A cross-domain physical layer security implementation method

Abstract

The present invention discloses a method for implementing cross-domain physical layer security. First, pre-processing and post-processing matrices are designed for the MIMO-OTFS system. Specifically, the equivalent channel matrix of the legitimate channel (DD) domain is subjected to singular value decomposition (SVD). The right singular matrix is ​​selected to design the pre-processing matrix, and the left singular matrix is ​​selected to design the post-processing matrix. Secondly, the null space matrix of the time domain AN is calculated according to the MIMO-OTFS system processing flow and a zero-mean circularly symmetric complex Gaussian vector is generated, finally generating the time domain AN. The AN design of this method can achieve self-cancellation in the DD domain of the legitimate receiver, while forming interference at the eavesdropper, thereby widening the quality gap between the legitimate channel and the eavesdropped channel, and achieving signal security for the MIMO-OTFS system.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a method for implementing cross-domain physical layer security. Background Art

[0002] Orthogonal frequency division multiplexing (OFDM) multicarrier technology, widely used in 4G and 5G systems, is sensitive to high Doppler shifts caused by high-speed mobility. This severely disrupts the orthogonality between its subcarriers, significantly reducing communication reliability. Orthogonal time-frequency space (OTFS) multicarrier technology has been proposed and applied to high-speed mobile communication scenarios. OTFS technology uses a two-dimensional transformation to convert information symbols from the time-frequency (TF) domain to the delay-Doppler (DD) domain for transmission. The channel experienced by the information symbols is transformed from a time-frequency selective fading channel in the TF domain to a nearly time-invariant stationary channel in the DD domain. This ensures that all OTFS symbols experience approximately the same channel gain, achieving better bit error performance than OFDM modulation in high-speed mobility scenarios.

[0003] Research on Multiple Input Multiple Output (MIMO-OTFS) systems (MIMO-OTFS) focuses primarily on feasibility and equalization algorithms. Feasibility studies primarily involve implementing a MIMO-OTFS system by adding precoders and postprocessors before and after a MIMO-OFDM system, and comparing the complexity and error performance of these two implementations. Equalization algorithm research focuses on designing low-complexity equalization receivers by leveraging the inherent sparsity of the DD-domain equivalent channel of the MIMO-OTFS system. Alternatively, cross-domain iterative equalization receivers can be designed by leveraging the fact that OTFS symbols pass through the time, TF, and DD domains during receiver processing.

[0004] Currently, there is sufficient research on the feasibility, signal detection, and equalization of MIMO-OTFS systems. However, considering the vulnerability of wireless communication signals to eavesdropping, there is still a lack of work dedicated to achieving multi-antenna OTFS signal security. Summary of the Invention

[0005] In order to overcome the shortcomings of the prior art, the present invention provides a cross-domain physical layer security implementation method. First, the pre-processing and post-processing matrices of the MIMO-OTFS system are designed. Specifically, the singular value decomposition (SVD) of the equivalent channel matrix of the legal channel DD domain is decomposed, and the right singular matrix is ​​selected to design the pre-processing matrix, and the left singular matrix is ​​selected to design the post-processing matrix. Secondly, according to the MIMO-OTFS system processing flow, the null space matrix of the time domain AN is calculated and a zero-mean circularly symmetric complex Gaussian vector is generated, and finally the time domain AN is generated. The AN design of this method can achieve self-cancellation in the DD domain of the legal receiver, while forming interference at the eavesdropper, thereby widening the quality gap between the legal channel and the eavesdropping channel, and realizing the signal security of the MIMO-OTFS system.

[0006] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0007] Step 1: For the single-input single-output SISO-OTFS system in the form of a MIMO-OTFS system reference rectangular pulse, the system processing is as follows;

[0008] Step 1-1: For an OTFS system, the system has M subcarriers with a subcarrier spacing of Δf and N symbols with a symbol time of T, the total bandwidth is B = MΔf, and the signal frame duration is T f =NT; OTFS system is critical sampling, that is, T△f=1;

[0009] Step 1-2: At the transmitter, the symbols after constellation mapping First, it is placed on the delay-Doppler grid, that is, x is arranged into a matrix by column Satisfy X DD =unvec M,N (x); then use the inverse symplectic Fourier transform ISFFT to transform X DD Convert the symbolic matrix X to the TF domain TF , X TF It is expressed as follows:

[0010]

[0011] Among them, F, F H They represent the discrete Fourier transform matrix and the discrete inverse Fourier transform matrix respectively;

[0012] In the case of rectangular pulse shaping, the TF domain symbol matrix X is transformed by discrete Heisenberg transform TF Convert to time domain signal s represents the following:

[0013]

[0014] Among them, vec(·) represents column-wise vectorization operation;

[0015] Then, the length N cp CP is added to the beginning of s, where N cp ≥L, L is the maximum delay spread; the time domain signal is transmitted on a time-frequency dual-selective channel, and the channel response h(τ,ν) is expressed as:

[0016]

[0017] Where P is the number of transmission paths, h i , τ i ∈[0,τ max ]、ν i ∈[-ν max ,ν max ] are the channel coefficient, delay, and Doppler shift of the i-th path respectively; here, τ max 、ν max are the maximum delay and Doppler shift respectively, and the delay tap and Doppler shift tap of the i-th path are l i =M△fτ i 、k i =NTν i ;

[0018] Step 1-3: At the receiver, the signal after removing the CP is expressed as:

[0019] r=Hs+w

[0020] The channel noise is the channel matrix containing the addition and subtraction CP operations, which is expressed as follows:

[0021]

[0022] Where π is the permutation matrix:

[0023]

[0024] Δ is a diagonal matrix of MN×MN:

[0025] Δ=diag[z 0 ,z 1 ,…,z MN-1 ]

[0026] In the formula

[0027] The received signal r is processed by Wigner transform and sigmoid Fourier transform SFFT, and the received symbol in DD domain is expressed as:

[0028]

[0029] Where R = unvec M,N (r);

[0030] The DD domain input and output relationship is written as:

[0031]

[0032] The DD domain input and output relationship is rewritten as:

[0033]

[0034] Among them, add CP matrix Remove CP matrix The unit matrix I is of size MN×MN MN The last N cp OK;

[0035] The DD domain equivalent channel matrix is ​​defined as:

[0036]

[0037] Step 2: In the MIMO-OTFS system, the number of transmitting antennas is N t , the number of receiving antennas is N r , the time domain transmission signal of the i-th transmitting antenna is expressed as:

[0038]

[0039] The time domain received signal of the jth receiving antenna can be expressed as:

[0040]

[0041] The corresponding DD domain received signal is:

[0042]

[0043] The time domain input and output relationship of the MIMO-OTFS system is written as:

[0044]

[0045] make The above formula is expressed as:

[0046]

[0047] Combining the transformation of the time domain and DD domain at the transmitter and receiver, let Then the DD domain input and output relationship of the MIMO-OTFS system is written as:

[0048]

[0049] The DD domain equivalent channel matrix of the MIMO-OTFS system is defined as:

[0050]

[0051] Step 3: Based on the time domain and DD domain processing, the MIMO-OTFS system generates the time domain AN. The transmitter performs the following processing:

[0052] Step 3-1: Convert the DD domain equivalent channel matrix Perform SVD decomposition, expressed as:

[0053]

[0054] For transmission N s , N s <N t data streams, each of which is MN in length, and the first N left singular matrices U are selected. s Columns as post-processing matrix W r , select the first N of matrix V s Columns are used as preprocessing matrix W t ;

[0055] Step 3-2: In the DD domain, s The data stream after constellation mapping Perform preprocessing, namely:

[0056] x MIMO =W t x S

[0057] in, so Contains N t data streams;

[0058] Step 3-3: For x MIMO N t The data streams are subjected to ISFFT transformation and discrete Heisenberg transform based on rectangular pulses, namely:

[0059]

[0060] in Contains N t data streams, s MIMO is the time domain signal;

[0061] Step 3-4: s MIMO N t Add a data stream of length N cpCP, that is:

[0062]

[0063] in Contains N t data streams;

[0064] Step 3-5: Injection time domain AN, that is:

[0065]

[0066] Where a is the injected time domain AN; a is designed to fall into the legal channel null space, let:

[0067] a=Qd t

[0068] Where Q is a semi-unitary matrix that satisfies:

[0069]

[0070]

