FDA-MIMO radar communication integrated transmit beam forming method

Abstract

The application discloses a FDA-MIMO radar communication integrated transmitting beam forming method, comprising the following steps: constructing a FDA-MIMO radar communication integrated signal model; deducing a signal processing model of a communication receiving end; realizing communication information embedding based on beam pattern modulation through transmitting beam forming; designing a transmitting beam forming matrix to ensure radar detection performance; establishing a FDA-MIMO radar communication integrated transmitting beam forming optimization model; and solving the optimization model by using an obstacle function algorithm. The application not only satisfies the beam performance of radar detection, realizes multi-user communication information embedding, prevents a eavesdropping user from intercepting multi-user communication information at one time, but also applies the optimal transmitting beam forming matrix obtained by solving the optimization model to a FDA-MIMO-based radar communication integrated transmitting end, effectively improving the detection and communication performance of the radar communication integrated system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of beam forming and signal processing, and particularly relates to a FDA-MIMO radar-communication integrated transmitting beam forming method. BACKGROUND

[0002] With the rapid development and wide application of modern electronic information technology, the airborne combat platform has higher requirements for radar target detection and wireless communication performance. However, with the increasing number of various detection and communication devices, the complexity and hardware cost of the airborne system are also increased, the spectrum resources are crowded, and the electromagnetic environment is gradually deteriorated. Dual-function radar-communication (DFRC) is considered as a key technology to solve the above problems. The integration of radar and communication systems can make radar and communication share spectrum resources, effectively reduce the electromagnetic interference between airborne radar and communication systems, and reduce the number and cost of airborne terminals. In fact, there are similarities between radar and communication in hardware structure and working principle, which lays a foundation for the realization of the radar-communication integrated system.

[0003] At present, most of the existing radar-communication integrated design schemes are based on single antenna and phased array systems. These schemes all have the disadvantage that the radar or communication performance cannot achieve the expected effect. The early single antenna radar-communication integrated system has many bottleneck problems that cannot be broken through, such as high bit error rate, poor security, low beam design freedom, etc. The radar-communication integrated system based on phased array uses the transmitting beam forming of phased array antenna. Although it has the advantages of high beam gain, strong directivity, narrow beam, and low sidelobe, the beam pointing of the transmitting beam formed by the phased array antenna is constant in the single pulse duration. This leads to the phased array being unable to realize the application of the radar-communication integrated system in distance-angle two-dimensional power control, main lobe clutter interference suppression, physical layer secure communication, and multi-user communication.

[0004] Therefore, the frequency control array (FDA) changes the transmitting beam pattern into a time, angle, and distance multi-dimensional function by introducing a stepped carrier frequency increment between each transmitting array element. And by combining the frequency control array with the multiple-input multiple-output (MIMO) technology, the distance-angle two-dimensional point beam pattern can be obtained through frequency diversity control and orthogonal waveform transmission. Based on the unique advantages of the two-dimensional distance-angle transmitting beam pattern, the radar-communication integrated system can realize wider range of full-space coverage, higher precision of radar detection, higher efficiency of wireless communication, lower interception radar detection, and secure wireless communication.

[0005] Currently, optimized design of transmit beamforming for integrated radar and communication has become a research hotspot. However, most existing designs only focus on the radar and communication performance of the beam in the angular domain, neglecting the performance in the range-angle two-dimensional region. Therefore, researching a transmit beamforming design method for integrated radar and communication based on FDA-MIMO is of great significance. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to provide an FDA-MIMO radar communication integrated transmission beamforming method for realizing two-dimensional range-angle point-to-point radar detection and wireless communication.

[0007] Technical solution: The FDA-MIMO radar communication integrated transmit beamforming method of the present invention includes the following steps:

[0008] Construct an integrated radar-communication signal model based on beammap modulation (FDA-MIMO);

[0009] The signal processing model of the communication receiver is derived, and the closed-form expression of the weighted range-angle two-dimensional equivalent transmit beam pattern of the receiver is obtained.

[0010] Using the distance-angle of the communication user as prior information, information embedding is achieved by constraining the amplitude and phase degrees of freedom of the equivalent transmission beam pattern at the communication user's location based on the distance-angle location.

[0011] Design the transmit beamforming matrix to ensure radar detection performance;

[0012] To meet the constraints of communication information embedding and eavesdropping user restrictions, and to minimize the mean square error between the transmitted beamforming matrix and the radar desired beamforming matrix as the optimization objective function, an FDA-MIMO radar-communication integrated transmitted beamforming optimization model is established.

[0013] The obstacle function algorithm is used to solve the optimization model.

[0014] Furthermore, an integrated radar-communication signal model based on beammap modulation is constructed, specifically including:

[0015] (A1) FDA-MIMO architecture radar communication integrated system, with M T There are 1 transmitting antenna, and all transmitting antennas simultaneously transmit M orthogonal waveforms ψ. m (t), m=1,…,M,T p Given the pulse duration, M orthogonal waveforms satisfy the strict orthogonality condition.

[0016] (A2) Introduce the frequency increment Δf of the frequency control array between different orthogonal waveforms, and calculate the transmission frequency f of the m-th orthogonal waveform. m for:

[0017]

[0018] Among them, f c Indicates the carrier frequency of the transmitted signal;

[0019] (A3) Calculate the m-th baseband transmitted signal s, which is composed of orthogonal waveforms and frequency increments. m (t) is:

[0020]

[0021] Where t represents the pulse time-domain sampling time;

[0022] (A4) Employs a transmit beamforming matrix For transmitted signals Beammap modulation is performed, where s1(t) is the first baseband transmitted signal, s M (t) represents the baseband transmission signal of the Mth path; the integrated radar-communication transmission signal S(t) is calculated as follows:

[0023] S(t)=Ws(t)

[0024] (A5) The far-field signal at a distance of R and an azimuth angle of θ is calculated as follows:

[0025] s T (t-τ,θ)=a H (θ)Ws(t-τ)

[0026] Among them, s T (t-τ,θ) represents the far-field signal at a distance R and an azimuth angle θ, where τ = R / c is the time delay, c is the speed of light, and s(t-τ) is the baseband transmitted signal vector. The launch steering vector is expressed as follows:

[0027]

[0028] Where d represents the spacing between array elements.

