Elastic doppler complementary waveform design method combined with signal strength and sidelobe suppression optimization

Abstract

The application discloses a signal strength and sidelobe suppression combined optimization elastic Doppler complementary waveform design method, first proposes a Pareto effective framework for Golay complementary waveform design, and the framework jointly optimizes a Doppler elastic transceiving sequence pair. The framework considers a constrained optimization problem in terms of SMR and SNR, constructs a loss function of a Pareto multi-objective optimization problem by using an epsilon-constraint method, and obtains all possible Pareto optimal solutions. Secondly, in order to solve the optimization problem, a model-driven machine learning algorithm is innovatively designed to process the multi-objective optimization problem. The application effectively reduces the interference of sidelobes on weak target detection, improves the accuracy and reliability of target detection of a radar system, can more clearly detect and distinguish multiple targets, and enhances the overall performance of the radar system.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, specifically relating to a method for designing elastic Doppler complementary waveforms that jointly optimizes signal strength and sidelobe suppression. Background Technology

[0002] In modern radar technology, pulse compression radar is an important technique. It improves ranging resolution by utilizing a large bandwidth while simultaneously acquiring high pulse energy using a pulse matched filter. This technique enables radar to more accurately determine the distance information of targets during detection. Golay Complementary Pair (GCP) waveforms are widely used in radar systems due to their unique properties. GCP possesses ideal autocorrelation characteristics, giving it a significant advantage in radar ranging applications. For example, it is considered a potential solution in the ongoing development of IEEE 802.11ad, which incorporates radar sensing capabilities.

[0003] However, GCP is not without its flaws. It is highly sensitive to mobility; when the radar detects a moving target, the Doppler frequency shift of the moving target disrupts the complementary characteristics of the received sequence pairs. This disruption, in turn, leads to a severe range-Doppler sidelobe problem.

[0004] The presence of range-Doppler sidelobes poses a significant challenge to multi-target radar detection. In real-world scenarios, such as autonomous vehicle scenarios, if the sidelobe problem cannot be effectively addressed, the sidelobes of strong targets may overwhelm the signals of weak targets, leading to inaccurate detection of weak targets and impacting the performance and reliability of the entire radar system. To address the Doppler elasticity problem of range-Doppler (GCP), the Doppler elasticity technique using Golay complementary waveforms has been extensively studied, and these studies can be broadly categorized into two types.

[0005] The first type of technique optimizes the transmitted pulse sequence under the matched filter reception assumption. For example, some methods construct the transmitted pulse sequence by coordinating transmission through a specific sequence, which can suppress sidelobes to some extent. However, this type of method has some limitations, such as the applicable Doppler range is often relatively limited, and it cannot adapt well to various practical situations.

[0006] The second type of technique involves orchestrating transmit-receive sequences, prioritizing the reduction of sidelobes near the zero Doppler axis. However, this approach comes at the cost of signal-to-noise ratio (SNR). In practical applications, a decrease in SNR can affect the radar's ability and accuracy in detecting targets.

[0007] More importantly, existing Doppler elasticity schemes are significantly inadequate in handling the trade-off between the two key performance indicators, sidelobe-to-main-lobe ratio (SMR) and signal-to-noise ratio (SNR). They typically simplify non-convex optimization problems, resulting in transmit-receive sequence pairs that only reflect a compromise rather than the optimal solution that simultaneously optimizes SMR and SNR. This creates a bottleneck in improving radar performance with current technology, failing to meet the ever-increasing practical demands. Summary of the Invention

[0008] To overcome the shortcomings of existing technologies, this invention provides a method for designing elastic Doppler complementary waveforms by jointly optimizing signal strength and sidelobe suppression. First, a Pareto efficient framework for Golay complementary waveform design is proposed, which jointly optimizes Doppler elastic transmit / receive sequence pairs. This framework considers constrained optimization problems on both SMR and SNR metrics, using the ε-constraint method to construct the loss function for a Pareto multi-objective optimization problem, and finding all possible Pareto optimal solutions. Second, to solve the optimization problem, a model-driven machine learning algorithm is innovatively designed to handle the multi-objective optimization problem. This invention effectively reduces the interference of sidelobes on weak target detection, improves the accuracy and reliability of radar system target detection, enables clearer detection and differentiation of multiple targets, and enhances the overall performance of the radar system.

