Satellite physical layer secure transmission method based on EWFRFT

Abstract

The invention discloses a satellite physical layer secure transmission method based on EWFRFT, and belongs to the technical field of wireless communication. The problem that a traditional satellite communication physical layer security method is poor in security performance is solved. The invention provides a physical layer secure transmission method for bidirectional communication between ground stations and application of extended weighted fractional Fourier transform. EWFRFT is carried out on transmitted signals by the modulators of the two ground stations, and the signals of the ground stations are superposed and forwarded in the satellite transparent transponder. For the condition that transmission needs to be carried out through an inter-satellite link, after the satellites receive superposed signals, EWFRFT inverse transformation, interception and conventional demodulation are carried out on the superposed signals to obtain signal data sent by a ground station, then the demodulated signal data are transmitted through the inter-satellite link, and the satellites responsible for sending downlink signals carry out zero padding, EWFRFT, PN sequence adding and signal superposition on the signals. And the ground station performs EWFRFT inverse transformation, interception and conventional demodulation on the received signal to obtain signal data to be received. The method can be applied to the field of wireless communication.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communication technology, and particularly relates to a satellite physical layer security transmission method based on EWFRFT. Background Art

[0002] In the next-generation wireless communication technology, due to the demand for high-speed data transmission and the ability to provide wide broadband coverage for global users, satellite communication plays an increasingly important role. However, due to the broadcast mechanism of satellites, illegal nodes are prone to intercepting transmitted signals, and the secure transmission problem of satellite communication is becoming more and more important. Physical layer security of satellite communication is a very important research content. At the same time, due to the limited coverage of a single satellite and the increasing maturity of the technology for realizing information exchange between satellites through inter-satellite links, compatible inter-satellite links can achieve information transmission over longer distances.

[0003] Traditional satellite communication physical layer security methods mainly focus on spread spectrum and frequency hopping. In recent years, the weighted fractional Fourier transform has gradually been introduced into the field of physical layer security. However, with the maturity of eavesdropping technology and the improvement of the computing power of eavesdroppers, the security performance of this traditional technology is greatly limited. Therefore, satellite communication requires new physical layer security methods to ensure the secure transmission of signals, and it is necessary to continue to explore methods to further improve system performance in terms of signal form design and communication process. Summary of the Invention

[0004] The purpose of the present invention is to improve the security performance of satellite communication physical layer security methods, and a satellite physical layer security transmission method based on EWFRFT is proposed.

[0005] The technical solution adopted by the present invention to solve the above technical problems is as follows:

[0006] Based on one aspect of the present invention, a satellite physical layer security transmission method based on EWFRFT, the method specifically includes the following steps:

[0007] Step 1: A ground station performs digital baseband modulation on the 0 and 1 bit data generated by a pair of information sources to obtain a modulation result X after constellation mapping;

[0008] Step 2: Group the modulation result X obtained in Step 1, and then perform zero-padding processing on each frame of data obtained by grouping to obtain each frame of data after zero-padding processing;

[0009] Perform extended weighted fractional Fourier transform on each frame of data after zero-padding processing to obtain an output signal obtained by extended weighted fractional Fourier transform of each frame of data;

[0010] Step 3: Add a PN sequence to the output signal obtained in Step 2, and use the output signal after adding the PN sequence to form a serial digital signal X S ;

[0011] Pass the serial digital signal X S through a digital-to-analog converter to obtain an analog modulation signal X to be transmitted S0 , and up-convert the analog modulation signal X S0 to the uplink frequency and then transmit it;

[0012] Step 4: Ground station 2 performs digital baseband modulation on the 0 and 1 bit data generated by the data source to obtain the modulated result X' after constellation mapping;

[0013] Step 5: Group the modulation result X' obtained in Step 4, and then perform zero-padding processing on each frame of data obtained by grouping to obtain each frame of data after zero-padding processing;

[0014] Perform extended weighted fractional Fourier transform on each frame of data after zero-padding processing respectively to obtain the output signal obtained by the extended weighted fractional Fourier transform of each frame of data;

[0015] Step 6: Add a PN sequence to the output signal obtained in Step 5, and use the output signal after adding the PN sequence to form a serial digital signal X S1 ;

[0016] Pass the serial digital signal X S1 through a digital-to-analog converter to obtain an analog modulation signal X to be transmitted S1 , and up-convert the analog modulation signal X S1 to the uplink frequency and then transmit it;

[0017] Step 7: After satellite 0 receives the superimposed signals from ground station 1 and ground station 2, pass the received superimposed signals through a low-noise amplifier, down-conversion, and analog-to-digital converter in sequence to obtain a received signal Y r ';

[0018] Step 8: Perform sliding cross-correlation, timing metric, and peak detection on the received signal Y r ' obtained in Step 7 with the PN sequence of ground station 1 stored in the memory of satellite 0 to locate the position of the PN sequence in the received signal Y r ';

[0019] Delete the PN sequence from the received signal Y r ', and then perform inverse extended weighted fractional Fourier transform on each frame of the remaining signal respectively. Extract the first half of the time slot from the inverse transform results of each frame to obtain the data sent by ground station 1, and extract the second half of the time slot from the inverse transform results of each frame to obtain the data sent by ground station 2;

[0020] Step 9: Satellite 0 connects the data of each frame sent by Ground Station 1 into an output signal Y1′, and then performs constellation demapping on the signal Y1′ to obtain the demodulated bit data Y1 of Ground Station 1;

[0021] Satellite 0 connects the data of each frame sent by Ground Station 2 into an output signal Y2′, and then performs constellation demapping on the signal Y2′ to obtain the demodulated bit data Y2 of Ground Station 2;

[0022] After Satellite 0 modulates the bit data Y1 and Y2 of Ground Station 1 and Ground Station 2 respectively, the modulated data is processed by a digital-to-analog converter and up-conversion, and then the processed data is transmitted separately;

[0023] Step 10: The two signals transmitted in Step 9 are transmitted through the inter-satellite link to the transponder of Satellite N. The transponder of Satellite N performs down-conversion and analog-to-digital conversion processing on the received two signals, and then sequentially performs zero-padding, extended weighted fractional Fourier transform, and PN sequence addition processing on the two signals. The two signals after adding the PN sequence are then processed by digital-to-analog conversion and up-conversion, and then the two up-converted signals are superimposed and the superimposed signal is forwarded;

