An OFDM-based integrated radar and communication secure transmission method

Abstract

The present invention discloses a secure transmission method for radar-communication integration based on OFDM, which improves the security of communication on the premise of ensuring the radar detection performance. In the present invention, artificial noise is added to the transmitted communication information at the base station and the power is allocated through the power allocation weight. It mainly interferes with the eavesdropping of the eavesdropper through the injection of AN to improve the secure transmission rate of communication. At the communication receiving end, the injected artificial noise can be effectively eliminated. At the radar receiving end, a series of operations such as matched filtering are performed to obtain the target reflection signal, and the Cramer-Rao lower bound (CRLB) of the target's angle and coordinates is calculated accordingly. Finally, with the constraint of the CRLB at the radar receiving end, maximizing the secure transmission rate at the communication receiving end is taken as an optimization problem. The present invention proposes an algorithm based on the Lagrangian dual method, which can effectively ensure the secure transmission rate and realize communication security and radar detection performance.

Description

Technical Field

[0001] The present invention belongs to the field of radar communication, and particularly relates to a secure transmission method for integrated radar communication based on OFDM (Orthogonal Frequency-Division Multiplexing). Background Art

[0002] With the continuous development of communication systems and radar systems, the two systems usually need to work together to simultaneously meet communication and sensing requirements. Therefore, integrated communication-radar systems have emerged. Compared with traditional independent radar systems and communication systems, integrated communication-radar systems can effectively reduce costs, save spectrum resources, and have a wide range of application scenarios. There are three ways to implement integrated communication-radar systems: time division, space division, and signal sharing.

[0003] OFDM technology is widely used in communication systems due to its flexible resource allocation and high spectrum utilization rate. At the same time, OFDM has the advantage of becoming an integrated waveform due to its stable performance in multipath fading and relatively simple synchronization. In addition, OFDM signals are often used as detection signals in radar systems because of their high bandwidth and flexible coding methods. Therefore, OFDM is used again as the transmission signal for integrated radar communication systems due to its strong advantages.

[0004] In existing integrated radar communication systems, although information transmission in communication and radar detection are achieved, there is still a bias towards one of the functions. To achieve good radar detection performance, the information transmission rate in communication will decrease. Similarly, an increase in the communication information transmission rate will reduce the radar detection performance. How to balance the performance of the two in different physical environments to achieve the best performance requires further research. Summary of the Invention

[0005] Object of the Invention: Aiming at the problems and deficiencies existing in the above-mentioned prior art, the object of the present invention is to propose a secure transmission method for integrated radar communication based on OFDM on the basis of traditional OFDM signals, to ensure the security of communication while ensuring radar detection performance.

[0006] Technical Solution: To achieve the above object of the invention, the technical solution adopted by the present invention is a secure transmission method for integrated radar communication based on OFDM, including the following steps:

[0007] (1) At the transmitting end, artificial noise is added to the communication information through power allocation weights and modulated onto the OFDM signal to obtain an integrated radar-communication signal;

[0008] (2) The communication receiver and the target process the received integrated radar-communication signal, and then respectively obtain the information transmission rates from the base station to the communication receiver and the target, thereby obtaining the total secure transmission rate;

[0009] (3) Meanwhile, the radar receiver processes the received target echo signal to obtain the Cramér-Rao lower bounds of the target's velocity and coordinates.

[0010] (4) Maximize the secure transmission rate under the constraint of the Cramér-Rao lower bounds, and obtain the optimized carrier allocation, power allocation, and power weight allocation through the proposed algorithm.

