A transmission encryption method and system based on massive MIMO antenna array technology

Abstract

This invention discloses a transmission encryption method and system based on massive MIMO (Multi-Site Array) technology. This invention incorporates the physical transmission process of MIMO into the entire encryption process. By processing the message and using precoding within the MIMO system, the information transmitted through the corresponding physical channel becomes difficult for eavesdroppers to decrypt, while legitimate recipients can obtain the transmitted information normally. The main innovation of this invention is the ingenious integration of the physical transmission process of MIMO and existing MIMO technology into the entire encryption algorithm to ensure the security and correctness of the entire cryptographic algorithm, greatly reducing the complexity of the encryption process.

Description

Technical Field

[0001] This invention relates to the fields of information security technology and data encryption management methods, and in particular to a transmission encryption method and system for Massive MIMO technology. Background Technology

[0002] Massive MIMO is an extension of MIMO (Multi-Input Multiple-Output) antenna array technology. MIMO, a concept proposed and utilized in the 3G and 4G eras, achieves multiple transmissions and receptions of signals through multiple transmit and receive antennas. Without increasing spectrum resources or antenna transmit power, it fully utilizes spatial resources, improving communication quality and multiplying system channel capacity, making it an indispensable technology in the communications field. As an emerging technology after 5G, Massive MIMO inherits many advantages of MIMO. The increased number of transmit and receive antennas further develops beamforming, spatial diversity, and other characteristics, making the channel state more complex. From a cryptographic perspective, more random factors participate in the spatial transmission process of MIMO, making it feasible to combine physical layer security—a technology utilizing these random factors—with MIMO.

[0003] Research on physical layer security can be traced back to Wyner's (W. Diffie and M. Hellman, "New Directions incryptography," IEEE Trans. on Inform. Theory, vol. 22, no. 6, pp. 644-654, Nov. 1976) theoretical exploration of the concept of eavesdropping channels. Based on the physical assumptions of communication channels, various secure communication technologies are implemented by utilizing the differences in channels between the sender and the legitimate receiver, and between the sender and the eavesdropper. In the context of wireless communication, the beamforming properties brought about by MIMO ensure that when the distance between the eavesdropper and the legitimate receiver is sufficiently large, auxiliary channel differences are used to achieve security. However, most existing MIMO physical layer security technologies require additional restrictions on the capabilities of eavesdroppers to achieve secure communication. For example, Oggier and Hassibi (F. Oggierand B. Hassibi, “The secrecycapacity of the MIMO wiretap channel,” IEEE Trans. on Inform. Theory, vol. 57, no. 8, pp. 4961–4972, Oct. 2011.) need to assume that the signal-to-noise ratio (SNR) in the eavesdropping channel between the sender and the eavesdropper is less than the SNR in the legitimate channel between the sender and the legitimate receiver; Zhu et al. (J. Zhu, R. Schober, and V. B. Hargava, “Linear Precoding of Data and Artificial Noise in Secure Massive MIMO Systems,” IEEE Trans. on Wireless Commun., vol. 15, no. 3, pp. 2245–2261, March 2016.) need to assume that the number of receiving antennas used by the eavesdropper is less than the number of receiving antennas used by the legitimate receiver; in (Bellare... M, Tessaro S, Vardy A. Semantic Security for the Wiredap Channel[J]. Advances in Cryptology–CRYPTO 2012. Springer, Berlin, Heidelberg, 2012.) achieves security by adding additional cryptographic components.Dean and Goldsmith, in their paper "Physical-layer cryptography through massive MIMO," *IEEE Transactions on Information Theory*, vol. 63, no. 8, pp. 5419–5436, Aug. 2017, present a novel method for achieving physical layer security based on Massive-MIMO communication systems. They attempt to avoid making additional assumptions about the eavesdropping channel, assuming that the channel state information (CSI) between the legitimate receiver and sender is known to all three parties. The main idea is to replace the information theory security assumptions used in physical layer security methods with weaker complexity-based security assumptions in cryptography. This involves reducing the problem of the eavesdropper correctly decoding to a difficult problem based on computational complexity, thereby avoiding some impractical assumptions in existing information theory techniques. However, this novel method for achieving physical layer security based on Massive-MIMO communication systems was proven by Sakzad and Steinfeld (Amin Sakzad and Ron Steinfeld. Comments on "Physical-layer cryptography through massive MIMO" [J]. 2020.) to have security and correctness issues. The core reason is that the decoding capabilities of the legitimate receiver and the eavesdropper do not actually differ in the above eavesdropping model, making it impossible to simultaneously satisfy security and correctness under normal circumstances. Therefore, existing MIMO physical layer security schemes still require reasonable additional security assumptions for eavesdropping channel models. The assumptions regarding the eavesdropping channel model were further discussed in (C. Paschou, O. Johnsont, Z. Zhu and A. Doufexi, "Re-Defining Secure Distance for CSI-based Key Generation Protocols," 2022 IEEE 95th Vehicular Technology Conference: (VTC2022-Spring), 2022), which considers the influence of physical factors on the eavesdropper's initiative, thus limiting the eavesdropper's ability to obtain legitimate CSI channels under passive eavesdropping conditions. This patent will consider providing a new secure encryption method under a new eavesdropping channel model, thereby simultaneously achieving the goals of ensuring security and correctness. Summary of the Invention