[0024] Step 11: The signal transmitted by Satellite N reaches the receiving end of Ground Station N′ through the downlink channel. The receiver of the ground station receiving end sequentially passes the received signal through a low-noise amplifier, down-conversion, and analog-to-digital converter to obtain the received signal y R ′;

[0025] Step 12: Ground Station N′ performs sliding cross-correlation, timing metric, and peak detection on the received signal y R ′ and the PN sequence added by Satellite N in the local signal memory, and deletes the PN sequence in the received signal y R ′ according to the peak detection result to obtain the signal after deleting the PN sequence;

[0026] Perform inverse extended weighted fractional Fourier transform on each frame of the signal after deleting the PN sequence, and then respectively extract the signals of Ground Station 1 and Ground Station 2 from the inverse transform results of each frame. Represent the signal of Ground Station 1 as a serial digital signal, and then demodulate the signal of Ground Station 1, and use the demodulation result as the signal sent by Ground Station 1;

[0027] Similarly, represent the signal of Ground Station 2 as a serial digital signal, and then demodulate the signal of Ground Station 2, and use the demodulation result as the signal sent by Ground Station 2.

[0028] Based on another aspect of the present invention, a satellite physical layer secure transmission method based on EWFRFT, the method specifically includes the following steps:

[0029] Step 1: The ground station 1 performs digital baseband modulation on the 0 and 1 bit data generated by the data source to obtain the modulation result X after constellation mapping;

[0030] Step 2: Group the modulation result X obtained in Step 1, and then perform zero-padding processing on each frame of data obtained by grouping to obtain each frame of data after zero-padding processing;

[0031] Perform extended weighted fractional Fourier transform on each frame of data after zero-padding processing respectively to obtain the output signal obtained by extended weighted fractional Fourier transform of each frame of data;

[0032] Step 3: Add a PN sequence to the output signal obtained in Step 2, and use the output signal after adding the PN sequence to form a serial digital signal X S ;

[0033] Pass the serial digital signal X S through a digital-to-analog converter to obtain the analog modulation signal X to be transmitted S0 , and up-convert the analog modulation signal X S0 to the uplink frequency and then transmit it;

[0034] Step 4: The ground station 2 performs digital baseband modulation on the 0 and 1 bit data generated by the data source to obtain the modulation result X′ after constellation mapping;

[0035] Step 5: Group the modulation result X′ obtained in Step 4, and then perform zero-padding processing on each frame of data obtained by grouping to obtain each frame of data after zero-padding processing;

[0036] Perform extended weighted fractional Fourier transform on each frame of data after zero-padding processing respectively to obtain the output signal obtained by extended weighted fractional Fourier transform of each frame of data;

[0037] Step 6: Add a PN sequence to the output signal obtained in Step 5, and use the output signal after adding the PN sequence to form a serial digital signal X S1 ;

[0038] Pass the serial digital signal X S1 through a digital-to-analog converter to obtain the analog modulation signal X to be transmitted S1 , and up-convert the analog modulation signal X S1 to the uplink frequency and then transmit it;

[0039] Step 7: After the satellite 0 receives the superimposed signals from the ground station 1 and the ground station 2, it forwards the received superimposed signals to the ground station 1 and the ground station 2;

[0040] Step 8: The receiver of Ground Station 1 sequentially passes the received superimposed signal through a low-noise amplifier, down-conversion, and an analog-to-digital converter to obtain the received signal Y R ′;

[0041] Step 9: Ground Station 1 performs a sliding cross-correlation between the received signal Y R ′ and the PN sequence of Ground Station 2 stored in the local memory to obtain a sliding cross-correlation function;

[0042] Step 10: Ground Station 1 performs timing metric on the sliding cross-correlation function obtained in Step 9 to obtain a timing metric result;

[0043] Step 11: Ground Station 1 performs peak detection on the timing metric result obtained in Step 10. According to the peak detection result, the position of the PN sequence in the received signal Y R ′ is obtained. After deleting the PN sequence part from the received signal Y R ′, each data frame is obtained;

[0044] Step 12: Ground Station 1 respectively performs an extended weighted inverse fractional Fourier transform on each data frame obtained in Step 11, and extracts the second half of the data from the inverse transform result of each frame to obtain the data of each frame sent by Ground Station 2;

[0045] Step 13: Express each frame of data Y i2 , i = 1, 2, 3,..., A′ sent by Ground Station 2 as a serial digital signal Y2, Y2 = [Y 12 Y 22 …Y i2 …Y A′2 . Perform constellation demapping on the signal Y2 to recover the 0 and 1 bit data, and obtain the demodulated bit data of Ground Station 2;

[0046] Step 14: Ground Station 2 repeats the process of Steps 8 to 13 to obtain the demodulated bit data of Ground Station 1.

[0047] The beneficial effects of the present invention are:

[0048] The present invention proposes a physical layer security transmission method in the scenarios of satellite transparent relay and inter-satellite link, through two-way communication between ground stations and applying extended weighted fractional Fourier transform. For the modulators of two communication ground stations, perform EWFRFT on the transmitted signals respectively, and the ground station signals are directly superimposed and relayed in the satellite transparent transponder. For the case that needs to be transmitted through the inter-satellite link, after the satellite receives the superimposed signal, perform the inverse EWFRFT, intercept and conventional demodulation respectively to obtain the signal data sent by the ground station, then transmit the demodulated signal data through the inter-satellite link, and finally, the satellite N responsible for transmitting the downlink signal performs zero-padding, extended weighted fractional Fourier transform, adding PN sequence and signal superposition on the signal. The ground station performs inverse EWFRFT, intercept and conventional demodulation on the received signal to obtain the signal data to be received. In the method of the present invention, the transmitted signals of a pair of ground stations are strong mutual interferences, and it is difficult for an eavesdropping node to separate the signals of the two ground stations, and the signal-to-interference-plus-noise ratio deteriorates severely. At the same time, it is very difficult for the eavesdropping node to scan out the parameters of the extended weighted fractional Fourier transform, which can guarantee the transmission security of the uplink, effectively reduce the eavesdropping capacity of the channel, improve the security capacity, and ensure the security performance. Brief Description of the Drawings

[0049] Figure 1 is the overall flowchart of the inter-satellite link transmission method of the present invention;

[0050] Figure 2 is the data packet structure of the present invention;

[0051] The first row and the second row are the data packet structures of a pair of ground stations after zero-padding respectively;