[0009] The technical solution adopted by this invention to solve its technical problem is as follows:

[0010] Step 1: Establish a system model;

[0011] A pulse compression radar system consists of a transmitter, a receiver, and a signal processing unit. The baseband signal in the transmitter is phase-coded using a GCP (Government-Pulse Coding Process), and then the encoded signal is transmitted through a phase-coded modulator. After receiving the reflected signal, the receiver processes it through a pulse compression filter, and finally the target information is detected by a detector.

[0012] At the transmitting end, the basic waveforms Sx(t) and Sy(t) encoded by GCP are transmitted according to the characteristic binary vector p, forming a P-pulse sequence Z. P(t) At the receiving end, the Q-pulse sequence Z Q(t) Defined by the coefficient vector q, the signal input to the matched filter is Z. P(t) e jvt Where v = 2πf d For Doppler frequency shift;

[0013] Signal Model: Golay complementary pairs are defined as two single-mode complex sequences x[·] and y[·] of length L, satisfying that for all lags k = -(L-1), -(L-2), ..., 0, ..., (L-1), C x [k]+C y [k]=2Lδ k C x (k) and C y (k) are the autocorrelation functions of sequences x and y at lag k, respectively, and δ k The Kronecker delta function; the basic Golay complementary waveform. and Where u(t) is the baseband pulse shape with unit energy, T c This refers to the chip length;

[0014] P-pulse sequence:

[0015]

[0016] Q-pulse sequence:

[0017]

[0018] Let Z p (t) represents the transmitted signal, Z Q (t) represents the time-domain response of the received signal, with the input of the receiver matched filter set to Z. p (t)e jυt Where v = 2πf d f d Z represents the Doppler frequency shift, measured in Hz. p (t)e jυt The impulse response is Z * Q A linear filter with (-t); the output of the matched filter, i.e., the cross-blur function, is:

[0019]

[0020] This cross-fuzzy function is also Z. p (t) and Z Q A continuous cross-fuzzy function of (t);

[0021] Through algebraic processing, the discrete cross-fuzzy function is:

[0022]

[0023] Where θ = vT = 2πf d T is the Doppler frequency shift within each pulse repetition interval T;

[0024] Step 2: ε-constraint method;

[0025] Step 2-1: Optimize the target definition;

[0026] SMR: For GCP-coded waveforms, the phase-coded modulator and pulse compression filter of the Golay waveform are controlled by the transmit vector p and the receive vector q; according to formula (4), when k≠0, This represents the range sidelobe that needs to be suppressed; when k = 0 and θ = 0, This represents the main lobe energy; therefore, SMR is defined as:

[0027]

[0028] SNR is:

[0029]

[0030] Among them Target power, N0 is the receiver white noise power spectral density;

[0031] The multi-objective optimization problem is formulated as follows:

[0032]

[0033] Its optimal solution is a set of trade-off solutions, which are solved using the ε-constraint method;

[0034] Step 2-2: Two cases of the ε-constraint method:

[0035] The optimization problem constrained by SNR is expressed as follows:

[0036]

[0037] The optimization problem constrained by SMR is expressed as follows:

[0038]

[0039] Where δ is the preset SNR constraint parameter, and ∈ is the preset SMR constraint parameter;

[0040] Steps 2-3: Penalty Function Method

[0041] Based on formulas (8) and (9), the penalty function method is used to approximate the constrained optimization problem as an unconstrained problem. For formula (4), the objective function is transformed into:

[0042]

[0043] Where σ is the penalty coefficient for SNR;

[0044] For formula (5), the objective function is transformed into:

[0045]

[0046] Where λ is the penalty coefficient of SMR;

[0047] Step 3: Model-driven machine learning approach;

[0048] Machine learning algorithms are used to solve optimization problems. The stochastic gradient descent (SGD) algorithm is employed to learn the model parameters.