[0029] Furthermore, the signal processing model of the communication receiver is derived, and a closed-form expression for the weighted range-angle two-dimensional equivalent transmit beammap of the receiver is obtained; specifically including:

[0030] (B1) has N j J communication users with one receiving antenna, with a distance and azimuth angle of R relative to the integrated radar-communication transmitter. j and θ jThe received signal of the j-th communication user is calculated as follows:

[0031] y j (t-τ j ,θ j )=β1b(θ j )s T (t-τ j ,θ j )+n j (t), j=1,…,J

[0032] Where yj(t-τj,θj) is the received signal of the j-th communication user, τ j Let be the latency of the j-th communication user, b(θj) be the receive steering vector of the j-th communication user, and s be the latency of the j-th communication user. T (t-τ j ,θ j ) represents the far-field transmitted signal, and β1 represents the signal propagation loss coefficient. Indicates received noise;

[0033] (B2) Adopt After performing matched filtering on the received signal, the output signal of the nth array element receiving the mth transmitted signal is calculated as follows:

[0034]

[0035] Among them, y n,m For the nth array element to receive the output signal of the mth transmitted signal, a represents the weighted transmitted beam space vector. w,1 (θ) is the first element of the weighted transmitted beam space vector, a w,2 (θ) is the second element of the weighted transmitted beam space vector, and aw,M(θ) is the Mth element of the weighted transmitted beam space vector. j ) represents the m-th element of the weighted transmitted beam space vector;

[0036] (B3) The multi-channel matched filter output signals are superimposed into an extended vector, represented as:

[0037]

[0038] in, It is an extended vector formed by the superposition of the output signals from multiple matched filters. Indicates the Kronecker product. The range-angle two-dimensional equivalent launch steering vector is expressed as follows:

[0039]

[0040] Furthermore, using the distance-angle of the communication user as prior information, information embedding is achieved by constraining the amplitude and phase degrees of freedom of the equivalent transmission beammap at the communication user's location based on the distance-angle position; specifically including:

[0041] (C1) J communication users are located at arbitrary distances and angle gates within the coverage area of ​​the transmit beam, and the location information of each user is known a priori; during each transmit pulse, phase constellation modulation is used to characterize the communication symbols; the communication information of the j-th user... The calculation is as follows:

[0042]

[0043] in, Represents the original communication phase, whose values ​​are derived from the set. Randomly selected from L B p represents the number of bits in a single communication symbol. i This represents the i-th phase point within a constellation;

[0044] (C2) A beammap modulation method is adopted, and a two-dimensional equivalent transmission steering vector a with respect to range and angle is introduced into the optimization problem. r The equality constraint of (τ,θ) is expressed as:

[0045]

[0046] Among them, a r (τ j ,θ j ) represents the range-angle two-dimensional equivalent launch steering vector, and ⊙ represents the Hadamard product. For power parameters, Δ j (1) is the first power parameter, Δ j (M) represents the Mth power parameter;

[0047] In scenario (C3), there are H threatening eavesdropping users, whose distances and angles relative to the radar-communication integrated transmitter are R and R, respectively. h and θ h , h=1,…,H; In the optimization problem, the following equality constraint is introduced to eliminate the phase information of the beam pattern at the location of the eavesdropping user:

[0048]

[0049] Where ar(τh,θ) h τ is the distance-angle two-dimensional equivalent transmission guidance vector for the h-th eavesdropping user. h For the h-th eavesdropping user, The power factor for the beammap at the eavesdropping user's location can be set to a number close to 0 to generate a beam null at the eavesdropping user's location.

[0050] Furthermore, the design of the transmit beamforming matrix to ensure radar detection performance includes the following steps:

[0051] (D1) Based on the transmit steering vector of the azimuth angle of the detected target, the desired transmit beamforming matrix of the radar is designed as follows:

[0052]

[0053] Where (:,m) represents all row elements in the m-th column of the matrix, W radar (:,m) represents all row elements in the m-th column of the radar's desired transmit beamforming matrix, θ t Let a(θ) be the azimuth angle of the target. t () represents the launch steering vector at the target angle;

[0054] (D2) The objective function is to minimize the mean square error between the transmitted beamforming matrix and the radar's desired transmitted beamforming matrix:

[0055]

[0056] Among them, W radar This is the desired transmit beamforming matrix for the radar.

[0057] Furthermore, taking the constraints of communication information embedding and eavesdropping user restrictions as the conditions, and minimizing the mean square error between the transmitted beamforming matrix and the radar desired beamforming matrix as the optimization objective, an FDA-MIMO radar-communication integrated transmitted beamforming optimization design model is established: Specifically:

[0058]

[0059] The first constraint represents the phase embedding and power control of the communication user; the second constraint represents the phase constraint and power limitation of the eavesdropping user; the objective function represents the radar transmit beamforming matrix that minimizes the mean square error under the premise of communication symbol embedding.

[0060] Furthermore, the obstacle function algorithm is used to solve the optimization model, specifically including:

[0061] (E1) The feasible region is denoted as:

[0062] (E2) Define the barrier function:

[0063] in, B(W) is a continuous function whose independent variable is the transmitted beamforming matrix W. As the independent variable W approaches the feasible region boundary, B(W) → +∞. Its expression can be chosen from the following two forms:

[0064]

[0065] (E3) Initialization: Given an initial interior point W( 0 )∈S, error threshold ε>0, initial parameters of the algorithm The reduction factor β∈(0,1), the maximum number of iterations K max Set the current iteration step k = 1;

[0066] (E4)If k≤K max If the calculation is successful, proceed with the calculation; otherwise, stop the calculation and proceed to step E7.

