Time reversal filtering, power allocation and artificial noise design method to enhance the security performance of OFDM system

Abstract

The present invention discloses a time reversal filtering, power allocation and artificial noise design method for enhancing the security performance of OFDM system. For OFDM transmission system with eavesdroppers, time reversal pre-filtering is used to increase the difference between the characteristics of legal channel and eavesdropping channel, and the covariance matrix of the carrier power allocation and artificial noise of the transmitting terminal is jointly optimized with the goal of maximizing the system confidentiality rate. The power allocation problem is solved by finding a solution that satisfies the first-order necessary conditions of Karush-Kuhn-Tucker (KKT), and the time domain null space artificial noise is constructed using the degrees of freedom provided by the cyclic prefix. A joint iterative optimization method for the subcarrier power allocation and the covariance matrix of the artificial noise is further provided.

Description

Technical Field

[0001] The invention relates to the field of information communication, and in particular to a time reversal filtering, power allocation and artificial noise design method for enhancing the safety performance of an OFDM system. Background Art

[0002] The security of information transmission is one of the key issues in the field of communication. Due to the openness of the transmission medium, the broadcast characteristics of the wireless channel, and the instability of the network structure, wireless communication systems are vulnerable to attacks, and the reliability and security of information transmission face major challenges. Physical layer security is an anti-eavesdropping technology that does not rely on upper layer encryption, but instead uses the randomness and diversity of the wireless channel to achieve secure information transmission at the physical layer by using signal processing, coding and other technologies. Confidentiality capacity is an indicator for evaluating the security performance of the physical layer based on information theory security. It is the maximum transmission rate of confidential information under the condition that the legitimate receiving end can reliably receive it and the eavesdropper cannot obtain confidential information. At present, the main method to achieve physical layer security is to increase the quality difference between the main channel and the eavesdropping channel through multiple antennas, beamforming, artificial noise (AN) and other signal processing technologies, thereby obtaining and improving confidentiality capacity, and then through secure channel coding, the legitimate receiving end can reliably receive information while preventing eavesdropping, thereby achieving confidential information transmission. Many existing solutions for enhancing physical layer security are based on the spatial freedom provided by multi-antenna systems. For example, beamforming can be used to direct the signal to the legitimate receiver and the nulling can be used to enhance the quality advantage of the legitimate receiver over the eavesdropping receiver. Artificial noise is a technology that enhances physical layer security by active interference and is often used in conjunction with multi-antenna technology. By utilizing the spatial freedom provided by multiple transmitting antennas, the direction of the artificial noise emission can be controlled through beamforming to effectively interfere with eavesdroppers. Even if it may have a slight impact on the legitimate receiver, it can significantly improve the system's confidentiality transmission capability. The literature [Khisti A, Wornell G W. Secure transmission with multiple antennas I: The MISOME wiretap channel [J]. IEEE Transactions on Information Theory, 2010, 56 (7): 3088-3104.] proposed a physical layer security solution that uses beamforming and artificial noise together. By using beamforming to direct the transmitted signal to the legitimate receiving end, and placing the artificial noise in the null space of the legitimate channel, it effectively interferes with potential eavesdroppers without interfering with the legitimate receiving end, thereby improving the confidentiality capacity of the system. Artificial noise is an important technical means to enhance the security performance of the physical layer, especially when the state information of the eavesdropping channel cannot be obtained or is incomplete. Many literatures have conducted in-depth research on the design and application of artificial noise.For example, in the literature [Wang B, Mu PC, Li Z Z. Artificial-noise-aided beamforming design in the MISOME wiretap channel under the secrecy outage probability constraint [J]. IEEE Transactions on wireless communications, 2017, 16 (11): 7207-7220.], the optimization problem of beamforming design assisted by artificial noise is studied for a multiple-input single-output (MISO) system with multiple eavesdroppers, and the confidentiality rate of the system is maximized under the constraint of confidentiality interruption probability. The research results of this literature show that artificial noise can not only interfere with eavesdropping nodes, but also improve the performance of legitimate users under certain circumstances. Beamforming and artificial noise are important methods to enhance physical layer security, but they need to rely on the spatial freedom of the multi-antenna system to achieve better results. In some nodes that are limited by volume, power consumption, etc., since they can only be equipped with a single antenna, the improvement of physical layer security transmission performance is greatly restricted.

