CN114337749B - Cooperative MIMO (multiple input multiple output) safety precoding method for spectrum sensing network - Google Patents
Cooperative MIMO (multiple input multiple output) safety precoding method for spectrum sensing network Download PDFInfo
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Abstract
The invention discloses a cooperative MIMO (multiple input multiple output) safety precoding method for a spectrum sensing network, belonging to the technical field of wireless communication physical layer safety. Aiming at the interference control and bottom physical layer safety problems existing in a CRN (China railway network) and the practical requirement that an ideal eavesdropping channel CSI (channel state information) is difficult to obtain in a practical scene, a cooperative MIMO (multiple input multiple output) safety precoding design method facing a spectrum sensing network is adopted, and the method comprises safety precoding based on the secondary user channel characteristics, safety precoding based on the main user channel null space, distributed transmitting node selection, artificial noise-assisted safety precoding scheme selection and differential convex programming problem solving by using an iterative outlier approximation method, so that the safety rate of the CRN secondary network is maximized while the interference power of a main user is controlled. The invention can be used in the fields of intelligent manufacturing, logistics, warehousing and the like, and realizes the balance of safety rate and interference control in the spectrum sensing network.
Description
Technical Field
The invention relates to a cooperative MIMO (multiple input multiple output) safety precoding method for a spectrum sensing network, belonging to the technical field of wireless communication physical layer safety.
Background
Due to the advantages of high spectrum utilization rate, low deployment cost and the like, a Cognitive Radio Network (CRN) is considered as an important deployment form of the future Industrial Internet of Things (IIoT). Based on the form, the unauthorized user can transmit own confidential information by utilizing the exclusive spectrum of the authorized user when the master user is idle, thereby realizing the improvement of the whole spectrum efficiency of the network. Especially in IIoT scenarios, for example, inside an intelligent manufacturing shop of a factory, a large number of sensors with radio frequency sensing function communicate with each other, and at the same time, a broadband data link also exists between them and a data acquisition site outside the factory. Because the space scope is limited in the factory, information security can be basically realized through means such as physical isolation, but potential eavesdropping nodes distributed discretely in the periphery of the factory threaten the security uploading of encrypted information greatly, and especially when an eavesdropper is in a hidden eavesdropping state, the security production is threatened greatly. Therefore, information security and interference management become two major issues that need to be solved in the above scenario.
The physical layer security technology can effectively improve the security rate of the spectrum sensing network, when the channel condition of a legal user is worse than that of an eavesdropping user, the scheme of artificial Noise injection can greatly reduce the Signal-to-Interference plus Noise Ratio (SINR) of the eavesdropping node, even if the eavesdropping device has strong enough decryption capability, the security interruption probability can be eliminated, and enough security rate redundancy is provided. However, in the underlying CRN network, the secondary user occupies the authorized spectrum of the primary user to perform communication, which inevitably causes interference to the normal communication of the primary user. Some existing works propose some solutions to the problem, l.sibomana sets an interruption probability lower limit for communication of a master user, t.hu proposes a more direct interference power constraint upper limit, f.zhu simultaneously limits the lowest received SINR of the master user and the highest SINR of an eavesdropper, and the above measures can ensure that a basic communication link of the master user is not affected, but have a certain safe interruption probability, and most assume that channel prior information of a malicious eavesdropper user is known, which is obviously difficult to implement in a real eavesdropping scene. Meanwhile, the multiple antennas play an important role in expanding the spatial freedom of the safety signals and improving the safety capacity of the system, Y.Pei researches a closed expression of the safety capacity of the MISOSE channel under the condition of assuming known ideal CSI, and an optimal signal covariance matrix is obtained by solving an optimization problem; similarly, assuming that the transmitting end knows ideal CSI, b.fang deduces the safe capacity under the mimo me channel, and the scheme of null-space artificial noise injection in the main channel improves the safe transmission performance of the system, but the null-space channel transmission scheme is limited by the relationship of the transmitting and receiving antennas and is difficult to be generalized to a more general situation.
Although the research of the safe transmission technology can control the interference level to the primary user, the safe rate of the secondary network system is improved or the interruption probability is reduced; however, it is assumed that the transmitting end knows the Channel States Information (CSI) of the overheard link or that the overhearr is "ubiquitous", and the ideal CSI of the overhearr is often difficult to obtain in a real-world scenario. Therefore, the problem of confidentiality optimization more in accordance with the actual industrial internet of things scene is not effectively solved, a large optimization space still exists under the condition that the channel condition of an eavesdropper is unknown or only offline statistical channel information is known, and meanwhile, how to design a scheme to better realize the balance between the security rate and the interference suppression of a master user is a problem to be solved urgently.
Disclosure of Invention
Aiming at the problem of safety performance optimization of an actual industrial Internet of things scene, the invention mainly aims to provide a cooperative MIMO safety precoding method facing a spectrum sensing network, which aims to thoroughly eliminate the safety interruption probability of a secondary network under the condition of ensuring that the interference power aiming at a main user in the spectrum sensing network meets certain upper limit constraint, and improves the safety transmission rate of the secondary network by combining an artificial noise injection method.
The purpose of the invention is realized by the following technical scheme:
the invention provides a spectrum sensing network-oriented collaborative MIMO secure precoding method aiming at the interference control and bottom physical layer security problems existing in a CRN network and the practical requirement that ideal eavesdropping channel CSI is difficult to obtain in a practical scene, and the method comprises the steps of secure precoding based on secondary user channel characteristics, secure precoding based on main user channel null space, distributed transmitting node selection, artificial noise-assisted secure precoding scheme selection, and differential convex programming problem solving by using an iterative outlier approximation method, so that the safe rate of the CRN secondary network is maximized while the interference power of the main user is controlled.