[0049] Step 3-1: Overall structure and function;

[0050] The neural network structure based on machine learning algorithms consists of a forward propagation module and a back propagation module. The forward propagation module calculates the normalized random Doppler frequency shift phase of the input. The back propagation module calculates the loss function according to formula (10) or (11), and then updates the weight vector in the forward propagation module. The weights trained in the neural network are set as the output feature vector. The weight vector is updated using the Adam optimizer by minimizing the loss function. The bias of the forward propagation is set to zero.

[0051] Step 3-1-1: Input the design;

[0052] The model's input is set to a phase value vector. Where θ d It is a Doppler frequency shift, in the Doppler interval [0, 2πf] d Randomly selected from T], where index d represents the number of iterations; after training, the loss is minimized over the entire Doppler interval to suppress sidelobes;

[0053] Step 3-1-2: Optimization Goal:

[0054] To find the optimal transmit-receive sequence pair {p,q}, a neural network is trained to minimize the loss function, as shown in Equation (12), where Let θ represent the loss function, and let θ represent the initial input phase in the Doppler interval.

[0055]

[0056] Step 3-1-3: Backpropagation module design;

[0057] Treating the product of p and q as a single parameter z, the backpropagation module minimizes the loss function. To update the feature vector z = [z1, z2, ..., z N-1 The feature vector z comes from the weight vector of the last layer of the neural network; the loss function... It is derived from the objective function in formula (10) or (11);

[0058] In the ε-constraint method, the constraint metric is multiplied by a penalty coefficient, and the loss functions for the constraint signal-to-noise ratio (SNR) and sidelobe-to-main-lobe ratio (SMR) are defined by equations (13) and (14), respectively.

[0059]

[0060] Where z n =p n *q n p n According to z n The polarity of the real part is shown in formula (15):

[0061]

[0062] q n As defined in formula (16):

[0063]

[0064] For the Doppler frequency shift θ, e jnθ The result, calculated using Euler's formula, is cos(nθ) + jsin(nθ). For a complex weight vector z, this can be written as z = z r +jz i , where z r Let z be the real part of z. i The imaginary part of z is represented; the multiplication of two complex numbers is shown in formula (17), which converts complex number multiplication into a series of real number multiplications;

[0065]

[0066] Finally, we obtain p and q.

[0067] Preferably, the p n The value is ±1, and the range of θ is [0, 2πf]. d T].

[0068] A computer program that causes a computer to execute the above-described elastic Doppler complementary waveform design method.

[0069] An electronic device includes: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to enable the electronic device to perform the above-described elastic Doppler complementary waveform design method.

[0070] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described elastic Doppler complementary waveform design method.

[0071] A chip includes a processor for retrieving and running a computer program from a memory, causing a device on which the chip is mounted to perform the above-described elastic Doppler complementary waveform design method.

[0072] A computer program product includes a computer storage medium storing a computer program, the computer program including instructions executable by at least one processor, which, when executed by the at least one processor, implement the above-described elastic Doppler complementary waveform design method.

[0073] The beneficial effects of this invention are as follows:

[0074] 1. Improved sidelobe suppression performance: The technical solution of this invention can suppress the range-Doppler sidelobe to an extremely low level in the Doppler interval [0,π), which is a significant improvement compared with traditional solutions (such as the NS solution), and effectively reduces the interference of sidelobe on weak target detection.

[0075] 2. Signal-to-noise ratio performance optimization: In the process of waveform optimization, the SNR can be better balanced, with less SNR loss compared with the existing scheme, which improves the accuracy and reliability of the radar system for target detection.