[0003] Time reversal (TR) technology uses multipath transmission of wireless channels to achieve energy focusing of signals in the time domain and space domain, which can improve the strength of received signals with very low system complexity. In the TR transmission system, the signal must be filtered by a TR filter before being sent into the channel. The impulse response of the TR pre-filter is the time-reversed conjugate of the channel impulse response (CIR), which makes the multipath channel a matched filter for the transmitted signal. After TR filtering and multipath channel transmission, the signal will have an obvious energy peak at the target receiver at a specific time, and the energy will be significantly attenuated at the time away from the peak. The literature [Wang B, Wu YL, Han F, et al. Green wireless communications: a time-reversal paradigm [J]. IEEE Journal on Selected Areas in Communications, 2011, 29 (8): 1698-1710.] verified the spatial and temporal focusing characteristics of TR and proved that TR preprocessing can improve the signal strength of the target receiver while reducing the energy leakage at the non-target receiver. The spatial and temporal focusing characteristics of TR technology make it very suitable for application in physical layer security transmission systems. The literature [Tan VT, Ha DB, TranD D. Evaluation of physical layer secrecy in MIMO ultra-wideband system using time-reversal techniques [C] / / 2014 International Conference on Computing, Management and Telecommunications (ComManTel). Da Nang, Vietnam: IEEE Press, 2014: 70-74.] studied the confidentiality transmission performance of TR transmission technology in the Multiple-Input Multiple-Output (MIMO) system. The results show that TR transmission technology can significantly improve the confidentiality capacity of the system. By combining TR technology with artificial noise technology, the physical layer security performance of the system can also be effectively improved under a single transmitting antenna.The literature [Lei WJ, Zhang WH, Yang MM, et al. Optimization of pre-processing filter for time-reversal multi-user secure transmission systems based on artificial noise [J]. Digital Signal Processing, 2021, 109 (102933).] studied the design and optimization of artificial noise security schemes with and without eavesdropper channel state information (CSI) in TR multi-user downlink multiple access systems. When the eavesdropping channel CSI is not available, zero-space artificial noise is used to minimize the signal power under the target constraint of each user's signal to interference plus noise ratio (SINR), maximize the artificial noise power, and minimize the eavesdropping rate; when the eavesdropping channel CSI is known, the TR pre-filter and artificial noise are jointly optimized to maximize the confidentiality rate. Reference [[9]XU Q,REN PY,DU QH,et al.Security-aware waveform and artificial noise design for time-reversal-based transmission[J].IEEE Transactions on Vehicular Technology,2018,67(6):5486-5490.] studied a scheme to improve the security transmission performance of the system by combining artificial noise and TR technology. Based on the two conditions of whether the CSI of the eavesdropping channel is known or not, three security transmission schemes that jointly optimize the TR pre-filter and artificial noise are proposed. The simulation verifies that the security performance of the proposed scheme is better than that of the scheme using conventional matched pre-filtering.

[0004] Orthogonal Frequency Division Multiplexing (OFDM) is a key technology in the 4th and 5th generation mobile communication systems, and will also be a key technology in the next generation of mobile communication systems. The space-time focusing effect of TR is also beneficial to improving the performance of OFDM systems. The literature [Liu Z, Yang T C. On the design of cyclic prefix length for Time-Reversed OFDM [J]. IEEE Transactions on Wireless Communications, 2012, 11 (10): 3723-3733.] studied the problem of using TR technology to shorten the cyclic prefix (CP) length of OFDM systems and improve the system spectrum efficiency. When the CP length is insufficient, the space-time focusing characteristics of TR are used to reduce inter-symbol interference (ISI) and inter-carrier interference (ICI), and a quantitative mathematical relationship between signal-to-interference-to-noise ratio (SINR), bit error performance and CP length is established. The literature [Aminjavaheri A, FARHANG A, rezazadehreyhani A, et al. OFDM without CP in massive MIMO [J]. IEEE Transactions on Wireless Communications, 2017, 16 (11): 7619-7633.] studied the relationship between the number of antennas and SINR in massive MIMO OFDM systems. The results of theoretical analysis and simulation show that in the absence of CP, even if the number of antennas increases infinitely, ISI and ICI cannot continue to decrease. However, after adding TR pre-filtering, ISI and ICI can approach zero as the number of antennas increases, thereby improving SINR and significantly improving the bandwidth efficiency of the system. For OFDM systems, TR pre-processing in the time domain can also be implemented in the frequency domain.The literature [Nguyen T, Monfared S, Determe J, et al. Performance analysis of frequency domain precoding time-reversal MISO OFDM systems [J]. IEEE Communications Letters, 2020, 24 (1): 48-51.] proposed a method for frequency domain TR precoding in MISO OFDM communication systems, derived a closed-form expression for the root mean square error of the received signal, and analyzed the relationship between the root mean square error and different rate back-off factors (Bof). The simulation results show that increasing the BOF or the number of antennas can improve the signal-to-noise ratio (SNR) gain of the system. Physical layer security in OFDM systems is also one of the key issues studied by the academic community. Power allocation, beamforming, artificial noise, and differentiated channel estimation are technologies that have been studied more to enhance the confidentiality of OFDM systems. Reference [Samara L, Alabbasi AO, Gouissem A, et al. A novel OFDM waveform with enhanced physical layer security [J]. IEEE Communications Letters, 2021, 25 (2): 387-391.] proposed a method to enhance physical layer security by optimizing the OFDM waveform design, and randomly adjusted the length of the CP through the key shared by the legitimate parties to randomize the duration of the OFDM symbol, thereby increasing the detection complexity of the eavesdropping node. Reference [Qin H, Suny, Chang TH, Chen X, et al. Power allocation and time-domain artificial noise design for wiretap OFDM with discrete inputs [J]. IEEE Transactions on Wireless Communications, 2013, 12 (6): 2717-2729.] studied the scheme of combining power allocation and artificial noise to improve the security performance of the OFDM system under the condition of discrete input character set, and proposed an iterative optimization algorithm based on Lagrangian dual optimization and an artificial noise design method. The simulation results show that the proposed scheme can significantly improve the system confidentiality rate. The spatial focusing effect of TR can also improve the security performance of OFDM.The literature [Cao W, Lei J, Liu W, et al. Secure performance of time reversal precoding technique in MISO OFDM systems [C] / / 2014 Communications Security Conference (CSC). Beijing, China: IEEE Press, 2014: 1-5.] compared the security performance of TR precoding and maximum ratio transmission (MRT) precoding techniques in MISO OFDM systems in terms of achievable confidentiality rate. The results show that when the number of transmitting antennas is small, the achievable confidentiality rate of the TR scheme is better than that of the MRT scheme. When the number of transmitting antennas is large, the confidentiality performance of the two precoding techniques is almost the same. The literature [Golstein S, Nguyen T, Horlin F, et al. Physical layer security in frequency-domain time-reversal SISO OFDM communication [C] / / 2020 International Conference on Computing, Networking and Communications (ICNC), Big Island, HI, USA: IEEE Press 2020: 222-227.] studied the method of achieving secure communication by combining frequency-domain TR precoding and artificial noise in SISO OFDM communication system, and verified the performance of the proposed scheme through simulation. Summary of the invention

