Transmit waveform design method for embedding amplitude modulation communication information in MIMO radar

Abstract

The application discloses a transmitting waveform design method for embedding amplitude modulation communication information in a MIMO radar, comprising the following steps: establishing a transmitting waveform design model for embedding an amplitude modulation signal in a transmitting direction pattern of the MIMO radar; converting the transmitting waveform design model into an equivalent unconstrained optimization model; and determining an optimal transmitting waveform by using a combined gradient descent method according to the unconstrained optimization model. In the application, a multi-waveform design optimization problem under a constant modulus constraint with transmitting direction pattern matching as a design target is constructed by using given azimuth angles of a plurality of detection targets and a plurality of communication receiving devices, and an algorithm for combining a descending direction is designed, so that the joint optimal design of the transmitting direction pattern of the radar and the amplitude modulation of the communication can be realized, and thus the optimal transmitting waveform is formed.

Description

Technical Field

[0001] This invention relates to the field of MIMO radar technology, and in particular to a method for designing a transmission waveform that embeds amplitude modulation communication information in MIMO radar. Background Technology

[0002] With the development of radar and wireless communication technologies, wireless spectrum resources are becoming increasingly scarce. Against this backdrop, integrated radar and communication design technology has attracted significant attention from industry and academia. Specifically, integrated radar and communication technology embeds modulated communication information into the radar's detection waveform, simultaneously transmitting information to the receiving device without significantly affecting the radar's detection capabilities. Therefore, this technology not only helps alleviate spectrum scarcity but also promises to reduce the hardware design costs of radar and communication systems.

[0003] Currently, a single-waveform design method for transmitting communication information using orthogonal amplitude modulation in the sidelobes of radar detection waves has been proposed. However, due to the limitations of a single transmitted waveform—such as the limited number of simultaneously detectable targets and poor sidelobe suppression—the designed transmitted waveform cannot meet the requirements. Summary of the Invention

[0004] Based on this, it is necessary to provide a method for designing the transmission waveform of MIMO radar that embeds amplitude modulation communication information to address the above-mentioned technical problems. This method aims to solve the problem that the transmission waveform cannot meet the requirements due to the existence of a single transmission waveform, which results in a small number of targets that can be detected at the same time and poor sidelobe suppression capability.

[0005] This application provides a method for designing a transmit waveform that embeds amplitude modulation communication information in a MIMO radar, including:

[0006] Establish a design model for the transmission waveform of a MIMO radar with an embedded amplitude modulation signal in the transmission pattern;

[0007] The transmitted waveform design model is transformed into an equivalent unconstrained optimization model;

[0008] Based on the unconstrained optimization model, the optimal transmission waveform is determined using a combined gradient descent method.

[0009] In one embodiment, determining the optimal transmission waveform using a combined gradient descent method based on the unconstrained optimization model includes:

[0010] Step a: Calculate the first descent direction and the second descent direction according to the unconstrained optimization model;

[0011] Step b: Calculate the optimal update step size and maximum descent amount of the unconstrained optimization model in the first descent direction and the second descent direction;

[0012] Step c: Calculate the combination coefficients based on the optimal update step size and the maximum descent amount;

[0013] Step d: Calculate the optimal transmission waveform using the gradient descent method based on the combined coefficients.

[0014] In one embodiment, calculating the first descent direction and the second descent direction according to the unconstrained optimization model includes:

[0015] Let Y1 be a feasible solution for the reference transmitted waveform, t = 1 be the initial iteration variable, and let M0 and V0 be an M-row N-column complex matrix of the reference transmitted waveform.

[0016] The first and second descent directions are obtained using the following formulas:

[0017] First descent direction

[0018] Second descent direction

[0019] In one embodiment, calculating the combination coefficients based on the optimal update step size and the maximum descent amount includes:

[0020] The optimal update step size corresponding to the first descent direction is α. t,GD The maximum decrease is D t，GD The optimal update step size corresponding to the second descent direction is α. t,Amsgrad The maximum decrease is D t,Amsgrad ;

[0021] The combination coefficient

[0022] The step of calculating the optimal transmission waveform using the gradient descent method based on the combination coefficients includes:

[0023] Substituting the combination coefficients into the preset formula, we get:

[0024] Y t+1 =Y t +w t ×(α t,GD ΔY t,GD )+(1-w t )×(α t,Amsgrad ΔY t,Amsgrad );

[0025] Update the variable t = t + 1 iteratively, and repeat steps a through c until Y is reached. t =Y t+1The optimal transmission waveform is obtained.

[0026] In one embodiment, the first descent direction is the negative gradient direction, and the second descent direction is the AMS gradient direction.

