CN108337028A - The safe rate based on broad sense inverse iteration maximizes synthetic method in the modulation of direction - Google Patents
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Abstract
本发明提供了方向调制中基于广义逆迭代的安全速率最大化合成方法，在设计有用信号波束成形向量和人工噪声投影矩阵前，先利用泄露的概念对两者进行初始化，然后利用广义逆迭代算法(General power iterative,GPI)更新人工噪声投影矩阵，同时通过Rayleigh‑Ritz方法更新有用信号波束成形向量。为了最大化安全速率，在设计有用信号波束成形向量和人工噪声投影矩阵时要用到交替迭代结构(Alternatively iterative structure,AIS )，并且需要及时更新对应的安全速率。本发明与传统的方向调制技术相比安全速率在中高信噪比时得到了极大的提升，并且在期望方向能够很好的解调出有用信号，在非期望方向难以恢复出有用信号，从而能够更好地提升系统的安全性能。
The invention provides a safe rate maximization synthesis method based on generalized inverse iteration in direction modulation. Before designing the useful signal beamforming vector and the artificial noise projection matrix, the concept of leakage is used to initialize the two, and then the generalized inverse iterative algorithm is used to (General power iterative, GPI) updates the artificial noise projection matrix, and at the same time updates the useful signal beamforming vector through the Rayleigh-Ritz method. In order to maximize the safe rate, an Alternatively iterative structure (AIS ) is used when designing the useful signal beamforming vector and the artificial noise projection matrix, and the corresponding safe rate needs to be updated in time. Compared with the traditional direction modulation technology, the safety rate of the present invention is greatly improved when the signal-to-noise ratio is high, and the useful signal can be well demodulated in the desired direction, and it is difficult to recover the useful signal in the undesired direction, thus It can better improve the security performance of the system.
Description
技术领域technical field
本发明涉及无线通信技术领域，特别涉及方向调制中基于广义逆迭代的安全速率最大化合成方法。The invention relates to the technical field of wireless communication, in particular to a synthesis method for maximum security rate based on generalized inverse iteration in direction modulation.
背景技术Background technique
近年来，随着移动通信网络的迅猛发展，信息的私密性也变得尤为重要，传统的上层加密技术仅仅通过数学方法解决问题，倘若有关数学问题的解决方案一旦被找到则通信过程就极易受到非法用户的攻击。于是，研究人员开始将目光投向底层的安全传输技术，即物理层安全传输技术。为保证安全传输最重要的一点是提升期望信道的通信质量，降低窃听信道的质量，从而保证信息的安全传输。In recent years, with the rapid development of mobile communication networks, the privacy of information has become particularly important. The traditional upper-level encryption technology only solves problems through mathematical methods. Once the solution to the mathematical problem is found, the communication process is very easy. Attacked by illegal users. Therefore, researchers began to turn their attention to the underlying security transmission technology, that is, the physical layer security transmission technology. The most important point to ensure safe transmission is to improve the communication quality of the expected channel and reduce the quality of the eavesdropping channel, so as to ensure the safe transmission of information.
方向调制技术能够使期望方向解调出有用信号，同时模糊非期望方向的信号，使其无法恢复出有用信号。最初，Wyner提出了Wire-tap模型，并将其与信息论知识相结合证明了可靠传输在完美的信道条件下是可以实现的。随后，人工噪声的概念被引入无线通信，发射机在发送私密信息的同时发送人工噪声，使人工噪声位于合法用户方向的零空间，即对合法用户不造成影响，同时最大化其在非法用户方向的能量，使得非期望方向星座图扭曲，从而保证私密信息的安全传输。另外，符号级预编码方案和协作中继也都被考虑用来提升系统的安全性能。The direction modulation technology can demodulate the useful signal in the desired direction, and at the same time blur the signal in the undesired direction, making it impossible to recover the useful signal. Initially, Wyner proposed the Wire-tap model and combined it with information theory knowledge to prove that reliable transmission is achievable under perfect channel conditions. Subsequently, the concept of artificial noise was introduced into wireless communication. The transmitter sends artificial noise while sending private information, so that the artificial noise is located in the null space in the direction of legitimate users, that is, it does not affect legitimate users, and at the same time maximizes its influence on the direction of illegal users. The energy of the undesired direction constellation is distorted, so as to ensure the safe transmission of private information. In addition, symbol-level precoding schemes and cooperative relay are also considered to improve the security performance of the system.