[0004] This invention provides a transmission encryption method and system combining large-scale antenna array (MIMO) transmission technology. By embedding the encryption method into the physical transmission process and combining it with existing computational processes in MIMO transmission, transmission security is ensured. Compared to traditional MIMO physical layer security schemes, it has less impact on communication quality and leverages the high utilization of spatial resources inherent in MIMO technology to utilize the physical random source—a highly reliable true random source. Furthermore, it incorporates the skeptical entropy of an eavesdropper's estimation of the legitimate channel matrix into the algorithm, using this skeptical entropy to specifically construct the precoding mechanism, thereby ensuring security.

[0005] The technical solution of the present invention is as follows:

[0006] A transmission encryption method based on massive MIMO antenna array transmission technology includes the following steps:

[0007] 1) The legitimate sender determines the plaintext information m and estimates the CSI. The legitimate receiver sends a pilot signal to the legitimate sender. The legitimate sender then solves the channel estimation equation by receiving the pilot signal to obtain the legitimate channel matrix H. b and the number of transmitting antennas n t Number of antennas n for legitimate receivers r It is modulated using M-QAM modulation.

[0008] 2) The legitimate sender obtains the channel matrix H b Perform SVD decomposition to obtain H b =UΣV H The corresponding eigenvector matrices U and V are obtained. H And the eigenvalue matrix Σ, and according to the channel matrix H b Construct a random matrix K, and then use VK as the precoding matrix W, where V and V H The two matrices are conjugate transposes of each other, U and U H These are conjugate transposes of each other.

[0009] 3) Calculate matrix K′U for the legitimate sender H This is used as a decoding matrix, and the decoding matrix is ​​sent directly to the legitimate recipient.

[0010] 4) The legitimate receiver receives the decoding matrix K′U H Then, an acknowledgment signal k is sent to the legitimate sender to indicate that the decoding matrix has been received, where k is the public plaintext information.

[0011] 5) The legitimate sender re-evaluates the channel using the received acknowledgment signal k, obtaining the new channel matrix within the relevant time period. V is obtained through SVD decomposition. H t and V Ht K serves as the precoding matrix, which modulates the plaintext information m to obtain the signal x, which is then precoded and sent to the legitimate receiver.

[0012] 6) After receiving the received signal y, calculate using the decoding matrix. Then, the processed received signal y t The plaintext information m is obtained by performing decoding methods such as maximum likelihood decoding.

[0013] The specific steps for a legitimate sender to calculate the decoding matrix and the precoding matrix are as follows:

[0014] 1) Estimate the legal channel matrix H using the obtained CSI. b The obtained channel matrix H b Perform SVD decomposition to obtain the corresponding eigenvector matrices U and V. H , and the eigenvalue matrix Σ.

