An ultra-low range-doppler sidelobe gray complementary waveform design method

Abstract

The application discloses a kind of ultra-low range-doppler sidelobe Golay complementary waveform design methods, first, a kind of Pareto effective Golay complementary waveform design framework is proposed, the framework is jointly optimized to Doppler elastic transceiving sequence pair, to achieve the trade-off between SMR and SNR performance.This framework considers the unconstrained optimization problem with variable weight on these two indicators, a series of loss functions of Pareto multi-objective optimization problem are constructed using weighted sum method, and all possible Pareto optimal solutions are obtained.Secondly, in order to solve the optimization problem, a model-driven machine learning algorithm is designed to carry out multi-objective optimization.The method of the application can suppress the Doppler sidelobe to an extremely low level of-80.38dB, but the loss of signal-to-noise ratio is small, only 2.8dB, which is 5dB and 0.3dB higher than the traditional Doppler elastic scheme respectively.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, specifically relating to an ultra-low range Doppler sidelobe Gray complementary waveform design method. Background Technology

[0002] Pulse compression radar can improve ranging resolution with its large bandwidth and obtain high pulse energy using pulse matched filters. Since the energy of a single pulse may be insufficient to detect a target, a specific length sequence can be modulated onto the pulse sequence to construct the transmitted waveform, enabling the receiver to collect sufficient energy; this is commonly referred to as phase-coded radar. However, if the coded pulse is reflected by a highly maneuverable target, the pulse compression radar receiver output may produce undesirable range sidelobes. Given that the sidelobes of strong targets tend to suppress the main lobe of weak targets, this can lead to missed detections of weak targets. Therefore, for multi-target radar detection missions involving at least one moving target, designing a low-range sidelobe waveform with non-zero Doppler is crucial.

[0003] Doppler elasticity techniques using Golay complementary waveforms have been extensively studied. These techniques can be broadly categorized into two types. In the first type, the transmitted pulse sequence is optimized based on the matched filter receiver assumption (i.e., conjugate transpose operation). In the second type, the transmit-receive sequence pair is orchestrated to preferentially reduce range sidelobes near the zero Doppler axis, but this comes at the cost of signal-to-noise ratio (SNR) because it does not employ matched filter operation on the receiver. Dang et al. proposed a binomial design (BD) for the transmit-receive sequence pair, aiming to reduce the range sidelobes of the ambiguity function within an expanded Doppler range (i.e., up to -70 dB within the radian range [-1, 1]). Compared to the first type of PTM technique, it achieves higher-order spectral zeros in the pulse sequence ambiguity function, but at a SNR loss of 5.1 dB.

[0004] However, for these existing Doppler elastic schemes, the non-convex optimization problem of achieving a tradeoff between two conflicting metrics (i.e., sidelobe to main lobe ratio (SMR) and signal-to-noise ratio (SNR)) is transformed into a simpler problem: achieving the maximum SNR to suppress sidelobes within a given Doppler frequency shift range.

[0005] Therefore, the single numerical value of the resulting transmit / receive sequence pair can only reflect a certain trade-off between these two objectives, which is actually a suboptimal solution that simultaneously minimizes SMR and maximizes SNR. However, in the design of Doppler elastic Golay complementary waveforms, achieving the optimal trade-off between these two conflicting objectives remains a key and unsolved problem. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, this invention provides an ultra-low-range Doppler sidelobe Gray complement waveform design method. First, a Pareto-efficient Golay complement waveform design framework is proposed, which jointly optimizes Doppler elastic transmit / receive sequence pairs to achieve a trade-off between SMR and SNR performance. This framework considers an unconstrained optimization problem with variable weights on these two metrics, constructing a series of Pareto multi-objective optimization loss functions using a weighted sum method to find all possible Pareto optimal solutions. Second, to solve the optimization problem, a model-driven machine learning algorithm is innovatively designed for multi-objective optimization. The method of this invention can suppress Doppler sidelobes to an extremely low level of -80.38 dB, while maintaining a small signal-to-noise ratio loss of only 2.8 dB, which is 5 dB and 0.3 dB higher than traditional Doppler elastic schemes, respectively.