[0011] Further, the step (1) includes the following steps:

[0012] 1) Add the artificial noise z n，m (k) to the communication signal x m (k) through the power allocation weight α n，m (k), where n is the OFDM symbol number, m is the communication receiver number, and k is the subcarrier number; obtain the signal of the mixed communication information and artificial noise ρ m (k) is a variable for carrier allocation, taking only two values of 0 or 1. When ρ m (k) = 1, it means that subcarrier k is allocated to communication receiver m. When ρ m (k) = 0, subcarrier k is not allocated to communication receiver m. p m (k) represents the power allocated to the m-th communication receiver on the k-th subcarrier;

[0013] 2) Modulate b n (k) onto the OFDM signal with length N b to obtain the integrated radar-communication signal where T s = (N d + N p )T, T is the sampling period, N d and N p are the number of carriers and the number of cyclic prefixes respectively, and u(t) is a rectangular pulse signal with amplitude A and duration T s ;

[0014] 2) Modulate b n (k) onto the OFDM signal with length N b to obtain the final integrated radar-communication signal where T s =(N d +N p )T, where T is the sampling period, and N d and N p are the number of carriers and the number of cyclic prefixes respectively.

[0015] Furthermore, the step (2) includes the following steps:

[0016] ① After the k-th subcarrier signal in the n-th OFDM symbol at the transmitting end propagates through space, the first received signal at the communication receiver m is Y n，m (k). The first received signal Y n，m (k) only contains the communication signal x n，m (t), and the artificial noise signal z n，m (t) can be eliminated by the corresponding communication receiver m. Meanwhile, the second received signal at the target is E n，m (k). The second received signal E n，m (k) contains the communication signal and artificial noise;

[0017] ② Calculate the information transmission rate R n，m (k) corresponding to the communication receiver m and the information transmission rate corresponding to the target n，m (k) respectively according to the first received signal Y m (k) and the second received signal E denotes the secure transmission rate. Sum the secure transmission rates of all subcarriers and communication receivers to obtain the total secure transmission rate

[0018] Furthermore, the step (3) includes the following steps:

[0019] I If the radar receiver knows the transmitted signal and the clutter signal of the surrounding scatterers, then the r-th radar receiver can receive the target echo signal y r (t). Perform matched filtering on the target echo signal y r (t), and the signal on the k-th subcarrier in the n-th OFDM symbol is

[0020] II According to and the Doppler frequency shift and time delay formula of the target, obtain the Cramer-Rao lower bounds of the target velocity and coordinates.

[0021] Furthermore, the step (1) includes the following steps:

[0022] (i) Formulate an optimization problem to maximize the total secure transmission rate For the purpose of satisfying the following constraint problems: the total transmit power, the Cramer-Rao lower bounds of the target coordinates and velocity, the uniqueness of carrier allocation, the power allocation, and its weight allocation requirements;

[0023] (2) Derive the Lagrangian function through the Lagrangian dual method and split it into k*m sub-functions according to the problem characteristics

[0024] (3) Solve the sub-functions Classify and discuss according to the comparison of the advantages and disadvantages of the communication channel and the eavesdropping channel, and let Derive the values of the power allocation weight α m (k) and the power allocation p m (k) with respect to α m (k) and p m (k) respectively;

[0025] (4) Substitute the obtained α m (k) into p m (k), classify and discuss according to the value range of α m (k), and obtain the optimal solutions (α m (k), p m (k)) under different conditions;

[0026] (5) Based on the optimal α m (k) and p m (k), set the optimal carrier allocation ρ m (k). For the sub-carrier k, the corresponding optimal communication receiver m should make take the maximum value;

[0027] (6) Finally, obtain the stable value of the Lagrange multiplier through the sub-gradient iteration algorithm. At this time, α m (k), p m (k), and ρ m (k) are also optimal.

[0028] Beneficial effects: The present invention is applicable to the communication between base stations and users and the ranging and angle measurement of radars. Through the integrated signal design, the radar communication shared signal is realized, which can effectively reduce the transmission cost and save the spectrum resources. The OFDM radar communication integrated security transmission method proposed by the present invention not only has the advantages of flexible resource allocation of OFDM signals, but also has high radar performance for detecting targets. At the same time, in the present invention, by injecting artificial noise into the communication signal, the channel capacity is improved, and the security of signal transmission can be guaranteed. Through the CRLB (Cramer-Rao Lower Bound) constraint of the target parameters, good radar detection performance can be guaranteed. Description of the Drawings

[0029] Figure 1 It is the system application scenario diagram of the OFDM-based integrated radar and communication security transmission method of the present invention;

[0030] Figure 2 It is the trade-off performance diagram between the communication secure transmission rate and the average CRLB of the position under different numbers of radar receivers;

[0031] Figure 3 It is the trade-off performance diagram between the communication secure transmission rate and the average CRLB of the speed under different numbers of radar receivers. Detailed implementation manners

[0032] The following will describe in detail the implementation manners of the present invention with reference to the accompanying drawings. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent forms of modification by those skilled in the art fall within the scope defined by the appended claims of the present invention.