[0052] The third row and the fourth row are the data packet structures of a pair of ground stations after performing extended weighted fractional Fourier transform and adding PN sequence respectively;

[0053] The fifth row is the data packet structure of the satellite after receiving the superposition;

[0054] Figure 3 is the block diagram of the transmitter and receiver of the two ground stations of the present invention when not in inter-satellite link transmission;

[0055] Figure 4 is the receiving and processing block diagram of satellite 0 when in inter-satellite link transmission;

[0056] Figure 5 is the receiving and processing block diagram of satellite N when in inter-satellite link transmission;

[0057] Figure 6 is the receiving and processing block diagram of ground stations N' and N" when in inter-satellite link transmission. Detailed Embodiment

[0058] Detailed Embodiment 1: Combine Figure 1 andFigure 2 , Figure 4 and Figure 5 illustrate this embodiment. A satellite physical layer security transmission method based on EWFRFT described in this embodiment specifically includes the following steps:

[0059] Step 1: A ground station pair digitally baseband modulates the 0 and 1 bit data generated by the data source to obtain the modulation result X after constellation mapping;

[0060] Step 2: Group the modulation result X obtained in Step 1, and then perform zero-padding processing on each frame of data obtained by grouping to obtain each frame of data after zero-padding processing;

[0061] Perform extended weighted fractional Fourier transform (EWFRFT) on each frame of data after zero-padding processing to obtain the output signal obtained by the extended weighted fractional Fourier transform of each frame of data;

[0062] Step 3: Add a PN sequence to the output signal obtained in Step 2, and use the output signal after adding the PN sequence to form a serial digital signal X S ;

[0063] Pass the serial digital signal X S through a digital-to-analog converter to obtain the analog modulation signal X to be transmitted S0 , and up-convert the analog modulation signal X S0 to the uplink frequency and then transmit it;

[0064] Step 4: A ground station pair digitally baseband modulates the 0 and 1 bit data generated by the data source to obtain the modulation result X';

[0065] Step 5: Group the modulation result X' obtained in Step 4, and then perform zero-padding processing on each frame of data obtained by grouping to obtain each frame of data after zero-padding processing;

[0066] Perform extended weighted fractional Fourier transform on each frame of data after zero-padding processing to obtain the output signal obtained by the extended weighted fractional Fourier transform of each frame of data;

[0067] Step 6: Add a PN sequence to the output signal obtained in Step 5, and use the output signal after adding the PN sequence to form a serial digital signal X S1 ; It should be noted that the method of adding the PN sequence by the second ground station is the same as that of the first ground station;

[0068] Pass the serial digital signal X S1 through a digital-to-analog converter to obtain the analog modulation signal X to be transmitted S1 , and up-convert the analog modulation signal X S1It is up-converted to the uplink frequency and then transmitted (the transmission frequency and bandwidth are the same as those of Ground Station 1).

[0069] Step 7: After Satellite 0 receives the superimposed signals from Ground Station 1 and Ground Station 2, the received superimposed signals are successively passed through a low-noise amplifier (LNA), down-converted, and an analog-to-digital converter to obtain the received signal Y r ′ (this received signal is the digital sampling of the baseband analog signal).

[0070] It should be noted that: the length of each frame of data in Ground Station 1 and Ground Station 2 is the same, and the zero-padding length is the same as the length of each frame of data. Also, the lengths of the PN sequences added by Ground Station 1 and Ground Station 2 are the same. As Figure 2 shown, in the superimposed signal, the PN sequences of the two ground stations are superimposed together, the EWFRFT data of the two ground stations are superimposed together, and the effective signal sent by one ground station occupies the first half of the time slot, while the effective signal sent by the other ground station occupies the second half of the time slot. The position of the superimposed PN sequence can be located through sliding cross-correlation detection, the PN sequence is deleted to obtain the position where the EWFRFT data are superimposed, and then the superimposed data are subjected to an inverse EWFRFT based on the transformation parameters of Ground Station 1, and the first half of the data is intercepted from the inverse transformation result to obtain the data of Ground Station 1; the superimposed data are subjected to an inverse EWFRFT based on the transformation parameters of Ground Station 2, and the second half of the data is intercepted from the inverse transformation result to obtain the data of Ground Station 2. In particular, when the total lengths of the data sent by Ground Station 1 and Ground Station 2 are different, the data sent by Ground Station 1 and Ground Station 2 can be framed according to a fixed frame length, and the length of the last frame of data can be less than the frame length. When padding with zeros, each frame of data can be padded with zeros to 2 times the frame length, which does not affect the signal superposition.

[0071] Step 8: Perform sliding cross-correlation, timing metric, and peak detection on the received signal Y r ′ obtained in Step 7 and the PN sequence of Ground Station 1 (or the PN sequence of Ground Station 2) stored in the memory of Satellite 0 to locate the position of the PN sequence in the received signal Y r ′;

[0072] Delete the PN sequence from the received signal Y r ′, and then perform an inverse extended weighted fractional Fourier transform on each frame of the remaining signal respectively. The first half of the time slot is intercepted from the inverse transformation results of each frame to obtain the data sent by Ground Station 1, and the second half of the time slot is intercepted from the inverse transformation results of each frame to obtain the data sent by Ground Station 2;

[0073] The specific process of sliding cross-correlation, timing metric, and peak detection is as follows:

[0074] Taking the PN sequence of Ground Station 1 as an example, a sliding cross-correlation is performed between a PN sequence of Ground Station 1 and the received signal Y r ′ to obtain the sliding cross-correlation function:

[0075]

[0076] where n is the time-domain sample position index of the received sequence, d is the time-domain sample position index of the sliding cross-correlation function, B is the length of a data frame sequence, P is the length of the local PN sequence, y(n + d) is the received signal sequence, and p(n) is the local PN sequence. The length of the received sequence participating in the sliding cross-correlation calculation is set to the length of one data frame plus the lengths of two segments of the local PN sequence to ensure that there is at least one continuous and complete PN sequence in the received sequence.