[0005] The purpose of the present invention is to provide a method for an OFDM transmission system with an eavesdropper, in which, when the eavesdropping channel state information (CSI) is known, time reversal pre-filtering is used to increase the difference between the legitimate channel and the eavesdropping channel characteristics, and a method for jointly optimizing the carrier power allocation of the transmitting terminal and the covariance matrix of artificial noise with the goal of maximizing the system confidentiality rate is provided. The method allocates power according to the channel state information, and adds artificial noise to interfere with the eavesdropping terminal in the null space of the legitimate channel to maximize the system confidentiality rate.

[0006] In order to achieve the above purpose, the present invention adopts the following technical scheme: based on the OFDM communication system, a TR pre-filter is applied to derive the system confidentiality rate formula, and a joint optimization problem of subcarrier power allocation and the covariance matrix of artificial noise with the goal of maximizing the system confidentiality rate is constructed, the problem is converted into a two-layer optimization problem, and finally an alternating iterative algorithm is used to jointly optimize the subcarrier power allocation and the covariance matrix of artificial noise. The specific steps are as follows:

[0007] (1) Construct a communication system model and obtain the achievable confidentiality rate of the system based on the constructed system model;

[0008] (2) Taking the maximization of the achievable confidentiality rate as the optimization goal, a joint optimization mathematical model of power allocation and artificial noise covariance matrix under the condition of transmission power constraint is constructed;

[0009] (3) The mathematical model in step (2) is transformed into a two-level optimization problem, wherein the first-level optimization problem determines the optimal power allocation factor, and the second-level optimization problem is the iterative optimization of the subcarrier power allocation and the artificial noise covariance matrix given the power allocation factor;

[0010] (4) The optimal power allocation factor, the power allocation of all subcarriers and the artificial noise covariance matrix are obtained through iteration.

[0011] The present invention utilizes the spatiotemporal focusing characteristics of TR to improve the anti-eavesdropping capability of the system, and jointly optimizes the carrier power allocation of the transmitting terminal and the artificial noise covariance matrix with the goal of maximizing the confidentiality rate. Simulation experiments show that the achievable confidentiality rate of the system optimized by the method given in the present invention is significantly improved compared with the unoptimized system or the partially optimized system. By using zero-space artificial noise, the achievable confidentiality rate is significantly improved, and the confidentiality rate can continue to increase with the increase of the transmission power. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 This is the system model diagram under the optimized power allocation scheme only;

[0013] Figure 2 This is the system model diagram under the artificial noise auxiliary scheme;

[0014] Figure 3 This is a system model diagram with multiple antennas;

[0015] Figure 4 Comparison of the confidentiality rates achievable by the time-reversal pre-filtering scheme and the direct transmission scheme when there is no artificial noise;

[0016] Figure 5 Comparison of confidentiality rates between schemes with and without artificial noise;

[0017] Figure 6 Comparison of the confidentiality rates of the two optimization schemes under different numbers of antennas;

[0018] Figure 7 Comparison of confidentiality rates under optimized and fixed power allocation factors. DETAILED DESCRIPTION

[0019] Symbol description: Underlined letters represent frequency domain symbols, ununderlined letters represent time domain symbols; lowercase bold letters represent vectors, uppercase bold letters represent matrices, and white letters represent scalars; |·|, (·) T 、(·) * 、(·) H , tr(A), A≥0 represent absolute value or modulus, transpose, conjugate, conjugate transpose, convolution, trace, and semi-positive definite, respectively; [x] + Represents the larger value between x and 0.