[0067] (E5) The transmitted beamforming matrix W calculated in the (k-1)th iteration ( k-1 Starting from point , solve the following unconstrained optimization problem to obtain the minimum value W( of the transmit beamforming matrix calculated in the k-th iteration). k ):

[0068]

[0069] (E6) Convergence Criterion: If r( k )B(W( k If ε < ε, stop the calculation and jump to step E7; otherwise, r(k+1) = βr ( k), k = k + 1, return to step E4; where r( k+1 ) and r( k ) are the algorithm parameters for the (k-1)th and kth calculations, respectively;

[0070] (E7) Output W opt =W( k ), where W opt This is the optimal transmit beamforming matrix.

[0071] The systems corresponding to the above methods include:

[0072] The signal model building unit is used to build an integrated signal model for radar and communication based on beammap modulation (FDA-MIMO).

[0073] The communication signal processing unit is used to derive the signal processing model of the communication receiver and obtain the closed-form expression of the weighted range-angle two-dimensional equivalent transmit beam pattern of the receiver.

[0074] The communication information embedding unit is used to embed information by constraining the amplitude and phase degrees of freedom of the equivalent transmission beam pattern at the location of the communication user, using the distance-angle of the communication user as prior information;

[0075] Transmit beamforming matrix design unit, used to design the transmit beamforming matrix to ensure radar detection performance;

[0076] An optimization model building unit is used to establish an FDA-MIMO radar-communication integrated transmit beamforming optimization model with the constraints of communication information embedding and eavesdropping user restrictions, and with the objective function of minimizing the mean square error between the transmit beamforming matrix and the radar desired beam matrix.

[0077] The optimization model solving unit is used to solve the optimization model using the obstacle function algorithm.

[0078] The control device for storing and processing the above methods includes a processor, a communication interface, a memory, and a communication bus;

[0079] The processor, the communication interface, and the memory communicate with each other through the communication bus.

[0080] The memory is used to store computer programs;

[0081] When the processor executes the program stored in the memory, it implements the steps of the FDA-MIMO radar-communication integrated transmission beamforming method.

[0082] A storage medium for storing the execution of the method, the storage medium storing a computer program that, when executed by at least one processor, implements the steps of the FDA-MIMO radar-communication integrated transmit beamforming method.

[0083] Beneficial effects: Compared with the prior art, the significant advantages of the present invention are: (1) By optimizing the design of the transmit beamforming matrix of FDA-MIMO, phase modulation communication information is adopted and embedded into the beam diagram for transmission. The communication information is embedded in the weighted range-angle two-dimensional equivalent transmit beam diagram using equality constraints. Under the constraints of communication information embedding and eavesdropping user restrictions, the mean square error between the transmit beamforming matrix and the radar desired beam matrix is ​​minimized as the optimization objective function. An optimization model for the transmit beamforming of FDA-MIMO radar communication integration is established, and the optimal transmit beamforming matrix is ​​obtained by using a convex optimization algorithm. Thus, the range-angle beam diagram of FDA-MIMO is used to realize two-dimensional point-to-point radar target detection and secure wireless communication, thereby improving radar detection performance and communication reliability; (2) It not only satisfies the beam performance of radar detection and realizes the embedding of communication information of multiple users, preventing eavesdropping users from intercepting the communication information of multiple users at one time, but also applies the optimal transmit beamforming matrix obtained by solving the proposed optimization model to the radar communication integration transmitter based on FDA-MIMO, effectively improving the detection and communication performance of the radar communication integration system. Attached Figure Description

[0084] Figure 1 A flowchart of an FDA-MIMO radar communication integrated transmit beamforming method;

[0085] Figure 2 This is a design scenario for an integrated transmit beamforming system for FDA-MIMO radar and communication.

[0086] Figure 3 This is a beam pattern for angular transmission.

[0087] Figure 4 This is a range-angle transmit-receive beammap for the radar target.

[0088] Figure 5 Distance-angle transmit-receive beam diagram for communication users;

[0089] Figure 6 The distance-angle two-dimensional bit error rate;

[0090] Figure 7 For the angle dimension, the bit error rate;

[0091] Figure 8 Let be the bit error rate in the distance dimension. Detailed Implementation

[0092] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0093] This invention, starting from the practical scenarios of radar detection and wireless communication, proposes an FDA-MIMO radar communication integrated transmit beamforming method, system, device and storage medium. Under the condition of satisfying the communication information embedding constraint of beam pattern modulation, it minimizes the mean square error between the transmit beamforming matrix and the radar desired beam matrix, thereby realizing point-to-point radar detection and wireless communication in two dimensions of range and angle.

[0094] This invention considers an integrated radar-communication scenario where the integrated system simultaneously detects a target and transmits information to multiple communication users. The transmitter of the integrated system adopts an FDA-MIMO architecture, meaning the transmitted signal is a group of orthogonal waveforms with stepped frequency diversity, and a digital transmit beamformer is used to weight the orthogonal waveforms. First, an integrated radar-communication signal model based on FDA-MIMO is constructed, and the communication signal processing method for integrated FDA-MIMO radar-communication is derived to obtain a closed-form expression for the weighted range-angle two-dimensional equivalent transmit steering vector at the receiver. Second, using the range-angle of the communication users as prior information, communication information is embedded based on beammap modulation through transmit beamforming. The optimization objective function is to minimize the mean square error between the transmit beamforming matrix and the radar's desired beam matrix, establishing an optimization model for the transmit beamforming of integrated FDA-MIMO radar-communication. Finally, a barrier function algorithm is used to solve the established optimization problem.