[0007] The technical solution adopted by this invention to solve its technical problem is as follows:

[0008] Step 1: Construct a signal model;

[0009] Step 1-1: Define the Golay complementary pair as two simple modulus complex sequences of length L, namely x[·] and y[·]. The sum of the values ​​of the autocorrelation function is:

[0010] C x (k) + C y (k) = 2Lδ k (1)

[0011] Where, k = -(L-1), -(L-2), ..., 0, ..., (L-1), C x (k) and C y (k) are the autocorrelation functions of sequences x and y at lag k, respectively, and δ k Let x be a Kronecker function, where x = [x[0], x[1], ..., x[L-1]]. T y = [y[0], y[1], ..., y[L-1]] T ;

[0012] Steps 1-2: Golay complementary waveforms x (t) and s y (t) Phase encoding is performed using x and y, i.e. and In the formula, u(t) is the shape of the unit energy baseband pulse, and satisfies T c Chip length;

[0013] Steps 1-3: During transmission, s x (t) and s y(t) is further derived from the eigenvalued binary vector p = [p0, p1, ..., p n ,…,p N-1 ] T Control, where N represents a positive number, p n =1 or -1; when p n When = 1, transmission s x (t), when p n When = -1, the transmission s y (t); therefore, the P-pulse sequence Z P (t) is defined as:

[0014]

[0015] In the formula, T is the pulse repetition interval PRI;

[0016] Steps 1-4: Let q = [q0, q1, ..., q N-1 [ ] represents the coefficient vector of the receiving filter, and the Q-pulse sequence Z Q (t) is defined as:

[0017]

[0018] in, Represents the complex conjugate of the receiver filter coefficients;

[0019] Steps 1-5: 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 υ=2πf d f d Z represents the Doppler frequency shift, measured in Hz. P (t)e jυt The impulse response is Z * Q For a linear filter with (-t), the output of the matched filter, i.e., the cross-ambiguity function, is:

[0020]

[0021] The cross-ambiguity function is also Z. P (t) and Z Q A continuous cross-fuzzy function of (t);

[0022] The discrete cross-fuzzy function is written as:

[0023]

[0024] In the formula, θ = υT = 2πf dT is the Doppler frequency shift in radians over a pulse repetition interval PRI, due to C x (k)+C y (k) = 2Lδk, the discrete fuzzy function is further simplified to:

[0025]

[0026] In the formula, k≠0 represents the range of sidelobes that need to be suppressed; when k=0, θ=0, it represents the main lobe energy.

[0027] Step 2: Pareto optimizes the framework;

[0028] Step 2-1: The side lobe to main lobe ratio (SMR) is defined as:

[0029]

[0030] Signal-to-noise ratio is defined as:

[0031]

[0032] in Let N0 be the power of the target, N0 be the power spectral density (PSD) of the receiver white noise, and q be the coefficient vector of the receiver filter.

[0033] Step 2-2: The multi-objective optimization problem is expressed as:

[0034]

[0035] Using a weighted sum method, the objective function is constructed from the weighted sum of all objectives. Within the Pareto framework, a set of transmit-receive sequence pairs {p, q} is searched based on the target's velocity range to minimize the given objective function. The single-objective non-convex optimization problem can be expressed as:

[0036]

[0037] Where w1 and w2 represent weight coefficients, and the weight values ​​represent the relative importance of the metric;

[0038] Step 3: Solve using machine learning algorithms:

[0039] Step 3-1: Solve the optimization problem using machine learning-based algorithms, and learn the model parameters using the stochastic gradient descent (SGD) algorithm;

[0040] The neural network structure based on machine learning algorithms consists of a forward propagation module and a backward propagation module. The forward propagation module calculates the input normalized random phase with Doppler frequency shift in radians. The backward propagation module calculates the loss function according to Equation (10) 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 z. By minimizing the loss function, the weight vector is updated using the Adam optimizer. The bias of the forward propagation is set to zero.