The invention discloses a cooperative MIMO secure precoding method facing a spectrum sensing network, which comprises the following steps:
initializing system configuration such as the number, distribution and user number of initialization antennas, the number of eavesdropping nodes, transmitting power and the like of the bottom CRN system;
the number of distributed transmitting antenna nodes Alice is recorded as K; the number of PU antennae of the master user is recorded as N P A plurality of; the number of the secondary user Bob antennae is marked as N B A plurality of; l eavesdropping users Eve, and the number of each antenna is recorded as N E A plurality of; the center of the distributed transmitting node is marked as O, and the distance from the distributed transmitting node to the main user is marked as p 0 And the distance to the secondary user is denoted b 0 The minimum distance to all eavesdropping nodes is denoted as e 0 (ii) a The range radius of the distributed antenna is recorded as r; the total power ceiling of the distributed transmitting nodes is denoted as Γ T (ii) a The upper limit of the interference power which can be tolerated by the primary user PU is recorded as gamma I 。
Secondly, designing a safety pre-coding scheme by utilizing the main channel characteristics of the secondary users and combining artificial noise injection, and showing that the safety rate optimization problem of the system is specifically as follows:
step 2.1: designing a sending signal into a form of weighted addition of secret information and artificial noise; namely:
wherein, the secret signal s and the artificial noise a with normalized power respectively obey a complex Gaussian Independent Identity Distribution (GIID) with a mean value of 0 and a covariance matrix of a unit matrix; power allocation matrix Ψ for a secure signal s Power allocation matrix psi with artificial noise a Expressed as a non-negative diagonal matrix, is a variable to be optimized; the kth diagonal element on the diagonal represents correspondencesTransmitting a kth symbol of a signal; the precoding matrices for the secret signal and the artificial noise are respectively V s And V a And mapping the mixed signal to be transmitted to a transmitting antenna.
Step 2.2: designing a precoding matrix in the step 2.1 according to the main channel characteristics of the secondary user;
SVD decomposition is carried out on the secondary user main channel matrix in the CRN network, and a singular matrix V is taken out H As a precoding matrix for the security signal and the artificial noise. Compared with the situation that the precoding matrix adopts the channel orthogonal matrix in the artificial noise injection scheme based on the channel null space, the precoding scheme has generality and is not limited by the number of the antennas at the transmitting and receiving ends.
Step 2.3: and (3) according to the MIMO channel capacity expression and the precoding matrix designed in the step 2.2, representing the information rate of the legal secondary user, the maximum information rate of the eavesdropping node and the worst safety rate of the system. Namely: worst security rate = information rate of secondary user Bob-maximum value of information rate of multiple eavesdropping users Eve, which corresponds to the worst-case security rate of the system, i.e. the lower limit of the security rate.
According to the Gaussian MIMO channel capacity expression, calculating the effective information rates of the secondary user Bob and the eavesdropping node Eve under the condition of artificial noise injection, namely:
wherein H in the upper right brackets indicates the adoption of V H A precoding scheme.
Step 2.4: setting total emission power constraint that total power of artificial noise and secret information is less than or equal to preset threshold gamma T 。
Step 2.5: setting interference power constraint aiming at the primary user PU, namely setting the power of the total power reaching the receiving end of the primary user PU to be less than or equal to a preset threshold value gamma I 。
Step 2.6: according to step 2.2 based on the secondary user BobMain channel eigenvector V H Precoding 2.4, and step 2.5, designing an optimization problem of maximizing the worst secret rate of the system under the constraint of the total transmission power of the system and the constraint of interference suppression.
Step three, similar to step two, designing a safety precoding scheme by utilizing a channel null space of a primary user PU and combining an artificial noise injection scheme, and expressing a safety rate optimization problem, specifically:
step 3.1: designing a sending signal into a form of weighted addition of secret information and artificial noise;
wherein, the secret signal s and the artificial noise a with normalized power respectively obey a complex Gaussian independent equal Distribution (GIID) with a mean value of 0 and a covariance matrix as a unit matrix; power allocation matrix psi for secret signals s Power allocation matrix psi with artificial noise a Expressed as a non-negative diagonal matrix, is a variable to be optimized; the kth diagonal element on the diagonal represents the kth symbol of the corresponding transmitted signal; the precoding matrices for the secret signal and the artificial noise are respectively V s And V a And mapping the mixed signal to be transmitted to a transmitting antenna.
Step 3.2: designing a precoding matrix in the step 3.1 according to a channel orthogonal null space of a main user PU;
taking orthogonal matrix V of primary user PU channel matrix G As precoding matrices for artifacts and security signals, i.e. GV G =0; the requirement here is that the number of Alice transmitting antennas is greater than the number of primary user PU receiving antennas;
step 3.3: and (3) according to the MIMO channel capacity expression and the precoding matrix designed in the step (3.2), representing the information rate of the legal secondary user, the maximum information rate of the eavesdropping node and the worst safety rate of the system. Namely: worst security rate = information rate of secondary user Bob-maximum value of information rate of multiple eavesdropping users Eve, which corresponds to the worst-case security rate of the system, i.e. the lower limit of the security rate.
According to the Gaussian MIMO channel capacity expression, calculating the effective information rates of the secondary user Bob and the eavesdropping node Eve under the condition of artificial noise injection, namely:
wherein G in parentheses in the upper right corner represents the adoption of V G A precoding scheme.
Step 3.4: setting a total transmission power constraint that the total power of the artificial noise and the secret information is less than or equal to a preset threshold value gamma T 。
Step 3.5: according to the primary channel eigenvector V based on the secondary user Bob in step 3.2 G And precoding 3.4, and designing an optimization problem of the worst secret keeping rate of the maximized system under the constraint of the total transmission power of the system.
Step four: according to the non-convex secret rate optimization problem designed in the second step and the third step, the problem of maximizing the safety rate is converted into a differential convex programming problem of minimizing the auxiliary variable t through a series of equation replacement and approximation;
step 4.1: calculating the approximate traversal safety capacity of the system under a plurality of position-limited eavesdropping nodes;
the traversal safety rate is expressed by a diagonal matrix X, wherein a Haar random matrix phi is used and combined with a Jensen inequality to replace an original channel right singular matrix V x ；
Wherein phi is a random unitary matrix, and elements therein are all randomly obtained by Haar measurement; this safe capacity requires simultaneous calculation expectations for W and Φ;
step 4.2: because the optimization problems in the second step and the third step are in a subtraction form of two non-convex optimization problems, the finally obtained optimization target expression is still a non-convex function. And replacing the safe speed optimization target expression in the second step and the safe speed optimization target expression in the third step by using the approximate traversal safe speed expression in the step 4.1 to obtain an optimized target after approximate replacement.
Step 4.3: and rewriting the maximum interception speed expression in the optimized target expression in the 4.2 into the total interception speed of all the interception nodes, namely the interception speed of other nodes except the optimal interception node i.
Step 4.4: since the first term of the expression in step 4.3 has no relation to i, the first term is taken out of the summation term, resulting in the reintegrated expression.
Wherein, the integrated expression is expressed in a subtraction form of two parts; the first part is q (x) (Ψ s ,Ψ a ) It means that the sum of the total eavesdropping rate and the rate of invalid information of the secondary users in the total power representation is inverted; the second part is p (x) (Ψ s ,Ψ a ) Adding the information rate of the secondary user under the total power to the invalid eavesdropping rate of the eavesdropping node i and the total eavesdropping rate of other nodes except the eavesdropping node i under the total power, acquiring a reverse number, and finally acquiring the maximum value of the calculation result after traversing all the eavesdropping nodes i;
step 4.5: since the maximum and finite number summation is a convex problem, the problem p in step 4.4 (x) (. Cndot.) and q (x) (. Is) convex, reintegrating the above expression by introducing auxiliary variables t and s;
where t ≦ 0 and s is a real number.