[0077] And a timing metric is performed on the sliding cross-correlation function (i.e., taking the modulus square of the sliding cross-correlation function):

[0078] M n (d) = |c n (d)| 2

[0079] According to the PN sequence structure, the timing metric function will exhibit a relatively large correlation peak, which is the result of the cross-correlation between the received sequence and the local PN sequence;

[0080] Then, peak detection is performed on the timing metric result. If a correlation peak is detected, the position of the correlation peak is the position index of the PN sequence symbol synchronization. If no correlation peak is detected, the next PN sequence of Ground Station 1 in the local signal memory is continued to be used for sliding cross-correlation with the received signal Y r ′ until the position of the correlation peak is detected. According to the detected position of the correlation peak, the PN sequence is deleted from the received signal Y r ′;

[0081] Step Nine: Satellite 0 connects the data of each frame sent by Ground Station 1 into an output signal Y1′, and then performs constellation demapping on the signal Y1′ to obtain the demodulated bit data Y1 of Ground Station 1;

[0082] Satellite 0 connects the data of each frame sent by Ground Station 2 into an output signal Y2′, and then performs constellation demapping on the signal Y2′ to obtain the demodulated bit data Y2 of Ground Station 2;

[0083] Satellite 0 modulates the bit data Y1 and Y2 of Ground Station 1 and Ground Station 2 respectively, then processes the modulated data through a digital-to-analog converter and up-conversion, and then transmits the processed data respectively (i.e., transmits through the inter-satellite link);

[0084] Step Ten: The two signals transmitted in Step Nine are transmitted through the inter-satellite link and reach the transponder of Satellite N. After the transponder of Satellite N performs down-conversion and analog-to-digital conversion on the received two signals, zero-padding (for one of the two signals, zeros are padded at the front, and for the other, zeros are padded at the back), extended weighted fractional Fourier transform, and PN sequence addition are successively performed on the two signals. After the PN sequence is added to the two signals, digital-to-analog conversion and up-conversion processing are performed, and then the two up-converted signals are superimposed and the superimposed signal is forwarded;

[0085] Step Eleven: The signal sent by Satellite N reaches the receiving end of Ground Station N′ through the transmission of the downlink channel. The receiver at the receiving end of the ground station successively passes the received signal through a low-noise amplifier (LNA), down-conversion, and an analog-to-digital converter to obtain the received signal y R ′ (this received signal is the digital sampling of the baseband analog signal);

[0086] Step Twelve: Ground Station N′ performs sliding cross-correlation, timing metric, and peak detection on the received signal y R ′ and the PN sequence added by Satellite N in the local signal memory, and deletes the PN sequence in the received signal y R ′ according to the peak detection result to obtain the signal after deleting the PN sequence;

[0087] Perform extended weighted inverse fractional Fourier transform on each frame of the signal after deleting the PN sequence, and then respectively extract the signals of Ground Station One and Ground Station Two from the inverse transform results of each frame. Represent the signal of Ground Station One as a serial digital signal, and then demodulate the signal of Ground Station One, and use the demodulation result as the signal sent by Ground Station One;

[0088] Similarly, represent the signal of Ground Station Two as a serial digital signal, and then demodulate the signal of Ground Station Two, and use the demodulation result as the signal sent by Ground Station Two.

[0089] (1) It should be noted that the processes in the above Step Ten to Step Twelve are described by taking the example that only one ground station N′ (i.e., other ground stations except Ground Station One and Ground Station Two) needs to receive data and needs to receive the data of Ground Station One and Ground Station Two simultaneously. During processing, Satellite N needs to perform zero-padding at the front and zero-padding at the back on the data corresponding to Ground Station One and Ground Station Two respectively, so that Ground Station N′ can separate the data sent by Ground Station One and Ground Station Two respectively.

[0090] (2) When only one ground station N′ needs to receive data and Ground Station N′ only needs to receive the data of Ground Station One or Ground Station Two, taking the example that Ground Station N′ only needs to receive the data of Ground Station One, then according to the time slot occupancy of Ground Station N′:

[0091] 1) If the ground station N' needs to occupy the first half of the time slot, the satellite N needs to pad zeros at the end of the data of ground station one, simulate the data of ground station two using artificial noise, pad zeros at the beginning of each frame of artificial noise, obtain a superimposed signal based on the data of ground station one and the artificial noise. Subsequently, after the ground station N' deletes the PN sequence from the received signal, it can obtain the data of ground station one by intercepting the first half;

[0092] 2) If the ground station N' needs to occupy the second half of the time slot, the satellite N needs to pad zeros at the beginning of the data of ground station one, simulate the data of ground station two using artificial noise, pad zeros at the end of each frame of artificial noise, obtain a superimposed signal based on the data of ground station one and the artificial noise. Subsequently, after the ground station N' deletes the PN sequence from the received signal, it can obtain the data of ground station one by intercepting the second half;

[0093] (3) As Figure 6 shown, when there are two ground stations N' and N'' that need to receive data, and the ground station N' needs to receive the data of ground station one and the ground station N'' needs to receive the data of ground station two, then according to the time slot occupancy of the ground stations N' and N'', pad zeros at the beginning and end of the data of ground station one and the data of ground station two respectively, or pad zeros at the end and beginning of the data of ground station one and the data of ground station two respectively, and then send the superimposed signals of ground station one and ground station two. After the two ground stations N' and N'' perform sliding cross-correlation, timing metric, and peak detection based on the locally stored PN sequence, they intercept the signals according to the time slots they occupy to obtain the received target signals.

[0094] Specific implementation method two: The difference between this implementation method and the first implementation method is that the specific process of step two is as follows:

[0095] Starting from the first digit of the modulation result X, divide the modulation result into A data blocks of equal length, and pad zeros starting from the end of each data block (that is, start supplementing the number 0 after the last digit of each data block, which is equivalent to occupying the first half of the time slot resources), and the length B of each data block obtained after padding zeros is 2 C , where C is a positive integer;

[0096] Take each data block obtained after padding zeros as a frame of data, and denote the a-th frame of data as X a , a = 1, 2, 3,..., A, where A is the total number of frames of data. Among them, X a = [x0 x1…x B-1 , and x0, x1,..., x B-1 are the 1st, 2nd,..., 2 a th data in the a-th frame of data X C respectively;

[0097] Denote the data of the a-th frame as X a The output signal obtained through the extended weighted fractional Fourier transform is denoted as X a1 , X a1 Specifically:

[0098]

[0099] Among them, the superscript T represents transpose, denotes the cumulative multiplication of the transformation iteration matrix F j ;

[0100] The transformation iteration matrix F j is a block diagonal matrix of size C*C, j = 0, 1,..., C - 1, C = log2B, and the k-th sub-block [F j j of the transformation iteration matrix F k is:

[0101]

[0102] In the formula, is an identity matrix of size 2 j+1 *2 j+1 , is a Fourier transform matrix of size 2 j+1 *2 j+1 , is a permutation matrix, is a weighting coefficient.