[0015] 2) Construct a unitary matrix K′ based on the randomness of the eigenvalue matrix Σ, and then decompose the resulting diagonal matrix V using SVD. H The eigenvalue matrix ∑ is obtained by calculating the eigenvalues. V This yields two real diagonal matrices R(∑ V ) and ξ(∑ V ), R(∑ V The elements in ) are ∑ V The real part of the elements, ξ(∑ V ) by ∑ V The imaginary part is composed of elements.

[0016] 3) Construct n t If R(∑)′ and ξ(I)′ are dimensional identity matrices, then R(∑)′, ξ(I ... V The corresponding diagonal element Then the diagonal elements in R(I)′ Similarly, through ξ(∑ V ) Process ξ(I)′, if ξ(∑ V The corresponding diagonal element Then the diagonal elements in ξ(I)′ Finally, calculate K = R(I)′ × ξ(I)′.

[0017] 4) When n r ≤n t When, take the first n of K r row and first n r Construct K′ in the column, when n r >n t At that time, construct Calculate K′U H As a decoding matrix.

[0018] 5) Obtain the channel matrix within the relevant time period by performing channel estimation again using the received acknowledgment signal k. V is obtained through SVD decomposition. H t And calculate V H t K is the precoding matrix.

[0019] A transmission encryption system based on massive MIMO technology, characterized in that it includes a sender and a receiver;

[0020] The sender determines the plaintext information m and estimates the channel state information (CSI) between the sender and receiver; when it receives a pilot signal from the receiver, the sender obtains the channel matrix H based on the CSI and the received pilot signal. b The sender modulates the plaintext information m; and modulates the channel matrix H. b Perform SVD decomposition to obtain the corresponding eigenvector matrices U and V. H And the eigenvalue matrix Σ; according to the channel matrix H b Construct a random matrix K, then use VK as the precoding matrix W; compute matrix K′U H The decoded matrix is ​​used as the decoding matrix and sent to the receiver; and the channel estimation is re-performed based on the received acknowledgment signal k to obtain the new channel matrix within the relevant time period. And for the channel matrix Performing SVD decomposition yields the eigenvector matrix V. H t and V H t K is used as the precoding matrix, and then the modulated plaintext information m is precoded using the precoding matrix to obtain signal y, which is then sent to the receiver; where V and V H The two matrices are conjugate transposes of each other, U and U H matrices that are conjugate transposes of each other;

[0021] After receiving the decoding matrix, the receiver sends an acknowledgment signal k to the sender; and after receiving the signal y, it calculates y using the decoding matrix. t and for signal y t Decoding yields the plaintext information m.

[0022] Furthermore, the method by which the sender obtains the decoding matrix is ​​as follows: first, a monomodular matrix K′ is constructed based on the eigenvalue matrix Σ, and then the monomodular matrix K′ is used to process V. H V is obtained by eigenvalue calculation. H eigenvalue matrix ∑ V , matrix ∑V Including the real diagonal matrix R(∑ V ) and ξ(∑ V ), R(∑ V The elements in ) are ∑ V The real part of the elements, ξ(∑ V ) by Σ V The imaginary part is composed of elements; then construct n. t If R(I)′ and ξ(I)′ are dimensional identity matrices, then R(∑ V The corresponding diagonal element Then the diagonal elements in R(I)′ If ξ(∑ V The corresponding diagonal element Then the corresponding diagonal element in ξ(I)′ takes the value -1; then calculate the random matrix K = R(I)′ × ξ(I)′, when n r ≤n t When, take the first n of the random matrix K. r row and first n r Construct matrix K′ from columns, when n r >n t When constructing a matrix Then calculate K′U H As the decoding matrix; where n t n is the number of transmit antennas of the sender. r This represents the number of receiving antennas at the receiver.

[0023] Furthermore, signals e represents the channel noise between the sender and receiver, and x represents the plaintext information m modulated into a signal.

[0024] Furthermore, the sender uses M-QAM modulation to modulate the plaintext information m.

[0025] Furthermore, the receiver calculates y using the decoding matrix. t =K′U H y.

