A system configuration based interference alignment secure transmission method

Abstract

The application belongs to the technical field of wireless communication, and particularly relates to a system configuration-based interference alignment security transmission method; the method proposes an improved interference alignment simplified algorithm based on an improved interference alignment algorithm, determines to execute which algorithm through the system configuration antenna number, and simultaneously analyzes the feasibility of the algorithm; the application can ensure that the artificial noise and the inter-user interference are aligned at the legal receiving end, the obtained signal transmission and receiving scheme is more stable, and the system operation complexity is effectively reduced.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of wireless communication, and particularly relates to a system configuration-based interference alignment secure transmission method. BACKGROUND

[0002] Multi-user interference is a basic characteristic of wireless communication network, which is extremely unfavorable for secure communication. Therefore, interference management becomes a key problem of modern wireless communication. Through designing transmission and reception strategies, interference alignment (IA) can effectively solve the interference management problem in multi-user network. Interference alignment makes the interference overlap together at the receiving end through precoding technology, maximally compresses the interference signal into the interference subspace, and makes the signal space and the interference subspace orthogonal, so as to completely eliminate the influence of interference on the expected signal, improve the information transmission rate, and make the system obtain the maximum degree of freedom. In the document "A Distributed Numerical Approach to Interference Alignment and Applications to Wireless Interference Networks", the minimum leakage interference alignment (ILM) algorithm is proposed, which uses the reciprocity of the channel to iterate between the transmission matrix and the receiving matrix. In the document "Interference Alignment via Alternating Minimization", an alternating minimization (AM) interference alignment scheme is proposed for the IA problem of any number of antennas, users and spatial streams in the MIMO interference channel, which is a method of iterating the transmission matrix and the receiving subspace without explicitly assuming the reciprocity of the channel, so as to realize the alternating minimization.

[0003] In order to solve the IA problem, a sufficient number of antennas need to be equipped on the transceiver of each user, and the number of antennas required can be determined according to the feasibility condition of the IA problem. In the document "On Feasibility of Interference Alignment in MIMO Interference Networks", the feasibility problem is related to the solvability problem of the polynomial system, and it is proposed that the IA problem can be divided into proper or improper according to the number of equations and variables, and it is proved that the relationship between the feasibility and the properness of the system can be further strengthened.

[0004] In multi-user interference networks, adding artificial noise (AN) to the transmitted signal is a simple and effective method to achieve secure communication. On the basis of interference alignment, AN can eliminate interference while avoiding eavesdropping, further improving security performance. The literature《Anti-Eavesdropping Schemes for Interference Alignment (IA)-Based Wireless Networks》 introduces an ILM interference alignment scheme with AN, which aligns the interference from the legitimate user and the artificial noise at the target user end to achieve secure communication. The literature《An Artificial Noise-Based Security Scheme for Interference Alignment-Based Wireless Networks》 proposes a scheme based on IA and AN to achieve anti-eavesdropping, which aligns the artificial noise and interference from different transmitters in two different subspaces of the legitimate receiver, which can effectively confuse the eavesdropper while enhancing the desired signal.

[0005] However, the traditional interference alignment algorithm may have the risk of eliminating useful signals. The literature《A Distributed Numerical Approach to Interference Alignment and Applications to Wireless Interference Networks》 and《Interference Alignment as a Rank Constrained Rank Minimization》 both discuss this problem. Both of these two literatures use the minimum leakage interference alignment (ILM) algorithm, and both may lead to the elimination of useful signals. The signal elimination problem will seriously affect the effective performance of the interference alignment algorithm. In the patent《An Improved Interference Alignment Security Transmission Method for Avoiding Elimination of Useful Signals》, the signal elimination problem has been improved based on the ILM algorithm, and the maximum eigenmode beamforming transmission scheme is adopted. In addition, the minimum leakage interference alignment (ILM) algorithm uses the reciprocity of the two-way channel to achieve interference alignment through iteration, and in the iteration process, the transmit precoding matrix and the receive interference suppression matrix are obtained through eigenvalue decomposition, so the system has too high computational complexity. SUMMARY

[0006] To solve the above problems, the present application provides a system configuration-based interference alignment security transmission method, comprising the following steps:

[0007] S1. Constructing a wireless communication system, the sending end of the system comprising a secure sending end Alice and non-secure sending ends Txk, and the receiving end comprising a secure receiving end Bob, non-secure receiving ends Rxk and an eavesdropper Eve;

[0008] K represents the total number of non-secure sending ends and the total number of non-secure receiving ends;

[0009] S2. The secure sending end Alice sends a secure signal to the receiving end, and the non-secure sending end Txk sends a common signal to the receiving end;

[0010] S3. Judging whether the number of antennas of the wireless communication system satisfies a first condition; if yes, executing step S4, and if not, executing step S5;

[0011] S4. Processing the sending signal and the receiving signal by using a first interference alignment algorithm to obtain a sending scheme and a receiving scheme, and executing step S6;

[0012] S5. Processing the sending signal and the receiving signal by using a second interference alignment algorithm to obtain a sending scheme and a receiving scheme, and executing step S6;

[0013] S6. Performing secure signal transmission according to the sending scheme and the receiving scheme.