然而，在诸多的不考虑估计角度误差的三点(发射机、期望接收机、窃听接收机)方向调制方案中，如何实现安全速率最大化是一个NP-hard问题。因此，本发明提出了方向调制中基于广义逆迭代的安全速率最大化合成方法，通过交替迭代结构合理设计有用信号波束成形向量和人工噪声投影矩阵，使安全速率得到提升，同时实现信息的可靠传输。However, in many three-point (transmitter, desired receiver, eavesdropping receiver) directional modulation schemes that do not consider the estimated angle error, how to maximize the security rate is an NP-hard problem. Therefore, the present invention proposes a synthesis method based on generalized inverse iteration to maximize the safe rate in direction modulation, and rationally design useful signal beamforming vectors and artificial noise projection matrices through alternating iterative structures, so that the safe rate can be improved, and at the same time, reliable transmission of information can be realized .
发明内容Contents of the invention
为了克服现有技术中存在的不足，本发明提供方向调制中基于广义逆迭代的安全速率最大化合成方法，先利用泄露的概念对有用信号波束成形向量和人工噪声投影矩阵进行初始化，接着利用广义逆迭代算法更新人工噪声投影矩阵，同时通过Rayleigh-Ritz方法更新有用信号波束成形向量。另外，在设计有用信号波束成形向量和人工噪声投影矩阵时要用到交替迭代结构，并且需要实时计算对应的安全速率，直到满足终止条件迭代结束，从而实现安全速率最大化。In order to overcome the deficiencies in the prior art, the present invention provides a safe rate maximization synthesis method based on generalized inverse iteration in direction modulation. First, the concept of leakage is used to initialize the useful signal beamforming vector and artificial noise projection matrix, and then use the generalized The artificial noise projection matrix is updated by the inverse iterative algorithm, and the useful signal beamforming vector is updated by the Rayleigh-Ritz method. In addition, an alternate iterative structure is used when designing the useful signal beamforming vector and the artificial noise projection matrix, and the corresponding safe rate needs to be calculated in real time until the termination condition is satisfied and the iteration ends, so as to maximize the safe rate.
为实现上述目的，本发明所采用的技术方案包括：利用泄露的概念对有用信号波束成形向量和人工噪声投影矩阵进行初始化；通过广义逆迭代算法和Rayleigh-Ritz方法更新人工噪声投影矩阵和有用信号波束成形向量；设计有用信号波束成形向量和人工噪声投影矩阵时要用到交替迭代结构，同时更新对应的安全速率。In order to achieve the above object, the technical solution adopted by the present invention includes: using the concept of leakage to initialize the useful signal beamforming vector and the artificial noise projection matrix; updating the artificial noise projection matrix and the useful signal by generalized inverse iterative algorithm and Rayleigh-Ritz method Beamforming vectors; the design of useful signal beamforming vectors and artificial noise projection matrices uses an alternate iterative structure while updating the corresponding security rates.
进一步地，具体过程包括：S1.利用泄露的概念初始化有用信号波束成形向量和人工噪声投影矩阵，在初始化人工噪声投影矩阵时把人工噪声当作有用信号，同理，在初始化有用信号波束成形向量时把私密信息当作有用信号；S2.利用广义逆迭代算法优化人工噪声投影矩阵需固定对应的有用信号波束成形向量，并且需要对其人工噪声投影矩阵进行拉直操作；S3.利用Rayleigh-Ritz方法优化有用信号波束成形向量时需固定相应的人工噪声投影矩阵，并取最大特征值所对应的特征向量；S4.计算人工噪声投影矩阵和有用信号波束成形向量更新前后所对应的安全速率之差的绝对值，直到满足终止条件。Further, the specific process includes: S1. Use the concept of leakage to initialize the useful signal beamforming vector and the artificial noise projection matrix. When initializing the artificial noise projection matrix, the artificial noise is regarded as a useful signal. Similarly, when initializing the useful signal beamforming vector When using private information as a useful signal; S2. Using the generalized inverse iterative algorithm to optimize the artificial noise projection matrix needs to fix the corresponding useful signal beamforming vector, and need to straighten the artificial noise projection matrix; S3. Use Rayleigh-Ritz Method When optimizing the useful signal beamforming vector, it is necessary to fix the corresponding artificial noise projection matrix, and take the eigenvector corresponding to the largest eigenvalue; S4. Calculate the difference between the artificial noise projection matrix and the security rate corresponding to the update of the useful signal beamforming vector The absolute value of , until the termination condition is met.