[0041] Step 3-2: Input Design:

[0042] Set the input of the model as a phase value vector. Where θ d The Doppler frequency shift is expressed in radians, within the Doppler interval [0, 2πf]. d Randomly selected within T], with index d representing the number of iterations; after training, minimize the loss over the entire Doppler interval to suppress sidelobes;

[0043] Step 3-3: Optimization Goal:

[0044] To find the optimal transmit / receive sequence pair {p,q}, a neural network is trained to minimize the loss function. In the formula Let θ represent the loss function, and let θ represent the initial input phase within the Doppler interval;

[0045] Steps 3-4: Backpropagation module design:

[0046] The backpropagation module minimizes the loss function. Update the feature vector z = [z1, z2] 2, ···,z N-1 The feature vector z is derived from the weight vector of the last layer of the neural network; the loss function. The loss function is derived from the objective function in equation (10); for the weighted sum method, the loss function is given by the following equation:

[0047]

[0048] Among them, z n =p n *q n p n From equation (12) z n polarity acquisition, q n Defined in equation (13):

[0049]

[0050] Steps 3-5: For the Doppler frequency shift θ, e jnθ Calculated using Euler's formula, it is e. jnθ=cos(nθ)+j sin(nθ); For the 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 Represent the imaginary part of z; two complex numbers e jnθ The multiplication with z is given by equation (14):

[0051]

[0052] Therefore, complex number multiplication is performed as a series of real number multiplications.

[0053] A computer program that causes a computer to execute the above-described complementary waveform design method.

[0054] 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 complementary waveform design method.

[0055] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described complementary waveform design method.

[0056] 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 complementary waveform design method described above.

[0057] 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 complementary waveform design method.

[0058] The beneficial effects of this invention are as follows:

[0059] 1. Improved sidelobe suppression performance and signal-to-noise ratio: Since these sequences are obtained from the Pareto optimal set that simultaneously optimizes SMR and SNR objectives, the transceiver framework is theoretically optimal. Numerical results show that within the Doppler time interval [0, π], the method of this invention can suppress Doppler sidelobes to an extremely low level of -80.38 dB, while the signal-to-noise ratio loss is small, only 2.8 dB, which is 5 dB and 0.3 dB higher than the traditional Doppler elastic scheme, respectively.

[0060] 2. More Flexible Golay Waveform Design: The machine learning framework proposed in this invention provides a more flexible method for designing Golay waveforms. On the one hand, the priorities of the two sub-objectives, SMR and SNR, can be flexibly adjusted according to actual needs to design complementary Golay waveforms. On the other hand, waveform parameters, such as the length of the transmit and receive sequences and the range of the Doppler interval, can be customized in the method of this invention. Attached Figure Description

[0061] Figure 1 This is an overall structural diagram of the method of the present invention;

[0062] Figure 2 This is a schematic diagram of the machine learning model structure in this area;

[0063] Figure 3 This is a schematic diagram of the Pareto front for achieving the trade-off between SMR and SNR within the Doppler interval [0, π] according to an embodiment of the present invention;

[0064] Figure 4 The distance measurement results are for the ordinary GCP scheme, NS scheme, and the proposed multi-target detection method in the embodiments of the present invention. Detailed Implementation

[0065] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0066] This invention proposes an ultra-low range Doppler sidelobe Gray complement waveform design method to improve the radar signal's resistance to Doppler jitter. First, a Pareto-efficient Golay complement waveform design framework is proposed, which jointly optimizes Doppler elastic transmit / receive sequence pairs to achieve a trade-off between SMR and SNR performance. This framework considers an unconstrained optimization problem with variable weights on these two metrics, constructing a series of Pareto multi-objective optimization loss functions using a weighted sum method to find all possible Pareto optimal solutions. Second, to solve the optimization problem, a model-driven machine learning algorithm is innovatively designed for multi-objective optimization. The overall structure of the method is shown in the figure below. Figure 1 As shown.

[0067] First, system and signal models were established. Pulse compression radar combines the energy advantage of ultra-long pulses with the range resolution advantage of extremely short pulses. The transmitted pulses are frequency / phase encoded and modulated, and received by correlating with the transmitted signal.

[0068] At the transmitter, the baseband waveform is phase-coded using GCP. Due to the bipolar nature of GCP, the pulse phase for each bit duration either maintains its initial phase or flips by 180 degrees. The received delayed signal is then correlated with different transmitted delayed pulse sequences to obtain the autocorrelation of the Golay complementary waveform. Because GCP has ideal aperiodic autocorrelation, the peak value of the autocorrelation function at zero delay hysteresis equals the number of transmitted pulses per unit energy, and equals zero at delay hysteresis of every other pulse duration. However, this pulse-like autocorrelation is not suitable for high mobility scenarios. When a moving target is detected, the Doppler frequency of the moving target causes a phase rotation on the received Golay complementary waveform. This destroys the complementary properties, generating range-Doppler sidelobes, which complicates multi-target detection.