[0014] Further, in step S3, if the number of antennas of each non-secure sending end in the wireless communication system satisfies the first condition, step S4 is executed; the first condition is expressed as:

[0015]

[0016] wherein M k represents the number of antennas of the kth non-secure sending end Txk, d k represents the number of data streams of the kth non-secure sending end Txk.

[0017] Further, the process of step S4 of processing the sending signal and the receiving signal by using the first interference alignment algorithm is as follows:

[0018] S41. Selecting the right singular vector and the left singular vector corresponding to the maximum singular value of the main channel as the secure beamforming vector v a of the secure sending end Alice and the receiving vector u b of the secure receiving end Bob, respectively;

[0019] S42. Judging whether the number of antennas M a of the secure sending end Alice satisfies If yes, executing step S43, and if not, executing step S44;

[0020] S43. Based on the constraint matrix, the zero-forcing method is used to calculate the artificial noise precoding matrix W of the secure transmitter Alice a , the receiving matrix U of the non-secure receiver Rxk k , and the precoding matrix V of the non-secure transmitter Txk k ; then step S46 is performed;

[0021] S44. Determine whether the number of data streams d k of the non-secure transmitter Txk and the number of artificial noise data streams d an of the secure transmitter Alice satisfy the simplified algorithm constraint condition. If yes, step S45 is performed; if no, reduce the number of data streams d k or the number of artificial noise data streams d an , and return to step S44;

[0022] S45. Perform the improved interference alignment simplified algorithm and determine whether interference alignment is achieved. If yes, step S46 is performed; if no, reduce the number of data streams d k or the number of artificial noise data streams d an , and return to step S45;

[0023] S46. Output the artificial noise precoding matrix W of the secure transmitter Alice a , the receiving matrix U of the non-secure receiver Rxk k , the precoding matrix V of the non-secure transmitter Txk k , the secure beamforming vector v of the secure transmitter Alice a , and the receiving vector u of the secure receiver Bob b .

[0024] Further, the process of step S45 performing the improved interference alignment simplified algorithm includes:

[0025] S451. Initialize the receiving matrix U of the non-secure receiver Rxk k , and satisfy

[0026] S452. Calculate the interference covariance matrix of the secure transmitter Alice according to the receiving matrix U k and the receiving vector u of the secure receiver Bob b . Obtain the artificial noise precoding matrix W of the secure transmitter Alice through the interference covariance matrix . a ;

[0027] S453. Calculate the artificial noise precoding matrix W of the secure transmitter Alice according to the artificial noise precoding matrix Wa computing the interference covariance matrix Q of the non-secure receiver Rxk k by the interference covariance matrix Q k updating the receive matrix U of the non-secure receiver Rxk k ;

[0028] S454. computing the system interference leakage according to the receive vector u of the secure receiver Bob, the interference covariance matrix Q b , the interference covariance matrix Q k , the interference covariance matrix Q b and the receive matrix U k ;

[0029] S455. If the system interference leakage converges or exceeds the preset iteration number, ending the loop and executing step S46, otherwise returning to step S452.

[0030] Further, the formula for computing the system interference leakage is:

[0031]

[0032]

[0033] wherein I represents the system interference leakage, Tr[] represents the trace operation on a matrix, Q b represents the interference covariance matrix of the secure receiver Bob, P k represents the transmission power of the non-secure transmitter Txk, P a represents the transmission power of the secure transmitter Alice, H bj represents the channel between the non-secure transmitter Txj and the secure receiver Bob, d an represents the number of artificial noise data streams, H ba represents the channel between the secure transmitter Alice and the secure receiver Bob.

[0034] Further, the constraint matrix of step S43 is represented as:

[0035]

[0036] wherein X represents the interference matrix related to the artificial noise signal, Y represents the interference matrix related to the secure signal transmitted by the secure transmitter Alice, Z k represents the interference matrix related to the common signal transmitted by the non-secure transmitter Txk, represents the conjugate transpose of the receive vector u b of the secure receiver Bob, H ba represents the channel between the secure transmitter Alice and the secure receiver Bob, H bkThis represents the channel between the unsecured transmitter Txk and the secure receiver Bob;

[0037] The artificial noise precoding matrix W is calculated using the zero-forcing method. a Receiver matrix U k and precoding matrix V k :

[0038] Artificial noise precoding matrix W a The column vectors of null(X) are vectors in an orthonormal basis;

[0039] Let the precoding matrix V k The column vector is null(Z) k Vectors in a set of orthonormal bases;

[0040] Let the receiver matrix U k The column vector is Vectors in a set of orthonormal bases.

[0041] Furthermore, the simplified algorithm constraints described in step S44 include:

[0042]

[0043]

[0044] Where, N k This represents the number of antennas in the k-th unsecured receiver, Rxk.