[0026] The advantages of this invention are as follows:

[0027] This invention has less impact on communication quality than traditional MIMO physical layer security schemes, and leverages the high utilization of spatial resources inherent in MIMO technology to utilize the physical random source, a truly random source. Simultaneously, it incorporates the skeptical entropy of an eavesdropper's estimation of the legitimate channel matrix into the algorithm, using this skeptical entropy to specifically construct the precoding mechanism to ensure security. Attached Figure Description

[0028] Figure 1This is an overall architecture diagram of the large-scale antenna array transmission encryption method described in the embodiments of the present invention.

[0029] Figure 2 This is the eavesdropping channel model in the method described in the embodiments of the present invention.

[0030] Figure 3 This refers to the legal channel transmission process in the method described in the embodiments of the present invention.

[0031] Figure 4 These are experimental data from the MIMO eavesdropping channel model using SVD precoding in the method described in this embodiment of the invention.

[0032] Figure 5 These are experimental data from the MIMO eavesdropping channel model using SVD precoding in the method described in this embodiment of the invention.

[0033] Figure 6 These are experimental data of the MIMO eavesdropping channel model precoded using the method described in the embodiments of the present invention.

[0034] Figure 7 These are experimental data of the MIMO eavesdropping channel model precoded using the method described in the embodiments of the present invention. Detailed Implementation

[0035] To make the objectives, technical solutions, correctness, safety and advantages of the present invention clearer, the present invention will be further described in detail below.

[0036] Table 1. Explanation of symbols in the scheme.

[0037] symbol significance <![CDATA[n r ]]> Number of receiving antennas for legitimate receivers <![CDATA[n′ r ]]> Number of receiving antennas of the eavesdropper <![CDATA[n t ]]> Number of transmitting antennas of legitimate senders <![CDATA[H b ]]> Channel matrix of legitimate channels <![CDATA[H e ]]> Channel matrix of the eavesdropping channel e Channel noise of legitimate channels e′ Channel noise in eavesdropping channels M Constellation chart size <![CDATA[CN α ]]> <![CDATA[Complex Gaussian distribution CN(0, α 2 )]]> eig(A) Find the eigenvalue diagonal matrix of matrix A.

[0038] 1. Eavesdropping Channel Model

[0039] Let n represent the number of transmitting antennas of the legitimate sender Alice. t The number of receiving antennas for the legitimate receiver Bob is represented by n. r The number of receiving antennas for the eavesdropper Eve is denoted as n′. r The channel matrix H between the sender and the legitimate receiver can be obtained. b For n r ×n t The channel matrix H between the sender and the eavesdropper. e For n′ r ×n t Dimension. Because MIMO possesses beamforming capabilities, and considering the different positions of the eavesdropper and the legitimate receiver, and taking channel normalization into account, we can derive H. b With H eThe distributions are assumed to be independent and identically distributed CN1. Furthermore, assuming these channel matrices do not change over a period of time, and considering only the channels without precoding, the eavesdropping channel model can be written in the form of the following equation:

[0040]

[0041] Where e represents the noise between the sender and the legitimate receiver's channel, and e′ represents the noise between the sender and the eavesdropper's channel. In the case of QAM modulation, M is the constellation size, and e and e′ are CN. α and CN β The distribution is assumed to be such that the channel state of the legitimate receiver is not inferior to that of the eavesdropping channel, which is reflected in the channel noise distribution, i.e., α ≤ β. The eavesdropper knows the CSI of the eavesdropping channel and part of the CSI of the sender and the legitimate receiver, while the legitimate sender only knows the CSI of the legitimate channel. Therefore, the sender can only rely on the known channel matrix H between itself and the legitimate receiver. b This information is used to calculate the relevant precoding matrix, and assuming the precoding matrix is ​​W, we can obtain the following: Under these conditions, the eavesdropping channel model can be further improved as follows:

[0042]