Step 4.6: rewriting the inequality into two new inequality constraints, namely;
(1) s and p (x) (Ψ s ,Ψ a ) The sum is less than or equal to 0;
(2) t and s, q (x) The sum of (c) is equal to or greater than 0;
step 4.7: the problem of maximizing the worst safe rate in the step 4.2 can be converted into the problem of minimizing the auxiliary variable t, and the problem is equivalent to the classical differential convex programming problem by combining two inequality constraints in the step 4.6, namely the auxiliary variable t is minimized under the condition of meeting the inequality constraint, the total transmission power constraint and the interference power constraint;
similarly, when a primary user-based PU channel null space feature vector is adopted, the safety rate optimization problem can be rewritten into a similar differential convex programming problem;
step five, solving the differential convex programming problem in the step four by adopting an iterative outlier approximation method, which specifically comprises the following steps:
step 5.1: finding boundary points by adopting an inner point interpolation method and an outer point interpolation method, namely initializing a feasible solution
Step 5.2: initializing according to step 5.1, starting iterative solution until convergence, and outputting w = { Ψ = { (Ψ) } a ,Ψ s S, t }; wherein epsilon represents the introduced relaxation factor, and when epsilon =0, the iterative optimization algorithm can obtain a global optimal solution.
And step six, calculating the worst safety capacity of the system according to the number and the distribution of the set nodes of the distributed MIMO under the condition of only considering large-scale fading, comparing the worst safety capacity with a preset safety lower limit, and selecting a distributed structure at least meeting the safety lower limit. And calculating an Interference to Noise Ratio (INR) of the PU of the main user, comparing the INR with a preset value, selecting a proper safe precoding scheme, feeding the scheme back to a sending end, periodically iterating the process, and adjusting the sending end precoding scheme in real time according to the INR change of the main user.
Step 6.1: the quantity and the distribution of a group of distributed nodes are random, and the safe rate R of the water injection method is calculated by adopting water injection power distribution under the condition of only considering large-scale fading s (Ψ water )；
Step 6.2: taking water injection method safe speed R s (Ψ water ) Same target safety rate gamma x R s ' ec Comparing if it is greater than gamma × R s ' ec If so, selecting the distributed node parameters and continuing to perform the next precoding scheme selection operation; otherwise, repeating the step 6.1 until the distributed nodes meeting the conditions are found, and stopping iteration;
step 6.3: according to the off-line test results of the precoding schemes in the second step and the third step, selecting the precoding scheme and the INR threshold eta corresponding to the optimal safe rate, namely when the INR is less than or equal to the eta, under the same INR constraint, the safe rate which can be provided by adopting the precoding scheme in the third step is superior to that in the second step, and vice versa, so that the eta is used as the decision threshold for selecting the precoding scheme;
step 6.4: determining the judgment INR at the position of the main user PU as eta according to the step 6.3, and calculating the ratio of the actual interference power and the noise power at the receiving end of the main user PU, namely the actual INR;
step 6.5: judging the actual INR and a preset INR value eta, and feeding back a judgment result to a sending end for executing the transmission of the next time slot;
step 6.6: at the transmitting end, when INR is greater than eta, the precoding scheme in the step two is executed, and a precoding matrix V is adopted s ＝V a ＝V H And solving the V adopted in the step 4.7 according to the power distribution algorithm of the step five H A differential convex programming problem from precoding equivalent transformation; when INR is less than or equal to eta, executing the precoding scheme in the step three, and adopting a precoding matrix V s ＝V a ＝V G Likewise, V is adopted in the step 4.7 according to the power distribution algorithm of the step five G Precoding the differential convex programming problem of the equivalent transformation.
Has the beneficial effects that:
compared with the prior art, the cooperative MIMO secure precoding method for the spectrum sensing network has the following beneficial effects:
1. the method adopts a safety pre-coding design method based on artificial noise and main channel characteristics, can effectively improve the safety rate of a bottom CRN network under the condition of meeting the control of the minimum interference power aiming at a main user, eliminates the safety interruption probability, and can realize safety transmission under any receiving and transmitting antenna relationship.
2. The safe precoding design method based on the PU channel null space of the main user can completely eliminate the interference aiming at the main user, and effectively improve the safe transmission rate of the bottom CRN network on the premise that the interference power of the main user is 0.
Drawings
FIG. 1 is a schematic diagram of a cooperative MIMO secure precoding method and an embodiment of the invention based on artificial noise, transmission node selection and channel characteristic selection for spectrum sensing network oriented secure precoding;
FIG. 2 is a schematic diagram of an outlier approximation iterative optimization algorithm in the cooperative MIMO secure precoding method and the embodiment of the invention for the spectrum sensing network;
fig. 3 is a graph of performance of change of a safe rate Cumulative Distribution Function (CDF) along with an eavesdropping Distribution range after implementing a precoding scheme based on artificial noise and secondary user channel characteristics under different eavesdropping ranges in the cooperative MIMO secure precoding method and embodiment of the invention facing a spectrum sensing network;
FIG. 4 is a graph showing performance of a safe rate CDF after an artificial noise and secondary user channel characteristic precoding scheme changes with a distribution range of distributed transmitting nodes in different distribution ranges in the spectrum-aware-network-oriented collaborative MIMO secure precoding method and embodiment of the present invention;
fig. 5 is a graph of average safe rates of two precoding schemes with different channel characteristics implemented under the constraint of different main user interference in the cooperative MIMO safe precoding method and embodiment of the invention for the spectrum sensing network.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples. The technical problems and the advantages solved by the technical solutions of the present invention are also described, and it should be noted that the described embodiments are only intended to facilitate the understanding of the present invention, and do not have any limiting effect.
The embodiment details steps of the cooperative MIMO secure precoding method for a spectrum sensing network of the present invention when implemented specifically in different distributed transmission node cooperative ranges and different eavesdropping ranges.