[0020] The time reversal orthogonal frequency division multiplexing (TR-OFDM) system is studied. The system model is as follows: Figure 1 As shown. The system includes a transmitter Alice and two receivers. The transmitter will send information to the two receivers in time, but the information sent to the two receivers needs to be kept confidential. The target receiver of the current information transmission is called the legitimate receiver Bob, and the other receiver is called the eavesdropping terminal Eve. Since they are all users in the system, the present invention assumes that the transmitter can obtain the CSI of the channel between it and the two receivers. The two receivers are equipped with a single antenna. First, consider the case where the transmitter is equipped with a single antenna, and then generalize it to the scenario of multiple antennas. The system model diagram under the multi-antenna scenario is shown in the figure Figure 3 As shown. The channel is a frequency selective fading channel. For the convenience of description, the present invention assumes that the CIR length of the channel from the transmitter to the two receiving ends is L, and the CIR of the channel from the transmitter to the legitimate receiving end and the eavesdropping end is recorded as h B [l]、h E [l], l = 0, ..., L-1, and its vector form is represented by h B =[h B [0],h B [1],…,h B [L-1]] T 、h E =[h E [0],h E [1],…,h E [L-1]] TThe TR pre-filter adopts the form of a conventional matched filter, with the number of taps being L, and the tap coefficient being the time-reversed conjugate of the CIR of the legal channel, that is, the impulse response of the TR pre-filter is

[0021]

[0022] In the formula, is the normalization coefficient. Considering the cascade of TR prefilter and multipath channel as an equivalent channel, the length of its impulse response is 2L-1, then the equivalent CIR of the legitimate channel and the wiretap channel are

[0023]

[0024]

[0025] The transmitter first transforms the frequency domain symbol s into a time domain symbol through an inverse fast Fourier transform (IFFT), where: s =[ s 1, s 2,…, s N ] T is a zero-mean, unit-variance information symbol vector, and N is the number of OFDM subcarriers. The time-domain symbol sequence is inserted into the CP to form an OFDM symbol. The sample value sequence in the time-domain symbol is sent to the channel after parallel / serial conversion and TR pre-filter. The signal is transmitted through the multipath channel to the receiving end. The receiver performs serial / parallel conversion, removes the CP, and then transforms the time-domain symbol to the frequency domain through Fast Fourier Transform (FFT). In order to eliminate inter-symbol interference, the length of the CP is N cp It should be greater than the equivalent channel delay spread. The process of inserting CP can be expressed as the time domain sequence after IFFT and the inserted CP matrix Multiply, where Represents the N×N dimensional identity matrix I N After N cp The process of removing CP can be expressed as receiving OFDM symbols and removing CP matrix Multiply, where Represents N×N cp dimensional zero matrix. The process of OFDM symbols passing through TR pre-filtering and multipath channel can be expressed as the convolution operation of the sample sequence in the OFDM symbol and the impulse response of the equivalent channel, which is equivalent to the multiplication of the OFDM symbol sample vector and the Toeplitz channel matrix. In this way, the frequency domain symbols received by the legitimate receiving end and the eavesdropping end can be expressed as

[0026]

[0027]

[0028] Where P = diag(P1, P2, ..., P N ) is the subchannel power diagonal matrix, which determines the signal power of each subchannel; P 1 / 2 It means that the diagonal elements of the matrix are the square roots of the diagonal elements in P; w =[ w 1, w 2,…, w N ] T and v =[ v 1, v 2,…, v N ] T are the channel additive noise vectors of the legitimate end and the eavesdropper end, respectively, and their elements are independent complex Gaussian random variables with zero mean and unit variance. F is the Fourier transform matrix, T cp and R cp are the insertion and removal of CP matrices, respectively. H0 and G0 are the Toeplitz channel matrices corresponding to the equivalent legal channel and the equivalent eavesdropping channel, respectively, which are expressed as:

[0029]

[0030]

[0031] Where L is the number of channel multipaths, g[l]、h B [l]、h E [l] represents the impulse response of the TR pre-filter, the channel impulse response from the transmitter to the legitimate receiver and the eavesdropper, respectively.

[0032] The sending and receiving processing and multipath channels from the sending end IFFT to the receiving end FFT are regarded as equivalent frequency domain parallel channels, that is,

[0033] H =FR cp H0T cp F H =diag( H 1, H 2,…, H N )

[0034] G =FR cp G0T cp F H =diag( G 1,G 2,…, G N )

[0035] in, H i and G i represent the complex channel coefficients of the i-th subchannel from the transmitting end to the legitimate end and the eavesdropping end respectively.

[0036] Under the system model of the present invention, the achievable confidentiality rate is:

[0037]

[0038] Among them, P i Represents the signal power allocated on the i-th subchannel.

[0039] Under the limitation of total transmission power, the power allocation of each subcarrier at the transmitting end is optimized to maximize the achievable confidentiality rate. The optimization problem can be expressed as

[0040]

[0041]

[0042] P max is the average maximum transmit power allowed for each subchannel, which is equivalent to limiting the total transmit power to NP max .

[0043] R s (P) is an upward convex function, which must have a maximum value. The optimization is a convex optimization problem and can be solved by the first-order KKT condition. The expression for the optimal power solution is:

[0044]

[0045] Among them, λ≥0 is the Lagrange multiplier. It is not difficult to see that the optimal solution P i * is a function of λ, and λ is determined by the power constraint, that is, the KKT condition, that is,

[0046]

[0047] It is very difficult to directly solve λ that satisfies the above equation. First, determine the solution of the equation, let Taking the first-order derivative of f(λ) with respect to λ, we get

[0048]

[0049] Note that when | H i | 2 >|G i | 2 When , f′(λ) is strictly less than zero, that is, f(λ) is a strictly monotonically decreasing function of λ, and when λ→0, f(λ)→+∞, when λ→∞, f(λ)<0, so f(λ) must have a zero point between (0, +∞), that is, there must be a non-negative λ that satisfies the KKT condition, which can be solved by numerical methods. The present invention first uses a one-dimensional forward and backward search method to find the interval [a, b] containing the zero point of f(λ), and then uses a binary search method to find the zero point of f(λ), that is, it satisfies The solution λ * . Solve for the optimal Lagrange multiplier λ * Algorithm 1 is summarized in Table 1, where ε1 is the relative difference between the interval endpoints required when the iteration terminates, that is, the convergence factor.