[0027] In one embodiment, establishing the transmission waveform design model with the amplitude modulation signal embedded in the MIMO radar transmission pattern includes:

[0028] Determine the number of antennas, the number of transmitted waveform sequences, the desired transmitted pattern, and the reference transmitted waveform for the MIMO radar;

[0029] Obtain the angles of all communication receiving devices and the amplitude of the amplitude-modulated communication signal;

[0030] Based on the number of antennas of the MIMO radar, the number of transmitted waveform sequences, the desired transmission pattern, the reference transmitted waveform, the angles of all communication receiving devices, and the amplitude of the amplitude-modulated communication signal, a transmission waveform design model for embedding amplitude-modulated signals in the transmission pattern of the MIMO radar is established.

[0031] In one embodiment, establishing the design model for the transmitted waveform embedding the amplitude modulation signal in the MIMO radar transmit pattern includes:

[0032] Establish the directional pattern and design the loss function;

[0033] Establish a cross-correlation loss function;

[0034] Establish a waveform similarity loss function;

[0035] Establish the loss function for amplitude modulation communication design;

[0036] Based on the aforementioned pattern design loss function, cross-correlation loss function, waveform similarity loss function, and amplitude modulation communication design loss function, a constant modulus constraint-based transmission waveform design model is constructed.

[0037] In one embodiment, the transmit waveform design model P1 is shown below:

[0038]

[0039]

[0040] Wherein, the f BM (α, X) is the design loss function for the radiation pattern, f CC (X) is the cross-correlation loss function, f RS (X) represents the waveform similarity loss function, f CP(X) represents the amplitude modulation communication design loss function, X is the transmitted waveform, ω, ρ, and τ are harmonic coefficients, and the variable α is used to match the amplitude difference between the actual transmission pattern and the desired transmission pattern.

[0041] In one embodiment, converting the transmit waveform design model into an equivalent unconstrained optimization model includes:

[0042] The optimal solution for calculating the amplitude difference between the actual and desired transmission patterns;

[0043] Substituting the optimal solution into the pattern design loss function yields a function that is only related to the transmitted waveform X;

[0044] Replace the transmitted waveform X with The function relating only to the transmitted waveform, and the Substituting these values ​​into the transmitted waveform design model yields the equivalent unconstrained optimization model.

[0045] In one embodiment, the unconstrained optimization model P2 is as follows:

[0046]

[0047] in, The function is only related to the transmitted waveform. For the cross-correlation loss function, This represents the waveform similarity loss function. Let ω, ρ, and τ represent the loss function for amplitude modulation communication design, where ω, ρ, and τ are harmonic coefficients.

[0048] The aforementioned method for designing a transmit waveform for embedding amplitude modulation communication information in a MIMO radar includes: establishing a transmit waveform design model for embedding amplitude modulation signals in the MIMO radar transmit pattern; converting the transmit waveform design model into an equivalent unconstrained optimization model; and determining the optimal transmit waveform using a combined gradient descent method based on the unconstrained optimization model. In this application, a multi-waveform design optimization problem under constant modulus constraints is constructed using given azimuth angles of multiple detection targets and multiple communication receiving devices, with transmit pattern matching as the design objective. An algorithm combining descent directions is designed to achieve joint optimization design of the radar transmit pattern and communication amplitude modulation, thereby forming the optimal transmit waveform. Attached Figure Description

[0049] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a flowchart illustrating a method for designing a transmit waveform that embeds amplitude modulation communication information in a MIMO radar according to an embodiment of the present invention.

[0051] Figure 2 This is a flowchart illustrating a calculation method for determining the optimal transmission waveform using a combined gradient descent method in one embodiment of the present invention. Detailed Implementation

[0052] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] In one embodiment, such as Figure 1 As shown, a method for designing a transmit waveform for embedding amplitude modulation communication information in a MIMO radar is provided, including the following steps:

[0054] In step S110, a design model for the transmission waveform of the MIMO radar with the amplitude modulation signal embedded in the transmission pattern is established;

[0055] In one embodiment of this application, a design model for the transmission waveform of a MIMO radar with an embedded amplitude modulation signal in the transmission pattern is established, specifically including:

[0056] Determine the number of antennas, the number of transmitted waveform sequences, the desired transmitted pattern, and the reference transmitted waveform for the MIMO radar;

[0057] Obtain the angles of all communication receiving devices and the amplitude of the amplitude-modulated communication signal;

[0058] Based on the number of antennas of the MIMO radar, the number of transmitted waveform sequences, the desired transmission pattern, the reference transmitted waveform, the angles of all communication receiving devices, and the amplitude of the amplitude-modulated communication signal, a transmission waveform design model for embedding amplitude-modulated signals in the transmission pattern of the MIMO radar is established.