[0103] Other steps and parameters are the same as those in the first specific implementation manner.

[0104] The third specific implementation manner: The difference between this implementation manner and the first or second specific implementation manner is that the weighting coefficient is specifically expressed as:

[0105]

[0106] Among them, is a transformation parameter, and i is the imaginary unit.

[0107] Other steps and parameters are the same as those in the first or second specific implementation manner.

[0108] The fourth specific implementation manner: The difference between this implementation manner and any one of the first to third specific implementation manners is that in step 3, a PN sequence (used for receiver signal detection) is added to the output signal obtained in step 2, and a serial digital signal X S is formed by using the output signal after adding the PN sequence; the specific process is:

[0109] X S = [P1 X​11 P2 X 21 … P a X a1 … P A X A1

[0110] Among them, P1 represents an m-sequence (Maximum Length Sequence) of length P, and P2, P3, …, P A are all sequences obtained by circularly shifting P1.

[0111] Other steps and parameters are the same as those in any one of the specific embodiments one to three.

[0112] In the present invention, ground station one and ground station two add PN sequences to the signal data blocks. The PN sequences added by the two ground stations are different pseudo-random sequences. Different circular shifts of the same pseudo-random sequence are used by the same ground station to distinguish data frames. The PN sequences added in the present invention are only stored in the two ground stations and the corresponding satellites. The signals transmitted through the inter-satellite link do not contain PN sequences. Therefore, the PN sequences used by non-corresponding satellites and ground stations can be the same or different. The PN sequence adopted is an m-sequence of length 255. Different circular shifts of the same m-sequence are added to each data block as time slot numbers and used for time synchronization. The present invention is compatible with various PN sequences. This embodiment takes the m-sequence of length 255 as an example.

[0113] Specific embodiment five: The difference between this embodiment and any one of the specific embodiments one to four is that in step five, the modulation result X′ obtained in step four is grouped, and then zero-padding processing is respectively performed on each frame of data obtained by grouping to obtain each frame of data after zero-padding processing; specifically:

[0114] Starting from the first bit of the modulation result X′, the modulation result is divided into A′ data blocks of equal length, and zero-padding is performed before the first bit of each data block (that is, the number 0 is added before the first bit of each data block, which is equivalent to occupying the second half of the time slot resource), and the length B of each data block obtained after zero-padding is 2 C , where C is a positive integer;

[0115] Each data block obtained after zero-padding is used as a frame of data, and the a′-th frame of data is denoted as X a ″.

[0116] Other steps and parameters are the same as those in any one of the specific embodiments one to four.

[0117] Specific embodiment six: Combining Figure 3 ​Describe this embodiment. A satellite physical layer security transmission method based on EWFRFT described in this embodiment specifically includes the following steps:

[0118] Step 1: A ground station pair digitally baseband modulates the 0 and 1 bit data generated by the data source to obtain the modulation result X after constellation mapping;

[0119] Step 2: Group the modulation result X obtained in Step 1, and then perform zero-padding processing on each frame of data obtained by grouping to obtain each frame of data after zero-padding processing;

[0120] Perform extended weighted fractional Fourier transform on each frame of data after zero-padding processing to obtain the output signal obtained by extended weighted fractional Fourier transform of each frame of data;

[0121] Step 3: Add a PN sequence to the output signal obtained in Step 2, and use the output signal after adding the PN sequence to form a serial digital signal X S ;

[0122] The serial digital signal X S Pass through a digital-to-analog converter to obtain the analog modulation signal X to be transmitted S0 , and the analog modulation signal X S0 Is up-converted to the uplink frequency and then transmitted;

[0123] Step 4: Another ground station pair digitally baseband modulates the 0 and 1 bit data generated by the data source to obtain the modulation result X';

[0124] Step 5: Group the modulation result X' obtained in Step 4, and then perform zero-padding processing on each frame of data obtained by grouping to obtain each frame of data after zero-padding processing;

[0125] Perform extended weighted fractional Fourier transform on each frame of data after zero-padding processing to obtain the output signal obtained by extended weighted fractional Fourier transform of each frame of data;

[0126] Step 6: Add a PN sequence to the output signal obtained in Step 5, and use the output signal after adding the PN sequence to form a serial digital signal X S1 ; It should be noted that the method of adding the PN sequence by the second ground station is the same as that of the first ground station;

[0127] The serial digital signal X S1 Pass through a digital-to-analog converter to obtain the analog modulation signal X to be transmitted S1 , and the analog modulation signal X S1 Is up-converted to the uplink frequency and then transmitted (the transmission frequency and bandwidth are the same as those of the first ground station);

[0128] Step 7: After satellite 0 receives the superimposed signals from Ground Station 1 and Ground Station 2, it forwards the received superimposed signals to Ground Station 1 and Ground Station 2;

[0129] Step 8: The receiver of Ground Station 1 sequentially passes the received superimposed signal through a low-noise amplifier (LNA), down-conversion, and an analog-to-digital converter to obtain the received signal Y R ′, which is the digital sampling of the baseband analog signal;

[0130] Step 9: Ground Station 1 performs a sliding cross-correlation between the received signal Y R ′ and the PN sequence of Ground Station 2 stored in the local memory to obtain a sliding cross-correlation function;

[0131] Step 10: Ground Station 1 performs timing metric on the sliding cross-correlation function obtained in Step 9 to obtain a timing metric result;

[0132] Step 11: Ground Station 1 performs peak detection on the timing metric result obtained in Step 10. According to the peak detection result, the position of the PN sequence in the received signal Y R ′ is obtained. After deleting the PN sequence part from the received signal Y R ′, each data frame is obtained;

[0133] If no correlation peak is detected using one PN sequence, the local PN sequence is adjusted, that is, the next PN sequence in the local memory is taken and the above process is repeated from Step 9. If a correlation peak is detected, it is considered that symbol synchronization is completed, and the sample point position of the correlation peak is the position index of the PN sequence symbol synchronization.