进一步地，所述的利用泄露的概念初始化有用信号波束成形向量和人工噪声投影矩阵相比随机产生的有用信号波束成形向量和人工噪声投影矩阵可以提升收敛速率，使期望方向能够恢复出有用信号，窃听方向无法恢复有用信号。Further, the use of leakage concept to initialize the useful signal beamforming vector and artificial noise projection matrix can improve the convergence rate compared with randomly generated useful signal beamforming vector and artificial noise projection matrix, so that the desired direction can restore the useful signal, Eavesdropping on directions cannot recover useful signals.
进一步地，所述利用广义逆迭代算法优化人工噪声投影矩阵需固定对应的有用信号波束成形向量，并且需要对其人工噪声投影矩阵进行拉直操作；利用Rayleigh-Ritz方法优化有用信号波束成形向量时需固定相应的人工噪声投影矩阵，并取最大特征值所对应的特征向量。Further, the optimization of the artificial noise projection matrix using the generalized inverse iterative algorithm needs to fix the corresponding useful signal beamforming vector, and the artificial noise projection matrix needs to be straightened; when using the Rayleigh-Ritz method to optimize the useful signal beamforming vector The corresponding artificial noise projection matrix needs to be fixed, and the eigenvector corresponding to the largest eigenvalue is taken.
与现有技术相比，通过本发明提出的方法能够实现安全速率最大化，同时保证期望接收机位置能够准确恢复出有用信号，而窃听接收机位置接收的信号星座图发生扭曲。利用泄露的概念初始化有用信号波束成形向量和人工噪声投影矩阵相比随机产生的有用信号波束成形向量和人工噪声投影矩阵可以提升收敛速率；通过广义逆迭代算法和Rayleigh-Ritz方法更新人工噪声投影矩阵和有用信号波束成形向量，并计算对应的安全速率，可以得到较高的安全速率，提升系统安全传输性能。Compared with the prior art, the method proposed by the invention can maximize the security rate, and at the same time ensure that the useful signal can be accurately recovered at the desired receiver position, while the signal constellation diagram received at the eavesdropping receiver position is distorted. Using the concept of leakage to initialize the useful signal beamforming vector and artificial noise projection matrix can improve the convergence rate compared with randomly generated useful signal beamforming vector and artificial noise projection matrix; the artificial noise projection matrix is updated by generalized inverse iterative algorithm and Rayleigh-Ritz method And useful signal beamforming vector, and calculate the corresponding security rate, can get a higher security rate, improve system security transmission performance.
本发明附加的方面和优点将在下面的描述中部分给出，这些将从下面的描述中变得明显，或通过本发明的实践了解到。Additional aspects and advantages of the invention will be set forth in part in the description which follows, and will become apparent from the description, or may be learned by practice of the invention.
附图说明Description of drawings
图1为方向调制中基于广义逆迭代的安全速率最大化合成方法。Fig. 1 shows the safe rate maximization synthesis method based on generalized inverse iteration in direction modulation.
具体实施方式Detailed ways
下面结合附图和具体实例，进一步阐明本发明，应理解这些实例仅用于说明本发明而不用于限制本发明的范围，在阅读了本发明之后，本领域技术人员对本发明的各种等价形式的修改均落于本申请所附权利要求所限定的范围。Below in conjunction with accompanying drawing and specific examples, further illustrate the present invention, should be understood that these examples are only used to illustrate the present invention and are not intended to limit the scope of the present invention, after having read the present invention, those skilled in the art will understand various equivalents of the present invention Modifications in form all fall within the scope defined by the appended claims of this application.