[0050] Table 1 Numerical algorithm for finding the optimal Lagrange multiplier

[0051]

[0052] The iterative power allocation algorithm (referred to as Algorithm 2) is summarized in Table 2. First, | H i | 2 <| G i | 2 The sub-channel power is set to zero, and the solution is obtained by Algorithm 1 to satisfy The Lagrange multiplier λ (1) , back to the expression of the optimal power solution to obtain the power allocation results of all sub-channels If the power allocated to any subchannel is negative, set the power of these subchannels to zero and solve the problem again to satisfy the constraint The Lagrange multiplier λ (2) , and the corresponding sub-carrier power allocation. Repeat the above process until the power allocation results of all sub-channels are positive or 0.

[0053] Table 2 Iterative power allocation algorithm

[0054]

[0055]

[0056] In order to further improve the safety performance of the system, time domain zero space artificial noise is added on the basis of the existing system. The system model is as follows Figure 2 The artificial noise vector a is superimposed on the time domain sequence before TR preprocessing and adding CP. After TR filtering and multipath channel transmission, the frequency domain symbol sequence received by the legitimate receiver and the eavesdropper can be expressed as

[0057] y B =FR cp H0(T cp F H P 1 / 2 s +a)+ w = H P 1 / 2 s +FR cp H0a+ w

[0058] y E =FR cp G0(T cp F H P 1 / 2 s +a)+ v = G P 1 / 2 s +FR cp G0a+ v

[0059] In order not to interfere with the legal receiver, the artificial noise should be located in the null space of the legal channel. The artificial noise can be designed as a = Qz, where z is a Gaussian random vector, obeying Among them, ∑ z is the diagonal covariance matrix of z. Q is a semi-unitary matrix whose column vectors span R cp The null space of H0 satisfies R cp H0Q=0. H0 and G0 are the Toeplitz channel matrices corresponding to the equivalent legal channel and the equivalent wiretap channel, respectively. Since the artificial noise a is set in the null space of the legal channel, the received signal on subchannel i can be expressed as

[0060]

[0061]

[0062] Among them, f i T is the i-th row of the FFT matrix F.

[0063] The system can achieve a confidentiality rate of

[0064]

[0065] Among them, q i =f i T R cp G0Q, [x] +represents the maximum value between 0 and x. The joint optimization problem of subcarrier power allocation and the covariance matrix of artificial noise to maximize the confidentiality rate can be expressed as

[0066]

[0067]

[0068] The problem is a non-convex problem with two optimization variables. The successive convex approximation algorithm is used to alternately optimize P and ∑ z , when optimizing one variable, fix the other variable, and obtain the optimal solution through alternating iterative optimization. But note that in P and ∑ z In the iterative solution process, the power of the transmitted data symbol and the artificial noise is required to be given. The power allocation factor α∈[0,1] is introduced as the ratio of the artificial noise power to the total power, and 1-α is the proportion of the power allocated to the data symbol. In this way, the optimization problem can be equivalently expressed as

[0069]

[0070]

[0071]

[0072] 0≤α≤1

[0073] The problem is further transformed into an equivalent two-level optimization problem: the first-level optimization problem is to find the value that maximizes the objective function within the range of α.

[0074]

[0075] st0≤α≤1

[0076] in When α is fixed, P and ∑ z is the maximum value of the confidentiality rate of the variable, that is And finding this maximum value is the second-level optimization problem:

[0077]

[0078]

[0079]

[0080] For the first-level optimization problem, it is easy to see that there must be an optimal α *To maximize the confidentiality rate, the golden section method is used here to solve. In the search process, it is necessary to solve the second-level optimization problem according to the α value corresponding to the golden section point. Through iteration, the search interval is continuously narrowed until the difference between the confidentiality rates of the two α values ​​corresponding to the interval is less than a pre-set value. Solve the optimal power allocation factor α * The algorithm (referred to as Algorithm 3) is summarized in Table 3.

[0081] Table 3 Golden section algorithm for solving the optimal power allocation factor

[0082]

[0083]

[0084] The solution to the second-level optimization problem is discussed below.

[0085] The second-level optimization problem is to optimize the artificial noise covariance matrix and power allocation under a given power allocation factor. It is decomposed into two sub-problems that need to be solved iteratively. Sub-problem 1 is to optimize the artificial noise covariance matrix ∑ z Under fixed conditions, the power allocation P of the subcarrier is optimized to maximize the confidentiality rate:

[0086]

[0087]

[0088] Sub-problem 2 is to optimize the covariance matrix ∑ of the artificial noise under the condition that the subcarrier power allocation P is fixed. z Minimize the eavesdropping channel capacity:

[0089]

[0090]

[0091] The covariance matrix of artificial noise ∑ z Given the situation, the optimization subproblem 1 is a convex optimization problem, which can be solved by the first-order KKT condition. The expression of the power optimal solution is

[0092]

[0093] in, This optimization subproblem is completely similar to the power allocation problem without artificial noise, so it can be solved using Algorithm 2.