[0045] Furthermore, step S5 involves processing the transmitted and received signals using the second interference alignment algorithm:

[0046] S51. Reduce the number of data streams d at the non-confidential sender Txk. k Or reduce the number of artificial noise data streams d at the secure transmitting end. an ;

[0047] S52. Execute the improved interference alignment algorithm;

[0048] S53. Determine if alignment is interfered with; if yes, proceed to step S54; otherwise, reduce the number of data streams by d. k Or reduce the number of artificial noise data streams d an and return to step S52;

[0049] S54. Output transmission and reception schemes.

[0050] The beneficial effects of this invention are:

[0051] The present application considers system configuration problems, and proposes a complete secure transmission process based on an improved interference alignment algorithm, so as to select a suitable transmission scheme according to the number of antennas of the system configuration. The artificial noise and inter-user interference are completely aligned at the legal receiving end, and the obtained signal transmission and reception scheme is more stable. The present application also simplifies the improved interference alignment algorithm, and the simplified algorithm can effectively reduce the computational complexity of interference alignment.

[0052] The present application considers the feasibility of the algorithm, and provides a feasibility judgment condition, which provides some reference for the setting of the interference alignment system configuration. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 The figure is a system configuration-based interference alignment secure transmission method block diagram of the present application;

[0054] Figure 2 The figure is a system configuration-based interference alignment secure transmission method block diagram of the present application;

[0055] Figure 3 The figure is a system configuration-based interference alignment secure transmission method block diagram of the present application;

[0056] Figure 4 The figure is a system configuration-based interference alignment secure transmission method block diagram of the present application;

[0057] Figure 5 The figure is a system configuration-based interference alignment secure transmission method block diagram of the present application;

[0058] Figure 6 The figure is a system configuration-based interference alignment secure transmission method block diagram of the present application;

[0059] Figure 7 The figure is a system configuration-based interference alignment secure transmission method block diagram of the present application;

[0060] Figure 8 The figure is a system configuration-based interference alignment secure transmission method block diagram of the present application; DETAILED DESCRIPTION

[0061] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0062] In the existing interference alignment transmission technology, the minimum leakage interference alignment (ILM) algorithm uses high complexity eigenvalue decomposition to obtain a precoding matrix Vk and receiving matrix U k , and iteration is carried out, so that the operation complexity of the system is too high. Actually, when the system configuration meets certain conditions, certain variables can not participate in iteration, so that the interference alignment algorithm can be simplified. Meanwhile, the ILM algorithm has the problem that the useful signal is eliminated, and in the patent 'Improved interference alignment secure transmission method for avoiding elimination of useful signal', the ILM algorithm is improved based on the ILM algorithm, but a clear determination condition for aligning interference for different system configurations is not given.

[0063] In view of the above problems, the present application provides an interference alignment secure transmission method based on system configuration, which is further simplified based on the improved interference alignment algorithm in the patent 'Improved interference alignment secure transmission method for avoiding elimination of useful signal', and an improved interference alignment simplified algorithm is provided, which only needs to obtain receiving matrix U k and artificial noise precoding matrix W a in the iteration process, so as to effectively reduce the operation complexity of the interference alignment. Secondly, the method provided by the present application also studies the feasibility of the improved interference alignment algorithm and the improved interference alignment simplified algorithm, and provides a complete interference alignment algorithm application process, which can ensure that the artificial noise and the interference between users are completely eliminated at the legal receiving end, and a better signal sending and transmission scheme is obtained.

[0064] In an embodiment, as shown in Figure 2 , in the presence of a passive eavesdropper Eve, a legal sender (secure sending end) Alice transmits secure information to a legal receiver (secure receiving end) Bob through artificial noise assisted secure beamforming. In addition, the multi-user interference wireless communication system also includes K pairs of legal transmitters-receivers that send common signals, which are also called K pairs of non-secure sending ends-non-secure receiving ends in the present application. It is assumed that Alice and Bob are respectively equipped with M a and N b antennas, K non-secure sending ends (Tx1, …, TxK) and non-secure receiving ends (Rx1, …, RxK) are respectively equipped with M k and N k antennas, the eavesdropper Eve is equipped with a single antenna. It is assumed that all legal channels meet the condition of being independent of each other in a quasi-flat fading environment, and the legal channels and the eavesdropping channels are subject to a circle symmetric complex Gaussian (CSCG) distribution with zero mean and unit variance. and respectively represent the channels between Alice and Bob, the non-secure receiving end Rxk and Eve. and denote the channel between non-secure transmitter Txkand Bob, non-secure receiver Rxjand Eve, respectively. In addition, the local channel state information (CSI) of the legitimate channel is known. Due to the passive nature of Eve, it is difficult for us to obtain the eavesdropping channel h e,a Therefore, we assume that only the statistical CSI of Eve is available. To achieve secure transmission from Alice to Bob, Alice transmits a secret signal and an artificial noise signal simultaneously.