[0076] 3. Enhanced multi-target detection capability: By achieving the optimal trade-off between sidelobe suppression ratio and signal-to-noise ratio, this invention improves the radar system's ability to distinguish between strong and weak targets in multi-target detection scenarios, enabling clearer detection and differentiation of multiple targets and enhancing the overall performance of the radar system. Attached Figure Description

[0077] Figure 1 This is a structural diagram of a pulse compression radar system;

[0078] Figure 2 This is a schematic diagram of the machine learning model structure of the present invention;

[0079] Figure 3 This is the Pareto front achieved by using the method of the present invention in the Doppler interval [0,π) to balance the signal-to-noise ratio and the sidelobe-to-mainlobe ratio. Detailed Implementation

[0080] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0081] This invention proposes a method for designing elastic Doppler complementary waveforms by jointly optimizing signal strength and sidelobe suppression. First, a Pareto efficient framework for Golay complementary waveform design is proposed, which jointly optimizes Doppler elastic transmit / receive sequence pairs. This framework considers constrained optimization problems on both SMR and SNR metrics, constructing a loss function for a Pareto multi-objective optimization problem using the ε-constraint method to find all possible Pareto optimal solutions. Second, to solve the optimization problem, a model-driven machine learning algorithm is innovatively designed to handle the multi-objective optimization problem.

[0082] 1. System Model Establishment (Reference) Figure 1 ):

[0083] A pulse compression radar system mainly consists of a transmitter, a receiver, and related signal processing components. The baseband signal in the transmitter is phase-coded using GCP (Gross Complementary Pairs), and then transmitted after passing through a phase-coded modulator. The receiver receives the reflected signal, processes it through a pulse compression filter, and finally, a detector detects the target information.

[0084] At the transmitting end, the basic waveforms Sx(t) and Sy(t) encoded by GCP are transmitted according to the characteristic binary vector p, forming a P-pulse sequence Z. P(t) At the receiving end, the Q-pulse sequence Z Q(t) Defined by the coefficient vector q, the signal input to the matched filter is Z. P(t) e jvt Where v = 2πf d This is due to the Doppler frequency shift.

[0085] Signal Model: Golay complementary pairs are defined as two single-mode complex sequences x[·] and y[·] of length L, satisfying that for all lags k = -(L-1), -(L-2), ..., 0, ..., (L-1), C x (k)+C y (k)=2Lδ k C x (k) and C y (k) are the autocorrelation functions of sequences x and y at lag k, respectively, and δ k This is the Kronecker delta function. Basic Golay complementary waveform. and Where u(t) is the baseband pulse shape with unit energy, T c This represents the chip length.

[0086] R-pulse sequence:

[0087]

[0088] S-pulse sequence:

[0089]

[0090] Let Z p (t) represents the transmitted signal, Z Q (t) represents the time-domain response of the received signal, with the input of the receiver matched filter set to Z. p (t)e jvt Where v = 2πf d f d Z represents the Doppler frequency shift, measured in Hz. p (t)e jvt The impulse response is Z* Q A linear filter with (-t) is then applied. The output of the matched filter, i.e., the cross-blur function, is...

[0091]

[0092] It is also Z p (t) and Z Q The continuous cross-fuzzy function of (t).

[0093] After certain approximations and simple algebraic processing, the discrete cross-fuzzy function is:

[0094]

[0095] Where θ = vT = 2πf d T is the Doppler frequency shift (in radians) within each pulse repetition interval (PRI)T.

[0096] 2. Principle and implementation of the ε-constraint method;

[0097] 2.1 Optimization Target Definition:

[0098] Definition of SMR: For a GCP-coded waveform, the phase-coded modulator and pulse compression filter of the basic Golay waveform are controlled by the transmit vector p and the receive vector q. According to formula (4), when k≠0, This represents the range sidelobe that needs to be suppressed; when k = 0 and θ = 0, This represents the main lobe energy. Therefore, SMR is defined as:

[0099]

[0100] (p n The value is ±1, and the range of θ is [0, 2πf]. d T].

[0101] SNR is:

[0102]

[0103] Among them Target power, N0 is the receiver white noise power spectral density.

[0104] An ideal radar system aims to simultaneously minimize SMR and maximize SNR (minimize its reciprocal), therefore the multi-objective optimization problem is formulated as:

[0105]

[0106] For the sake of brevity, constants have been omitted from the formula. and L, where the constraint condition is p n ∈{1,-1},θ∈[0,2πf d Since the two objectives conflict with each other, the optimal solution is usually a set of trade-off solutions, which are solved using the ε-constraint method.

[0107] 2.2 Two cases of the ε-constraint method:

[0108] Transform one of the objectives into a constraint.