[0033] The following will describe in detail the implementation manners of the present invention with reference to the accompanying drawings:

[0034] The application scenario of the present invention is as Figure 1 shown: We consider an integrated radar and communication integrated system. The base station sends an integrated signal to the communication receiver, and the communication receiver receives and processes the integrated signal to extract the communication information from it. At the same time, the radar receiver receives and processes the echo signal to extract the radar information from it. The communication receiver and the radar receiver in this system receive the same signal, but process the received signal independently. The artificial noise injected into the integrated signal is known to the communication receiver, and the target can be interfered while not interfering with the communication.

[0035] In the integrated radar and communication system of the present invention, assume that the number of communication receivers is M, the number of radar receivers is R, and the signal sent by the base station consists of N b OFDM symbols. Each symbol period T s =(N d +N p )T, where T is the sampling period, and N d , N p are the number of carriers and the number of cyclic prefixes respectively. Therefore, the transmitted signal waveform is as follows:

[0036]

[0037] where u(t) is a rectangular pulse signal with an amplitude of A and a duration of T s , and b n (k) is the symbol of the nth OFDM symbol on the kth subcarrier, which contains the transmitted communication information and artificial noise, and the waveform is as follows:

[0038]

[0039] Among them, and represent x n，m (k) and z n，m (k) are circularly symmetric complex Gaussian (CSCG) random variables with zero mean and unit variance, and are the communication information and artificial noise on the k-th subcarrier of the n-th OFDM symbol, respectively. ρ m (k), p m (k), a m (k) are the subcarrier allocation, transmit power, and power weight allocation factor, respectively. At the same time, α m (k) ∈ [0, 1], ρ m (k) ∈ {0, 1}. If subcarrier k is allocated to communication receiver m, ρ m (k) = 1; conversely, ρ m (k) = 0.

[0040] We assume that the channel between the base station and the communication receiver is a frequency-selective fading channel, that is, within the N b OFDM symbol periods, the communication channel is constant. In addition, the communication receiver can cancel the artificial noise injected into the transmitted signal. Therefore, if subcarrier k is allocated to communication receiver m, that is, ρ m (k) = 1, the signal received by communication receiver m on the k-th subcarrier of the n-th OFDM symbol is

[0041]

[0042] Among them, is the channel complex gain from subcarrier k to communication receiver m, G m (k) is the antenna gain at the transmitter, d m is the distance from the base station to communication receiver m, λ is the wavelength, ε l is the small-scale channel gain of the l-th scatterer and follows an independent and identical distribution, L is the total number of scatterers, v n，m (k) is additive white Gaussian noise with a mean of 0 and a variance of σ 2 . Since the target (potential eavesdropper) cannot cancel the artificial noise, the signal received by the target on the k-th subcarrier of the n-th OFDM symbol is

[0043]

[0044] Among them, is the channel complex gain from the signal sent from subcarrier k to communication receiver m from the base station to the target, G' m(k) is the antenna gain obtained by the target when the subcarrier k transmitted by the base station aligns the beam with the communication receiver m, and d t is the distance from the base station to the target, and ε′ l is the small-scale gain for the l-th scatterer of the target, is additive white Gaussian noise with a mean of 0 and a variance of σ 2 .

[0045] We let be the time delay from the base station to the radar receiver r reflected by the target, that is

[0046]

[0047] where x = [x x , x y T , are the positions of the target, the base station, and the radar receiver respectively, c is the speed of light in free space, and the corresponding Doppler shift is

[0048]

[0049] where v = [v x , v y T is the moving speed of the target, and λ is the wavelength of the carrier wave.