[0043] Meanwhile, based on the fundamental communication model, the eavesdropper is in a completely passive state throughout the process, hence it is a passive eavesdropping model. Building on this, Paschou and Johnsont, in (C. Paschou, O. Johnsont, Z. Zhu and A. Doufexi, "Re-Defining Secure Distance for CSI-based Key Generation Protocols," 2022 IEEE 95th Vehicular Technology Conference: (VTC2022-Spring), 2022), proposed a new definition of secure distance, reconsidering the eavesdropper's initiative in the passive eavesdropping model. Specifically, they argued that when the eavesdropper maintains a certain secure distance from legitimate senders and receivers, their ability to acquire CSI from legitimate channels weakens, and they provided a derivation of the relationship between relevant information entropy and secure distance. Therefore, this patent considers the impact of the eavesdropper's initiative in the passive model and proposes a new eavesdropping model that considers the eavesdropper's ability to acquire CSI from legitimate channels, which can be expressed as: Figure 3 The mathematical model is as follows:

[0044]

[0045] Where W′ is the relevant precoding matrix derived by the eavesdropper from the CSI information obtained from the legitimate channel, and H e (WW′)x is the error caused by the eavesdropper's inability to fully acquire legitimate channel CSI. The magnitude of this error is clearly related to the extent to which the eavesdropper acquires legitimate channel CSI. Therefore, the entropy of skepticism H(H′) for the eavesdropper regarding legitimate channel CSI is proposed. e |H e ). Where H′ e The legitimate channel matrix is ​​estimated by the eavesdropper using the relevant CSI obtained through the legitimate channel, while H e To determine the data, we can obtain H(H′). e |H e )=H(H e -H′ e The legitimate channel matrix and its estimated value both conform to a complex Gaussian distribution, and the matrix elements are independent of each other. The error matrix (H) can then be obtained. e -H′ e It also conforms to a complex Gaussian distribution, and the matrix elements are independent of each other. With an expectation of 0, a matrix rank of p, matrix elements that are independently and identically distributed, and a variance of σ, the Gaussian distribution matrix entropy (Ben-Naim, A.. Elements of Information Theory, p. 249) is:

[0046]

[0047] The above equation shows that the magnitude of the Gaussian distribution matrix entropy is influenced by the matrix's rank and the variance of its distribution, which can be determined through the error matrix (H). e -H′ e The variance of the distribution of ) characterizes the magnitude of the ambiguity entropy. Precoding matrices are generally related to the actual channel state to improve channel transmission quality; therefore, ambiguity entropy also affects the eavesdropper's estimation of the channel precoding matrix. The equivalent noise of the eavesdropper, H, can be obtained from an eavesdropping channel model considering ambiguity entropy. e (WW′)x+e′, which means the addition of the entropy of doubt increases the equivalent noise in the eavesdropper's decoding. Let x be a discrete variable and follow a uniform distribution, H e W and H e W′ are all complex Gaussian distributions, therefore we can obtain H e (WW′)x represents a discrete complex Gaussian distribution, and e represents a continuous complex Gaussian distribution. The addition of complex numbers actually involves calculating the real and imaginary parts separately, thus yielding the equivalent noise H. e (WW′)x+e′ is a continuous complex Gaussian distribution, and since the expectation is 0, the expectation of the equivalent noise is also 0.

[0048] H can be estimated by using information from legitimate channels. e The distribution of (WW′)x+e′, where x is a known quantity for the sender, H e H can be used b As an upper bound, (WW′) can be obtained from the ambiguous entropy estimated from the safe zone distance, and for e′, the lower bound of the covariance can be obtained from the channel noise e estimated from the legitimate channel. Therefore, in practice, the legitimate sender can estimate the equivalent noise H. e The lower bound of the variance of (WW′)x+e′ is H. b The variance of (WW′)x+e. Because for a legitimate sender, H b Both x and y are deterministic quantities. Based on the achievable secure distance, the magnitude of the entropy that the eavesdropper can obtain can be deduced. By substituting the calculated lower bound of variance into y, the upper bound of its flatness factor can be obtained. By comparing the computational precision that the receiver can achieve, it can be determined whether information-theoretic security can be achieved under the current application context of entropy and precoding. Figure 4 The example in the middle is when (H) e -H′ e The variance of ) is 10 -1 When using SVD precoding, the bit error rate changes for the eavesdropper Eve and the legitimate receiver Bob under different signal-to-noise ratios show that when the skeptical entropy is large enough, the equivalent noise itself is large enough to ensure the security of legitimate channel transmission when using SVD precoding; however, Figure 5 In the middle, when (H) e -H′ e The variance of ) is 10 -2 In such cases, the corresponding entropy is relatively small, making it difficult for traditional MIMO transmission methods to guarantee security.