[0094] Substituting the power allocation result obtained from solving subproblem 1 into subproblem 2, it is easy to see that this is a convex optimization problem that can be solved using the CVX toolbox.

[0095] To obtain the maximum confidentiality rate under a given power allocation factor α, we need to solve the optimal subcarrier power allocation P and the covariance matrix ∑ of the artificial noise. z , it is necessary to iterate between the solutions of subproblems 1 and 2. First, set the initial value of the artificial noise covariance matrix In this Next, solve subproblem 1 and obtain the solution P for power allocation. (1) , substitute into subproblem 2, and solve to obtain the solution of the artificial noise covariance matrix Substitute it into subproblem 1 and perform the second round of iteration. Repeat the iteration until convergence. The iterative algorithm (referred to as Algorithm 4) is summarized in Table 4, where P (k) and are the subcarrier power allocation and artificial noise covariance matrix obtained in the kth iteration respectively, and ε3 is the maximum value of the difference in confidentiality rate obtained in two iterations required when the iteration terminates, that is, the convergence factor.

[0096] Table 4 Successive convex approximation algorithm

[0097]

[0098] The present invention will be further described in detail below with reference to the accompanying drawings. This section simulates and verifies the performance of the proposed algorithm. The simulation results of the confidentiality rate in each of the following figures are 1×10 4 The average value of the group channel samples. In the simulation, the number of OFDM subcarriers N = 64, the cyclic prefix length N cp =16; the number of channel paths L = 8, the channel bandwidth B = 1MHz; the channel is a Rayleigh fading channel, the channel coefficients obey a zero-mean complex Gaussian distribution, and the variances of the l-th path coefficients of the legitimate channel and the eavesdropping channel are and l=0,1,…,L-1, where σ T =5 / B is the root mean square delay of the path, T s =1 / B is the sampling period, η B , η E are the large-scale fading coefficients of the legitimate channel and the eavesdropping channel, respectively. They are normalized to 1 in the simulation. The convergence factor in Algorithms 1, 3, and 4 is ε1 = 1 × 10 -4 ,ε2=ε3=1×10 -3 .

[0099] Figure 4 is the simulation result of the change of the confidentiality rate of the time reversal pre-filtering scheme and the direct transmission scheme with the transmission power when there is no artificial noise, where Figure 4 (a) is the simulation result with one transmitting antenna. Figure 4(b) is the simulation result under two transmitting antennas. In the figure, "TR" indicates that the signal has been time-reversed pre-filtered; "DT" indicates direct transmission, that is, the transmitted signal is not pre-processed by TR. The simulation results of the scheme of optimizing subcarrier power allocation and the scheme of equal power allocation according to the algorithm given in Algorithm 2 of the present invention are given respectively. The equal power allocation scheme means that power is evenly distributed on the subchannels with higher subchannel gains in all legal channels. From Figure 4 (a) It can be seen that, regardless of whether TR pre-filtering is performed or not, the confidentiality rate is significantly improved after power allocation optimization, and the smaller the transmission power, the more obvious the improvement, which proves the effectiveness of optimizing power allocation in improving confidentiality transmission performance. Comparing the simulation results of TR transmission and direct transmission, it can be seen that the confidentiality rate of TR transmission is higher than that of direct transmission at low transmission power, and the two are similar at high transmission power. This is because the impulse response of the TR pre-filter is the time-reversed conjugate of the CIR of the legitimate channel, and the convolution of the transmitted signal with it is equivalent to multiplying the symbol transmitted on each subchannel by the conjugate of the subchannel coefficient in the frequency domain. For the legitimate channel, the subchannel with a gain greater than 1 will show a higher channel gain after TR processing, and for the subchannel with a channel gain less than 1, its channel gain will become lower after TR processing, that is, TR processing will increase the difference between subchannel gains. For the undesired receiver, there is no similar effect. In other words, after TR pre-filtering, the subchannel with a high gain of the legitimate channel will have a higher quality advantage over the eavesdropping subchannel, while the subchannel with a low gain becomes worse than the corresponding subchannel of the eavesdropping channel. After optimizing the power allocation, the change in sub-channel performance differences is reflected in the increase in the capacity difference between the legitimate channel and the eavesdropped channel, thereby improving the confidentiality transmission rate. When the transmission power is high, the effect of power allocation on the transmission rate decreases, so the effect of improving the confidentiality rate through TR pre-filtering will also decrease. Figure 4 (b) The simulation results under two antennas show that when the number of antennas increases, the effect of improving the confidentiality rate by optimizing the power allocation is more obvious, especially at low transmit power; and comparing the simulation results of the two schemes with and without TR preprocessing, it can be seen that the confidentiality rate advantage of the scheme with TR preprocessing is greater than that of the single antenna. This is because TR preprocessing is performed on legal channels, and the increase in the number of antennas is equivalent to the increase in the number of paths, the space-time focusing effect is more obvious, and the capacity of legal channels will be more significantly improved.