[0065] Therefore, the signal transmitted by Alice can be expressed as:

[0066]

[0067] where P a is the transmission power of Alice, φ ∈ (0, 1] denotes the proportion of P a allocated to the secret signal. In addition, denotes the secret signal transmitted by Alice, denotes the secret beamforming vector. Similarly, denotes the d an -dimensional artificial noise vector (gaussian noise vector), denotes the artificial noise precoding matrix.

[0068] In addition, we assume that each of the K non-secure transmitters transmits a multi-data stream signal, and therefore the signal s k transmitted by non-secure transmitter Txkcan be expressed as:

[0069]

[0070] where and denote the signal vector transmitted by non-secure transmitter Txkand its corresponding precoding matrix, respectively, d k denotes the number of data streams transmitted by non-secure transmitter Txk, P k denotes the transmission power of non-secure transmitter Txk.

[0071] Therefore, the processed received signal of Bob, the received signal of non-secure receiver Rxk, and the received signal of Eve can be expressed as:

[0072]

[0073]

[0074]

[0075] wherein, represents the receive vector at Bob, represents the receive matrix of non-secret receiver Rxk. n e respectively represent the Additive Complex White Gaussian Noise (AWGN) vectors at Bob, receiver Rxk and Eve, obeying zero mean and unit variance.

[0076] Preferably, in the multi-user interference network with AN assistance, to achieve interference alignment, the following conditions need to be met simultaneously:

[0077]

[0078]

[0079]

[0080]

[0081]

[0082] wherein, (6)-(8) represent the cancellation of artificial noise and interference of other users at each legitimate receiver, and (9)-(10) represent the Rank Constraint Condition of IA.

[0083] Assuming all channels are generic channels (GC), when the precoding and receiving design of the signal is not associated with the direct link, it will not affect the dimension of the signal space. As can be seen from (6)-(8), the design of U k (V k ) is irrelevant to the direct link H kk , so condition (10) is almost certainly true. However, as can be seen from equation (6), the design of W a and u b needs to rely on the direct link H ba , so condition (9) is not necessarily true, resulting in the possibility of secret signals being cancelled. In summary, the traditional interference alignment algorithm may cause the secret signal to be cancelled, and the secret transmission loses its meaning. It should be particularly pointed out that the "traditional interference alignment algorithm" referred to in the present application specifically refers to the minimum leakage interference alignment (ILM) algorithm.

[0084] In order to avoid eliminating the secret signal, the ILM algorithm is improved to obtain an improved interference alignment algorithm, which optimizes the beamforming design of Alice and Bob, adopts a max-eigenmode beamforming scheme, and finally outputs a transmission scheme and a receiving scheme.

[0085] Specifically, the constraint conditions of (6)-(8) are defined as a constraint matrix, denoted as:

[0086]

[0087] wherein X is a matrix with a dimension of , Y is a matrix with a dimension of , and Z k is a matrix with a dimension of . It can be obtained from that Because Z k is a matrix with a dimension of , it satisfies Therefore, it can be obtained that wherein rank(Z k ) represents the rank of the matrix Z k , null(Z k ) represents the null space of Z k , and dim(null(Z k )) represents the dimension of the null space of Z k . Therefore, there must exist a matrix V k with non-zero column vectors that satisfies equation (8). However, because v a has been fixed, it is necessary to additionally design the receiving matrix U k of the non-secret receiving end Rxk to satisfy equation (7). In summary, for the improved interference alignment algorithm, under the condition of , only equations (6) and (7) need to be considered, so the improved interference alignment algorithm can be simplified.

[0088] In an embodiment, based on the above analysis, a system configuration-based interference alignment secure transmission method is proposed, as shown in Figure 1 , Figure 3 , which includes the following steps:

[0089] S1. Construct the wireless communication system described above, and group the secret receiving end Bob, the non-secret receiving end Rxk and the eavesdropper Eve into receiving ends;

[0090] S2. The secret sending end Alice sends a secret signal to the receiving end, and the non-secret sending end Txk sends a public signal to the receiving end;

[0091] S3. determining whether the number of antennas of the wireless communication system satisfies a first condition; if yes, performing step S4, and if no, performing step S5;

[0092] Specifically, if the number of antennas of each non-secure transmitter in the wireless communication system satisfies the first condition, step S4 is performed; the first condition is expressed as:

[0093]

[0094] wherein M k represents the number of antennas of the kth non-secure transmitter Txk, d k represents the number of data streams of the kth non-secure transmitter Txk.

[0095] S4. processing the transmitting signals and the receiving signals by using a first interference alignment algorithm to obtain a transmitting scheme and a receiving scheme, and performing step S6;

[0096] S5. processing the transmitting signals and the receiving signals by using a second interference alignment algorithm to obtain a transmitting scheme and a receiving scheme, and performing step S6;

[0097] S6. performing signal secure transmission according to the transmitting scheme and the receiving scheme.