[0071] d t is an artificially generated zero-mean circularly symmetric complex Gaussian noise, that is The dimension of the matrix multiplied by Q is N s MN×N t (MN+N cp ), the condition for the existence of the null space matrix Q is:

[0072]

[0073] Among them, when the data stream N is transmitted s Less than the number of transmitting antennas N t When , the condition for the existence of the null space matrix Q must be satisfied; Contains N t data streams;

[0074] Step 3-6: For step 3-5 N t The data streams are respectively digitally up-converted, digital-to-analog converted, radio frequency up-converted, and finally transmitted to N t Root antenna transmission;

[0075] Step 4: The time domain AN of the MIMO-OTFS system is generated based on time domain and DD domain processing. The receiving end processes it as follows:

[0076] Step 4-1: For N r The signal received by the antenna is subjected to RF down-conversion, analog-to-digital conversion, and digital down-conversion, and finally N rbaseband data streams, each of which has a length of MN+N cp ; N r The baseband data stream is recorded as:

[0077]

[0078] in, The data stream corresponding to the i-th antenna;

[0079] Step 4-2: For N r Each baseband data stream is subjected to CP removal operation, namely:

[0080]

[0081] in Contains N r data streams; MIMO is the time domain signal;

[0082] Step 4-3: For r MIMO N r Each data stream is subjected to SFFT transformation and discrete Wigner transform, namely:

[0083]

[0084] in Contains N r data stream; y MIMO It is the DD domain signal;

[0085] Step 4-4: For y MIMO Perform post-processing operations and convert into N s data streams, namely:

[0086] y S =W r y MIMO

[0087] in Contains N s data streams;

[0088] Step 5: Based on steps 3 and 4, the DD domain input and output relationship of the MIMO-OTFS system is written as:

[0089]

[0090] Preferably, the x MIMO According to the element sequence from small to large, each MN element is regarded as a data stream, forming N t data streams.

[0091] Preferably, the s MIMOAccording to the element sequence from small to large, each MN element is regarded as a data stream, forming N t data streams.

[0092] Preferably, According to the element number from small to large every MN+N cp elements as a data stream, forming N t data streams.

[0093] Preferably, the According to the element number from small to large every MN+N cp elements as a data stream, forming N t data streams.

[0094] Preferably, the r MIMO According to the element sequence from small to large, each MN element is regarded as a data stream, forming N r data streams.

[0095] Preferably, the y MIMO According to the element sequence from small to large, each MN element is regarded as a data stream, forming N r data streams.

[0096] Preferably, the y S According to the element sequence from small to large, each MN element is regarded as a data stream, forming N s data streams.

[0097] The beneficial effects of the present invention are as follows:

[0098] 1. The time-domain AN technique proposed in this method is applicable to MIMO-OTFS systems where the number of transmit antennas is smaller than the number of receive antennas. Traditional time-domain AN techniques can achieve AN cancellation at the legitimate receiving end only when the number of transmit antennas is greater than the number of receive antennas. Unlike traditional time-domain AN techniques, which inject AN in the time domain and then cancel it in the time domain, this method injects AN in the time domain and cancels it in the DD domain. This allows AN to be generated even when the number of transmit antennas is smaller than the number of receive antennas. Therefore, this method can inject AN in MIMO-OTFS systems with a wider range of antenna configurations.

[0099] 2. The equivalent channel matrix of the MIMO-OTFS system in this method, including pre-processing and post-processing operations, is a diagonal matrix, which can then be subjected to single-tap equalization. The single-tap equalization operation can be implemented using simple data division, avoiding more complex matrix operations. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] Figure 1 This is a block diagram of the SISO-OTFS system of the present invention.

[0101] Figure 2This is a flowchart of baseband signal processing by the sender Alice in an embodiment of the present invention.

[0102] Figure 3 This is a bit error rate-signal-to-noise ratio curve diagram of the legal receiver Bob and the eavesdropper Eve with and without AN in an embodiment of the present invention. DETAILED DESCRIPTION

[0103] The present invention will be further described below with reference to the accompanying drawings and examples.