[0134] Step 12: Ground Station 1 performs an extended weighted inverse fractional Fourier transform on each data frame obtained in Step 11 respectively, and intercepts the second half of the data from the inverse transform results of each frame to obtain the data of each frame sent by Ground Station 2;

[0135] Step 13: The data of each frame sent by Ground Station 2, Y i2 , i = 1, 2, 3,..., A′ is represented as a serial digital signal Y2, Y2 = [Y 12 Y 22 …Y i2 …Y A′2 . The signal Y2 is demapped by constellation to recover the 0 and 1 bit data, and the demodulated bit data of Ground Station 2 is obtained;

[0136] Step 14: Ground Station 2 repeats the process of Steps 8 to 13 to obtain the demodulated bit data of Ground Station 1. The difference is only that the first half of the data is intercepted after Ground Station 2 performs the extended weighted inverse fractional Fourier transform.

[0137] Specific Embodiment VII: The difference between this embodiment and Specific Embodiment VI is that the specific process of step two is as follows:

[0138] Starting from the first digit of the modulation result X, the modulation result is divided into A data blocks of equal length, and zeros are filled at the end of each data block respectively (that is, starting from the last digit of each data block, the number 0 is filled, which is equivalent to occupying the first half of the time slot resource), and the length B of each data block after filling zeros is 2 C , where C is a positive integer;

[0139] Each data block obtained after filling zeros is used as a frame of data, and the a-th frame of data is denoted as X a , a = 1, 2, 3,..., A, where A is the total number of frames of data. Among them, X a = [x0 x1...x B-1 , and x0, x1,..., x B-1 are the first, second,..., and 2 a -th data in the a-th frame of data X C respectively;

[0140] The output signal obtained by subjecting the a-th frame of data X a to the extended weighted fractional Fourier transform is denoted as X a1 , and X a1 is specifically:

[0141]

[0142] Among them, the superscript T represents transpose, represents the cumulative multiplication of the transformation iteration matrix F j ;

[0143] The transformation iteration matrix F j is a block diagonal matrix of size C*C, j = 0, 1,..., C - 1, C = log2B. The k-th sub-block [F j j of the transformation iteration matrix F k is:

[0144]

[0145] In the formula, is the identity matrix of size 2 j+1 * 2 j+1 , is the Fourier transform matrix of size 2 j+1 * 2 j+1 , is the permutation matrix, is the weighting coefficient;

[0146] ​

[0147] Among them, is a transformation parameter, and i is the imaginary unit.

[0148] Other steps and parameters are the same as those in the sixth specific implementation manner.

[0149] Eighth specific implementation manner: The difference between this implementation manner and the sixth or seventh specific implementation manner is that in step 3, a PN sequence (used for receiver signal detection) is added to the output signal obtained in step 2, and a serial digital signal X is formed using the output signal after adding the PN sequence S ; The specific process is as follows:

[0150] X S = [P1 X 11 P2 X 21 … P a X a1 … P A X A1

[0151] Among them, P1 represents an m-sequence (Maximum Length Sequence) of length P, and P2, P3, …, P A are all sequences obtained by circularly shifting P1.

[0152] Other steps and parameters are the same as those in the sixth or seventh specific implementation manner.

[0153] Ninth specific implementation manner: The difference between this implementation manner and any one of the sixth to eighth specific implementation manners is that in step 5, the modulation result X′ obtained in step 4 is grouped, and then zero-padding processing is performed on each frame of data obtained by grouping, resulting in each frame of data after zero-padding processing; specifically:

[0154] Starting from the first bit of the modulation result X′, the modulation result is divided into A′ data blocks of equal length, and zero-padding is performed before the first bit of each data block (i.e., adding the number 0 before the first bit of each data block, which is equivalent to occupying the second half of the time slot resource), and the length B of each data block obtained after zero-padding is 2 C , where C is a positive integer;

[0155] Each data block obtained after zero-padding is used as a frame of data, and the a′-th frame of data is denoted as X a ″.

[0156] Other steps and parameters are the same as any one of the sixth to eighth specific implementation manners.

[0157] ​Embodiment Ten: The difference between this embodiment and any one of Embodiments Six to Nine is that the ground station one performs an extended weighted inverse fractional Fourier transform on each data frame obtained in Step Eleven, specifically as follows:

[0158] The a'-th frame of data obtained in Step Eleven is represented as Y a′ =[y0 y1...y B-1 , where a' = 1, 2, 3,..., A', and y0, y1,..., y B-1 are the 1st, 2nd,..., 2 C th data in the a'-th frame of data respectively. The output signal obtained by performing an extended weighted inverse fractional Fourier transform on the a'-th frame of data is represented as Y a′2 ;

[0159] The expression of Y a′2 is specifically as follows:

[0160]

[0161] where The inverse transform iteration matrix is a block diagonal matrix of size C*C. The k-th sub-block of the inverse transform iteration matrix is represented as:

[0162]

[0163] where is the inverse transform weighting coefficient, which is specifically represented as:

[0164]

[0165] where is the transform parameter.

[0166] Other steps and parameters are the same as any one of Embodiments Six to Nine.