[0098] Preferably, the process of step S4 of processing the transmitting signals and the receiving signals by using the first interference alignment algorithm comprises:

[0099] S41. selecting the right singular vector and the left singular vector corresponding to the maximum singular value of the main channel as the secure beamforming vector v a of the secure transmitter Alice and the receiving vector u b of the secure receiver Bob, respectively;

[0100] S42. determining whether the number of antennas M a of the secure transmitter Alice satisfies if yes, performing step S43, and if no, performing step S44;

[0101] S43. calculating the artificial noise precoding matrix W a of the secure transmitter Alice, the receiving matrix U k of the non-secure receiver Rxk, and the precoding matrix V k of the non-secure transmitter Txk by using the zero-forcing method based on the constraint matrix; and then performing step S46;

[0102] S44. determining whether the number of data streams d k of the non-secure transmitter Txk and the number of artificial noise data streams d anDoes the simplified algorithm constraint condition meet? If it does, proceed to step S45; otherwise, reduce the number of data streams d. k Or reduce the number of artificial noise data streams d an and return to step S44;

[0103] S45. Execute the improved interference alignment simplification algorithm and determine whether interference alignment occurs; if yes, proceed to step S46; otherwise, reduce the number of data streams d. k Or reduce the number of artificial noise data streams d an and return to step S45;

[0104] S46. Output the artificial noise precoding matrix W of the secure transmitter Alice. a The receiver matrix U of the unsecured receiver Rxk k (or Bob's receive vector u at the secure receiver) b ) and the precoding matrix V of the unconfidential transmitter Txk k (or the secure beamforming vector v of the secure transmitter Alice) a ).

[0105] Specifically, the zero-forcing method is used to calculate the artificial noise precoding matrix W. a Receiver matrix U k and precoding matrix V k :

[0106] Artificial noise precoding matrix W a The column vectors of null(X) are vectors in an orthonormal basis;

[0107] Let the precoding matrix V k The column vector is null(Z) k Vectors in a set of orthonormal bases;

[0108] Let the receiver matrix U k The column vector is Vectors in a set of orthonormal bases.

[0109] Specifically, such as Figure 5 As shown, step S45, which executes the improved interference alignment simplification algorithm, includes:

[0110] S451. Initialize the receiver matrix U of the unsecured receiver Rxk. k and satisfy

[0111] S452. According to the receiver matrix U k The receive vector u of Bob at the secure receiver b Calculate the interference covariance matrix of the secure transmitter Alice. By interfering with the covariance matrix Obtain the artificial noise precoding matrix W from the secure transmitter Alice. a The calculation formula is:

[0112]

[0113]

[0114] Among them, (W) a ) ★d W a The d-th column vector, Representation matrix The eigenvector corresponding to the d-th smallest eigenvalue.

[0115] S453. Based on the artificial noise precoding matrix W of the secure transmitter Alice. a Calculate the interference covariance matrix Q of the unsecured receiver Rxk. k By interfering with the covariance matrix Q k Update the receiver matrix U of the unsecured receiver Rxk k The calculation formula is:

[0116]

[0117] (U k ) ★d =x d [Q k ],d=1,...,d k

[0118] Among them, (U) k ) ★d For U k The d-th column vector, x d [Q k ] represents matrix Q k The eigenvector corresponding to the d-th smallest eigenvalue.

[0119] S454. Based on the receive vector u of the secure receiver Bob. b Interference covariance matrix Q k Interference covariance matrix Q b and receiver matrix U k Interference leakage in computing systems;

[0120] Specifically, the formula for calculating system interference leakage is:

[0121]

[0122]

[0123]

[0124] where I denotes the system interference leakage, Tr[] denotes the trace operation on a matrix, Q b denotes the interference covariance matrix of the non-secure receiver Rxk, P k denotes the transmit power of the non-secure transmitter Txk, P a denotes the transmit power of the secure transmitter Alice, H bj denotes the channel between the non-secure transmitter Txj and the secure receiver Bob, d an denotes the number of artificial noise streams, H ba denotes the channel between the secure transmitter Alice and the secure receiver Bob.

[0125] S455. If the system interference leakage converges or exceeds the preset number of iterations, the loop is ended and step S46 is executed, otherwise step S452 is returned.

[0126] Preferably, step S5 adopts a second interference alignment algorithm to process the sending signal and the receiving signal:

[0127] S51. Reducing the number of data streams d k of the non-secure transmitter Txk or reducing the number of artificial noise streams d an of the secure transmitter;

[0128] S52. Executing an improved interference alignment algorithm;

[0129] S53. Judging whether the interference alignment is performed; if yes, step S54 is executed, if not, reducing the number of data streams d k or reducing the number of artificial noise streams d an and returning to step S52;

[0130] S54. Outputting the artificial noise precoding matrix W a of the secure transmitter Alice, the receiving matrix U k (or the receiving vector u b ) of the non-secure receiver Rxk and the precoding matrix V k (or the secure beamforming vector v a ) of the non-secure transmitter Txk.