[0104] like Figure 1 As shown, in order to achieve the physical layer signal security of the MIMO-OTFS system, the present invention provides a MIMO-OTFS system time domain artificial noise (AN) generation technology based on time domain and DD domain processing. The method first designs the pre-processing and post-processing matrices for the MIMO-OTFS system, specifically performs singular value decomposition (SVD) decomposition on the DD domain equivalent channel matrix of the legal channel, selects the right singular matrix to design the pre-processing matrix, and selects the left singular matrix to design the post-processing matrix. Secondly, according to the MIMO-OTFS system processing flow, the null space matrix of the time domain AN is calculated and a zero-mean circularly symmetric complex Gaussian vector is generated, and finally the time domain AN is generated. The AN design of this method can achieve self-cancellation in the DD domain of the legal receiver, while forming interference at the eavesdropper, thereby widening the quality gap between the legal channel and the eavesdropping channel, and achieving signal security of the MIMO-OTFS system.

[0105] Consider the MIMO-OTFS system as a reference to a single-input single-output (SISO) OTFS system in the form of rectangular pulses. First, the SISO-OTFS system based on rectangular pulses is processed as follows:

[0106] Without loss of generality, consider an OTFS system with M subcarriers with a subcarrier spacing of Δf and N symbols with a symbol time of T, a total bandwidth of B = MΔf, and a signal frame duration of T. f =NT. In addition, consider that the OTFS system is critically sampled, that is, TΔf=1.

[0107] At the transmitter, the symbols after constellation mapping First, it is placed on the delay-Doppler grid, that is, x is arranged into a matrix by column Satisfy X DD =unvec M,N (x). Then use the Inverse Symplectic Fast Fourier Transform (ISFFT) to transform XDD Convert the symbolic matrix X to the TF domain TF .X TF It is expressed as follows:

[0108]

[0109] Among them, F, F H They represent the discrete Fourier transform matrix and the discrete inverse Fourier transform matrix respectively.

[0110] Next, assuming a typical rectangular pulse shaping, the TF domain symbol matrix X is transformed into TF Convert to time domain signal s represents the following:

[0111]

[0112] Here, vec(·) represents a column-wise vectorized operation.

[0113] Then, the length N cp CP is added to the beginning of s, where N cp ≥L, L is the maximum delay spread. The time domain signal is transmitted on a time-frequency dual-selective channel, and the channel response h(τ,ν) is expressed as:

[0114]

[0115] Where P is the number of transmission paths, h i , τ i ∈[0,τ max ]、ν i ∈[-ν max ,ν max ] are the channel coefficient, delay, and Doppler shift of the i-th path respectively. Here, τ max 、ν max are the maximum delay and Doppler shift respectively. The delay tap and Doppler shift tap of the i-th path are l i =M△fτ i 、k i =NTν i Only the case of integer Doppler is considered here.

[0116] At the receiver, the signal after removing the CP can be expressed as:

[0117] r=Hs+w

[0118] The channel noise is the channel matrix containing the addition and subtraction CP operations, which is expressed as follows:

[0119]

[0120] Where π is the permutation matrix (forward cyclic shift),

[0121]

[0122] Δ is a diagonal matrix of MN×MN,

[0123] Δ=diag[z 0 ,z 1 ,…,z MN-1 ]

[0124] In the formula

[0125] The received signal r is then processed by Wigner transform and Symplectic Fast Fourier Transform (SFFT). The received symbol in the DD domain can be expressed as:

[0126]

[0127] Where R = unvec M,N (r). The input-output relationship of the DD domain can be written as:

[0128]

[0129] Considering the operations of adding and removing CP, the input and output relationship of the DD domain can be rewritten as:

[0130]

[0131] Among them, add CP matrix Remove CP matrix The unit matrix I is of size MN×MN MN The last N cp The DD domain equivalent channel matrix is ​​defined as:

[0132]

[0133] Secondly, consider the MIMO-OTFS system, where the number of transmitting antennas is N t , the number of receiving antennas is N r The time domain transmission signal of the i-th transmitting antenna can be expressed as:

[0134]

[0135] The time domain received signal of the jth receiving antenna can be expressed as:

[0136]

[0137] The corresponding DD domain received signal is:

[0138]

[0139] The time domain input and output relationship of the MIMO-OTFS system can be written as:

[0140]

[0141] make The above formula can be expressed as:

[0142]