In this embodiment, the spectrum sensing network is considered to be deployed in an industrial park, and the distributed transmitting antenna nodes Alice are distributed around the center of an O with radius r =1 meter, 3 meters, 5 metersSelecting the proper positions and the proper number of distributed nodes Alice in a circle of a meter through a node activation algorithm; alice uploads confidential data to data acquisition equipment (master user PU) outside a factory, and the number of equipped antennas is N P =2, the fixed distance between the collecting device and the circle center O is p 0 =10 meters; meanwhile, secondary users Bob which access in a competitive mode under the condition of existence of unauthorized frequency bands exist in the factory building, and the number of the equipped antennas is N B =2, fixed distance from center O
Rice; meanwhile, 10 single-antenna hidden eavesdropping nodes are arranged on the periphery of the factory building to prepare for intercepting confidential data at any time. Since it can only be guaranteed that there is no eavesdropping threat in a certain range near the factory, the location of the eavesdropping node can approach the minimum eavesdropping range infinitely, and the eavesdropping range is set as e in this embodiment 0 In three ranges of 6 meters, 8 meters and 10 meters, 10 eavesdroppers are all distributed in a manner of taking the center of the distributed transmitting node as the center of a circle, e, to ensure the optimal eavesdropping 0 Is a circle with a radius, and the spacing distance is random; the upper limit of the total power of the distributed transmitting nodes is set to be gamma T =30dBm. Under the scene, the problems of determining the deployment range of the distributed antenna, allocating power of confidential information and artificial noise, selecting a precoding scheme and the like need to be solved, and for this purpose, a cooperative MIMO secure precoding method facing a spectrum sensing network is adopted to improve the security performance of a secondary transmission network, eliminate the probability of security interruption, eliminate the influence of interference on main user equipment to the maximum extent, and solve the problems of power allocation, precoding scheme selection and the like;
fig. 1 shows a detailed process of precoding scheme design and selection based on the characteristics of the primary user channel null space and the secondary user channel in combination with artificial noise, specifically to this embodiment, the method has the following operation flow:
step one, setting system configurations such as the number of antennas and users of the bottom CRN system, the number of eavesdropping nodes, the transmitting power and the like;
the number of the initialized distributed transmitting nodes Alice is K =4; master user PThe number of U antennas is N P =2; the number of antennae of the secondary user Bob is N B =2;10 eavesdropping users Eve, each antenna number is N E =2; the center of the distributed transmitting node is marked as O, and the distance from the distributed transmitting node to the main user is marked as O
Distance to secondary user b 0 =10m, minimum distance e to all eavesdropping nodes 0 =6,8,10 m; the range radius of the distributed antenna is r =1,3,5 meters; the total power of the distributed transmitting nodes is limited to gamma T =30dBm; the upper limit of the interference power which can be tolerated by the primary user PU is recorded as gamma I ＝-15～-5dBm。
Secondly, designing a safety pre-coding scheme by utilizing the main channel characteristics of the secondary users and combining artificial noise injection, and showing that the safety rate optimization problem of the system is specifically as follows:
step 2.1: designing a sending signal into a form of weighted addition of secret information and artificial noise;
wherein the content of the first and second substances,
and
secret signal and artificial noise vectors respectively representing lengths corresponding to the number of transmitting antennas, non-negative diagonal matrix psi x The power distribution vector of the secret signals and the artificial noise is represented by ≧ 0,x ∈ { s, a }, which is a variable to be optimized, and the kth diagonal element ψ x,k More than or equal to 0 represents the k symbol of the corresponding transmission signal; at the same time, it is necessary to satisfy 0 ≦ tr (Ψ) s +Ψ a )≤Γ T ，Γ T An upper limit representing the total transmitted power of the security signal and the artificial noise; at the same time, V s And V a Representing precoding matrices for secret signals and artificial noise, respectively, of a hybrid signal to be transmittedThe signal is mapped onto the transmit antenna.
Step 2.2: designing a precoding matrix in the step 2.1 according to the main channel characteristics of the secondary user;
firstly, performing SVD on a secondary user main channel matrix in the CRN network, namely:
let V s ＝V a ＝V H In which V is H Is represented by the right singular vector of the secondary user primary channel H. Artificial noise injection scheme to null space
In the case of (2), the precoding scheme is more general and cannot be restricted by the number of antennas at the transmitting and receiving ends.
Step 2.3: and (3) calculating the information rate of the legal secondary user, the maximum information rate of the eavesdropping node and the approximate traversal security rate according to the pre-coding matrix designed in the step 2.2.
A pair of fixed power distribution coefficients { Ψ } s ,Ψ a Next, the worst secret rate of the system is calculated as follows:
wherein, the first and the second end of the pipe are connected with each other,
representing a safety rate corresponding to precoding designed based on a secondary user main channel characteristic vector;
indicating the information rate at the secondary user;
indicating potential eavesdropping at node iThe information rate of (d); max 1≤i≤L {. Cndot.) denotes that the eavesdropping rate for the best eavesdropping location is calculated and thus corresponds to the worst-case security rate of the system, i.e., the lower bound of the security rate.
And calculating the information rates of the secondary user Bob and the eavesdropping node Eve according to the Gaussian MIMO channel capacity expression:
wherein the content of the first and second substances,
denotes a semi-positive definite Hermitian matrix, here
And
is defined as:
in a bottom CRN network, the transmission of secret signals and artificial noise is simultaneously subjected to double constraints of total transmitting power and interference power suppression aiming at a main user; therefore, a primary channel eigenvector V based on the secondary user Bob is adopted H Precoding, under the condition of satisfying the constraint of total transmission power and the constraint of interference suppression of the system, maximizing the worst secret rate of the system:
wherein, gamma is I Represents an upper limit of the interference power for the primary user PU. [ x ] of] + Indicating taking the maximum of 0 and x. Therefore, a system security rate optimization objective function corresponding to the main channel special positive vector precoding based on the secondary user Bob is obtained.
Thirdly, designing a safe precoding scheme by utilizing the channel null space of a main user PU and combining an artificial noise injection scheme based on the MIMO channel safe capacity expression, and expressing the problem of safe rate optimization, wherein the safe precoding scheme specifically comprises the following steps:
step 3.1: designing the sending signal into a form of weighted addition of the secret information and the artificial noise similarly to the step two;
wherein the content of the first and second substances,
and
secret signal and artificial noise vectors respectively representing lengths corresponding to the number of transmitting antennas, non-negative diagonal matrix Ψ x The power distribution vector of the secret signals and the artificial noise is represented by ≧ 0,x ∈ { s, a }, which is a variable to be optimized, and the kth diagonal element ψ x,k More than or equal to 0 represents the k symbol of the corresponding transmission signal; at the same time, it is necessary to satisfy 0 ≦ tr (Ψ) s +Ψ a )≤Γ T ，Γ T An upper limit representing the total transmitted power of the security signal and the artificial noise; at the same time, V s And V a And respectively representing precoding matrixes for the secret signals and the artificial noise, and mapping the mixed signals to be transmitted to a transmitting antenna.