[0131] Specifically, as shown in Figure 4 , the process of step S52 executing the improved interference alignment algorithm includes:

[0132] S521. Initializing the artificial noise precoding matrix Wa The precoding matrix V of the unconfidential transmitter Txk k They respectively satisfy

[0133] S522. Select the main channel H respectively. ba The left and right singular vectors corresponding to the maximum singular value serve as the secure beamforming vector v for the secure transmitter Alice. a The receive vector u of Bob at the secure receiver b ;

[0134] S523. Based on the artificial noise precoding matrix W a and precoding matrix V k Calculate the interference covariance matrix Q of Bob at the secure receiver. b According to the artificial noise precoding matrix W a Precoding matrix V k and confidential beamforming vector v a Calculate the interference covariance matrix Q of the unsecured receiver Rxk. k ;

[0135] S524. Based on the interference covariance matrix Q of the unsecured receiver Rxk. k Calculate the receiver matrix U of the unsecured receiver Rxk. k ;

[0136] S525. Based on the receive vector u of the secure receiver Bob. b Interference covariance matrix Q k Interference covariance matrix Q b and receiver matrix U k Interference leakage in computing systems;

[0137] S526. Based on the receive vector u of the secure receiver Bob. b The receiver matrix U of the unconfidential receiver Rxk k Calculate the interference covariance matrix of the secure transmitter Alice and the unsecure transmitter Txk;

[0138] S527. If the system interference leakage converges or exceeds the iteration number threshold, output the artificial noise precoding matrix W of the secure transmitter Alice. a The receiver matrix U of the unsecured receiver Rxk k (or Bob's receive vector u at the secure receiver) b ) and the precoding matrix V of the unconfidential transmitter Txk k (or the secure beamforming vector v of the secure transmitter Alice) a Otherwise, return to step S523.

[0139] In IA-based multi-user interference networks, equations (6)-(8) can be solved only if both the transmitter and the receiver are equipped with sufficient number of antennas. The feasibility of the IA problem is equivalent to the solvability of non-zero solutions of a system of polynomial equations. A general system of polynomial equations can be solved only if the number of equations N E does not exceed the number of variables N V Therefore, a given IA system can be judged feasible or not by the relationship between the number of equations and the number of variables.

[0140] Thus, the total number of equations in equation (6) is:

[0141]

[0142] The total number of variables in equation (6) is:

[0143]

[0144] The total number of equations in equation (7) is:

[0145]

[0146] The total number of variables in equation (7) is:

[0147]

[0148] The total number of equations in equation (8) is:

[0149]

[0150] The total number of variables in equation (8) is:

[0151]

[0152] Preferably, the feasibility of the improved IA algorithm is equivalent to the solvability of the system of equations (6)-(8). If the improved IA algorithm is feasible, then the total number of variables of each subset of the system of equations (6)-(8) is greater than or equal to the total number of equations, thus there are the following three conditions:

[0153]

[0154]

[0155]

[0156] Equations (17)-(19) are called the feasibility conditions of the improved IA algorithm. When the number of data streams d k of the legitimate transmitter Txk and the number of data streams d anWhen conditions (17)-(19) are met, the improved interference alignment algorithm can be executed. If the feasibility conditions are not met, d can be appropriately reduced. k or d an Then determine whether the feasibility conditions are met.

[0157] Preferably, the feasibility of the improved interference alignment simplification algorithm is equivalent to the solvability of equations (6)-(7). If the improved interference alignment simplification algorithm is feasible, then the total number of variables in each subset of equations (6)-(7) must be greater than or equal to the total number of equations, thus there are two feasibility conditions in equations (17)-(18).

[0158] Specifically, the validity of equation (17) is equivalent to the validity of d. an The following constraints apply:

[0159]

[0160] Equation (12) holds true if and only if d k The following constraints apply:

[0161]

[0162] Therefore, when the number of data streams d of the legitimate transmitter Txk k The number of data streams d with artificial noise an When constraints (20) and (21) are met, the improved interference alignment simplification algorithm can be executed. If the constraints are not met, the number of data streams d of the legitimate transmitter Txk can be appropriately reduced. k The number of data streams d with artificial noise an Then determine whether the constraints are met.

[0163] However, under certain system configurations, even if the feasibility conditions are met, artificial noise and interference may not be perfectly aligned at the receiving end. In this case, residual interference will remain at each receiving end, affecting performance.