[0143] Combining the transformation of the time domain and DD domain at the transmitter and receiver, let Then the DD domain input and output relationship of the MIMO-OTFS system can be written as:

[0144]

[0145] The DD domain equivalent channel matrix of the MIMO-OTFS system is defined as:

[0146]

[0147] The present invention provides a MIMO-OTFS system time domain AN generation technology based on time domain and DD domain processing. The transmitter processing includes the following steps:

[0148] Step 1: Substitute the DD domain equivalent channel matrix Perform SVD decomposition, expressed as:

[0149]

[0150] For transmission N s (N s <N t ) data streams (each data stream is MN in length), select the first N left singular matrix U s Columns as post-processing matrix W r , select the first N of matrix V s Columns are used as preprocessing matrix W t .

[0151] Step 2: In the DD domain, s The data stream after constellation mapping Perform preprocessing, namely:

[0152] x MIMO =W t x S

[0153] in, so Contains N t Data streams (x MIMO According to the element sequence from small to large, each MN element is regarded as a data stream, which can form N t data streams).

[0154] Step 3: x MIMO N t The data streams are subjected to ISFFT transformation and discrete Heisenberg transform based on rectangular pulses, namely:

[0155]

[0156] in Contains N t Data streams (s MIMO According to the element sequence from small to large, each MN element is regarded as a data stream, which can form N t data streams). MIMO is a time domain signal.

[0157] Step 4: s MIMO N t Add a data stream of length N cp CP, that is:

[0158]

[0159] in Contains N t Data streams ( According to the element number from small to large every MN+N cp elements as a data stream, which can form N t data streams).

[0160] Step 5: Injection time domain AN, that is:

[0161]

[0162] Where a is the injected time domain AN. a is designed to fall into the legal channel null space, let:

[0163] a=Qd t

[0164] Where Q is a semi-unitary matrix that satisfies:

[0165]

[0166]

[0167] dt is an artificially generated zero-mean circularly symmetric complex Gaussian noise, that is The dimension of the matrix multiplied by Q is N s MN×N t (MN+N cp ), the condition for the existence of the null space matrix Q is:

[0168]

[0169] Among them, when the data stream N is transmitted s Less than the number of transmitting antennas N t When , the condition for the existence of the null space matrix Q must be satisfied. Contains N t Data streams ( According to the element number from small to large every MN+N cp elements as a data stream, which can form N t data streams).

[0170] Step 6: Step 5 N in t The data streams are respectively digitally up-converted, digital-to-analog converted, radio frequency up-converted, and finally transmitted to N t Antenna transmission.

[0171] The receiving end processing includes the following steps:

[0172] Step 7: N r The signal received by the antenna is subjected to RF down-conversion, analog-to-digital conversion, and digital down-conversion, and finally N r baseband data streams, each of which has a length of MN+N cp . N r The baseband data stream is recorded as:

[0173]

[0174] in, The data stream corresponding to the i-th antenna.

[0175] Step 8: N r Each baseband data stream is subjected to CP removal operation, namely:

[0176]

[0177] in Contains N r Data streams (r MIMO According to the element sequence from small to large, each MN element is regarded as a data stream, which can form N r data streams). MIMO is a time domain signal.

[0178] Step 9: MIMO N r Each data stream is subjected to SFFT transformation and discrete Wigner transform, namely:

[0179]

[0180] in Contains N r Data streams (y MIMO According to the element sequence from small to large, each MN element is regarded as a data stream, which can form N r data streams). MIMO It is a DD domain signal.

[0181] Step 10: y MIMO Perform post-processing operations and convert into N s data streams, namely:

[0182] y S =W r y MIMO

[0183] in Contains N s Data streams (y S According to the element sequence from small to large, each MN element is regarded as a data stream, which can form N s data streams).