[0109] The optimization problem constrained by SNR is expressed as follows:

[0110]

[0111] The optimization problem constrained by SMR is expressed as follows:

[0112]

[0113] Where δ is the preset SNR constraint parameter, and ∈ is the preset SMR constraint parameter.

[0114] 2.3 Penalty Function Method:

[0115] Since solving constrained optimization problems is more difficult than solving unconstrained optimization problems, the penalty function method is used to approximate constrained optimization problems as unconstrained problems based on equations (8) and (9). For equation (4), the objective function is transformed into:

[0116]

[0117] σ is the penalty coefficient for SNR.

[0118] For formula (5), the objective function is transformed into:

[0119]

[0120] Where λ is the penalty coefficient of SMR.

[0121] 3. Model-driven machine learning methods;

[0122] Due to the integer nature of p and the complex numerical nature of q, the multi-objective optimization problem under discussion is actually an NP-hard problem. In this section, we propose a machine learning-based algorithm to solve the optimization problem. We employ the stochastic gradient descent (SGD) algorithm to learn the model parameters.

[0123] 3.1 Overall structure and function;

[0124] Machine learning-based algorithm structures such as Figure 2 As shown, it consists of a forward propagation module and a backpropagation module. The forward propagation module calculates the normalized random Doppler shift phase of the input (in radians). The backpropagation module calculates the loss function according to formula (10) or (11), and then updates the weight vector in the forward propagation module. Here we set the weights obtained from training in the neural network as the output feature vector. The weight vector is updated using the Adam optimizer by minimizing the loss function. The bias of the forward propagation is set to zero.

[0125] 3.1.1 Input Design:

[0126] The model's input is set to a phase value vector. Where θ d It is the Doppler frequency shift (in radians), in the Doppler interval [0, 2πf]. d The index d represents the number of iterations. After multiple training iterations, the expected value θ is obtained. d As many samples as possible are selected to cover the entire Doppler range. After training, the loss is minimized across the entire Doppler range to suppress sidelobes, rather than just on uniformly spaced Doppler shift samples derived from the Doppler van der Mönch matrix in the null space method.

[0127] 3.1.2 Optimization Objective:

[0128] To find the optimal transmit-receive sequence pair {p,q}, a neural network is trained to minimize the loss function, as shown in Equation (12), where Let θ represent the loss function, and let θ represent the initial input phase in the Doppler interval.

[0129]

[0130] 3.1.3 Backpropagation Module Design:

[0131] The product of p and q is treated as a single parameter z. Figure 2 In the middle, the backpropagation module minimizes the loss function. To update the feature vector z = [z1, z2, ..., z N-1 The feature vector z comes from the weight vector of the last layer of the neural network. Loss function. It is derived from the objective function in formula (10) or (11).

[0132] In the ε-constraint method, the constraint metric is multiplied by a penalty coefficient. The loss functions for the constraint signal-to-noise ratio (SNR) and sidelobe-to-main-lobe ratio (SMR) are defined by equations (13) and (14), respectively.

[0133]

[0134] Where z n =p n *q n p n According to z n The polarity of the real part is shown in formula (15).

[0135]

[0136] q n As defined by formula (16).

[0137]

[0138] Since most machine learning models are designed to handle real-number problems, the optimization problem in this paper is solved by using two models to handle the real and imaginary parts separately. For the Doppler shift θ, e jnθ This can be calculated using Euler's formula as cos(nθ) + jsin(nθ). For a complex weight vector z, it can be written as z = z r +jz i , where z r Let z be the real part of z. i The imaginary part of z is represented. The multiplication of two complex numbers is shown in formula (17), which transforms complex number multiplication into a series of real number multiplications.

[0139]

[0140] 3.1.4 Algorithm Flow:

[0141] Input: Randomized normalized phase θ d The learning rate γ>0, the initial penalty coefficient σ0>0, the final penalty coefficient σ, the number of iterations D, and the growth parameter ρ>1.

[0142] Output: Optimized feature vector z.