[0095] Symbol explanation in this invention: bold lowercase 'a' represents a vector, bold uppercase 'A' represents a matrix, and (·) T ,(·) * ,(·) H These represent the transpose, conjugate, and conjugate transpose operations, respectively; |·| represents the absolute value operation; and ||·||2 and ||·|| F Representing the 2-norm and Frobenius norm, and Let I represent the sets of complex numbers, real numbers, and positive integers, respectively. N and 1 N Let represent an N×N identity matrix and an N-dimensional all-1 vector, respectively.

[0096] like Figure 1 As shown, the method of the present invention includes the following steps:

[0097] First, construct a design scenario for an integrated FDA-MIMO radar and communication system:

[0098] The transmitter of the integrated radar and communication system adopts an FDA-MIMO architecture, with an array configuration of a one-dimensional uniform linear array, and features M TThere are M transmitting antennas with an element spacing of d. All transmitting antennas simultaneously transmit M orthogonal waveforms that satisfy strict orthogonality conditions. The orthogonal waveforms from different channels are subjected to stepped frequency diversity modulation using a frequency-controlled array. There is a radar detection target and J communication users in the space, such as... Figure 2 As shown.

[0099] S1. Construct an integrated FDA-MIMO radar communication transmission signal model, which includes the following steps:

[0100] A1: All transmitting antennas simultaneously transmit M orthogonal waveforms ψ m (t), m=1,…,M,T p Let the pulse duration be M, and let the M orthogonal waveforms satisfy the strict orthogonality condition.

[0101] A2: Introduce the frequency increment Δf of the frequency control array between different orthogonal waveforms, and calculate the transmission frequency f of the m-th orthogonal waveform. m for:

[0102]

[0103] Among them, f c This indicates the carrier frequency of the transmitted signal.

[0104] A3: Calculate the m-th baseband transmitted signal s, which is composed of orthogonal waveforms and frequency increments. m (t) is:

[0105]

[0106] Where t represents the pulse time-domain sampling time.

[0107] A4: To control the transmission pattern and embed communication information, a transmission beamforming matrix is ​​used. For transmitted signals Beammap modulation is performed, where s1(t) is the first baseband transmitted signal, s M (t) represents the baseband transmitted signal of the Mth path. The integrated radar-communication transmitted signal S(t) is calculated as follows:

[0108] S(t)=Ws(t) (3)

[0109] A5: Under the assumption of narrowband signal, the far-field signal at a distance of R and an azimuth angle of θ is calculated as follows:

[0110] s T (t-τ,θ)=a H (θ)Ws(t-τ) (4)

[0111] Among them, s T(t-τ,θ) represents the far-field signal at a distance R and an azimuth angle θ, where τ = R / c is the time delay, c is the speed of light, and s(t-τ) is the baseband transmitted signal vector. The launch steering vector is expressed as follows:

[0112]

[0113] Where d represents the spacing between array elements.

[0114] S2. Derive the communication signal processing method for FDA-MIMO radar-communication integration, specifically including the following steps:

[0115] B1: Considering N j J communication users with one receiving antenna, with a distance and azimuth angle of R relative to the integrated radar-communication transmitter. j and θ j The received signal of the j-th communication user is calculated as follows:

[0116] y j (t-τ j ,θ j )=β1b(θ j )s T (t-τ j ,θ j )+n j (t), j=1,…,J (6)

[0117] Where yj(t-τj,θj) is the received signal of the j-th communication user, τ j Let be the latency of the j-th communication user, b(θj) be the receive steering vector of the j-th communication user, and s be the latency of the j-th communication user. T (t-τ j ,θ j ) represents the far-field transmitted signal, and β1 represents the signal propagation loss coefficient. This indicates received noise.

[0118] B2: Adopt After performing matched filtering on the received signal in equation (7), the output signal of the nth array element receiving the mth transmitted signal is calculated as follows:

[0119]

[0120] Among them, y n,m For the nth array element to receive the output signal of the mth transmitted signal, a represents the weighted transmitted beam space vector. w (θ) is the weighted transmitted beam space vector, a w,1(θ) is the first element of the weighted transmitted beam space vector, a w,2 (θ) is the second element of the weighted transmitted beam space vector, a w,M (θ) is the Mth element of the weighted transmitted beam space vector, a w,m (θ j ) is the m-th element of the weighted transmit beam space vector.

[0121] B3: The multi-channel matched filter output signals of equation (7) are superimposed into an extended vector, which is expressed as:

[0122]

[0123] in, It is an extended vector formed by the superposition of the output signals from multiple matched filters. This represents the Kronecker product. The range-angle two-dimensional equivalent launch steering vector is expressed as follows:

[0124]

[0125] S3. Embedding communication information based on beammap modulation through transmitted beamforming, specifically including the following steps:

[0126] C1: Assume J communication users are located at arbitrary distances and angle gates within the coverage area of ​​the transmit beam, and the location information of each user is known a priori. During each transmit pulse, phase constellation modulation is used to characterize the communication symbols. The communication information of the j-th user is... It can be calculated as follows:

[0127]

[0128] in, Represents the original communication phase, whose values ​​are derived from the set. Randomly selected from L B p represents the number of bits in a single communication symbol. i This represents the i-th phase point within a constellation.

[0129] C2: Using beammap modulation, a two-dimensional equivalent transmit steering vector a with respect to range and angle is introduced into the optimization problem. r The equality constraint of (τ,θ) can be expressed as:

[0130]

[0131] Among them, a r (τ j ,θ j) represents the range-angle two-dimensional equivalent launch steering vector, and ⊙ represents the Hadamard product. For power parameters, Δ j (1) is the first power parameter, Δ j (M) represents the Mth power parameter.

