates interference from the imaginary part of complex signals and highlights real-valued features that can be quantized; a dual-threshold quantization algorithm is used to quantize real-valued features. and The process involves mapping continuous real-number features to discrete binary bits using two preset quantization thresholds, resulting in the initial key bit sequence for both legitimate parties. and .

[0078] Combination Figure 1 process and Figure 3 A schematic diagram of the dual-gate quantization principle, based on the optimal fractional order determined in step S3. For complex signals in the transform domain and Real part extraction and double threshold quantization are performed to generate the initial key bit sequences for both A and B ends. The specific operations are as follows:

[0079] Extract the optimal order separately Below, complex signals in the transform domain and The real part of is used to obtain the corresponding real eigenvalue, where , ;pass Extracting the real part of a complex number can effectively eliminate the interference caused by the imaginary part of the complex signal, highlight the real number characteristics that can be used for quantization, and lay the foundation for subsequent quantization operations.

[0080] Combination Figure 3 A schematic diagram of dual-threshold quantization, illustrating the use of a dual-threshold quantization algorithm for real-valued features. and Processing is performed, with two preset quantization thresholds. and ( < The quantification rules are as follows:

[0081] If real characteristic quantity If so, the sample is quantized into a binary bit "1";

[0082] If real characteristic quantity If the sample is quantized into binary bits "0", then the sample is quantized into binary bits "0".

[0083] If the real characteristic quantity is in and If the sample is between these intervals, it should be removed to avoid key bit errors caused by noise interference within that interval.

[0084] Generate the initial key sequence: respectively for and After quantization, the initial key bit sequence at end A is finally obtained. and the initial key bit sequence at the B end .

[0085] , (7)

[0086] , (8)

[0087] In the formula The quantized bit value, The dynamic mean of the feature sequence. It is the standard deviation of the characteristic sequence. It is a quantization factor that uses double-threshold quantization to eliminate samples with high uncertainty, ultimately yielding the initial key bit sequences for ends A and B. and The dual-threshold mechanism can effectively reduce the impact of atmospheric turbulence noise on key consistency and improve the reliability of key generation.

[0088] According to an embodiment of the present invention, the two communicating parties, A and B, first acquire a time-domain direct observation sequence through atmospheric turbulence channel detection. and Fractional Fourier transform operations were performed on the two sets of observation sequences, and the results were mapped to different transform domains to obtain complex signals. and Subsequently, an optimization function was constructed. Iterate through the candidate fraction orders to determine the optimal transformation order. Then, extract the real part of the down-transform domain signal of that order to construct real feature quantities. and The initial key bit sequence is generated by quantizing the data using a dual-threshold quantization algorithm. and Therefore, the two ends of the communication can generate a shared initial key that combines consistency and randomness based on the optimal transform domain characteristics and quantization rules, thereby achieving high efficiency and robustness in physical layer key extraction under atmospheric turbulence channels, and providing a lightweight and highly secure key generation scheme for wireless communication systems.

[0089] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0090] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