[0143] 1) Perform the following operations when σk ≤ σ:

[0144] 2) Let d = 0, and according to Figure 2 Construct the forward propagation module;

[0145] 3) θ d The input is fed into the forward propagation module, and the weight vector z of the neural network layer is obtained;

[0146] 4) Calculate according to (13)

[0147] 5) Calculate in real number form

[0148] 6) Construct the loss function based on (9) or (10);

[0149] 7) Optimize the loss function using the Adam optimizer;

[0150] 8) If d = D, then output the result z. k Otherwise, update d to d:=d+1 and return to step 4;

[0151] 9) If σ k If the value is equal to σ, then stop and output z. k+1 Otherwise, update the penalty coefficient to σ. k+1 =ρσ k , k:=k+1, and use z k Return to step 2 as the initial guess;

[0152] 10) Obtain p and q based on (15) and (16).

[0153] Example:

[0154] Pareto frontier: achieving the optimal trade-off between signal-to-noise ratio and sidelobe-to-mainlobe ratio.

[0155] This paper discusses a constrained multi-objective optimization problem, aiming to achieve a trade-off between the signal-to-noise ratio (SNR) and the sidelobe-to-mainlobe ratio. An algorithm using a loss function is employed to achieve this trade-off among multiple sub-objectives.

[0156] loss function and It consists of an optimization index and a penalty term with another index. In the simulation, the initial and final values ​​of the penalty coefficient are set to 1 and 10, respectively. 6 The growth parameter is ρ = 10.

[0157] By appropriately designing the penalty coefficient, a Pareto optimal solution can be achieved through optimizing the reconstructed objective function. The boundary defined by the Pareto solution set forms the Pareto front.

[0158] Figure 3The Pareto front is shown, in which the proposed method achieves a trade-off between signal-to-noise ratio and sidelobe-to-mainlobe ratio in the Doppler interval [0,π).

[0159] Simulation results were performed under two conditions: an ε-constraint method with constraints on the signal-to-noise ratio and constraints on the sidelobe-to-mainlobe ratio. The Pareto fronts for these conditions were plotted on... Figure 3 middle.

[0160] Constraint signal-to-noise ratio: Figure 3 The Pareto front of the ε-constraint method with constrained signal-to-noise ratio (SNR) values ​​is shown, represented by the dashed line connecting the blue pentagons. The figure illustrates the trade-offs for constrained SNR values ​​of -1 dB, -2 dB, and -3 dB. It can be seen that the point representing the optimal solution appears above the points of other conventional schemes, indicating a better SNR and sidelobe-to-main-lobe ratio. From... Figure 3 As can be seen, the solution with a constrained signal-to-noise ratio of -3dB shows a sidelobe-to-main-lobe ratio gain of nearly 6dB and a signal-to-noise ratio gain of 0.1dB compared to the NS scheme. When the signal-to-noise ratio is close to 0dB, the proposed scheme's sidelobe-to-main-lobe ratio performance is 19dB better than the PTM scheme and 24dB better than the ordinary GCP scheme.

[0161] Constraint on sidelobe-to-mainlobe ratio: Figure 3 The Pareto front of the ε-divisor method with constrained sidelobe-to-mainlobe ratio is shown, represented by a dotted-dash line connecting pentagram markers. Here, the constrained sidelobe-to-mainlobe ratio is set to cover a range from -30dB to -80dB, and then the signal-to-noise ratio is maximized. The Pareto front can also be observed appearing above the conventional scheme. Figure 3 In the proposed solution, with a sidelobe-to-main-lobe ratio of -81.5 dB, the sidelobe-to-main-lobe ratio gain is 5.9 dB and the signal-to-noise ratio (SNR) gain is 0.1 dB compared to the NS scheme. The SNR performance improves when the requirements for the sidelobe-to-main-lobe ratio are relaxed. When the sidelobe-to-main-lobe ratio is -72 dB, the proposed scheme achieves an SNR of -2.6 dB, which is 0.5 dB better than the NS scheme.

[0162] from Figure 3 It can be seen that the obtained Pareto optimal sets are all superior to other traditional Doppler elastic GCP waveforms, and show better signal-to-noise ratio and sidelobe-to-mainlobe ratio performance.