Step 3.2: designing a precoding matrix in the step 3.1 according to a channel orthogonal null space of a main user PU;
according to primary user PU channel G, order
Therefore, for the primary user PU, the interference signal at the receiving end
The premise of design needs to be noticed, and the requirement that the number of the transmitting antennas of Alice is greater than that of the receiving antennas of the primary user PU is met;
step 3.3: likewise, the information rate of the legitimate secondary user Bob is calculated from the pre-coding matrix designed in step 3.2
Maximum information rate of eavesdropping node Eve
And approximate traversal safety rate
At this time, the power distribution coefficient { Ψ is fixed s ,Ψ a Next, the worst security rate of the system is calculated as follows:
wherein the content of the first and second substances,
representing a safety rate corresponding to a precoding scheme designed based on a channel zero space vector of a primary user PU;
represents the information rate of the secondary user Bob;
indicating the information rate at the ith eavesdropping node; max 1≤i≤L {. Represents calculationWhat is needed is an interception rate for the best interception location, and thus corresponds to the worst-case security rate of the system, i.e., the lower bound on the security rate.
And calculating the information rates of the secondary user Bob and the interception node Eve according to the Gaussian MIMO channel capacity expression:
wherein the content of the first and second substances,
denotes a semi-positive definite Hermitian matrix, here
And
is defined as:
channel null space vector V based on primary user PU is adopted G Precoding, maximizing the worst secret rate of the system under the condition of satisfying the constraint of the total transmission power of the system, and expressing the optimization problem as (15):
s.t.0≤tr(Ψ s +Ψ a )≤Γ T (16)
wherein, [ x ]] + This indicates taking the maximum of 0 and x. Unlike step one, here the interference power constraint Γ for the primary user is I And all interference signals realize signal null, namely, the signal and noise vectors are multiplied by the main user channel G to be 0, so that interference is completely eliminated, and only the constraint of total transmission power needs to be satisfied.
Step four: according to the non-convex secret rate optimization problem designed in the second step and the third step, the problem of maximizing the safety rate is converted into a differential convex programming problem of minimizing the auxiliary variable t through a series of equation replacement and approximation;
step 4.1: calculating the approximate traversal safety capacity of the system under a plurality of position-limited eavesdropping nodes;
wherein the content of the first and second substances,
x is a diagonal matrix, phi is a random unitary matrix, and elements in the matrix are all randomly obtained by Haar measurement; the above-mentioned ergodic safe rate approximate expression is expected to calculate W and phi simultaneously; in the comparison of the expressions xx, the,
here, a Haar random matrix phi is used in combination with a Jensen inequality to replace a right singular matrix V x ；
Step 4.2: since the optimization problem in step two and step three is the subtraction of two non-convex optimization problems, the resulting expressions (8) and (15) are still non-convex functions. Replacing expressions (8) and (15) with expression (24) in step 4.1
Obtaining an approximate expression (19):
step 4.3: rewriting the above equation into expression (20):
step 4.4: since the first term of the expression (20) has no relation with i, the first term is taken out of the summation term to obtain an expression (21);
wherein the content of the first and second substances,
step 4.5: since both the maximum and the finite number sum are convex problems, the problem p (x) (. Ang) and q (x) (. Cndot.) is convex, where auxiliary variables t and s are introduced, resulting in expression (24);
wherein t is less than or equal to 0 and s is a real number.
Step 4.6: rewriting the above inequality as follows;
step 4.7: comparing expressions (21) and (24), the problem of maximizing the worst safe rate can be converted into the problem of minimizing the auxiliary variable t, and in combination with the constraint (25), the above optimization problem can be equivalent to the classical differential convex programming problem, as shown below;
likewise, when a primary user PU channel-based null-space feature vector is employed, the security rate optimization problem can be written as:
wherein w = { Ψ = { (Ψ) a ,Ψ s ,s,t}
Fig. 2 shows a detailed process of initialization and iterative optimization based on the outlier approximation method in the present invention, which is more specific to the present embodiment, the method has the following operation flow:
step five, as the algorithm flow chart of fig. 2, solving the difference convex programming problem in step four by adopting an iterative outlier approximation method, specifically:
step 5.1:
first, a feasible solution is initialized
For simplicity, the above constraints are expressed as:
H (x) ＝{w:h (x) (w)≤0}，G (x) ＝{w:g (x) (w)≥0}
and
wherein
Represents G (x) The set of boundary points of (1);
step 5.2: finding boundary points, i.e. initialized feasible solution w, by adopting an interpolation method of inner and outer points 0 ：
First, it is necessary to findTo a suitable set of inner and outer points x ∈ G (x) ，
g (x) (x)＞0，g (x) (v) < 0, and t v ＜min{t w :w∈H (x) ∩G (x) }。
The interpolation points are represented as: pi (x) = vx + (1-v) v,0 < v < 1, i.e., g (x) (π(x))＝0；
Step 5.3: first, a suitable outlier v is found 0 ；
The secret power can be directly applied to a water injection algorithm Jie wf The noise power is initialized to 0, i.e.:
thus, the initialization outliers can be expressed as:
step 5.4: secondly, find a suitable interior point x 0 ；
Obtained by solving the following optimization problem:
max{g (x) (x):x∈H (x) } (30)
this results in an initialization feasible solution: w is a 0 ＝π(x 0 )＝vx 0 +(1-v)v 0
Step 5.5, starting iterative solution, and taking k to be more than or equal to 1;
solving the subproblems:
if g is (x) (z k )≥ε
Let w k ＝π(z k )，k＝k+1；
Otherwise
Output w * ＝z k ；
Wherein epsilon represents the introduced relaxation factor, and can balance the iteration complexity and the optimization result.
Step 5.6 the process of iterating step 4.E is repeated until convergence and the optimized w = { Ψ = is output a ,Ψ s S, t }; note that the iterative optimization algorithm can achieve a globally optimal solution when epsilon = 0.
And step six, setting the number and the distribution of the nodes of the distributed MIMO, calculating the water injection safety rate of the system under the condition of only considering large-scale fading, comparing the water injection safety rate with a preset safety lower limit, and selecting the distributed transmitting nodes at least meeting the safety lower limit. And calculating an Interference to Noise Ratio (INR) of the primary user PU, comparing the INR with a preset value, selecting a proper safety precoding scheme from the second step and the third step, feeding the scheme back to the sending end, periodically iterating the process, and adjusting the sending end precoding scheme in real time according to the INR change of the primary user.