[0100] Figure 5 The comparison of confidentiality rates of the schemes with and without artificial noise is shown, and the simulation results of TR transmission and direct transmission are given respectively. The scheme without artificial noise uses the algorithm 2 of the present invention to optimize the power allocation of subcarriers, and the scheme with artificial noise uses the algorithm 4 of the present invention to jointly optimize the subcarrier power allocation and the artificial noise covariance matrix. Figure 5 (a) is the simulation result with one transmitting antenna. Figure 5 (b) is the simulation result under two transmitting antennas. It can be seen from the figure that regardless of whether TR pre-filtering is used, the artificial noise scheme can significantly improve the system confidentiality rate, and the higher the transmission power, the more obvious the effect. When there is no artificial noise, the confidentiality rate will gradually approach an upper limit as the transmission power increases, while when there is artificial noise, there is no such upper limit, and the confidentiality rate will continue to increase with the increase of transmission power. This is because when there is no artificial noise, although the subcarrier power allocation is optimized to maximize the confidentiality rate, when the transmission power increases to a certain extent, the legal channel capacity and the eavesdropping channel capacity will gradually converge with the increase of transmission power, resulting in a gradual decrease in the growth rate of the confidentiality rate, and finally tending to a constant value. In the scheme using artificial noise, when the transmission power increases, the signal power and the power of artificial noise will increase after optimization. Since artificial noise will not affect the legal receiving end, the legal channel capacity increases, while the eavesdropping end increases due to the increase of artificial noise, resulting in the increase rate of the eavesdropping channel capacity is significantly lower than the legal channel. Therefore, the confidentiality rate will continue to increase rapidly with the increase of total transmission power. Compared with Figure 5 (a) and Figure 5 From the simulation results of (b), we can see that when the number of antennas increases, the confidentiality rate of the direct transmission system only increases slightly, while the confidentiality rate of the TR transmission system increases significantly. This is because TR transmission uses channel multipath to concentrate the transmission energy at the legitimate receiving end. The increase in the number of antennas is equivalent to the increase in the number of channel paths, and the space-time focusing effect is more obvious. The received signal strength of the legitimate end increases, which makes the confidentiality rate of TR transmission significantly improved. This shows that increasing the number of antennas can provide more spatial degrees of freedom, and TR transmission can make more full use of multipath channels to obtain better time and space focusing effects, thereby improving the physical layer security performance.

[0101] Figure 6 The simulation results of the confidentiality rates of the two schemes proposed by the present invention are compared under the conditions of one and two antennas. As can be seen from the figure, when the number of antennas increases, the confidentiality rates of the two schemes are significantly improved, and the confidentiality rate of the artificial noise scheme increases faster with the increase of the transmission power. This is because the increase in the number of antennas provides more channel transmission paths, and TR transmission can obtain better spatiotemporal focusing effects, improve the signal strength and legal channel capacity of the legal receiving end, while the eavesdropping end has no similar effect, thereby improving the confidentiality transmission rate. In the artificial noise scheme, when the transmission power increases, the power allocated to the artificial noise increases, and the rate of the eavesdropping end increases very slowly with the transmission power, and quickly tends to a constant value. Artificial noise will not affect the legal end, so the rate difference between the legal end and the eavesdropping end increases with the increase of the transmission power, thereby further improving the confidentiality transmission rate.

[0102] Figure 7 The scheme using artificial noise uses the algorithm 3 of the present invention to optimize the allocation factor of signal power and artificial noise power and compares the achievable confidentiality rate when the power allocation factor is fixed. When the power allocation factor is fixed, the subcarrier power allocation and the artificial noise covariance matrix are also optimized using the algorithm 4 of the present invention, where α=0 is a scheme without artificial noise and only optimizing the subcarrier power allocation. The number of antennas K=1 in the simulation. As can be seen from the figure, even the worst-performing artificial noise scheme with α fixed at 0.8 can continue to increase its achievable confidentiality rate as the transmission power increases. When the total transmission power increases to more than 1dBW, it is higher than the scheme without artificial noise, and the higher the total transmission power, the more obvious the performance advantage. In the scheme using artificial noise, the confidentiality rate of the α optimization scheme is always better than the scheme with fixed α, which shows that optimizing α is effective in improving the confidentiality rate. By comparing the simulation results when α is fixed, it can be seen that within the entire simulated power range, the achievable confidentiality rates when α=0.2 and α=0.4 are relatively close, and both are higher than when α=0.6 and 0.8. By carefully comparing the two curves when α=0.2 and α=0.4, we can see that the confidentiality rate of α=0.2 is slightly higher at low power, which means that when the total available power is low, it is better to allocate a smaller proportion of power to artificial noise because it does not carry information. This is in line with intuitive judgment. Figure 7 The simulation results show that only a small amount of power needs to be allocated to artificial noise to significantly improve the confidentiality rate, proving that artificial noise is an effective technical means to improve security performance with high power efficiency.