[0049] 2. Analysis of the correctness of the plan

[0050] An n-dimensional lattice in a linear space can be represented as:

[0051] Λ=L(B)={Bx:x∈Z n}

[0052] The columns of the generating basis real matrix B, which serves as the lattice, are linearly independent. Therefore, extending this to complex matrices, we can utilize the generating basis complex matrix B... c The definition of a complex lattice is obtained as follows:

[0053] Λ c =L(B c )={B c x:x∈Z n}

[0054] If we consider the complex matrix B c Represented as an equivalent real matrix, we have:

[0055]

[0056] Considering the case where x is a complex integer vector, we can then define B... c The calculation of x is equivalent to the calculation of a real matrix:

[0057]

[0058] Therefore, some existing security conclusions in the real lattice domain can be extended to the complex lattice domain for application, specifically for the complex lattice Λ. c The basic region can be directly defined as the basic region of the equivalent real lattice, F(Λ). c The size of the basic region is defined as F(Λ). c Then the complex lattice Λ can be defined. c Dual lattice Λ c * :

[0059]

[0060] The minimum basis of a given lattice Λ can be represented by the set of minimum distances between lattice points:

[0061] λ=dist(a,b), a, b∈Λ,

[0062] λ1=min{λ}=min{||a||:a∈Λ\{0}}

[0063] λ i =min{λ:λ i >λ i-1 ,2≤i≤dim(Λ)}

[0064] For the MIMO channel matrix H b With H e Both the channel noise and the probability density function of the n-dimensional Gaussian distribution are given below:

[0065]

[0066] When x is modulated as QAM, the channel matrix can be regarded as a generator basis, and x can be regarded as a complex integer vector, thus H can be obtained. b x and H e x can be considered as a complex lattice. Based on the lattice, the received signal y′=H e Based on the premise that the noise is Gaussian white noise, x+e′ can be considered as having a Gaussian distribution over a lattice, and Λ is defined.e =H e If x, then the distribution of y′ can be obtained as follows:

[0067]

[0068] For the lattice Λ and the variance σ, define the flatness factor:

[0069]

[0070] However, if we solve the lattice Λ e =H e The flatness factor of x can be obtained by constructing a lattice Λ from a valid channel matrix. b =H b x is estimated because the legitimate channel's channel state can be considered superior to the eavesdropping channel's channel state due to the beamforming characteristics of the MIMO channel. Therefore, we obtain:

[0071]

[0072] Therefore, it can be done through Λ b An estimation yields a insufficiently compressed upper bound. A method for calculating the flatness factor when the lattice is known is provided in (C. Ling, L. Luzzi, J.-C. Belfiore and D. Stehlé, "Semantically Secure Lattice Codes for the Gaussian Wiretap Channel," in IEEE Transactions on Information Theory, vol. 60, no. 10, pp. 6399-6416, Oct. 2014).

[0073]

[0074] The smaller the flatness factor, the closer the distribution of y′ is to a uniform distribution. The relationship between smoothing parameters commonly used in cryptography and the flatness factor is also given:

[0075] Theorem 1: For a lattice Λ, take ε>0, the smoothness parameter η ε (Λ) is able to satisfy The minimum value of σ > 0 under this condition. And when η ε When (Λ) = σ, ∈ Λ (σ)=ε.