Step 6.1: the quantity and the distribution of a group of distributed nodes are random, water injection power distribution is adopted under the condition of only considering large-scale fading, and the water injection safety rate of the system is calculated:
R s (Ψ s )＝R B (Ψ s )-max 1≤i≤L R E,i (Ψ s ) (31)
wherein the content of the first and second substances,
Ω＝diag{w 1 ,w 2 ,...,w K }；
alpha represents a path loss factor, and the representation in the third step is consistent; psi s ＝diag{ψ 1 ,ψ 2 ,...,ψ K Denotes the distributed antenna power distribution coefficient, distributed antenna power distribution vector psi under unit transmission power water And solving by a water injection power distribution algorithm:
wherein the content of the first and second substances,
step 6.2: safety rate R of water injection method s (Ψ water ) Same target safety rate gamma x R' sec If greater than gamma × R 'for comparison' sec If so, selecting the distributed node parameters and continuing to perform the next precoding scheme selection operation; otherwise, repeating the step 6.1 until the distributed nodes meeting the conditions are found, and stopping iteration;
R s (Ψ water )≥γ×R' sec (34)
wherein, gamma represents the diversity gain coefficient brought by considering the MIMO small-scale decay;
step 6.3: according to the off-line test results of the precoding schemes in the second step and the third step, selecting the precoding scheme and the INR threshold eta corresponding to the optimal safe rate, namely when the INR is less than or equal to the eta, under the same INR constraint, the safe rate which can be provided by adopting the precoding scheme in the third step is superior to that in the second step, and vice versa, so that the eta can be used as a critical value for selecting the precoding scheme;
step 6.4: determining the judgment INR at the position of the main user PU as eta according to the step 6.3, and calculating the ratio of interference power to noise power at the receiving end of the main user PU through an expression (31):
wherein N is 0 Representing the transmit side noise power; c. C 0 A reference path loss magnitude representing a signal unit distance; d represents the distance from the transmitter Alice to the primary user PU, and alpha represents a path loss factor which is related to the path loss influence factor of the actual signal transmission environment.
Step 6.5: judging the actual INR and the preset INR value eta by using the expression in the step 6.4, and feeding back the judgment result to the sending end for executing the transmission of the next time slot;
step 6.6: at the transmitting end, when INR is larger than eta, the precoding scheme in the second step is executed, and a precoding matrix V is adopted s ＝V a ＝V H And solving an optimization problem (26) according to the power distribution algorithm of the step five; when INR is less than or equal to eta, executing the precoding scheme in the step three, and adopting a precoding matrix V s ＝V a ＝V G Solving an optimization problem (27) according to the power distribution algorithm in the step five;
therefore, through the steps from the first step to the sixth step, all processes of the cooperative MIMO secure precoding method facing the spectrum sensing network are completed.
FIG. 3 is a diagram of simulation results of the worst privacy rate CDF with secondary user channel characteristics in different eavesdropping ranges and with or without artificial noise in the cooperative MIMO secure precoding method and embodiment for the spectrum sensing network of the present invention;
in FIG. 3, the safe rate is plotted on the abscissa, the range is 0 to 10nats/s/Hz, the CDF is plotted on the ordinate, and the simulation experiment carries out comparative analysis on six conditions: 1) Without artificial noise, eavesdropping range e 0 =6m, the upper limit of the total transmitting power is 30dBm, and the upper limit of the INR reaching the master user is 2.15dB; 2) Without artificial noise, eavesdropping range e 0 =8m, the upper limit of the total transmitting power is 30dBm, and the upper limit of INR reaching the master user is 2.15dB; 3) No artificial noise, eavesdropping range e 0 =10m, the upper limit of the total transmitting power is 30dBm, and the upper limit of INR reaching the master user is 2.15dB; 4) Combined with artificial noise, eavesdropping range e 0 =6m, the upper limit of the total transmitting power is 30dBm, and the upper limit of the INR reaching the master user is 2.15dB; 5) Combined with artificial noise, eavesdropping range e 0 =8m, the upper limit of the total transmitting power is 30dBm, and the upper limit of the INR reaching the master user is 2.15dB; 6) Combined with artificial noise, eavesdropping range being e 0 =10m, the upper limit of the total transmitting power is 30dBm, and the upper limit of INR reaching the master user is 2.15dB; from fig. 3, it can be seen that the precoding proposed by the present invention combines the artificial noise and the primary channel characteristics of the secondary usersThe scheme (solid line), the safe rate is significantly improved compared to the scheme without artificial noise (dotted line), at e 0 When the speed is not less than 8, the average speed is increased from 3nats/s/Hz to 5.5nats/s/Hz, the safety interruption probability is completely eliminated, the worst instantaneous safety speed is about 4nats/s/Hz, and the method aims at different eavesdropping ranges e 0 Stable safe speed improvement can be achieved;
FIG. 4 is a diagram of simulation results of the worst privacy rate CDF using the secondary user channel characteristics under different distributed node radii and with or without artificial noise in the cooperative MIMO secure precoding method and embodiment of the invention for the spectrum sensing network;
in FIG. 4, the safe rate is plotted on the abscissa, the range is 0 to 10nats/s/Hz, the CDF is plotted on the ordinate, and the simulation experiment performed comparative analysis on six conditions: 1) The radius of the distributed transmitting node is 1m, the upper limit of the total transmitting power is 30dBm, and the upper limit of the INR reaching the master user is 2.15dB without artificial noise; 2) The radius of the distributed transmitting node is 3m, the upper limit of the total transmitting power is 30dBm, and the upper limit of the INR reaching the master user is 2.15dB; 3) The artificial noise is avoided, the radius of the distributed transmitting node is 5m, the upper limit of the total transmitting power is 30dBm, and the upper limit of the INR reaching the master user is 2.15dB; 4) Combining artificial noise, the radius of the distributed transmitting node is 1m, the upper limit of the total transmitting power is 30dBm, and the upper limit of INR reaching a master user is 2.15dB; 5) By combining artificial noise, the radius of the distributed transmitting node is 3m, the upper limit of the total transmitting power is 30dBm, and the upper limit of the INR reaching the master user is 2.15dB; 6) Combining artificial noise, the radius of the distributed transmitting node is 5m, the upper limit of the total transmitting power is 30dBm, and the upper limit of INR reaching a master user is 2.15dB; fig. 4 shows that the precoding scheme combining the artificial noise and the secondary user main channel characteristics provided by the present invention significantly improves the security rate and completely eliminates the security outage probability compared to a scheme without artificial noise, and meanwhile, when the distributed radius is increased from 3m to 5m, the security rate is increased from 6nats/s/Hz to 8.5nats/s/Hz, so that the larger the distributed range is, the better the security performance is.