Claims

1. A time reversal filtering, power allocation and artificial noise design method for enhancing the security performance of OFDM system, characterized in that: The following steps are involved: (1) Construct a communication system model and obtain the achievable confidentiality rate of the system based on the constructed system model; This includes modeling the achievable confidentiality rates of the legitimate receiver and the eavesdropper, as follows: The received signals of the legitimate end and the eavesdropping end are expressed as: y B =FR cp H0(T cp F H P 1 / 2 s +a)+w=HP 1 / 2 s +FR cp H0a+ w y E =FR cp G0(T cp F H P 12 s+a)+v= G P 12 s+FR cp G0a+v in, s =[ s 1, s 2,…, s N ] T is the information symbol vector with zero mean and unit variance, F is the Fourier transform matrix, P = diag(P1, P2, ..., P N ) is the subchannel power diagonal matrix, T cp and R cp are inserting and removing CP matrices, respectively. w and v are the channel additive noise vectors of the legitimate end and the eavesdropper end respectively, a is the artificial noise vector, and the artificial noise is designed to be a = Qz, where z is a Gaussian random vector, obeying Among them, ∑ z is the diagonal covariance matrix of z, Q is a semi-unitary matrix, and its column vectors form R cp The null space of H0 satisfies R cp H0Q=0, the sending and receiving processing and multipath channel from the sending end IFFT to the receiving end FFT are regarded as equivalent frequency domain parallel channels, that is, H =FR cp H0T cp F H =diag( H 1, H 2,…, H N ), G =FR cp G0T cp F H =diag( G 1, G 2,…, G N ), H0 and G0 are the Toeplitz channel matrices corresponding to the equivalent legal channel and the equivalent eavesdropping channel, respectively, expressed as: Where L is the number of channel multipaths, g[l]、h B [l]、h E [l] represents the impulse response of the TR prefilter, the channel impulse response from the transmitter to the legitimate receiver and the eavesdropper, respectively; The system can achieve a confidentiality rate of Where N is the number of OFDM subcarriers, H i and G i represents the complex channel coefficients of the ith subchannel from the transmitter to the legitimate end and the eavesdropping end, respectively, P i represents the signal power allocated on the i-th subchannel, q i =f i T R cp G0Q, where f i T is the i-th row of the FFT matrix F, [x] + It means taking the maximum value between 0 and x; (2) Taking the maximization of the achievable confidentiality rate as the optimization goal, a joint optimization mathematical model of power allocation and artificial noise covariance matrix under the condition of transmission power constraint is constructed; The transmission power constraint is: Where P max is the average maximum transmit power allowed for each subchannel, which is equivalent to limiting the total transmit power to NP max ; The optimization problem is constructed as: (3) The mathematical model in step (2) is transformed into a two-level optimization problem, wherein the first-level optimization problem determines the optimal power allocation factor, and the second-level optimization problem is the iterative optimization of the subcarrier power allocation and the artificial noise covariance matrix given the power allocation factor; The optimization problem is transformed into an equivalent optimization problem, which includes: P and ∑ z In the iterative solution process, the power of sending data symbols and artificial noise is required to be fixed. The power allocation factor α∈[0,1] is introduced as the ratio of artificial noise power to total power, and 1-α is the proportion of power allocated to data symbols. The optimization problem is equivalent to: 0≤α≤1 The optimization problem is further transformed into an equivalent two-level optimization problem: the first-level optimization problem is to find the value that maximizes the objective function within the range of α. st0≤α≤1 in When α is fixed, P and ∑ z is the maximum value of the confidentiality rate of the variable, that is The second-level optimization problem is to optimize the artificial noise covariance matrix and power allocation under a given power allocation factor: The second-level optimization problem is decomposed into two sub-problems that need to be solved iteratively. Sub-problem 1 is to solve the covariance matrix ∑ z Under fixed conditions, the power allocation P of the subcarrier is optimized to maximize the confidentiality rate: The covariance matrix of artificial noise Σ z Given the situation, the optimization subproblem 1 is a convex optimization problem, which is solved by the first-order KKT condition, and the expression of the optimal power solution is obtained as follows: Optimal solution is a function of λ, and λ is determined by the power constraint, namely the KKT condition: in, Thus, the optimization problem is transformed into the problem of solving the optimal Lagrange multiplier; Sub-problem 2 is to optimize the covariance matrix ∑ of the artificial noise under the condition that the subcarrier power allocation P is fixed. z Minimize the eavesdropping channel capacity: (4) Obtaining the optimal power allocation factor, the power allocation of all subcarriers, and the artificial noise covariance matrix through iteration; The iterative algorithm specifically adopts the golden section method to solve the first-layer optimization problem. During the search process, the second-layer optimization problem needs to be solved according to the α value corresponding to the golden section point. The search interval is continuously narrowed by iteration until the difference between the confidentiality rates of the two α values ​​corresponding to the interval is less than a preset value. The solution of the second-layer optimization problem is specifically ∑ z Assign an initial value In this Next, solve subproblem 1 and obtain the solution P for power allocation. (1) , substitute into subproblem 2, and solve to obtain the solution of the artificial noise covariance matrix Substitute it into subproblem 1 and perform the second round of iteration; repeat the iteration until convergence.

2. The time reversal filtering, power allocation and artificial noise design method for enhancing the safety performance of OFDM system according to claim 1, characterized in that: The communication system model is based on the conventional OFDM secure communication system. The signal sent by the transmitter is first superimposed with time domain zero space artificial noise, and then enters the multipath channel after passing through a TR pre-filter. The TR pre-filter is a conventional matching pre-filter.

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