[0059] In this embodiment, the number of antennas and the number of transmitted waveform sequences of the MIMO radar can be determined according to the actual needs of the MIMO radar embedding amplitude signals. The desired transmission pattern and the reference transmitted waveform can be preset by the user. The angles of all communication receiving devices can be the azimuth angles of the receiving antennas of all communication receiving devices.

[0060] In this embodiment of the application, establishing the transmission waveform design model for embedding the amplitude modulation signal in the MIMO radar transmission pattern includes:

[0061] Establish the directional pattern and design the loss function;

[0062] Establish a cross-correlation loss function;

[0063] Establish a waveform similarity loss function;

[0064] Establish the loss function for amplitude modulation communication design;

[0065] Based on the aforementioned pattern design loss function, cross-correlation loss function, waveform similarity loss function, and amplitude modulation communication design loss function, a constant modulus constraint-based transmission waveform design model is constructed.

[0066] Specifically, in a MIMO radar with M antennas arranged linearly at half-wavelength intervals, the number of transmitted waveform sequences is set to N. Assume the transmitted waveform is X (X is an M x N complex matrix, where the element in the m x n row represents the nth waveform transmitted by the m x n antenna), and the desired transmission pattern P... d (θ), θ∈[0,180°], the reference waveform is X0, the angle of the communication equipment and the amplitude of the amplitude-modulated communication signal are (θ). l Δ l ),l=1,.....l.

[0067] Therefore, the pattern design loss function is as follows:

[0068]

[0069] The cross-correlation loss function is shown below:

[0070]

[0071] The waveform similarity loss function is shown below:

[0072]

[0073] The loss function for amplitude modulation communication is shown below:

[0074]

[0075] Here, the variable α is used to match the amplitude difference between the actual transmission pattern and the desired transmission pattern, a(θ)=[1,exp(jπsinθ),…,exp(jπ(M-1)sinθ)] T It is the guiding vector at angle θ, exp(x) represents the natural constant raised to the power of x, j is the imaginary unit, and P d (θ i ) refers to the angle θ i The expected direction pattern on the set Includes all angles that need to be tracked, X0 is a pre-set reference emission waveform, set It is the angle at which all communication receiving devices are located, Δ l It is a predefined direction at θ l The amplitude of the amplitude-modulated communication signal transmitted by the angle communication device. Considering the constant modulus constraint commonly used in practice, the design model of the transmitted waveform for embedding amplitude-modulated communication information in this MIMO radar is shown below:

[0076]

[0077]

[0078] Wherein, the f BM (α, X) is the design loss function for the radiation pattern, f CC (X) is the cross-correlation loss function, f RS (X) represents the waveform similarity loss function, f CP (X) represents the amplitude modulation communication design loss function, X is the transmitted waveform, ω, ρ, and τ are harmonic coefficients, the variable α is used to match the amplitude difference between the actual transmission pattern and the desired transmission pattern, and m and n represent the m-th row and n-th column in the transmitted waveform X matrix.

[0079] In step S120, the transmitted waveform design model is transformed into an equivalent unconstrained optimization model;

[0080] In this embodiment of the application, the transmit waveform design model is a constrained optimization problem, and therefore it can be converted into an equivalent unconstrained optimization problem.

[0081] In the embodiments of this application, the transmitted waveform design model is transformed into an equivalent unconstrained optimization model, including:

[0082] The optimal solution for calculating the amplitude difference between the actual and desired transmission patterns;

[0083] Substituting the optimal solution into the pattern design loss function yields a function that is only related to the transmitted waveform X;

[0084] Replace the transmitted waveform X with The function relating only to the transmitted waveform, and the Substituting these values ​​into the transmitted waveform design model yields the equivalent unconstrained optimization model.

[0085] Specifically, for a given transmitted waveform X, the optimal solution for variable α can be obtained using the following formula:

[0086]

[0087] Substituting this into the pattern design loss function f BM In (α, X), a function relating only to the transmitted waveform X can be obtained, as shown below:

[0088]

[0089] Then, replace the transmitted waveform X with If Y is an M-row N-column complex matrix, then problem P1 can be transformed into an unconstrained optimization problem P2 using the following formula.

[0090]

[0091] in, The function is only related to the transmitted waveform. For the cross-correlation loss function, This represents the waveform similarity loss function. Let ω, ρ, and τ represent the loss function for amplitude modulation communication design, where ω, ρ, and τ are harmonic coefficients.