[0076] It can be seen that with the orthogonal generating basis of the lattice remaining unchanged, the smoothness parameter of the lattice also remains unchanged with the flatness factor remaining unchanged. The received signal after processing by the decoding matrix by the final legitimate receiver is approximately:

[0077] K′U H y=K′U H H b Vkx+K′U H e=K′∑Kx+K′U H e=∑x+K′U H e

[0078] Considering the channel matrix after precoding using this method, since the V matrix is ​​a unitary matrix and K is a monomodular matrix, it has no effect on the orthogonal basis of the lattice; K′U H The same applies to e, in U H When the matrix is ​​a unitary matrix and K′ is a monomodular matrix, the noise level is not affected, and it can also be seen from the above formula that the final ∑ remains unchanged. Therefore, for a legitimate receiver, the precoding method of this method does not affect the transmission power, noise level, or eigenvalue matrix of the channel matrix. From the perspective of lattice cryptography, this method does not increase the decoding difficulty of the lattice formed by the legitimate channel matrix and plaintext information during transmission, and the legitimate receiver's ability to decode correctly remains unchanged.

[0079] 3. Analysis of the security of the solution

[0080] By employing the analysis method of Gaussian distribution over a lattice, this method estimates the magnitude of equivalent noise using ambiguity entropy. It then uses the eigenvalue matrix of the legitimate channel's channel matrix as an orthogonal basis of the lattice to calculate smoothness parameters and determine the decoding difficulty for the eavesdropper. However, when the ambiguity entropy is too small for the equivalent noise to guarantee security, this method utilizes the randomness introduced by the ambiguity entropy to amplify the equivalent noise, thereby ensuring the security of legitimate channel transmission. The eavesdropping channel model after applying this method can be represented as:

[0081]

[0082] Where V′P is the precoding matrix W′ calculated by the eavesdropper based on the estimated legitimate channel CSI. Compared to the traditional SVD precoding matrix, the eavesdropper also estimates the random matrix K to obtain K. eThe estimation error is larger for a matrix, while the diagonal elements of a random matrix R consist only of 1s and -1s, which does not affect the signal strength. For R′, if the estimation is wrong, the original subtraction will become addition. For traditional SVD precoding, it can be inferred that as the entropy decreases, the difference between the unitary matrices V and V′ will also decrease, and more corresponding matrix elements will have the same sign. By adding a random matrix K, the calculation between previously similar elements changes from subtraction to addition, increasing the number of corresponding difference matrix elements. As a result, the final equivalent noise is larger than that of traditional SVD precoding transmission, and the overall variance of the equivalent noise distribution is also larger. From a communication perspective, this increases the noise; from a lattice analysis perspective, increasing the noise distribution variance reduces the flatness factor, thus ensuring security from both analytical perspectives.

[0083] For a random matrix K, in the case of large-scale MIMO, the dimension of the channel matrix is ​​higher. Therefore, when solving for singular values, the error propagation and confusion of matrix elements are greater, thus ensuring that the random matrix K is difficult for eavesdroppers to guess and thus affect security.

[0084] The design method for the random matrix K in the precoding matrix is ​​as follows:

[0085]

[0086]

[0087]

[0088]

[0089] K=R(I)′×ξ(I)′

[0090] From Figure 6 as well as Figure 7 As seen in the text, even when (H) e -H e The variance of ′) is 10 -2 and variance of 10 -3 Even under conditions where the eavesdropper's entropy is low, this scheme can still provide security in the context of MIMO. It can also be seen that in the case of large-scale MIMO, where the number of antennas is increased to 80, the bit error rate can be kept at approximately 0.5% even with very low entropy, which proves the security of this scheme.

[0091] Although specific embodiments of the invention have been disclosed for illustrative purposes to aid in understanding and implementing the invention, those skilled in the art will understand that various substitutions, variations, and modifications are possible without departing from the spirit and scope of the invention and the appended claims. Therefore, the invention should not be limited to the content disclosed in the preferred embodiments, and the scope of protection claimed by the invention is defined by the claims.