[0163] The key points of this invention are as follows:

[0164] (I) Innovation in multi-objective optimization methods;

[0165] Problems with existing technologies: When dealing with radar waveform optimization, traditional Doppler elastic schemes often simplify non-convex multi-objective optimization problems, such as maximizing SNR under the zero-order spectral condition of given sidelobe suppression. This approach can only obtain a single compromise solution and cannot simultaneously achieve the optimal trade-off between sidelobe-to-main-lobe ratio (SMR) and SNR.

[0166] Innovation of this invention: Application of the ε-constraint method: The ε-constraint method proposed in this invention transforms multi-objective optimization problems more effectively. When SNR is used as the constraint, the optimization problem is...

[0167]

[0168] And converted through the penalty function method

[0169]

[0170] This method can obtain a series of Pareto optimal solutions, achieving a more flexible and better trade-off between SMR and SNR.

[0171] Obtaining the Pareto optimal solution: The Pareto optimal solution set obtained through the ε-constraint method allows for more reasonable adjustments between SMR and SNR in radar waveform design based on actual needs. For example, in scenarios with extremely high requirements for sidelobe suppression, a solution that favors reducing SMR can be selected; while in scenarios with high requirements for signal strength, a solution that is more conducive to improving SNR can be selected. This contrasts sharply with existing technologies that can only provide a single, fixed solution, greatly improving the adaptability and flexibility of radar waveform design.

[0172] (II) Unique applications of model-driven machine learning;

[0173] Problems with existing technologies: When solving radar waveform optimization problems, existing technologies rarely combine model-driven machine learning methods with ε-constraint methods, thus failing to fully utilize the advantages of machine learning in complex optimization problems.

[0174] Innovation of this invention:

[0175] The optimization process based on machine learning: This invention treats the transmit-receive sequence {p,q} as parameters in a machine learning model for training. In the model structure (see reference...) Figure 2 The forward propagation module calculates the Doppler frequency shift correlation value of the input normalized random phase, while the backpropagation module calculates the loss based on the constructed ε-constraint correlation loss function and updates the weight vector z using the Adam optimizer. Through multiple iterations of training, the model can automatically learn the optimal transmit-receive sequence pair, achieving optimized design of the radar waveform.

[0176] Improving optimization efficiency and performance: This machine learning-based approach can effectively handle complex complex value optimization problems by transforming complex value multiplication into a series of real number multiplications (e.g., using Euler's formula e^(-1 / 2)). jnθ =cos(nθ)+jsin(nθ) handles Doppler frequency shift related calculations, improving computational efficiency. Simultaneously, the machine learning model can perform calculations on a large amount of training data (by randomly selecting the Doppler frequency shift θ). d It learns better waveform parameters in the entire Doppler range, which, compared with traditional optimization methods based on mathematical derivation, can better adapt to different radar operating scenarios and further improve the performance of radar waveforms.