[0092] In step S130, the optimal transmission waveform is determined by using a combined gradient descent method based on the unconstrained optimization model.

[0093] See Figure 2 In this embodiment of the application, determining the optimal transmission waveform using a combined gradient descent method based on the unconstrained optimization model includes:

[0094] Step a: Calculate the first descent direction and the second descent direction according to the unconstrained optimization model;

[0095] Step b: Calculate the optimal update step size and maximum descent amount of the unconstrained optimization model in the first descent direction and the second descent direction;

[0096] Step c: Calculate the combination coefficients based on the optimal update step size and the maximum descent amount;

[0097] Step d: Calculate the optimal transmission waveform using the gradient descent method based on the combined coefficients.

[0098] Specifically, calculating the first descent direction and the second descent direction according to the unconstrained optimization model includes:

[0099] Let Y1 be the feasible solution of the initial transmission waveform, t = 1 be the initial iteration variable, and set the auxiliary variables M0 and V0 as an M-row N-column complex matrix of the initial transmission waveform.

[0100] The first and second descent directions are obtained using the following formulas:

[0101] First descent direction

[0102] Second descent direction

[0103] The first descent direction is the negative gradient direction of the traditional objective function, while the second descent direction is the AMS gradient direction. This AMS gradient direction can be obtained using the following formula:

[0104] M t =βM t-1 +(1-β1)G t ;

[0105]

[0106]

[0107]

[0108]

[0109] Then, the optimal update step size and maximum descent amount can be calculated for f(Y) in the first descent direction and the second descent direction.

[0110] Specifically, for Y t Given a descent direction ΔY, the optimal update step size can be obtained by solving the following problem:

[0111] α ★ =argmin α f(Y t +αΔY);

[0112] This problem is a one-dimensional search problem, which can be solved directly using optimization toolkits, such as the fminbnd method built into MATLAB, or by exhaustive search. The corresponding maximum descent is: f(Y) t )-f(Y t +αΔY).

[0113] From the above formula, the optimal update step size corresponding to the first descent direction can be obtained as α.t,GD The maximum decrease is D t，GD The optimal update step size corresponding to the second descent direction is α. t,Amsgrad The maximum decrease is D t,Amsgrad .

[0114] The calculation of the combination coefficients based on the optimal update step size and the maximum descent amount includes:

[0115] The combination coefficients: e is a natural constant.

[0116] The step of calculating the optimal transmission waveform using the gradient descent method based on the combination coefficients includes:

[0117] Substituting the combination coefficients into the preset formula, we get:

[0118] Y t+1 =Y t +w t ×(α t,GD ΔY t,GD )+(1-w t )×(α t,Amsgrad ΔY t,Amsgrad );

[0119] Update the variable t = t + 1 iteratively, and repeat steps a through c until Y is reached. t =Y t+1 The optimal transmission waveform is obtained.

[0120] This application provides a method for designing a transmit waveform that embeds amplitude modulation communication information in a MIMO radar. The method includes: establishing a transmit waveform design model with an amplitude modulation signal embedded in the MIMO radar transmit pattern; converting the transmit waveform design model into an equivalent unconstrained optimization model; and determining the optimal transmit waveform using a combined gradient descent method based on the unconstrained optimization model. In this application, a multi-waveform design optimization problem under constant modulus constraints is constructed using multiple given detection targets and azimuth angles of multiple communication receiving devices, with transmit pattern matching as the design objective. An algorithm combining descent directions is designed to achieve joint optimization design of the radar transmit pattern and communication amplitude modulation, thereby forming the optimal transmit waveform.

[0121] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0122] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A method for designing a transmit waveform for embedding amplitude-modulated communication information in a MIMO radar, characterized in that, The method includes: Establish a design model for the transmission waveform of a MIMO radar with an embedded amplitude modulation signal in the transmission pattern; The establishment of the transmission waveform design model for embedding amplitude modulation signals in the MIMO radar transmission pattern includes: Determine the number of antennas, the number of transmitted waveform sequences, the desired transmitted pattern, and the reference transmitted waveform for the MIMO radar; Obtain the angles of all communication receiving devices and the amplitude of the amplitude-modulated communication signal; Based on the number of antennas of the MIMO radar, the number of sequences of transmitted waveforms, the desired transmission pattern, the reference transmitted waveform, the angles of all communication receiving devices, and the amplitude of the amplitude-modulated communication signal, a transmission waveform design model for embedding amplitude-modulated signals in the transmission pattern of the MIMO radar is established. The transmitted waveform design model is transformed into an equivalent unconstrained optimization model; Based on the unconstrained optimization model, the optimal transmission waveform is determined using a combined gradient descent method.