[0050] The echo signal received by the radar receiver r combines the communication receiver, the target, and the surrounding scatterers. To simplify the analysis of the target, we consider that the communication receiver and the surrounding scatterers are known to the radar receiver. Therefore, the parameter estimation of the target depends on the target echo signal obtained by processing the radar receiver as follows:

[0051]

[0052] where is the channel complex gain from the base station to the radar receiver via the target, RCS is the scattering cross-section of the target, is the distance from the target to the base station, is the distance from the base station to the r-th radar receiver, and w r (t) is additive white Gaussian noise with a mean of 0 and a power density of n0,

[0053] We set Therefore, after matched filtering, the signal transmitted by the radar receiver on the k-th subcarrier of the n-th OFDM symbol is

[0054] ​​

[0055] wherein, is additive white Gaussian noise with a mean of 0 and a variance of .

[0056] We assume that the communication receiver and the target move slowly, so their position changes within N b symbol periods are very small and negligible. Therefore, we can obtain the information rate of the communication receiver m on subcarrier k as

[0057]

[0058] The information rate of the target is

[0059]

[0060] Therefore, the secure transmission rate of the communication receiver m on subcarrier k is

[0061]

[0062] wherein, According to the definition of ρ m (k), the total secure transmission rate is given by

[0063]

[0064] Next, we calculate the Cramer-Rao lower bounds of the target velocity and coordinates from the signals received by the radar receiver. We define the following estimation parameters:

[0065] u = [x x , x y , v x , v y , c] T (13)

[0066] wherein, c = [c1, c2,..., c R is the attenuation coefficient including path loss, reflection, and channel gain. To obtain the CRLB from y n，r (k), we need to calculate the Fisher information matrix (FIM) using the chain rule as follows:

[0067] J(u) = QJ(γ)Q T (14)

[0068] wherein, γ = [τ, f, c], and Q is a Jacobian matrix as follows

[0069]

[0070] wherein, I is an R×R identity matrix.

[0071] We let y be a Gaussian vector with mean It can be obtained that

[0072]

[0073] where, γ i represents the i-th element of γ, and according to the calculation, it can be obtained that

[0074]

[0075] where, A ij is an R×R diagonal matrix, that is

[0076]

[0077]

[0078]

[0079]

[0080] From this, J(u) can be obtained as follows

[0081]

[0082] where, B ij is a 2×2 matrix, and C ij is a 2×R matrix.

[0083] The CRLB is determined by the diagonal elements of the inverse matrix of J(u), but the calculation of the inverse matrix of J(u) is very complex. Therefore, we further relax the lower bound, and the obtained CRLB is as follows:

[0084]

[0085]

[0086]

[0087]

[0088] where,

[0089] The object of the present invention aims to achieve secure transmission of communication, that is, to maximize the secure transmission rate Meet the radar detection performance, that is, the CRLB constraints of the target speed and coordinates, and optimize the power allocation, carrier allocation, and power weight allocation according to their respective requirements. Therefore, the optimization problem can be given as:

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100] Among them, η1, η2, η1, η2 are CRLB constraint parameters, P t is the total transmission power, P peak is the maximum transmission power constraint on a single subcarrier.

[0101] Our optimization problem is non-convex, and the Lagrangian dual method can solve this problem. When the number of subcarriers is large enough, the duality gap approaches 0. First, the Lagrangian function is obtained

[0102]

[0103] Among them, λ = [λ1, λ2, λ3, λ4, λ5] is the Lagrangian multiplier vector,

[0104] The corresponding Lagrangian dual function is

[0105]

[0106] s.t.(27f)-(27i)

[0107] According to the convex optimization theory, by solving the following convex problem, the optimal Lagrangian multiplier vector λ can make the duality gap approach 0,

[0108]

[0109] The next task is to maximize under the condition of satisfying the constraints as follows:

[0110]

[0111] s.t. (27f)-(27i)

[0112] The communication receiver m corresponding to subcarrier k can be obtained as follows

[0113]

[0114] When, we can obtain Let It can be written as

[0115]

[0116] Next, according to |h m (k)| 2 and |g m (k)| 2 for size classification and discussion.