[0132] C3: Consider the scenario with H threatening eavesdropping users, whose distances and angles relative to the radar-communication integrated transmitter are R and R, respectively. h and θ h Let h = 1, ..., H. To prevent eavesdropping users from intercepting communication information, the following equality constraint is introduced into the optimization problem to eliminate the phase information of the beam pattern at the location of the eavesdropping user:

[0133]

[0134] Among them, a r (τ h ,θ h Let τ be the distance-angle two-dimensional equivalent transmission steering vector of the h-th eavesdropping user, and τh be the time delay of the h-th eavesdropping user. The power factor for the beammap at the eavesdropping user's location can be set to a number close to 0 to generate a beam null at the eavesdropping user's location.

[0135] S4. Design the transmit beamforming matrix to ensure radar detection performance, specifically including the following steps:

[0136] D1: To achieve a high radar detection signal-to-noise ratio, the desired transmit beamforming matrix of the radar is designed based on the transmit steering vector of the azimuth angle of the detected target:

[0137]

[0138] Where (:,m) represents all row elements in the m-th column of the matrix, W radar (:,m) represents all row elements in the m-th column of the radar's desired transmit beamforming matrix, θ t Let a(θ) be the azimuth angle of the target. t ) is the launch guidance vector at the target angle.

[0139] D2: The objective function is to minimize the mean square error between the transmitted beamforming matrix and the radar's desired transmitted beamforming matrix.

[0140]

[0141] Among them, W radar This is the desired transmit beamforming matrix for the radar.

[0142] S5. Taking the constraints of communication information embedding and eavesdropping user limitations as constraints, and minimizing the mean square error between the transmitted beamforming matrix and the radar's desired beamforming matrix as the optimization objective, an optimization design model for the integrated transmitted beamforming of FDA-MIMO radar and communication is established:

[0143]

[0144] In Equation (15), the first constraint represents the phase embedding and power control of the communication user; the second constraint represents the phase constraint and power limitation of the eavesdropping user; the objective function represents the radar transmit beamforming matrix that minimizes the mean square error under the premise of communication symbol embedding.

[0145] S6. The obstacle function algorithm is used to solve the optimization design problem of the integrated radar-communication transmit beamforming of the FDA-MIMO radar, which includes the following steps:

[0146] E1: The feasible region is denoted as:

[0147] E2: Define the barrier function:

[0148] in, B(W) is a continuous function whose independent variable is the transmitted beamforming matrix W. As the independent variable W approaches the feasible region boundary, B(W) → +∞. Its expression can be chosen from the following two forms:

[0149]

[0150] E3: Initialization: Given an initial interior point W( 0 )∈S, error threshold ε>0, initial parameters of the algorithm The reduction factor β∈(0,1), the maximum number of iterations K max Set the current iteration step k = 1.

[0151] E4: If k≤K max If the calculation is not performed, proceed to step E7; otherwise, stop the calculation and proceed to step E7.

[0152] E5: The transmitted beamforming matrix W calculated in the (k-1)th iteration ( k-1 Starting from point , solve the following unconstrained optimization problem to obtain the minimum value W( of the transmit beamforming matrix calculated in the k-th iteration). k ):

[0153]

[0154] E6: Convergence check: If r(k)B(W(k))<ε, stop the calculation and jump to step E7; otherwise, r (k+1)=βr (k) , k = k + 1, return to step E4; where, r (k+1) and r (k) These are the algorithm parameters for the (k-1)th and kth calculations, respectively.

[0155] E7: Output W opt =W( k ), where W opt This is the optimal transmit beamforming matrix.

[0156] The systems corresponding to the above methods include:

[0157] The signal model building unit is used to build an integrated signal model for radar and communication based on beammap modulation (FDA-MIMO).

[0158] The communication signal processing unit is used to derive the signal processing model of the communication receiver and obtain the closed-form expression of the weighted range-angle two-dimensional equivalent transmit beam pattern of the receiver.

[0159] The communication information embedding unit is used to embed information by constraining the amplitude and phase degrees of freedom of the equivalent transmission beam pattern at the location of the communication user, using the distance-angle of the communication user as prior information;

[0160] Transmit beamforming matrix design unit, used to design the transmit beamforming matrix to ensure radar detection performance;

[0161] An optimization model building unit is used to establish an FDA-MIMO radar-communication integrated transmit beamforming optimization model with the constraints of communication information embedding and eavesdropping user restrictions, and with the objective function of minimizing the mean square error between the transmit beamforming matrix and the radar desired beam matrix.

[0162] The optimization model solving unit is used to solve the optimization model using the obstacle function algorithm.

[0163] The control device for the above method includes a processor, a communication interface, a memory, and a communication bus;

[0164] The processor, the communication interface, and the memory communicate with each other through the communication bus.

[0165] The memory is used to store computer programs;

[0166] When the processor executes the program stored in the memory, it implements the steps of the FDA-MIMO radar-communication integrated transmission beamforming method.

[0167] The storage medium of the above method stores a computer program, which, when executed by at least one processor, implements the steps of the FDA-MIMO radar-communication integrated transmit beamforming method.

[0168] Simulation results:

[0169] To verify the feasibility and superiority of the proposed method, the following simulation scenario was designed: Assume a distance gate of 10m, a monitoring range of 150 distance gates, and a target located at R. t =0.75km,θ t At θ = 0°, there are three communication users located at R1 = 0.4km, θ1 = -50°, R2 = 1.3km, θ1 = -30°, and R3 = 1.0km, θ3 = 40°, respectively, i.e., J = 3. The radar-communication integrated system simultaneously performs radar target detection and communication information transmission.