给定一个三节点方向调制系统模型，即源节点、目的节点、窃听节点，其中基站采用N阵元均匀线性阵列天线，期望用户和窃听用户均为单天线接收机，系统工作在直达路径中。在这种情况下，发射机端传输的基带信号向量表示为Given a three-node directional modulation system model, that is, source node, destination node, and eavesdropping node, the base station uses an N-element uniform linear array antenna, the desired user and the eavesdropping user are both single-antenna receivers, and the system works in the direct path. In this case, the baseband signal vector transmitted at the transmitter end is expressed as
式中，Ps表示总的发射功率；β1和β2分别表示有用信号和人工噪声的功率分配因子，并且满足x表示有用信号并满足z表示人工噪声向量且服从复高斯分布 表示期望用户的归一化波束成形向量，即可将有用信号汇聚到期望方向；表示人工噪声投影矩阵，可将发射的人工噪声功率集中到窃听方向从而干扰非法用户的窃听；α表示功率归一化因子，满足 In the formula, P s represents the total transmission power; β 1 and β 2 represent the power allocation factors of useful signal and artificial noise respectively, and satisfy x represents a useful signal and satisfies z represents the artificial noise vector and obeys the complex Gaussian distribution Denotes the normalized beamforming vector of the desired user, namely Useful signals can be converged to the desired direction; Represents the artificial noise projection matrix, which can concentrate the transmitted artificial noise power to the eavesdropping direction to interfere with the eavesdropping of illegal users; α represents the power normalization factor, which satisfies
经过line of sight(LoS)信道后，在方向角θ处接收到的信号为After passing through the line of sight (LoS) channel, the signal received at the direction angle θ is
其中，nr表示接收机加性高斯白噪声，服从分布；表示归一化导向向量，可表示为Among them, n r represents the receiver additive white Gaussian noise, subject to distributed; Represents the normalized steering vector, which can be expressed as
上式中In the above formula
其中n表示第n根发射天线，d表示发射机相邻两天线的间隔，λ表示发射载波信号的波长。同理，期望接收机和窃听接收机的接收信号可分别表示为Among them, n represents the nth transmitting antenna, d represents the interval between two adjacent antennas of the transmitter, and λ represents the wavelength of the transmitted carrier signal. Similarly, the received signals of the desired receiver and the eavesdropping receiver can be expressed as
和and
其中nd表示期望接收机噪声，服从分布；ne表示窃听接收机噪声，服从分布。通常，我们假定 where n d represents the desired receiver noise, subject to distribution; ne represents the noise of the eavesdropping receiver, obeying distributed. Usually, we assume
由式(5)和(6)分别获得期望方向和非期望方向的可实现速率，即The achievable speeds of the desired direction and the undesired direction can be obtained from equations (5) and (6), respectively, that is,
和and
因此，安全速率可以定义为期望方向和非期望方向的可实现速率之差即Therefore, the safe rate can be defined as the difference between the achievable rates in the desired and undesired directions, namely
其中 in
为了最大化安全速率，我们需要优化有用信号波束成形向量和人工噪声投影矩阵，该优化问题可以表示为In order to maximize the safe rate, we need to optimize the useful signal beamforming vector and the artificial noise projection matrix, the optimization problem can be expressed as
明显地，上式优化问题是一个NP-hard问题，故难以找到直接的或相近形式的解析解。为此，我们可将上述优化问题转换成两个相互关联的子问题，并且在这两个子问题之间建立一个迭代结构。Obviously, the above optimization problem is an NP-hard problem, so it is difficult to find a direct or similar analytical solution. To this end, we can convert the above optimization problem into two interrelated sub-problems, and establish an iterative structure between these two sub-problems.
在优化有用信号波束成形向量和人工噪声投影矩阵之前，需要先对两者进行初始化操作，具体过程如下：Before optimizing the useful signal beamforming vector and the artificial noise projection matrix, both need to be initialized first, and the specific process is as follows:
S1.利用泄露的概念初始化有用信号波束成形向量和人工噪声投影矩阵，在初始化人工噪声投影矩阵时把人工噪声当作有用信号，同理，在初始化有用信号波束成形向量时把私密信息当作有用信号。S1. Use the concept of leakage to initialize the useful signal beamforming vector and the artificial noise projection matrix. When initializing the artificial noise projection matrix, artificial noise is regarded as a useful signal. Similarly, private information is regarded as useful when initializing the useful signal beamforming vector. Signal.