[0184] According to the processing from step 1 to step 10, the DD domain input-output relationship of the MIMO-OTFS system using the time domain AN generation technology proposed by this method can be written as:

[0185]

[0186] Example:

[0187] This method is applicable to MIMO-OTFS systems in TDD mode or in FDD mode that feed back channel state information (CSI). According to the time domain AN generation technology proposed in this invention, it is assumed that the number of antennas of the sender Alice is N. t =3, the number of antennas of the legal receiver Bob Number of Eve antennas Transmit data stream N s =2, the data streams are all power-normalized QPSK modulated signals, the number of OTFS modulated subcarriers M = 8, the number of time slots N = 4, and the CP length N cp= 4. Considering the case where the eavesdropping channel quality is superior to the legitimate channel quality, the eavesdropping channel maximum speed is lower than the legitimate channel maximum speed, and the corresponding Doppler tap parameter in the channel parameter setting is smaller. Specific channel parameter settings are shown in the attached table. Consider that the signal power and AN power each account for half of the transmit power. Because the CP length is shorter than the data stream length, this embodiment does not consider the signal CP portion when calculating signal power.

[0188] Step 1: If Figure 2 As shown, the sender Alice obtains the CSI fed back by the legitimate receiver Bob. For the DD domain equivalent channel matrix Perform SVD decomposition, expressed as:

[0189]

[0190] To transmit two data streams (each data stream is 32 in length), the first two columns of the left singular matrix U are selected as the post-processing matrix W r , select the first two columns of matrix V as the preprocessing matrix W t .

[0191] Step 2: In the DD domain, the data stream after mapping the two constellations Perform preprocessing, namely:

[0192] x MIMO =W t x S

[0193] in, so Contains 3 data streams (x MIMO According to the element sequence from small to large, every 32 elements are regarded as a data stream, which can constitute 3 data streams).

[0194] Step 3: x MIMO The three data streams are subjected to ISFFT transformation and discrete Heisenberg transform respectively, namely:

[0195]

[0196] in Contains 3 data streams (s MIMO According to the element sequence from small to large, every 32 elements are regarded as a data stream, which can form 3 data streams). MIMO is a time domain signal.

[0197] Step 4: s MIMO The three data streams are added with a CP of length 4, namely:

[0198]

[0199] in Contains 3 data streams (s MIMO According to the element sequence from small to large, every 36 elements are regarded as a data stream, which can constitute 3 data streams).

[0200] Step 5: Injection time domain AN, that is:

[0201]

[0202] Where a is the injected time domain AN. a should fall into the legal channel null space, let:

[0203] a=Qd t

[0204] The null space matrix Q is solved by the following formula:

[0205]

[0206] d t is an artificially generated zero-mean circularly symmetric complex Gaussian white noise, AN power The signal power is calculated as follows:

[0207]

[0208] Since it is assumed that the signal power is equal to the AN power, the AN variance can be calculated Then you can generate d t , added to Contains 3 data streams ( According to the element sequence from small to large, every 36 elements are regarded as a data stream, which can constitute 3 data streams).

[0209] Step 6: Step 5 The three data streams in the system are respectively digitally up-converted, digital-to-analog converted, and radio frequency up-converted, and finally transmitted to three antennas for transmission.

[0210] like Figure 3 As shown, Bob and Eve perform the following steps respectively:

[0211] Step 7: Perform RF down-conversion, analog-to-digital conversion, and digital down-conversion on the signals received by the two antennas, and finally obtain two baseband data streams, each with a length of 36. The two baseband data streams are recorded as:

[0212]

[0213] in, The data stream corresponding to the i-th antenna.

[0214] Step 8: Remove the CP from the two baseband data streams separately, namely:

[0215]

[0216] in Contains 2 data streams (r MIMO According to the element sequence from small to large, every 32 elements are regarded as a data stream, which can form 2 data streams). MIMO is a time domain signal.

[0217] Step 9: MIMO The two data streams are subjected to SFFT transformation and discrete Wigner transform respectively, namely:

[0218]

[0219] in Contains 2 data streams (y MIMO According to the element sequence from small to large, every 32 elements are regarded as a data stream, which can form 2 data streams). MIMO It is a DD domain signal.

[0220] Step 10: y MIMO Perform post-processing operations and convert them into two data streams, namely:

[0221] y S =W r y MIMO

[0222] in Contains 2 data streams (y MIMO According to the element sequence from small to large, every 32 elements are regarded as a data stream, which can constitute 2 data streams).

[0223] Step 11: Consider the worst case, the eavesdropper Eve knows the legitimate, eavesdropping channel CSI, that is, knows W t 、W r To achieve better communication performance, Bob and Eve both use the y obtained in step 10. S Minimum mean square error equalization is performed. Constellation demapping is then performed to recover the 0 and 1 bit streams. Table 1 shows the channel parameter settings.