[0170] The specific experimental procedure is as follows:

[0171] Step 1: Modeling Radar Detection and Communication Scenarios

[0172] The radar-communication integrated system uses a one-dimensional uniform linear array with an element spacing of half a wavelength d = λ / 2, and has M transmitting and receiving antennas. T =M R =21. The carrier frequency of the transmitted signal is f. c =3GHz, the frequency control array step frequency increment is Δf = 200kHz, and the signal bandwidth is B = 100MHz. The number of orthogonal waveforms M = 5, using Oppermann sequences as the orthogonal waveforms, with parameters set to q = 1, n = 3, and p = 1. Assuming a range gate of 10m, a monitoring range of 150 range gates, and a target located at R... t =0.75km,θ t At θ = 0°, there are three communication users located at R1 = 0.4 km, θ1 = -50°, R2 = 1.3 km, θ1 = -30°, and R3 = 1.0 km, θ3 = 40°, i.e., J = 3. Each communication user's receiving array has... Each antenna has a power level set to embed communication information. A total of 1000 Monte Carlo experiments were conducted, with 10 rockets launched each time. 7 Each pulse. The communication channel coefficients are modeled as random variables with unit size and uniformly distributed phase.

[0173] Step 2: Optimization solution of the transmitted beamforming matrix

[0174] A convex optimization algorithm is used to iteratively solve the optimization model of the transmitted beamforming to obtain the transmitted beamforming matrix, which is then used to model the transmitted signal. Specific solution methods can be achieved using various convex optimization algorithm toolboxes, such as the CVX toolbox in MATLAB.

[0175] Step 3: Beammap Simulation

[0176] Figure 3 The diagram shows the transmit beam pattern, where the green dashed lines represent the azimuth angles of the three communication users, and the pink dashed lines represent the azimuth angle of the radar target. Without considering time delay, the FDA-MIMO transmit beam pattern proposed in this invention maintains high-gain azimuth directivity through transmit beamforming technology, achieving high gain at every preset desired angle. Figure 4 and Figure 5 This is a transmit-receive two-way beammap for radar targets and communication users, with red indicating high-gain regions and blue indicating low-gain regions. Normalized non-adaptive weight vectors are used here. Achieving receive beamforming, where u TR (τ′,θ′) is the receiving beamforming weight vector, b(θ′) is the angular-dimensional receiving beamforming weight vector, and a r (τ′, θ′) represents the range-angle two-dimensional receiving beamforming weight vector, where τ′ is the beamforming range and θ′ is the beamforming angle. Clearly, after matched filtering, channel separation, and receiving beamforming processing, the two-dimensional coupled range-angle degrees of freedom in the FDA-MIMO transmit signal can be successfully separated. The transmit-receive two-way pattern generates a high-gain region only at the radar target and the locations of the three preset communication users, enabling point-to-point two-dimensional detection and transmission.

[0177] Step 4: Communication demodulation and bit error rate simulation

[0178] With the received signal-to-noise ratio (SNR) fixed at 11 dB, the bit error rate (BER) for the three communication users was calculated at all distance and angle gates. To clearly illustrate the two-dimensional relationship between BER and distance-angle, the BER values ​​were logarithmically normalized, i.e., P0. ee = -log10(BER) / max(-log10(BER)), where P ee P represents the bit error rate after logarithmic normalization. ee A higher value indicates a lower bit error rate. Figure 6 Simulation results of the range-angle two-dimensional bit error rate are presented. It can be seen that only three preset communication users can achieve communication information demodulation in the scenario. High bit error rates are observed in non-preset sidelobe regions and at the radar target, indicating that the proposed method can achieve low intercept characteristics in both range and angle dimensions. Furthermore, Figure 7and Figure 8 The bit error rate profiles for the angular and distance dimensions are presented. It can be seen that the communication information of the three users can only be demodulated and recovered at their corresponding positions, indicating that the method proposed in this invention can achieve single-pulse multi-user communication capability.

[0179] The working principle and process of this invention:

[0180] Consider an integrated radar-communication scenario where the integrated system simultaneously detects targets and transmits downlink symbol information to multiple communication users. The transmitter of the integrated system adopts an FDA-MIMO architecture, meaning the transmitted signal is a group of orthogonal waveforms with stepped frequency diversity, and a digital transmit beamformer is used to weight the orthogonal waveforms to achieve beammap modulation. First, an integrated FDA-MIMO radar-communication signal model based on beammap modulation is constructed, the signal processing model of the communication receiver is derived, and a closed-form expression for the weighted range-angle two-dimensional equivalent transmit beammap at the receiver is obtained. Second, using the range-angle of the communication users as prior information, information embedding is achieved by constraining the amplitude and phase degrees of freedom of the range-angle equivalent transmit beammap at the communication user's location. Under the constraints of communication information embedding and eavesdropping user limitations, an optimization model for the FDA-MIMO radar-communication integrated transmit beamforming is established with the objective function of minimizing the mean square error between the transmit beamforming matrix and the radar's desired beam matrix. Finally, a convex optimization algorithm is used to solve the established optimization problem.