Claims

1. A method for flexible Doppler complementary waveform design with joint optimization of signal strength and sidelobe suppression, characterized in that, Comprising the following steps: Step 1: Establishing system model; The pulse compression radar system is composed of a transmitter, a receiver and a signal processing part; the baseband signal in the transmitter is phase encoded by GCP, and then the encoded signal is transmitted by the phase encoding modulator; After the receiver receives the reflected signal, it is processed by the pulse compression filter, and finally the detector detects the target information; At the transmitting end, the basic waveforms Sx(t) and Sy(t) of GCP coding control the transmission according to the characteristic binary vector p, forming a P-pulse sequence Z P(t) ; at the receiving end, the Q-pulse sequence Z Q(t) defined by the coefficient vector q, the signal input to the matched filter is Z P(t) , wherein is the Doppler shift; Signal model: Golay complementary pair defined as two single-mode complex sequences of length L , satisfying for all lags where and are the sequences and respectively, the autocorrelation function at lag , is the Kronecker function; basic Golay complementary waveforms where is a unit-energy baseband pulse shape, is the chip length; P-pulse sequence: （1） Q-pulse sequence: （2） Let be the transmitted signal, be the time-domain response of the received signal, and let the input of the receiver matched filter be where , is the Doppler shift in Hz; The matched filter output, i.e., the cross ambiguity function, is given by the impulse response of the linear filter * Q t).​ （3） The cross ambiguity function is also and the continuous cross ambiguity function; Through algebraic processing, the discrete cross ambiguity function is: （4） wherein = vT = T for each pulse repetition interval T Doppler shift within Step 2: - Constraint method; Step 2-1: Optimization target definition; SMR: For GCP coded waveforms, the phase encoding modulator and pulse compression filter of the Golay waveform are controlled by the transmit vector p and receive vector q; according to equation (4), when k ≠ 0, denotes the distance sidelobes that need to be suppressed; when and k = 0 and = 0, denotes the mainlobe energy; the SMR is defined as: （5） SNR is: （6） wherein target power, is the receiver white noise power spectral density; The multi-objective optimization problem is expressed as: （7） The optimal solution is a set of trade-off solutions, which are solved by - constraint method; Step 2-2: Two cases of constraint method: The optimization problem formula with SNR as the constraint is expressed as: （8） The optimization problem formula with SMR as the constraint is expressed as: （9） wherein is a preset SNR constraint parameter, is a preset SMR constraint parameter; Step 2-3: Penalty function method: On the basis of formula (8) and (9), the penalty function method is used to approximate the constrained optimization problem to an unconstrained problem. For formula (4), the objective function is converted to: （10） wherein, is a penalty coefficient for SNR; For formula (5), the objective function is converted to: （11） wherein, is a penalty coefficient for SMR; Step 3: Model-driven machine learning method; The algorithm based on machine learning is used to solve the optimization problem, and the stochastic gradient descent (SGD) algorithm is used to learn the model parameters; Step 3-1: Overall structure and function; The neural network structure of the algorithm based on machine learning is composed of a forward propagation module and a back propagation module; the forward propagation module calculates the normalized random Doppler frequency phase of the input; the back propagation module calculates the loss function according to formula (10) or (11), and then updates the weight vector in the forward propagation module; the weights trained in the neural network are set as the output feature vector; the weights are updated using the Adam optimizer by minimizing the loss function; the bias of the forward propagation is set to zero; Step 3-1-1: Input design; The input of the model is set to a vector of phase values where is the Doppler shift, randomly selected in a Doppler interval with index denotes the number of iterations; after training, the loss is minimized over the entire Doppler interval to suppress sidelobes; Step 3-1-2: Optimization target: To find the optimal transmit-receive sequence pair {p,q} , the neural network is trained to minimize a loss function, as shown in equation (12), where represents the loss function; （12） Step 3-1-3: Back propagation module design; The product of p and q is considered as a single parameter z The feature vector is updated by the back propagation module by minimizing the loss function The feature vector z is from the weight vector of the last layer of the neural network; the loss function is converted from the objective function in equation (10) or (11); In In the constrained approach, the constraint metric is multiplied by a penalty coefficient, the loss functions for the constraint signal-to-noise ratio SNR and the side-lobe-to-main-lobe ratio SMR are defined as in equations (13) and (14), respectively; （13） （14） wherein , According to the real part of the polar value, as shown in equation (15): （15） As defined by equation (16): （16） For Doppler shift , By Euler's formula , for complex weight vector , write where denotes the real part of , denotes the imaginary part of ; multiplication of two complex numbers as shown in equation (17) converts complex multiplication into a series of real number multiplications; （17） obtained p and q .

2. The method of claim 1, wherein, The is ±1, range is .

3. An electronic device, comprising: Comprising: A processor and a memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to enable the electronic device to perform the method of any one of claims 1-2.

4. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to implement the method of any one of claims 1-2.

5. A chip, characterized by Comprising: A processor for calling and running a computer program from a memory, so that a device installed with the chip executes the method of any one of claims 1-2.

6. A computer program product, characterised in that, The computer program product comprises a computer storage medium storing a computer program, and the computer program comprises instructions executable by at least one processor, which implement the method of any one of claims 1-2 when executed by the at least one processor.

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