FIG. 5 shows a collaborative MIMO secure precoding method and embodiment of the invention for spectrum sensing networkNull space V with primary user PU channel G Precoding and exploiting secondary user channel characteristics V H Average privacy rate of precoding under different interference power constraints Γ I A simulation result graph under the condition;
FIG. 5 abscissa is interference power constraint Γ I The range is-15 dBm to-5 dBm; the ordinate is the average safe rate, the unit is nats/s/Hz, and the simulation experiment contrasts and analyzes four conditions: 1) V H Precoding + absence of artifacts, 2) V H Precoding + combining artificial noise, 3) V G Precoding + absence of artifacts 4) V G Precoding + combining with artificial noise. It can be seen from FIG. 5 that the scheme proposed by the present invention adopts V when the interference power is less than-11.6 dBm, according to the formula (31), i.e. when the INR of the primary user is less than or equal to-2.22 dB G The precoding scheme can achieve higher average safe rate; when INR of a main user is > -2.22dB, V is adopted H The precoding scheme can achieve a higher average security rate.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (7)
1. The cooperative MIMO secure precoding method facing the spectrum sensing network is characterized in that: comprises the following steps of (a) carrying out,
initializing system configuration such as the number, distribution and user number of initialization antennas of a bottom CRN system, the number of eavesdropping nodes, transmitting power and the like;
designing a safety pre-coding scheme by utilizing the characteristics of a secondary user main channel and combining artificial noise injection, and expressing the problem of system safety rate optimization;
thirdly, designing a safety pre-coding scheme by utilizing a channel null space of a primary user PU and combining an artificial noise injection scheme, and expressing a safety rate optimization problem;
step four: according to the non-convex secret rate optimization problem designed in the second step and the third step, the problem of maximizing the safety rate is converted into a differential convex programming problem of minimizing the auxiliary variable t through a series of equation replacement and approximation;
step five, solving the differential convex programming problem in the step four by adopting an iterative outlier approximation method;
step six, according to the number and the distribution of the set distributed MIMO nodes, under the condition of only considering large-scale fading, calculating the worst safe rate of the system, comparing the worst safe rate with a preset safe lower limit, and selecting a distributed structure at least meeting the safe lower limit; and calculating the interference-to-noise ratio of the PU of the main user, comparing the interference-to-noise ratio with a preset value, selecting a proper safety precoding scheme, feeding the scheme back to a sending end, periodically iterating the process, and adjusting the sending-end precoding scheme in real time according to the INR change of the main user, namely realizing the cooperative MIMO safety precoding facing the spectrum sensing network.
2. The cooperative MIMO secure precoding method for spectrum-aware networks as claimed in claim 1, wherein: the implementation method of the step one is that,
the number of the distributed transmitting antenna nodes Alice is recorded as K; the number of primary user PU antennas is recorded as N P A plurality of; the number of the secondary user Bob antennae is marked as N B A plurality of; l eavesdropping users Eve, and the number of each antenna is recorded as N E A plurality of; the center of the distributed transmitting node is marked as O, and the distance from the distributed transmitting node to the main user is marked as p 0 And the distance to the secondary user is denoted b 0 The minimum distance to all eavesdropping nodes is denoted as e 0 (ii) a The range radius of the distributed antenna is recorded as r; the total power of the distributed transmitting nodes is limited by Γ T (ii) a The upper limit of the interference power which can be tolerated by the primary user PU is recorded as gamma I 。
3. The cooperative MIMO secure precoding method for spectrum-aware networks as claimed in claim 1, wherein: the implementation method of the second step is that,
step 2.1: designing a sending signal into a form of weighted addition of secret information and artificial noise; namely:
wherein, the secret signal s and the artificial noise a with normalized power respectively obey a complex Gaussian Independent Identity Distribution (GIID) with a mean value of 0 and a covariance matrix of a unit matrix; power allocation matrix Ψ for a secure signal s Power allocation matrix psi with artificial noise a Expressed as a non-negative diagonal matrix, is a variable to be optimized; the kth diagonal element on the diagonal represents the kth symbol of the corresponding transmitted signal; the precoding matrices for the secret signal and the artificial noise are respectively V s And V a Mapping a mixed signal to be transmitted to a transmitting antenna;
step 2.2: designing a precoding matrix in the step 2.1 according to the main channel characteristics of the secondary user;
SVD decomposition is carried out on the secondary user main channel matrix in the CRN network, and a singular matrix V is taken out H A pre-coding matrix as a secret signal and artificial noise; compared with the situation that a precoding matrix adopts a channel orthogonal matrix in an artificial noise injection scheme based on a channel null space, the precoding scheme is more general and is not limited by the number of antennas at a transmitting end and a receiving end;
step 2.3: according to the MIMO channel capacity expression and the pre-coding matrix designed in the step 2.2, the information rate of a legal secondary user, the maximum information rate of a wiretap node and the worst safety rate of a system are represented; namely: worst security rate = information rate of secondary user Bob — maximum value of information rate of multiple eavesdropping users Eve, and the calculated value corresponds to security rate in worst case of system, i.e. lower limit of security rate;
according to the Gaussian MIMO channel capacity expression, calculating the effective information rates of the secondary user Bob and the interception node Eve under the condition of artificial noise injection, namely:
wherein H in the upper right brackets indicates the adoption of V H A precoding scheme;
step 2.4: setting total emission power constraint that total power of artificial noise and secret information is less than or equal to preset threshold gamma T ；
Step 2.5: setting interference power constraint aiming at the primary user PU, namely setting the power of the total power reaching the receiving end of the primary user PU to be less than or equal to a preset threshold gamma I ；
Step 2.6: according to the primary channel feature vector V based on the secondary user Bob in step 2.2 H And precoding 2.4, and step 2.5, designing an optimization problem of the worst secret rate of the maximized system under the constraint of the total transmission power of the system and the constraint of interference suppression.