Claims

1. A method for integrated transmit beamforming of FDA-MIMO radar communication, characterized in that, Includes the following steps: Construct an integrated radar-communication signal model based on beammap modulation (FDA-MIMO); The signal processing model of the communication receiver is derived, and a closed-form expression for the weighted range-angle two-dimensional equivalent transmit beammap of the receiver is obtained; specifically including: (B1) has J communication users with one receiving antenna, with a distance and azimuth angle relative to the integrated radar-communication transmitter as follows: and ; Calculate the received signal of the j-th communication user; (B2) Adopt After performing matched filtering on the received signal, the output signal of the nth array element receiving the mth transmitted signal is calculated, where, It is an orthogonal waveform. Let m be the transmission frequency of the m-th orthogonal waveform. Indicates the pulse time-domain sampling time; (B3) Superimpose the multi-channel matched filter output signals into an extended vector; Using the distance-angle of the communication user as prior information, information embedding is achieved by constraining the amplitude and phase degrees of freedom of the equivalent transmission beammap at the communication user's location based on the distance-angle; specifically including: (C1) J communication users are located at arbitrary distances and angle gates within the coverage area of ​​the transmitted beam, and the location information of each user is known a priori; during each transmitted pulse, phase constellation modulation is used to characterize the communication symbols; the communication information of the j-th user... The calculation is as follows: ； in, Represents the original communication phase, whose values ​​are derived from the set. Randomly selected from the middle, This represents the number of orthogonal waveforms transmitted simultaneously by all transmitting antennas. This represents the number of bits in a single communication symbol. This represents the i-th phase point within a constellation; (C2) A beammap modulation method is adopted, and a two-dimensional equivalent transmission steering vector with respect to range and angle is introduced into the optimization problem. The equality constraint is expressed as: ； in, The range-angle two-dimensional equivalent launch guidance vector. Represents the Hadamard product. For power parameters, This is the first power parameter. This is the Mth power parameter; In scenario (C3), there are H threatening eavesdropping users, whose distances and angles relative to the radar-communication integrated transmitter are respectively... and , The following equality constraint is introduced into the optimization problem to eliminate the phase information of the beammap at the location of the eavesdropping user: ； in, Let h be the distance-angle two-dimensional equivalent transmission guidance vector for the h-th eavesdropping user. For the h-th eavesdropping user, The power factor of the beammap at the eavesdropping user's location can be set to a number close to 0 to generate beam nulls at the eavesdropping user's location. for A 1-dimensional vector; The transmit beamforming matrix is ​​designed to ensure radar detection performance; specifically, the desired transmit beamforming matrix of the radar is designed based on the transmit steering vector of the azimuth angle of the target location: ； in, This represents all row elements in the m-th column of the matrix. Let m be all the row elements of the m-th column of the radar's desired transmit beamforming matrix. The azimuth of the target. The launch guidance vector at the target angle; The number of transmitting antennas, Let be the number of orthogonal waveforms transmitted simultaneously by all transmitting antennas; with constraints on communication information embedding and eavesdropping user limitations, and with the objective function being minimizing the mean square error between the transmitted beamforming matrix and the radar desired beam matrix, an FDA-MIMO radar-communication integrated transmitted beamforming optimization model is established, specifically as follows: ； in, For transmitting beamforming matrix, To form the matrix of the radar's desired transmit beam, The range-angle two-dimensional equivalent launch guidance vector. Let the delay be that of the j-th communication user. Let be the azimuth angle of the j-th communication user relative to the radar-communication integrated transmitter; Represents the Hadamard product. For power parameters, For the communication information of the j-th communication user, Let h be the distance-angle two-dimensional equivalent transmission guidance vector for the h-th eavesdropping user. For the h-th eavesdropping user, Let h be the angle of the h-th eavesdropping user relative to the radar-communication integrated transmitter. In order to eavesdrop on the power coefficient of the user's beammap, Let J be an M-dimensional vector of all ones, and J be the number of communication users. The objective function represents the number of eavesdropping users. The first constraint represents the phase embedding and power control of the communication users; the second constraint represents the phase constraint and power limitation of the eavesdropping users. This represents the radar transmit beamforming matrix that minimizes the mean square error under the premise of communication symbol embedding; the obstacle function algorithm is used to solve the optimization model.

2. The FDA-MIMO radar communication integrated transmit beamforming method according to claim 1, characterized in that, Constructing an integrated radar-communication signal model based on beammap modulation (FDA-MIMO), specifically including: (A1) FDA-MIMO architecture radar communication integrated system, with There are one transmitting antenna, and all transmitting antennas simultaneously transmit M orthogonal waveforms. , Given the pulse duration, M orthogonal waveforms satisfy the strict orthogonality condition. ; (A2) Introducing frequency increments of a frequency control array between different orthogonal waveforms Calculate the transmission frequency of the m-th orthogonal waveform. for: ； in, Indicates the carrier frequency of the transmitted signal; (A3) Calculate the m-th baseband transmitted signal composed of orthogonal waveforms and frequency increments. for: ； in, Indicates the pulse time-domain sampling time; (A4) Employing a transmit beamforming matrix For transmitted signals Beam pattern modulation is performed, where This is the first baseband transmission signal. For the Mth baseband transmission signal; calculate the integrated radar and communication transmission signal. for: ； (A5) The far-field signal at a distance of R and an azimuth angle of θ is calculated as follows: ； in, This represents the far-field signal at a distance of R and an azimuth angle of θ. where c is the time delay and c is the speed of light. for The transmission signal at any moment, for The conjugate transpose of . The launch steering vector is expressed as follows: ； Where d represents the spacing between array elements.

3. The FDA-MIMO radar communication integrated transmit beamforming method according to claim 1, characterized in that, The formula for calculating the received signal of the j-th communication user is: ； in, For the received signal of the j-th communication user, Let the delay be that of the j-th communication user. Let j be the receive steering vector for the j-th communication user. For far-field transmission signals, The loss coefficient for signal propagation. Indicates received noise; The formula for calculating the output signal of the nth array element receiving the mth transmitted signal is: ； in, The nth array element receives the output signal of the mth transmitted signal, where d represents the element spacing. , This represents the weighted transmitted beam space vector. The first element of the weighted transmit beam space vector. The second element of the weighted transmit beam space vector. The Mth element of the weighted transmit beam space vector. This is the m-th element of the weighted transmitted beam space vector; The extended vector is represented as: ； in, It is an extended vector formed by the superposition of the output signals of multiple matched filters. Indicates the Kronecker product. The range-angle two-dimensional equivalent launch steering vector is expressed as follows: 。 4. The FDA-MIMO radar communication integrated transmit beamforming method according to claim 1, characterized in that, The obstacle function algorithm is used to solve the optimization model, specifically including: (E1) The feasible region is denoted as: ; (E2) Define the barrier function: ; in, , It is a continuous function with the transmitted beamforming matrix W as the independent variable. When the independent variable W approaches the boundary of the feasible region, Its expression can be chosen from the following two forms: ； ； (E3) Initialization: Given an initial interior point Error threshold The initial parameters of the algorithm Reduction factor Maximum number of iterations Set the current iteration step k=1; (E4) If If the calculation is successful, proceed with the calculation; otherwise, stop the calculation and proceed to step E7. (E5) The transmitted beamforming matrix calculated using the (k-1)th time. Starting from a given point, solve the following unconstrained optimization problem to obtain the minimum value of the transmit beamforming matrix calculated in the k-th iteration. : ； (E6) Convergence Criterion: If Stop the calculation and proceed to step E7; otherwise, , k = k+1, return to step E4; where, and These are the algorithm parameters calculated in the (k-1)th and kth iterations, respectively; (E7) Output ,in, This is the optimal transmit beamforming matrix.