根据泄露的概念，在初始化人工噪声投影矩阵时沿窃听方向的人工噪声被看作有用信号，沿期望方向的人工噪声被看作干扰，因此，可定义相应的人工噪声信泄噪比(AN-to-leakage-plus-noise ratio ANLNR)为According to the concept of leakage, when initializing the artificial noise projection matrix, the artificial noise along the eavesdropping direction is regarded as a useful signal, and the artificial noise along the desired direction is regarded as interference. Therefore, the corresponding artificial noise signal-to-noise ratio (AN- to-leakage-plus-noise ratio ANLNR) is
为了最大化信泄噪比得到初始化矩阵PAN，我们需通过拉直操作将矩阵PAN转化为一个列向量故上式可写成In order to maximize the signal-to-noise ratio to obtain the initialization matrix P AN , we need to convert the matrix P AN into a column vector through a straightening operation Therefore, the above formula can be written as
因此，通过最大化上述目标函数和Rayleigh-Ritz定理，我们可以求得优化变量w由矩阵Therefore, by maximizing the above objective function and the Rayleigh-Ritz theorem, we can obtain the optimization variable w by the matrix
的最大特征值所对应的特征向量组成。由此，我们可以得到初始化的人工噪声矩阵PAN。The eigenvector corresponding to the largest eigenvalue of . Thus, we can obtain the initialized artificial noise matrix P AN .
同理，期望用户希望有用信息尽可能少地泄露到窃听用户，因此，我们定义私密信号信泄噪比(Confidential signal-to-leakage-plus-noise ratio ANLNR)为Similarly, users are expected to want useful information to be leaked to eavesdropping users as little as possible, so we define the confidential signal-to-leakage-plus-noise ratio (ANLNR) as
根据最大化信泄噪比准则以及Rayleigh-Ritz定理可以求得vd的初始值为矩阵According to the principle of maximizing the signal-to-noise ratio and the Rayleigh-Ritz theorem, the initial value of v d can be obtained as a matrix
的最大特征值所对应的特征向量组成。The eigenvector corresponding to the largest eigenvalue of .
S2.利用广义逆迭代算法优化人工噪声投影矩阵需固定对应的有用信号波束成形向量，并且需要对其人工噪声投影矩阵进行拉直操作。S2. Optimizing the artificial noise projection matrix using the generalized inverse iterative algorithm requires fixing the corresponding useful signal beamforming vector and straightening the artificial noise projection matrix.
当优化问题P1中波束成形向量固定时，优化问题P1可以写成When the beamforming vector in optimization problem P1 is fixed, the optimization problem P1 can be written as
此时，目标函数Rs(fixed vd,PAN)可以写成At this point, the objective function R s (fixed v d ,P AN ) can be written as
其中in
考虑到PAN的伸缩并不改变式(20)的比值，因此，问题P1.1可等效为Considering that the expansion and contraction of P AN does not change the ratio of formula (20), therefore, problem P1.1 can be equivalent to
由于式(25)是一个非凸二次分式函数，和均为半正定矩阵，因此w可以利用GPI算法解得，由此即可得到相应的PAN。Since equation (25) is a non-convex quadratic fraction function, and Both are positive semi-definite matrices, so w can be solved using the GPI algorithm, and the corresponding P AN can be obtained from this.
S3.利用Rayleigh-Ritz方法优化有用信号波束成形向量时需固定相应的人工噪声投影矩阵，并取最大特征值所对应的特征向量。S3. When using the Rayleigh-Ritz method to optimize the useful signal beamforming vector, it is necessary to fix the corresponding artificial noise projection matrix, and take the eigenvector corresponding to the largest eigenvalue.
当优化问题P1中人工噪声矩阵固定时，优化问题P1可以写成When the artificial noise matrix in the optimization problem P1 is fixed, the optimization problem P1 can be written as
由式(9)可以发现上述优化问题可以等效为From formula (9), it can be found that the above optimization problem can be equivalent to
事实上，这是一个Rayleigh-Ritz比值问题，最优的vd可由矩阵In fact, this is a Rayleigh-Ritz ratio problem, and the optimal v d can be obtained by the matrix
(He+AeIN)-1(Hd+AdIN) (28)(H e +A e I N ) -1 (H d +A d I N ) (28)
的最大特征值所对应的特征向量得到。The eigenvector corresponding to the largest eigenvalue of is obtained.
S4.计算人工噪声投影矩阵和有用信号波束成形向量更新前后所对应的安全速率之差的绝对值，直到满足终止条件。S4. Calculate the absolute value of the difference between the artificial noise projection matrix and the corresponding safe rate before and after updating the useful signal beamforming vector, until the termination condition is met.
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