[0117] (1) |h m (k)| 2 <|g m (k)| 2

[0118] In the case of, there is α m (k) = 1 or

[0119]

[0120] Considering α m (k) = 1, it can be seen that is a linear function, and the solution set Ψ1 of the optimal solution (p m (k), α m (k)) is

[0121]

[0122] In the case of

[0123]

[0124] We let to obtain the optimal as

[0125]

[0126] Then let to obtain

[0127]

[0128] where a1, b1, c1, d1 are coefficients containing of

[0129] Substitute into the above formula to obtain the one containing the optimal Then substitute into to obtain the feasible solution which needs to satisfy

[0130] When At this time the optimal solution is the same as Ψ1.

[0131] When let Φ1 be the solution that satisfies of

[0132] When the optimal solution is also located at P peak In summary, all feasible solutions can be summarized as

[0133]

[0134] (II)|h m (k)| 2 ≥|g m (k)| 2

[0135] In this case always holds and is similar to |h m (k)| 2 <|g m (k)| 2 For p m (k), α m (k), take the derivative and substitute to obtain At this time always holds. In order to satisfy

[0136] when

[0137] When let Φ2 be the one that satisfies solution. When the feasible solution obtains P peak . So all feasible solutions for these two cases are

[0138]

[0139] When we let obtain the solution Let Φ3 be the solution that satisfies , and all feasible solutions are

[0140]

[0141] When the obtained feasible solutions are the same as Ψ4.

[0142] The final solution set

[0143]

[0144] We can obtain an optimal solution from all feasible solutions:

[0145]

[0146] To solve our overall optimization problem, select the following gradient iteration more Lagrange multipliers here:

[0147]

[0148]

[0149]

[0150]

[0151]

[0152] where t ≥ 0 represents the number of iterations, represents the optimal solution, and ξ1, ξ2, ξ3, ξ4, ξ5 represent the step sizes for updating the corresponding Lagrange multipliers.

[0153] After each of our Lagrange multipliers converges, the optimization problem of the present invention obtains an optimal solution.

[0154] Such as Figure 2As shown, the simulation shows the impact of the Cramer-Rao lower bound (CRLB) of the radar detection target position on the secure communication transmission rate under different numbers of radar receivers. It can be seen from the figure that as the position CRLB increases, the secure communication transmission rate gradually increases and finally approaches a steady state. Through theory, it is known that when the CRLB increases to a certain value, that is, when the Lagrange multipliers are all 0, our secure communication transmission rate becomes a fixed value. That is to say, the CRLB after this has no impact on the secure communication transmission rate, and the CRLB under this secure communication transmission rate can all achieve the performance at the steady state.

[0155] As Figure 3 shown, the simulation demonstrates the impact of the radar detection target speed on the secure communication transmission rate under different numbers of radar receivers. Compared with the Cramer-Rao lower bound of the position, the increase in the CRLB of the speed will also bring an increase in the secure communication transmission rate. Similarly, the secure communication transmission rate will not change after the CRLB reaches a threshold. It can be found that to achieve good radar detection performance, the confidentiality of communication will be affected to a certain extent. The two can be compromised by taking the minimum CRLB at the fixed value of the secure communication transmission rate, so that both good communication confidentiality and accurate radar detection can be achieved.

[0156] The simulation shows that the proposed OFDM-based integrated radar and communication secure transmission method can achieve good detection performance, and the injection of artificial noise can interfere with unknown targets (eavesdroppers) to achieve communication confidentiality.