5. An FDA-MIMO radar-communication integrated transmit beamforming system, characterized in that, include: The signal model building unit is used to build an integrated signal model for radar and communication based on beammap modulation (FDA-MIMO). The communication signal processing unit is used to derive the signal processing model of the communication receiver and obtain the closed-form expression of the weighted range-angle two-dimensional equivalent transmit beammap at the receiver; specifically, it includes: (B1) has J communication users with one receiving antenna, with a distance and azimuth angle relative to the integrated radar-communication transmitter as follows: and ; Calculate the received signal of the j-th communication user; (B2) Adopt After performing matched filtering on the received signal, the output signal of the nth array element receiving the mth transmitted signal is calculated, where, It is an orthogonal waveform. Let m be the transmission frequency of the m-th orthogonal waveform. Indicates the pulse time-domain sampling time; (B3) Superimpose the multi-channel matched filter output signals into an extended vector; A communication information embedding unit is used to embed information by constraining the amplitude and phase degrees of freedom of the equivalent transmission beam pattern at the communication user's location, using the distance-angle position of the communication user as prior information; specifically, it includes: (C1) J communication users are located at arbitrary distances and angle gates within the coverage area of ​​the transmitted beam, and the location information of each user is known a priori; during each transmitted pulse, phase constellation modulation is used to characterize the communication symbols; the communication information of the j-th user... The calculation is as follows: ； in, Represents the original communication phase, whose values ​​are derived from the set. Randomly selected from the middle, This represents the number of orthogonal waveforms transmitted simultaneously by all transmitting antennas. This represents the number of bits in a single communication symbol. This represents the i-th phase point within a constellation; (C2) A beammap modulation method is adopted, and a two-dimensional equivalent transmission steering vector with respect to range and angle is introduced into the optimization problem. The equality constraint is expressed as: ； in, The range-angle two-dimensional equivalent launch guidance vector. Represents the Hadamard product. For power parameters, This is the first power parameter. For the first One power parameter; In scenario (C3), there are H threatening eavesdropping users, whose distances and angles relative to the radar-communication integrated transmitter are respectively... and , The following equality constraint is introduced into the optimization problem to eliminate the phase information of the beammap at the location of the eavesdropping user: ； in, Let h be the distance-angle two-dimensional equivalent transmission guidance vector for the h-th eavesdropping user. For the h-th eavesdropping user, The power factor of the beammap at the eavesdropping user's location can be set to a number close to 0 to generate beam nulls at the eavesdropping user's location. for A 1-dimensional vector; The transmit beamforming matrix design unit is used to design the transmit beamforming matrix to ensure radar detection performance; specifically, it designs the desired transmit beamforming matrix of the radar based on the transmit steering vector of the azimuth angle of the detected target. ； in, This represents all row elements in the m-th column of the matrix. Let m be all the row elements of the m-th column of the radar's desired transmit beamforming matrix. The azimuth of the target. The launch guidance vector at the target angle; Where is the number of transmitting antennas, and M is the number of orthogonal waveforms transmitted simultaneously by all transmitting antennas; An optimization model building unit is used to establish an FDA-MIMO radar-communication integrated transmit beamforming optimization model, with the constraints of communication information embedding and eavesdropping user restrictions as the optimization objective function, and minimizing the mean square error between the transmitted beamforming matrix and the radar desired beamforming matrix; specifically: ； in, For transmitting beamforming matrix, To form the matrix of the radar's desired transmit beam, The range-angle two-dimensional equivalent launch guidance vector. Let the delay be that of the j-th communication user. Let be the azimuth angle of the j-th communication user relative to the radar-communication integrated transmitter; Represents the Hadamard product. For power parameters, For the communication information of the j-th communication user, Let h be the distance-angle two-dimensional equivalent transmission guidance vector for the h-th eavesdropping user. For the h-th eavesdropping user, Let h be the angle of the h-th eavesdropping user relative to the radar-communication integrated transmitter. The power coefficient of the beammap at the eavesdropping user's location, where J is the number of communication users. The objective function represents the number of eavesdropping users. The first constraint represents the phase embedding and power control of the communication users; the second constraint represents the phase constraint and power limitation of the eavesdropping users. This represents the radar transmit beamforming matrix that minimizes the mean square error under the premise of communication symbol embedding. The optimization model solving unit is used to solve the optimization model using the obstacle function algorithm.

6. A control device, characterized in that, Includes processor, communication interface, memory, and communication bus; The processor, the communication interface, and the memory communicate with each other through the communication bus. The memory is used to store computer programs; When the processor executes the program stored in the memory, it implements the steps of the FDA-MIMO radar-communication integrated transmission beamforming method according to any one of claims 1-4.

7. A storage medium, characterized in that, The storage medium stores a computer program that, when executed by at least one processor, implements the steps of the FDA-MIMO radar-communication integrated transmit beamforming method as described in any one of claims 1-4.

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