[0167] The above examples of the present invention are only for illustrating in detail the calculation model and calculation process of the present invention, rather than limiting the embodiments of the present invention. For those of ordinary skill in the art, other different forms of changes or variations can be made based on the above description. It is impossible to list all the embodiments here. Any obvious changes or variations derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A satellite physical layer security transmission method based on EWFRFT, characterized in that The method specifically includes the following steps: Step 1: The ground station 1 performs digital baseband modulation on the 0 and 1 bit data generated by the source, and obtains the modulation result X after constellation mapping; Step 2: Group the modulation result X obtained in Step 1, and then perform zero-padding processing on each frame of data obtained by grouping to obtain each frame of data after zero-padding processing; Perform extended weighted fractional Fourier transform on each frame of data after zero-padding processing respectively, and obtain the output signal obtained by the extended weighted fractional Fourier transform of each frame of data; Step 3: Add a PN sequence to the output signal obtained in Step 2, and use the output signal after adding the PN sequence to form a serial digital signal X S ; Convert the serial digital signal X S through a digital-to-analog converter to obtain the analog modulation signal X to be transmitted S0 , and up-convert the analog modulation signal X S0 to the uplink frequency and then transmit it Step 4: The ground station 2 performs digital baseband modulation on the 0 and 1 bit data generated by the source, and obtains the modulation result X' after constellation mapping; Step 5: Group the modulation result X' obtained in Step 4, and then perform zero-padding processing on each frame of data obtained by grouping to obtain each frame of data after zero-padding processing; Perform extended weighted fractional Fourier transform on each frame of data after zero-padding processing respectively, and obtain the output signal obtained by the extended weighted fractional Fourier transform of each frame of data; Step 6: Add a PN sequence to the output signal obtained in Step 5, and use the output signal after adding the PN sequence to form a serial digital signal X S1 ; Convert the serial digital signal X S1 through a digital-to-analog converter to obtain the analog modulation signal X to be transmitted S1 , up-convert the analog modulation signal X S1 to the uplink frequency and then transmit it Step 7: After satellite 0 receives the superimposed signals from ground station 1 and ground station 2, the received superimposed signals are successively passed through a low-noise amplifier, down-conversion, and an analog-to-digital converter to obtain the received signal Y r ′; Step 8: Perform sliding cross-correlation, timing metric calculation, and peak detection on the received signal Y obtained in Step 7 r ′ with the PN sequence of Ground Station 1 stored in the memory of Satellite 0 to locate the position of the PN sequence in the received signal Y r ′; Remove the PN sequence from the received signal Y r ′, then perform the inverse extended weighted fractional Fourier transform on each frame of the remaining signal respectively. Extract the first half of the time slot from the inverse transform results of each frame to obtain the data sent by Ground Station 1, and extract the second half of the time slot from the inverse transform results of each frame to obtain the data sent by Ground Station 2; Step 9: The satellite 0 connects each frame of data sent by the ground station 1 into an output signal Y1', and then performs constellation demapping on the signal Y1' to obtain the demodulated bit data Y1 of the ground station 1; The satellite 0 connects each frame of data sent by the ground station 2 into an output signal Y2', and then performs constellation demapping on the signal Y2' to obtain the demodulated bit data Y2 of the ground station 1; The satellite 0 modulates the bit data Y1 and Y2 of the ground station 1 and the ground station 2 respectively, then processes the modulated data through a digital-to-analog converter and up-conversion, and then transmits the processed data respectively; Step 10: The two signals transmitted in Step 9 are transmitted through the inter-satellite link to the transponder of the satellite N. The transponder of the satellite N performs down-conversion and analog-to-digital conversion processing on the received two signals, and then performs zero-padding, extended weighted fractional Fourier transform and PN sequence addition processing on the two signals in sequence. The two signals after adding the PN sequence are then processed through digital-to-analog conversion and up-conversion, and then the two up-converted signals are superimposed and the superimposed signal is forwarded; Step Eleven: The signal sent by satellite N reaches the receiving end of ground station N′ through the transmission of the downlink channel. The receiver at the receiving end of the ground station sequentially passes the received signal through a low-noise amplifier, down-conversion, and an analog-to-digital converter to obtain the received signal y R ′; Step Twelve: The ground station N′ performs sliding cross-correlation, timing metric, and peak detection on the received signal y R ′ and the PN sequence added by satellite N in the local signal memory, deletes the PN sequence in the received signal y R ′ according to the peak detection result, and obtains the signal after deleting the PN sequence; Perform inverse extended weighted fractional Fourier transform on each frame in the signal after deleting the PN sequence, and then respectively intercept the signals of the ground station 1 and the ground station 2 from the inverse transform results of each frame. Represent the signal of the ground station 1 as a serial digital signal, and then demodulate the signal of the ground station 1, and use the demodulation result as the signal sent by the ground station 1; Similarly, represent the signal of the ground station 2 as a serial digital signal, and then demodulate the signal of the ground station 2, and use the demodulation result as the signal sent by the ground station 2.

2. The satellite physical layer security transmission method based on EWFRFT according to claim 1, characterized in that, The specific process of Step 2 is as follows: Starting from the first digit of the modulation result X, the modulation result is divided into A data blocks of equal length, and zeros are padded starting from the end of each data block. Moreover, the length B of each data block obtained after padding is 2 C , where C is a positive integer; Each data block obtained after padding with zeros is taken as a frame of data, and the a-th frame of data is denoted as X a , where a = 1, 2, 3, ..., A, and A is the total number of frames of data. Among them, X a = [x0 x1...x B-1 , and x0, x1, …, x B-1 are respectively the 1st, 2nd, …, 2 a th data in the a-th frame of data X C ; Denote the data of the a-th frame as X a The output signal obtained by extended weighted fractional Fourier transform is denoted as X a1 , X a1 Specifically: where the superscript T represents transpose, denotes the cumulative multiplication of j the transformation iteration matrix F. Transformation iteration matrix F j is a block diagonal matrix of size C*C, where j = 0, 1,..., C - 1, C = log2B, and the transformation iteration matrix F j The k-th sub-block of j [F k is as follows: In the formula, is an identity matrix of size 2 j+1 *2 j+1 . is a Fourier transform matrix of size 2 j+1 *2 j+1 . is a permutation matrix, where m = 0, 1, 2, 3 are weighting coefficients.

3. A satellite physical layer security transmission method based on EWFRFT according to claim 2, characterized in that The weighted coefficient Specifically expressed as: wherein, n = 0, 1, 2, 3 is a transformation parameter, and i is the imaginary unit.

4. A satellite physical layer secure transmission method based on EWFRFT according to claim 3, characterized in that In the third step, a PN sequence is added to the output signal obtained in the second step, and a serial digital signal X is formed by using the output signal after adding the PN sequence. S The specific process is as follows: X S = [P1 X 11 P2 X 21 … P a X a1 … P A X A1 ​ Among them, P1 represents an m-sequence of length P, and P2, P3, …, P A are all sequences obtained by circularly shifting P1.