[0224] Table 1: Channel parameter settings in the embodiment

[0225] Channel parameters Legal recipient Bob Eve the Eavesdropper Carrier frequency (GHz) 3 3 Subcarrier bandwidth (kHz) 2 2 Number of paths 4 4 Maximum speed (km / h) 200 150 <![CDATA[Maximum Doppler Tap (k max )]]> 2 1 <![CDATA[Maximum delay tap (l max )]]> 3 3

[0226] Figure 3When the sender Alice uses the time domain AN generation technology proposed in this invention to perform secure transmission in the MIMO-OTFS system, it is assumed that the eavesdropper Eve knows the CSI of the legitimate and eavesdropped channels, and the legitimate receiver Bob and the eavesdropper Eve both use the error curve of the minimum mean square error equalization algorithm. Figure 3 As can be seen, the two curves with the best bit error rate performance are those without time-domain AN and with Bob and Eve performing MMSE equalization. In the case of time-domain AN, although Bob's received signal is unaffected by the time-domain AN, the SNR is calculated as the ratio of total signal power to channel noise power. Using a portion of the power to generate AN reduces the power available for signal generation, ultimately lowering the SINR and resulting in some loss in bit error rate performance. However, for Eve, the interference from the time-domain AN cannot be eliminated, resulting in a significant drop in bit error performance. Therefore, the time-domain AN generation technology proposed in this invention can widen the gap between legitimate and eavesdropped channels.