[0164] In one embodiment, experimental tests were conducted to verify the effectiveness of the method proposed in this invention. For example... Figure 6 The figure shows the relationship between the total system interference leakage and the number of iterations for the improved interference alignment simplification algorithm under different system configurations. Figure 6 In the meantime, when the total system interference leakage is less than 10 -10 This indicates that interference alignment is feasible. The system configuration is denoted as... It can be observed that the system configuration χ1 = (11×2,[1,6])(9×4,2) 4 and χ4=(10×2,[1,5])(9×4,2) 4The feasibility conditions of (17) - (18) are not satisfied, obviously the interference cannot be aligned, which means that the interference alignment is not feasible in this configuration. System configuration χ2= (11 x 2, [1, 5]) (9 x 4, 2) 4 χ3= (11 x 2, [1, 4]) (9 x 4, 2) 4 χ5= (10 x 2, [1, 4]) (9 x 4, 2) 4 and χ6= (10 x 2, [1, 3]) (9 x 4, 2) 4 All satisfy the feasibility conditions, but the system configuration

[0165] χ2= (11 x 2, [1, 5]) (9 x 4, 2) 4 and χ5= (10 x 2, [1, 4]) (9 x 4, 2) 4 The interference cannot be aligned, at this time, d k or d an should be reduced again and then the interference alignment algorithm is executed.

[0166] In an embodiment, the system is configured as:

[0167]

[0168] Figure 7 The relationship between the interference leakage of the system and the SINR of the confidential signal with the iteration number. In Figure 7 Figure (a), when the interference leakage is less than 10 -10 , it means that the interference alignment is feasible. In Figure (b), when the SINR of the confidential signal is less than 10 -10 , it means that the interference alignment causes the elimination of the confidential signal. From Figure (a), it can be seen that the interference leakage of the improved interference alignment algorithm and the traditional interference alignment algorithm can converge to a very small value with the increase of the iteration number, that is, both schemes can realize the interference alignment. However, from Figure (b), it can be seen that the signal-to-interference-and-noise ratio of the confidential signal in the traditional interference alignment algorithm gradually tends to 0 with the increase of the iteration number, which means that the scheme eliminates the confidential signal when realizing the interference alignment. The signal-to-interference-and-noise ratio of the improved interference alignment algorithm in this paper does not change with the increase of the iteration number, which can effectively preserve the confidential signal, and is therefore more stable and reliable.

[0169] Figure 8 The relationship between the interference leakage of the system and the iteration number. From Figure 8It can be seen that the interference leakage of the simplified algorithm of the improved interference alignment algorithm can still converge to a very small value with the increase of the iteration number, that is, the simplified algorithm of the improved interference alignment can still achieve interference alignment. In addition, it can be observed that the simplified algorithm proposed in this paper requires fewer iterations to achieve convergence compared with the corresponding original interference alignment algorithm, which also shows that the simplified algorithm has certain advantages.

[0170] Specifically, Table 1 shows the running time of the three algorithms. It can be seen that the simplified algorithm proposed in this paper has shorter running time compared with the corresponding original interference alignment algorithm, which also confirms that the simplified algorithm can reduce the computational complexity of the system.

[0171] Table 1 Running time of the three algorithms

[0172]

[0173] In the present application, unless otherwise explicitly specified and limited, the terms "mounting", "setting", "connecting", "fixing", "rotating" and the like should be understood in a broad sense, for example, can be fixedly connected, can also be detachably connected, or integrated; can be mechanically connected, can also be electrically connected; can be directly connected, can also be indirectly connected through an intermediate medium, can be the internal communication of two elements or the interaction relationship between two elements, unless otherwise explicitly limited, the above-mentioned terms in the present application can be understood according to the specific meaning of the above-mentioned terms in the present application by those skilled in the art.

[0174] Although the embodiments of the present application have been shown and described, those skilled in the art can understand that various changes, modifications, replacements and variations can be made to the embodiments without departing from the principles and spirits of the present application, and the scope of the present application is defined by the appended claims and their equivalents.