5. A satellite physical layer secure transmission method based on EWFRFT according to claim 4, characterized in that, In Step 5, group the modulation result X' obtained in Step 4, and then perform zero-padding processing on each frame of data obtained by grouping to obtain each frame of data after zero-padding processing; specifically: Starting from the first digit of the modulation result X′, the modulation result is divided into A′ data blocks of equal length, and zeros are padded before the first digit of each data block. After padding, the length B of each obtained data block is 2 C , where C is a positive integer; Each data block obtained after padding with zeros is used as a frame of data, and the a'-th frame of data is denoted as X'. a′ 。 6. A satellite physical layer security transmission method based on EWFRFT, characterized in that, The method specifically includes the following steps: Step 1: The ground station 1 performs digital baseband modulation on the 0 and 1 bit data generated by the source, and obtains the modulation result X after constellation mapping; Step 2: Group the modulation result X obtained in Step 1, and then perform zero-padding processing on each frame of data obtained by grouping to obtain each frame of data after zero-padding processing; Perform extended weighted fractional Fourier transform on each frame of data after zero-padding processing respectively to obtain the output signal obtained by the extended weighted fractional Fourier transform of each frame of data; Step 3: Add a PN sequence to the output signal obtained in Step 2, and use the output signal after adding the PN sequence to form a serial digital signal X S ; The serial digital signal X S is passed through a digital-to-analog converter to obtain an analog modulation signal X to be transmitted S0 , and the analog modulation signal X S0 is up-converted to the uplink frequency and then transmitted Step 4: Ground station 2 performs digital baseband modulation on the 0 and 1 bit data generated by the information source to obtain the modulation result X' after constellation mapping; Step 5: Group the modulation result X' obtained in Step 4, and then perform zero-padding processing on each frame of data obtained by grouping to obtain each frame of data after zero-padding processing; Perform extended weighted fractional Fourier transform on each frame of data after zero-padding processing respectively to obtain the output signal obtained by the extended weighted fractional Fourier transform of each frame of data; Step 6: Add a PN sequence to the output signal obtained in Step 5, and use the output signal after adding the PN sequence to form a serial digital signal X S1 ; The serial digital signal X S1 is converted into an analog modulation signal X to be transmitted through a digital-to-analog converter S1 , and the analog modulation signal X S1 is up-converted to the uplink frequency and then transmitted Step 7: After satellite 0 receives the superimposed signals from ground station 1 and ground station 2, forward the received superimposed signals to ground station 1 and ground station 2; Step 8: The receiver of Ground Station 1 sequentially passes the received superimposed signal through a low-noise amplifier, down-conversion, and an analog-to-digital converter to obtain the received signal Y R ′; Step Nine: Ground Station 1 performs a sliding cross-correlation between the received signal Y R ′ and the PN sequence of Ground Station 2 stored in the local memory to obtain a sliding cross-correlation function; Step 10: Ground station 1 performs timing metric on the sliding cross-correlation function obtained in Step 9 to obtain the timing metric result; Step Eleven: The ground station performs peak detection on the timing metric results obtained in Step Ten, and obtains the position of the PN sequence in the received signal Y R '. After deleting the PN sequence part from the received signal Y R ', each data frame is obtained; Step 12: Ground station 1 performs inverse extended weighted fractional Fourier transform on each of the data frames obtained in Step 11 respectively, and intercepts the second half of the data from the inverse transform results of each frame to obtain each frame of data sent by ground station 2; Step Thirteen: Each frame of data Y sent by Ground Station Two i2 , where i = 1, 2, 3,..., A′ is represented as a serial digital signal Y2, Y2 = [Y 12 Y 22 … Y i2 …Y A′2 . Perform constellation demapping on the signal Y2 to recover the 0 and 1 bit data, and obtain the demodulated bit data of Ground Station Two; Step 14: Ground station 2 repeats the process from Step 8 to Step 13 to obtain the demodulated bit data of ground station 1.

7. A satellite physical layer secure transmission method based on EWFRFT according to claim 6, characterized in that The specific process of Step 2 is as follows: Starting from the first digit of the modulation result X, divide the modulation result into A data blocks of equal length, and fill zeros from the end of each data block respectively. And the length B of each data block obtained after filling zeros is 2 C , where C is a positive integer; Each data block obtained after padding with zeros is regarded as a frame of data, and the a-th frame of data is denoted as X a , where a = 1, 2, 3, ..., A, and A is the total number of frames of data. Among them, X a = [x0 x1 ... x B-1 , and x0, x1, ..., x B-1 are respectively the 1st, 2nd, ..., 2 a th data in the a-th frame of data X C ; Denote the a-th frame data X a as the output signal X a1 obtained through the extended weighted fractional Fourier transform, a1 Specifically: where the superscript T represents transpose, denotes the successive multiplication of j the transformation iteration matrix F. Transformation iteration matrix F j is a block diagonal matrix of size C*C, where j = 0, 1,..., C - 1, C = log2B, and the transformation iteration matrix F j The k-th sub-block of [F j k is as follows:​ wherein, is an identity matrix of size 2 j+1 *2 j+1 , is a Fourier transform matrix of size 2 j+1 *2 j+1 , is a permutation matrix, m = 0, 1, 2, 3 are weighting coefficients; Among them, n = 0, 1, 2, 3 are transformation parameters, and i is the imaginary unit.

8. A satellite physical layer secure transmission method based on EWFRFT according to claim 7, characterized in that, In the third step, a PN sequence is added to the output signal obtained in the second step, and a serial digital signal X is formed by using the output signal after adding the PN sequence. S The specific process is as follows: X S = [P1 X 11 P2 X 21 … P a X a1 … P A X A1 ​ Among them, P1 represents an m-sequence of length P, and P2, P3, …, P A are all sequences obtained by circularly shifting P1.

9. A satellite physical layer secure transmission method based on EWFRFT according to claim 8, characterized in that, In Step 5, group the modulation result X' obtained in Step 4, and then perform zero-padding processing on each frame of data obtained by grouping to obtain each frame of data after zero-padding processing; specifically: Starting from the first digit of the modulation result X', the modulation result is divided into A' data blocks of equal length, and zeros are padded before the first digit of each data block. Moreover, the length B of each data block obtained after padding is 2 C , where C is a positive integer; Each data block obtained after padding with zeros is regarded as a frame of data, and the a'-th frame of data is denoted as X'. a′ .

10. A satellite physical layer security transmission method based on EWFRFT according to claim 9, characterized in that, Ground station 1 performs inverse extended weighted fractional Fourier transform on each of the data frames obtained in Step 11 respectively, specifically: Represent the a'-th frame data obtained in Step Eleven as Y a′ =[y0 y1... y B-1 , where a' = 1, 2, 3,..., A', and y0, y1,..., y B-1 are the 1st, 2nd,..., 2 C th data in the a'-th frame data respectively. The output signal obtained by the extended weighted inverse fractional Fourier transform of the a'-th frame data is represented as Y a′2 ; Y a′2 The expression of is specifically as follows: Among them, Inverse transform iteration matrix is a block diagonal matrix of size C*C, and the inverse transform iteration matrix The k-th sub-block of is expressed as: Among them, m = 0, 1, 2, 3 are inverse transformation weighting coefficients, Specifically expressed as: wherein, n = 0, 1, 2, 3 is a transformation parameter.

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