Claims

1. A secure transmission method for integrated radar and communication based on OFDM, comprising the following steps: (1) At the transmitter, artificial noise is added to the communication information through power allocation weights and modulated onto the OFDM signal to obtain an integrated radar and communication signal; (2) The communication receiver and the target process the received integrated radar and communication signal, and then respectively obtain the information transmission rates from the base station to the communication receiver and the target, so as to obtain the total secure transmission rate; (3) The radar receiver processes the received target echo signal to obtain the Cramer-Rao lower bounds of the target with respect to velocity and coordinates; (4) Maximize the secure transmission rate under the constraint of the Cramer-Rao lower bounds, and obtain the optimized carrier allocation, power allocation, and power weight allocation through the proposed algorithm; The steps in step (2) include the following steps: ① After the k-th subcarrier signal in the n-th OFDM symbol at the transmitting end propagates through space, the first received signal at the communication receiver m is Y n,m (k), and the first received signal Y n,m (k) only contains the communication signal x n,m (t), and the artificial noise signal z n,m (t) can be eliminated by the corresponding communication receiver m. At the same time, the second received signal at the target is E n,m (k), and the second received signal E n,m (k) contains the communication signal and artificial noise; ②According to the first received signal Y n,m (k) and the second received signal E n,m (k), calculate the first information transmission rate R m (k) corresponding to the communication receiver m and the second information transmission rate corresponding to the target indicating the secure transmission rate, sum the secure transmission rates of all subcarriers and communication receivers to obtain the total secure transmission rate The steps in step (4) include the following steps: (i) Formulate an optimization problem to maximize the total secure transmission rate for the purpose of satisfying the following constraint problems: total transmit power, Cramer-Rao lower bounds of the target coordinates and velocity, carrier allocation uniqueness, power allocation, and its weight allocation requirements; (ii) Obtain the Lagrangian function through the Lagrangian dual method and split it into k*m sub-functions according to the problem characteristics ㈢ Sub - function Solve it, and classify and discuss according to the comparison of the advantages and disadvantages of the communication channel and the eavesdropping channel, so that Derive the power - allocation weights α m (k) and the power allocation p m (k) respectively to obtain the values of α m (k) and p m (k); (4) Substitute the obtained α m (k) into p m (k), and classify and discuss according to the value range of α m (k) to obtain the optimal solutions (α m (k), p m (k)) under different conditions; (v) Based on the optimal α m (k) and p m (k) Set the optimal carrier allocation ρ m (k). For the optimal communication receiver m corresponding to subcarrier k, it should make the value the largest; (6) Finally, the stable value of the Lagrange multiplier is obtained through the subgradient iteration algorithm, and at this time, α m (k), p m (k), and ρ m (k) are the optimal ones.

2. The method for secure transmission of integrated OFDM radar communication according to claim 1, wherein The steps in step (1) include the following steps: 1) Add the artificial noise z n,m (k) to the communication signal x m (k) through the power allocation weight α n,m (k), where n is the OFDM symbol number, m is the communication receiver number, and k is the subcarrier number; obtain the signal of the mixed communication information and the artificial noise ρ m (k) is a variable for carrier allocation, taking only two values of 0 or 1. When ρ m (k) = 1, it means that the subcarrier k is allocated to the communication receiver m. When ρ m (k) = 0, the subcarrier k is not allocated to the communication receiver m. p m (k) represents the power of the k-th subcarrier allocated to the m-th communication receiver; 2) Modulate b n (k) onto an OFDM signal with length N b to obtain an integrated radar and communication signal where T s =(N d +N p )T, T is the sampling period, N d , N p are the number of carriers and the number of cyclic prefixes respectively, and u(t) is a rectangular pulse signal with amplitude A and duration T s .

3. The method for secure transmission of integrated OFDM radar communication according to claim 1, wherein The steps in step (3) include the following steps: Ⅰ If the radar receiver knows the transmitted signal and the clutter signal of surrounding scatterers, then the r-th radar receiver can receive the target echo signal y r (t). For the target echo signal y r (t), perform matched filtering, then the signal on the k-th subcarrier in the n-th OFDM symbol is ⅡAccording to and the Doppler frequency shift and time delay formula of the target, the Cramer-Rao lower bounds of the target velocity and coordinates are obtained.

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