4. The cooperative MIMO secure precoding method for spectrum-aware networks as claimed in claim 1, wherein: the third step is realized by the method that,
step 3.1: designing a sending signal into a form of weighted addition of secret information and artificial noise;
wherein, the secret signal s and the artificial noise a with normalized power respectively obey a complex Gaussian independent equal Distribution (GIID) with a mean value of 0 and a covariance matrix as a unit matrix; power allocation matrix psi for secret signals s Power allocation matrix psi with artificial noise a Expressed as a non-negative diagonal matrix, is a variable to be optimized; the kth diagonal element on the diagonal represents the kth symbol of the corresponding transmitted signal; the precoding matrices for the secret signal and the artificial noise are respectively V s And V a Mapping the mixed signal to be sent to a transmitting antenna;
step 3.2: designing a precoding matrix in the step 3.1 according to a channel orthogonal null space of a main user PU;
taking orthogonal matrix V of primary user PU channel matrix G As precoding matrices for artifacts and security signals, i.e. GV G =0; the requirement here is that the number of Alice transmitting antennas is greater than the number of primary user PU receiving antennas;
step 3.3: according to the MIMO channel capacity expression and the pre-coding matrix designed in the step 3.2, the information rate of a legal secondary user, the maximum information rate of an eavesdropping node and the worst safety rate of a system are represented; namely: worst security rate = information rate of secondary user Bob — maximum value of information rate of multiple eavesdropping users Eve, and the calculated value corresponds to security rate in worst case of system, i.e. lower limit of security rate;
according to the Gaussian MIMO channel capacity expression, calculating the effective information rates of the secondary user Bob and the eavesdropping node Eve under the condition of artificial noise injection, namely:
wherein G in parentheses in the upper right corner represents the adoption of V G A precoding scheme;
step 3.4: setting total emission power constraint that total power of artificial noise and secret information is less than or equal to preset threshold gamma T ；
Step 3.5: according to the primary channel eigenvector V based on the secondary user Bob in step 3.2 G And precoding 3.4, and designing an optimization problem of the worst secret rate of the maximized system under the constraint of the total transmission power of the system.
5. The cooperative MIMO secure precoding method for spectrum-aware networks as claimed in claim 1, wherein: the implementation method of the fourth step is that,
step 4.1: calculating the approximate traversal security rate of the system under a plurality of position-limited eavesdropping nodes;
the traversal safety rate is expressed by a diagonal matrix X, wherein a Haar random matrix phi is used and combined with a Jensen inequality to replace an original channel right singular matrix V x ；
Wherein phi is a random unitary matrix, and elements therein are all randomly obtained by Haar measurement; this safe rate requires computation of expectations for both W and Φ;
step 4.2: because the optimization problems in the second step and the third step are in a subtraction mode of two non-convex optimization problems, the finally obtained optimization target expression is still a non-convex function; replacing the safe speed optimization target expressions in the second step and the third step by the approximate traversal safe speed expressions in the step 4.1 to obtain an optimized target after approximate replacement;
step 4.3: rewriting the maximum eavesdropping speed expression in the optimized target expression in the 4.2 into the total eavesdropping speed of all eavesdropping nodes, namely the eavesdropping speed of other nodes except the optimal eavesdropping node i;
step 4.4: since the first term of the expression in step 4.3 has no relation with i, the first term is taken out of the summation term to obtain the expression after reintegration;
wherein, the integrated expression is expressed in a subtraction form of two parts; the first part is q (x) (Ψ s ,Ψ a ) It means that the sum of the total eavesdropping rate and the rate of invalid information of the secondary users in the total power representation is inverted; the second part is p (x) (Ψ s ,Ψ a ) Adding the information rate of the secondary user under the total power to the invalid eavesdropping rate of the eavesdropping node i and the total eavesdropping rate of other nodes except the eavesdropping node i under the total power, acquiring the opposite number, and finally acquiring the maximum value of the calculation result after traversing all the eavesdropping nodes i;
step 4.5: since the maximum and finite number summation is a convex problem, the problem p in step 4.4 (x) (. Ang) and q (x) (. Is) convex, reintegrating the above expression by introducing auxiliary variables t and s;
wherein t is less than or equal to 0 and s is a real number;
step 4.6: rewriting the inequality into two new inequality constraints, namely;
(1) s and p (x) (Ψ s ,Ψ a ) The sum is less than or equal to 0;
(2) t and s, q (x) The sum of (c) is equal to or greater than 0;
step 4.7: the problem of maximizing the worst safe rate in the step 4.2 can be converted into the problem of minimizing the auxiliary variable t, and the problem is equivalent to the classical differential convex programming problem by combining two inequality constraints in the step 4.6, namely the auxiliary variable t is minimized under the condition of meeting the inequality constraint, the total transmission power constraint and the interference power constraint;
similarly, when the primary user PU channel-based null-space feature vector is used, the security rate optimization problem can be rewritten to a similar differential convex programming problem.
6. The cooperative MIMO secure precoding method for spectrum-aware networks as claimed in claim 1, wherein: the implementation method of the fifth step is that,
step 5.1: finding boundary points by adopting an inner point interpolation method and an outer point interpolation method, namely initializing a feasible solution
And step 5.2: initializing according to the step 5.1, starting iterative solution by using an iterative optimization algorithm until convergence, and outputting w = { Ψ = to a ,Ψ s S, t }; wherein epsilon represents the introduced relaxation factor, and when epsilon =0, the iterative optimization algorithm can obtain a global optimal solution.
7. The cooperative MIMO secure precoding method for spectrum-aware networks as claimed in claim 1, wherein: the implementation method of the step six is that,
step 6.1: the quantity and the distribution of a group of distributed nodes are random, and the safe rate R of the water injection method is calculated by adopting water injection power distribution under the condition of only considering large-scale fading s (Ψ water )；
Step 6.2: taking water injection method safe speed R s (Ψ water ) Same target safety rate gamma x R' sec If greater than gamma × R 'for comparison' sec If so, selecting distributed node parameters and continuing to perform the next precoding scheme selection operation; otherwise, repeating the step 6.1 until the distributed nodes meeting the conditions are found, and stopping iteration;
step 6.3: according to the off-line test results of the precoding schemes in the second step and the third step, selecting the precoding scheme and the INR threshold eta corresponding to the optimal safe rate, namely when the INR is less than or equal to eta, under the same INR constraint, the safe rate which can be provided by adopting the precoding scheme in the third step is superior to that in the second step, and vice versa, and then eta is used as a decision threshold for selecting the precoding scheme;
step 6.4: determining the INR at the primary user PU as eta according to the step 6.3, and calculating the ratio of the actual interference power and the noise power, namely the actual INR at the receiving end of the primary user PU;
step 6.5: judging the actual INR and a preset INR value eta, and feeding back a judgment result to a sending end for executing the transmission of the next time slot;
step 6.6: at the transmitting end, when INR is greater than eta, the precoding scheme in the step two is executed, and a precoding matrix V is adopted s ＝V a ＝V H And solving the V adopted in the step 4.7 according to the power distribution algorithm of the step five H A differential convex programming problem from precoding equivalent transformation; when INR is less than or equal to eta, executing the pre-coding scheme in the third step, and adopting a pre-coding matrix V s ＝V a ＝V G Likewise, V is adopted in the step 4.7 according to the power distribution algorithm of the step five G Precoding the differential convex programming problem of the equivalent transformation.
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