Claims

1. A method for secure transmission with interference alignment based on system configuration, characterized in that, Includes the following steps: S1. Construct a wireless communication system, wherein the transmitting end of the system includes a secure transmitting end Alice and a non-secure transmitting end Txk, and the receiving end includes a secure receiving end Bob, a non-secure receiving end Rxk, and an eavesdropper Eve; K represents both the total number of unconfidential senders and the total number of unconfidential receivers. S2. The confidential transmitter Alice sends a confidential signal to the receiver, while the non-confidential transmitter Txk sends a common signal to the receiver; S3. Determine whether the number of antennas in the wireless communication system meets the first condition; if it does, proceed to step S4; if it does not, proceed to step S5. The first condition is expressed as: Among them, M k d represents the number of antennas in the k-th unsecured transmitter Txk. k This represents the number of data streams from the k-th unconfidential sender, Txk. S4. The first interference alignment algorithm is used to process the transmitted and received signals to obtain the transmission scheme and the reception scheme. Then, step S6 is executed. Step S4 is the process of processing the transmitted and received signals using the first interference alignment algorithm: S41. Select the right singular vector and left singular vector corresponding to the maximum singular value of the main channel as the secure beamforming vector v of the secure transmitter Alice. a The receive vector u of Bob at the secure receiver b ; S42. Determine the number of antennas M of the secure transmitter Alice. a Does it meet the requirements? If satisfied, proceed to step S43; otherwise, proceed to step S44. S43. Based on the constraint matrix, the zero-forcing method is used to calculate the artificial noise precoding matrix W of the secure transmitter Alice. a The receiver matrix U of the unsecured receiver Rxk k The precoding matrix V of the unconfidential sender Txk k Then proceed to step S46; S44. Determine the number d of data streams from the non-confidential sender Txk. k The number of artificial noise data streams d from the secure transmitter Alice an Does the simplified algorithm constraint condition meet? If it does, proceed to step S45; otherwise, reduce the number of data streams d. k Or reduce the number of artificial noise data streams d an and return to step S44; S45. Execute the improved interference alignment simplification algorithm and determine whether interference alignment occurs; if yes, proceed to step S46; otherwise, reduce the number of data streams d. k Or reduce the number of artificial noise data streams d an and return to step S45; S46. Output the artificial noise precoding matrix W of the secure transmitter Alice. a The receiver matrix U of the unsecured receiver Rxk k The precoding matrix V of the unconfidential transmitter Txk k The secure beamforming vector v of the secure transmitter Alice a The receive vector u of Bob at the secure receiver b ; S5. The second interference alignment algorithm is used to process the transmitted and received signals to obtain the transmission scheme and the reception scheme. Then, step S6 is executed. Step S5 involves processing the transmitted and received signals using the second interference alignment algorithm: S51. Reduce the number of data streams d at the non-confidential sender Txk. k Or reduce the number of artificial noise data streams d at the secure transmitting end. an ; S52. Execute the improved interference alignment algorithm; S53. Determine if alignment is interfered with; if yes, proceed to step S54; otherwise, reduce the number of data streams by d. k Or reduce the number of artificial noise data streams d an and return to step S52; S54. Output transmission and reception schemes; S6. Ensure secure signal transmission according to the transmission and reception schemes.

2. The interference-aligned secure transmission method based on system configuration according to claim 1, characterized in that, In step S3, if the number of antennas of each non-secret transmitter in the wireless communication system satisfies the first condition, then step S4 is executed.

3. The interference-aligned secure transmission method based on system configuration according to claim 1, characterized in that, Step S45, which involves executing the improved interference alignment simplification algorithm, includes: S451. Initialize the receiver matrix U of the unsecured receiver Rxk. k and satisfy S452. According to the receiver matrix U k The receive vector u of Bob at the secure receiver b Calculate the interference covariance matrix of the secure transmitter Alice. By interfering with the covariance matrix Obtain the artificial noise precoding matrix W from the secure transmitter Alice. a ; S453. Based on the artificial noise precoding matrix W of the secure transmitter Alice. a Calculate the interference covariance matrix Q of the unsecured receiver Rxk. k By interfering with the covariance matrix Q k Update the receiver matrix U of the unsecured receiver Rxk k ; S454. Based on the receive vector u of the secure receiver Bob. b Interference covariance matrix Q k and receiver matrix U k Interference leakage in computing systems; S455. If the system interference leakage converges or exceeds the preset number of iterations, the loop ends and step S46 is executed; otherwise, return to step S452.

4. The interference-aligned secure transmission method based on system configuration according to claim 3, characterized in that, The formula for calculating system interference leakage is: Where I represents system interference leakage, Tr[] represents the trace operation on the matrix, and Q b Let P represent the interference covariance matrix of Bob at the secure receiver. k P represents the transmit power of the unsecured transmitter Txk. a H represents the transmit power of the secure transmitter Alice. bj d represents the channel between the unsecured transmitter Txj and the secure receiver Bob. an H represents the number of artificial noise data streams. ba This represents the channel between the secure sender Alice and the secure receiver Bob.

5. The interference-aligned secure transmission method based on system configuration according to claim 1, characterized in that, The constraint matrix of step S43 is expressed as follows: Where X represents the interference matrix related to the artificial noise signal, Y represents the interference matrix related to the secure signal transmitted by the secure transmitter Alice, and Z represents the interference matrix related to the secure signal transmitted by Alice. k This represents the interference matrix related to the common signal transmitted by the unsecured transmitter Txk. The receive vector u represents Bob's secure receiver. b The conjugate transpose of H ba H represents the channel between the secure transmitter Alice and the secure receiver Bob. bk This represents the channel between the unsecured transmitter Txk and the secure receiver Bob; The artificial noise precoding matrix W is calculated using the zero-forcing method. a Receiver matrix U k and precoding matrix V k : Artificial noise precoding matrix W a The column vectors of null(X) are vectors in an orthonormal basis; Let the precoding matrix V k The column vector is null(Z) k Vectors in a set of orthonormal bases; Let the receiver matrix U k The column vector is Vectors in a set of orthonormal bases.

6. The interference-aligned secure transmission method based on system configuration according to claim 1, characterized in that, The simplified algorithm constraints described in step S44 include: Where, N k This represents the number of antennas in the k-th unsecured receiver, Rxk.

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