[0091] The specific embodiments of the present invention described above do not constitute a limitation on the scope of protection of the present invention. Any other corresponding changes and modifications made in accordance with the technical concept of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A quantization method suitable for atmospheric turbulent channel physical layer key extraction, characterized in that, Includes the following steps: S1. Channel sounding obtains a direct observation sequence; the legitimate communication parties perform a channel sounding operation through an atmospheric turbulence channel, respectively send a sounding signal to the other party and receive a sounding response of the other party, sample the received sounding response signal, and obtain a time domain direct observation sequence and ; S2. Fractional Fourier transform mapping transform domain; directly observing sequence in time domain and performing fractional Fourier transform operation respectively, mapping from time domain to fractional Fourier transform domain to obtain corresponding transform domain complex signal and ; S3. Establish an optimization function to find the optimal fractional order; construct the optimization function. This is used to comprehensively quantize the combined performance of key consistency and randomness; it iterates through all candidate score orders. Calculate the corresponding Value; find the value through an optimization algorithm. The order in which the optimal value is obtained is called the optimal fractional order. This is used to ensure that the characteristics of the complex signal in the transform domain at this order are best suited for generating a high-quality key; Optimization function The expression is: ； In the formula, Cross-correlation coefficient, used to measure the transformed characteristic sequences of two parties in legitimate communication. and The degree of consistency is calculated using the following formula: ； The closer the value is to 1, the better the consistency of the transform domain features between the two parties, and the lower the bit error rate after key generation. The autocorrelation function is used to measure the autocorrelation of a sequence in the transform domain. The randomness of the sequence is such that the smaller the integral of the denominator with respect to the absolute value of the autocorrelation function, the faster the correlation of the sequence decays and the stronger the randomness; the range of the fractional order traversal is set. With fixed step size Iterate through all candidate orders, and for each candidate order... Calculate the corresponding optimization function value ; Based on the discrete fractional Fourier transform matrix Time-domain sampled signal and Perform the transformation to obtain the discrete transform domain signal. and The calculation formula is as follows: ； in, for The elements of the discrete fractional Fourier transform matrix are given, where N is the number of sampling points. Consistency and randomness indices are calculated based on the transform domain signal, and the corresponding... The extreme value search algorithm is used to iterate through the obtained values. Analyze the sequence to find... The fractional order that yields the maximum value is the optimal fractional order. ; S4. Extract and quantize the real part of the complex signal in the transform domain; [This step involves] processing the complex signal in the transform domain. and Extract the real part separately and construct real feature quantities. and To eliminate interference from the imaginary part of complex signals and highlight real-number features that can be used for quantization; a dual-threshold quantization algorithm is used to quantize real-number features. and The process involves mapping continuous real-number features to discrete binary bits using two preset quantization thresholds, resulting in the initial key bit sequence for legitimate communication parties. and .

2. The quantization method for physical layer key extraction in atmospheric turbulence channels according to claim 1, characterized in that, In step S1, the detection signal is selected as a pseudo-random sequence or a single-frequency signal. For the observation sequence of one end of a legitimate communication between two parties, For the observation sequence at the other end, The number of sampling points; the two sets of observation sequences originate from independent measurements of the same channel, have natural reciprocity, and also include random disturbances and noise interference introduced by atmospheric turbulence.

3. The quantization method for physical layer key extraction in atmospheric turbulence channels according to claim 2, characterized in that, In step S2, the fractional Fourier transform formula is as follows: ； In the formula, Represents time-domain signal The fractional-domain complex signal obtained after fractional Fourier transform. For the generalized frequency coordinates in the fractional domain; This is the kernel function for the fractional Fourier transform; The input is a direct time-domain observation sequence. Use time coordinates; This fractional Fourier transform satisfies the principle of linear superposition, that is, for any time-domain signal... , Given constants a and b, we have: ； Transform kernel function It consists of a normalization factor and a phase modulation factor, and its specific form is as follows: ； In the formula, the normalization factor It is in complex form to ensure the energy conservation and invertibility of the fractional Fourier transform; when the transform order... When changing, Adjustments were made accordingly. The modulus and phase angle are adaptively varied to ensure the consistency of signal energy before and after transformation and to avoid energy distortion caused by phase rotation; Phase modulation factor , The introduction of time-domain linear frequency modulation is equivalent to performing linear frequency modulation filtering on the time-domain signal; The introduction of frequency domain linear frequency modulation is equivalent to performing linear frequency modulation filtering on the frequency domain signal; The term embodies the time-frequency coupling characteristics and corresponds to the cross term in the time-frequency plane rotation, realizing the fusion representation of time-domain and frequency-domain features.

4. The quantization method for physical layer key extraction in atmospheric turbulence channels according to claim 3, characterized in that, In step S4, the extraction and quantization of the real part of the transform domain signal is as follows: Based on the optimal fractional order obtained in step S3 For complex signals in the transform domain and Real part extraction and double threshold quantization are performed to generate the initial key bit sequence; First extract respectively and The real part is used to obtain the real eigenvalues: ； ； in, This means extracting the real part of a complex number. Extracting the real part features eliminates the interference of the imaginary part of the complex signal and highlights the real number features that can be used for quantization. Using a dual-gated quantization algorithm and Processing is performed based on the feature sequence. Two quantization thresholds are set for the mean and standard deviation. and , will be greater than The measured value is quantized to 1, which is less than The measured value is quantized to 0, and the value located at... and Feature sequence value removal between: ； ； In the formula, The quantized bit value, The dynamic mean of the feature sequence. It is the standard deviation of the characteristic sequence. It is a quantization factor that uses double-threshold quantization to eliminate uncertain samples, thus obtaining the initial key bit sequence for legitimate communication between the two parties. and .

Images