Claims

1. A cross-domain physical layer security implementation method, characterized in that: The steps include: Step 1: For the single-input single-output SISO-OTFS system in the form of a MIMO-OTFS system reference rectangular pulse, the system processing is as follows; Step 1-1: For an OTFS system, the system has M subcarriers with a subcarrier spacing of Δf and N symbols with a symbol time of T, the total bandwidth is B = MΔf, and the signal frame duration is T f =NT; OTFS system is critical sampling, that is, T△f=1; Step 1-2: At the transmitter, the symbols after constellation mapping First, it is placed on the delay-Doppler grid, that is, x is arranged into a matrix by column Satisfy X DD =unvec M,N (x); then use the inverse symplectic Fourier transform ISFFT to transform X DD Convert the symbolic matrix X to the TF domain TF , X TF It is expressed as follows: Among them, F, F H They represent the discrete Fourier transform matrix and the discrete inverse Fourier transform matrix respectively; In the case of rectangular pulse shaping, the TF domain symbol matrix X is transformed by discrete Heisenberg transform TF Convert to time domain signal s represents the following: Among them, vec(·) represents column-wise vectorization operation; Then, the length N cp Add CP to s The beginning of N cp ≥L, L is the maximum delay spread; the time domain signal is transmitted on a time-frequency dual-selective channel, and the channel response h(τ,ν) is expressed as: Where P is the number of transmission paths, h i , τ i ∈[0,τ max ]、ν i ∈[-ν max ,ν max ] are the channel coefficient, delay, and Doppler shift of the i-th path respectively; here, τ max 、ν max are the maximum delay and Doppler shift respectively, and the delay tap and Doppler shift tap of the i-th path are l i =M△fτ i 、k i =NTν i ; Step 1-3: At the receiver, the signal after removing the CP is expressed as: r=Hs+w The channel noise is the channel matrix containing the addition and subtraction CP operations, which is expressed as follows: Where π is the permutation matrix: Δ is a diagonal matrix of MN×MN: Δ=diag[z 0 ,With 1 ,…,With MN-1 ] In the formula The received signal is transformed by Wigner transform and sigmoid Fourier transform SFFT r After processing, the received symbol of the DD domain is represented as: Where R = unvec M,N (r); The DD domain input and output relationship is written as: The DD domain input and output relationship is rewritten as: Among them, add CP matrix Remove CP matrix The unit matrix I is of size MN×MN MN The last N cp OK; The DD domain equivalent channel matrix is ​​defined as: Step 2: In the MIMO-OTFS system, the number of transmitting antennas is N t , the number of receiving antennas is N r , the time domain transmission signal of the i-th transmitting antenna is expressed as: The time domain received signal of the jth receiving antenna can be expressed as: The corresponding DD domain received signal is: The time domain input and output relationship of the MIMO-OTFS system is written as: make The above formula is expressed as: Combining the transformation of the time domain and DD domain at the transmitter and receiver, let Then the DD domain input and output relationship of the MIMO-OTFS system is written as: The DD domain equivalent channel matrix of the MIMO-OTFS system is defined as: Step 3: Based on the time domain and DD domain processing, the MIMO-OTFS system generates the time domain AN. The transmitter performs the following processing: Step 3-1: Convert the DD domain equivalent channel matrix Perform SVD decomposition, expressed as: For transmission N s , N s <N t data streams, each of which is MN in length, and the first Ns columns of the left singular matrix U are selected as the post-processing matrix W r , select the first N of matrix V s Columns are used as preprocessing matrix W t ; Step 3-2: In the DD domain, s The data stream after constellation mapping Perform preprocessing, namely: x MIMO =W t x S in, so Contains N t data streams; Step 3-3: For x MIMO N t The data streams are subjected to ISFFT transformation and discrete Heisenberg transform based on rectangular pulses, namely: in Contains N t data streams, s MIMO is the time domain signal; Step 3-4: s MIMO N t Add a data stream of length N cp CP, that is: in Contains N t data streams; Step 3-5: Injection time domain AN, that is: Where a is the injected time domain AN; a is designed to fall into the legal channel null space, let: a=Qd t Where Q is a semi-unitary matrix that satisfies: d t is an artificially generated zero-mean circularly symmetric complex Gaussian noise, that is The dimension of the matrix multiplied by Q is N s MN×N t (MN+N cp ), the condition for the existence of the null space matrix Q is: Among them, when the data stream N is transmitted s Less than the number of transmitting antennas N t When , the condition for the existence of the null space matrix Q must be satisfied; Contains N t data streams; Step 3-6: For step 3-5 N t The data streams are respectively digitally up-converted, digital-to-analog converted, radio frequency up-converted, and finally transmitted to N t Root antenna transmission; Step 4: The time domain AN of the MIMO-OTFS system is generated based on time domain and DD domain processing. The receiving end processes it as follows: Step 4-1: For N r The signal received by the antenna is subjected to RF down-conversion, analog-to-digital conversion, and digital down-conversion, and finally N r baseband data streams, each of which has a length of MN+N cp ; N r The baseband data stream is recorded as: in, The data stream corresponding to the i-th antenna; Step 4-2: For N r Each baseband data stream is subjected to CP removal operation, namely: in Contains N r data streams; r MIMO is the time domain signal; Step 4-3: For r MIMO N r Each data stream is subjected to SFFT transformation and discrete Wigner transform, namely: in Contains N r data stream; y MIMO It is the DD domain signal; Step 4-4: For y MIMO Perform post-processing operations and convert into N s data streams, namely: y S =W r y MIMO in Contains N s data streams; Step 5: Based on steps 3 and 4, the DD domain input and output relationship of the MIMO-OTFS system is written as:

2. A cross-domain physical layer security implementation method according to claim 1, characterized in that: The x MIMO According to the element sequence from small to large, each MN element is regarded as a data stream, forming N t data streams.

3. A cross-domain physical layer security implementation method according to claim 1, characterized in that: The s MIMO According to the element sequence from small to large, each MN element is regarded as a data stream, forming N t data streams.

4. A cross-domain physical layer security implementation method according to claim 1, characterized in that: According to the element number from small to large every MN+N cp elements as a data stream, forming N t data streams.

5. A cross-domain physical layer security implementation method according to claim 1, characterized in that: described According to the element number from small to large every MN+N cp elements as a data stream, forming N t data streams.

6. A cross-domain physical layer security implementation method according to claim 1, characterized in that: The r MIMO According to the element sequence from small to large, each MN element is regarded as a data stream, forming N r data streams.

7. A cross-domain physical layer security implementation method according to claim 1, characterized in that: The y MIMO According to the element sequence from small to large, each MN element is regarded as a data stream, forming N r data streams.

8. A cross-domain physical layer security implementation method according to claim 1, characterized in that: The y S According to the element sequence from small to large, each MN element is regarded as a data stream, forming N s data streams.

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