Claims

1. A transmission encryption method based on large-scale antenna array technology, comprising the following steps: The sender determines the plaintext information m and estimates the channel state information (CSI) between the sender and receiver; When receiving the pilot sent by the receiving party, the sending party obtains a channel matrix according to the CSI and the received pilot signal ; The sender modulates the plaintext information m; The sender carries out SVD decomposition on the channel matrix to obtain a corresponding eigenvector matrix U and an eigenvalue matrix ; constructs a random matrix according to the channel matrix , and then takes K as a precoding matrix VK ; wherein W and V are conjugate transpose matrices of each other, and U are conjugate transpose matrices of each other; wherein the random matrix ; , , is an dimension unit matrix, if the corresponding diagonal element , then the diagonal element in is ; if the corresponding diagonal element , then the corresponding diagonal element in takes a value of ; Sender calculates matrix As a decoding matrix, the decoding matrix is ​​sent to the receiver; After receiving the decoding matrix, the receiver sends an acknowledgment signal to the sender. k ; The sender, based on the received confirmation signal k The channel estimation is performed again to obtain the channel matrix within the new correlation time. and the channel matrix SVD decomposition yields the eigenvector matrix. and will As a precoding matrix, the modulated plaintext information m is then precoded using the precoding matrix to obtain the signal. y And send it to the recipient; The receiver receives the signal. y Then, the result is obtained through decoding matrix calculation. and the signal Decoding yields the plaintext information m.

2. The method according to claim 1, characterized in that, The method by which the sender obtains the decoding matrix is ​​as follows: firstly, using the monomodulus matrix... right Eigenvalue calculation is performed to obtain eigenvalue matrix eigenvalue matrix Including real diagonal matrices and , The elements in are from The real part is composed of elements. Depend on The imaginary part is composed of elements; when When, take a random matrix K The former line and front Column construction matrix ,when When constructing a matrix Then calculate As the decoding matrix; where, The number of transmitting antennas of the sender. This represents the number of receiving antennas at the receiver.

3. The method according to claim 1 or 2, characterized in that, Signal = , The channel noise between the sender and receiver. The signal is the plaintext information m modulated by the signal.

4. The method according to claim 1 or 2, characterized in that, The sender uses M-QAM modulation to modulate the plaintext information m.

5. The method according to claim 1 or 2, characterized in that, The receiver calculates through the decoding matrix. .

6. A transmission encryption system based on large-scale antenna array technology, characterized in that, Including the sender and the receiver; The sender determines the plaintext information m and estimates the channel state information (CSI) between the sender and receiver; when it receives a pilot signal from the receiver, the sender obtains the channel matrix based on the CSI and the received pilot signal. ; The sender modulates the plaintext information m; and modulates the channel matrix. Perform SVD decomposition to obtain the corresponding eigenvector matrix. U and and eigenvalue matrix According to the channel matrix Constructing a random matrix K After that VK As a precoding matrix W ; Calculate the matrix As a decoding matrix, the decoding matrix is ​​sent to the receiver; and based on the received acknowledgment signal... k The channel estimation is performed again to obtain the channel matrix within the new correlation time. and the channel matrix SVD decomposition yields the eigenvector matrix. and will As a precoding matrix, the modulated plaintext information m is then precoded using the precoding matrix to obtain the signal. y And send it to the recipient; wherein V and Conjugate transposes of each other U and The random matrix is ​​a conjugate transpose of the random matrix. ; , for 1D identity matrix, if Corresponding diagonal elements ,but diagonal elements in ;if Corresponding diagonal elements ,but The corresponding diagonal element in the middle has the value of ; After receiving the decoding matrix, the receiver sends an acknowledgment signal to the sender. k ; and receiving the signal y Then, the result is obtained through decoding matrix calculation. and the signal Decoding yields the plaintext information m.

7. The system according to claim 6, characterized in that, The method by which the sender obtains the decoding matrix is ​​as follows: firstly, using a monomodulo matrix... right Eigenvalue calculation is performed to obtain eigenvalue matrix eigenvalue matrix Including real diagonal matrices and , The elements in are from The real part is composed of elements. Depend on The imaginary part is composed of elements; when When, take a random matrix K The former line and front Column construction matrix ,when When constructing a matrix Then calculate As the decoding matrix; where, The number of transmitting antennas of the sender. This represents the number of receiving antennas at the receiver.

8. The system according to claim 6 or 7, characterized in that, Signal = , The channel noise between the sender and receiver. The signal is the plaintext information m modulated by the signal.

9. The system according to claim 6 or 7, characterized in that, The sender modulates the plaintext information m using M-QAM modulation.

10. The system according to claim 6 or 7, characterized in that, The receiver calculates through the decoding matrix. .

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