2. The method for designing the transmit waveform for embedding amplitude modulation communication information in a MIMO radar as described in claim 1, characterized in that, The step of determining the optimal transmission waveform based on the unconstrained optimization model using a combined gradient descent method includes: Step a: Calculate the first descent direction and the second descent direction according to the unconstrained optimization model; Step b: Calculate the optimal update step size and maximum descent amount of the unconstrained optimization model in the first descent direction and the second descent direction; Step c: Calculate the combination coefficients based on the optimal update step size and the maximum descent amount; Step d: Calculate the optimal transmission waveform using the gradient descent method based on the combined coefficients.

3. The method for designing the transmit waveform for embedding amplitude modulation communication information in a MIMO radar as described in claim 2, characterized in that, The step of calculating the first descent direction and the second descent direction according to the unconstrained optimization model includes: Let Y1 be the feasible solution of the initial transmission waveform, t = 1 be the initial iteration variable, and set the auxiliary variables M0 and V0 as an M-row N-column complex matrix of the initial transmission waveform. The first and second descent directions are obtained using the following formulas: First descent direction Second descent direction Among them, Y t Let represent the feasible solution for the emission waveform at the t-th iteration.

4. The method for designing the transmit waveform for embedding amplitude modulation communication information in a MIMO radar as described in claim 3, characterized in that, The calculation of the combination coefficients based on the optimal update step size and the maximum descent amount includes: The optimal update step size corresponding to the first descent direction is α. t,GD The maximum decrease is D t，GD The optimal update step size corresponding to the second descent direction is α. t,Amsgrad The maximum decrease is D t,Amsgrad ; The combination coefficient The step of calculating the optimal transmission waveform using the gradient descent method based on the combination coefficients includes: Substituting the combination coefficients into the preset formula, we get: Y t+1 =Y t +w t ×(a t,GD Y t,GD )+(1-w t )×(a t,Amsgrad Y t,Amsgrad ); Update the variable t = t + 1 iteratively, and repeat steps a through c until Y is reached. t =Y t+1 The optimal transmission waveform is obtained, where Y t+1 Let represent the feasible solution of the emission waveform at the (t+1)th iteration.

5. The method for designing a transmission waveform for embedding amplitude modulation communication information in a MIMO radar as described in any one of claims 2-4, characterized in that, The first descent direction is the negative gradient direction, and the second descent direction is the AMS gradient direction.

6. The method for designing the transmit waveform for embedding amplitude modulation communication information in a MIMO radar as described in claim 1, characterized in that, The establishment of the transmission waveform design model for embedding the amplitude modulation signal in the transmission pattern of the MIMO radar includes: Establish the directional pattern and design the loss function; Establish a cross-correlation loss function; Establish a waveform similarity loss function; Establish the loss function for amplitude modulation communication design; Based on the aforementioned pattern design loss function, cross-correlation loss function, waveform similarity loss function, and amplitude modulation communication design loss function, a constant modulus constraint-based transmission waveform design model is constructed.

7. The method for designing a transmit waveform for embedding amplitude modulation communication information in a MIMO radar as described in claim 1, characterized in that, The transmitted waveform design model P1 is shown below: Wherein, the f BM (α, X) is the design loss function for the radiation pattern, f CC (X) is the cross-correlation loss function, f RS (X) represents the waveform similarity loss function, f CP (X) represents the amplitude modulation communication design loss function, X is the transmitted waveform, ω, ρ, and τ are harmonic coefficients, the variable α is used to match the amplitude difference between the actual transmission pattern and the desired transmission pattern, and m and n represent the m-th row and n-th column in the transmitted waveform X matrix.

8. The method for designing the transmit waveform for embedding amplitude modulation communication information in a MIMO radar as described in claim 7, characterized in that, The step of transforming the transmitted waveform design model into an equivalent unconstrained optimization model includes: The optimal solution for calculating the amplitude difference between the actual and desired transmission patterns; Substituting the optimal solution into the pattern design loss function yields a function that is only related to the transmitted waveform X; Replace the transmitted waveform X with The function relating only to the transmitted waveform X, and the... Substituting these values ​​into the transmitted waveform design model yields the equivalent unconstrained optimization model.

9. The method for designing the transmit waveform for embedding amplitude modulation communication information in a MIMO radar as described in claim 8, characterized in that, The unconstrained optimization model P2 is shown below: in, The function is only related to the transmitted waveform. For the cross-correlation loss function, This represents the waveform similarity loss function. Let ω, ρ, and τ represent the loss function for amplitude modulation communication design, where ω, ρ, and τ are harmonic coefficients.

Images