[0069] Signal model:

[0070] For the signal model, first define the Golay complementary pair as two single-mode complex sequences of length L, namely x[·] and y[·], and sum the values ​​of the autocorrelation function as:

[0071] C x (k) + C y (k) = 2Lδ k (1)

[0072] Where, k = -(L-1), -(L-2), ..., 0, ..., (L-1), C x (k) and C y (k) are the autocorrelation functions of sequences x and y at lag k, respectively, and δ k Let x be a Kronecker function, where x = [x[0], x[1], ..., x[L-1]]. T y = [y[0], y[1], ..., y[L-1]] T Under the aforementioned GCP, the basic Golay complementary waveform s x (t) and s y (t) Phase encoding is performed using x and y, i.e. and In the formula, u(t) is the shape of the unit energy baseband pulse, and satisfies T c This refers to the chip length. During transmission, s x (t) and s y (t) is further derived from the eigenvalued binary vector p = [p0, p1, ..., p N-1 ] T Control, where N represents a positive number, p n =1 or -1. When p n When = 1, transmission s x(t), when p n When = -1, the transmission s y (t). Therefore, the P-pulse sequence Z P (t) is defined as:

[0073]

[0074] In the formula, T is the pulse repetition interval (PRI).

[0075] Let q = [q0, q1, ..., q N-1 [ ] represents the coefficient vector of the receiving filter. Therefore, the Q-pulse sequence Z Q (t) is defined as:

[0076]

[0077] Launch Z P (t), setting the input of the receiver matched filter to Z P (t)e jυt , where υ=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) is used. The output of the matched filter, i.e., the cross-ambiguity function, is:

[0078]

[0079] It is also Z P (t) and Z Q The continuous cross-fuzzy function of (t).

[0080] After certain approximations and simple algebraic processing, the discrete cross-fuzzy function can be written as:

[0081]

[0082] In the formula, θ = υT = 2πf d T is the Doppler frequency shift in radians over a pulse repetition interval (PRI). Because C x [k]+C y [k] = 2Lδk, the discrete fuzzy function can be further simplified to:

[0083]

[0084] In the function, k≠0 represents the range of sidelobes that need to be suppressed; when k=0, θ=0, it represents the main lobe energy.

[0085] Therefore, based on the aforementioned GCP transmission, the objective of this invention is to carefully design p n and q n The value is used to suppress the sidelobes caused by k≠0 in the fuzzy function.

[0086] Pareto optimization framework design

[0087] Next, a Pareto optimization framework was designed for constructing complementary waveforms with low-range-Doppler sidelobes and high signal strength Golay. The sidelobe to main lobe ratio (SMR) is defined as:

[0088]

[0089] Besides SMR, signal-to-noise ratio (SNR) is also an important performance indicator for radar detection systems. The system's SNR is typically defined as:

[0090]

[0091] Where σ b 2 Let N be the target power, and N0 be the power spectral density (PSD) of the receiver white noise.

[0092] Therefore, it can be achieved by maximizing || To optimize the signal-to-noise ratio.

[0093] The ideal objective of a radar system is to minimize SMR while maximizing signal-to-noise ratio. Therefore, the multi-objective optimization problem can be expressed as:

[0094]

[0095] For the sake of simplicity, the constant in the discrete fuzzy function has been omitted. And L.

[0096] In (9), the two objectives are conflicting; improvement in one objective often leads to deterioration in the other. The optimal solution for such multi-objective optimization is usually not a single solution, but rather a set of trade-off solutions. This invention constructs a Pareto framework to generate a set of solutions that achieve a Pareto optimal trade-off between SMR and SNR. To transform the multi-objective optimization problem, scalarization techniques are used to merge multiple objectives into a single objective.

[0097] The scalarization method used in this invention is the weighted sum method, where the objective function is constructed from the weighted sum of all objectives. Within the Pareto framework, a set of transmit-receive sequence pairs {p, q} is searched based on the target's velocity range to minimize the given objective function. The single-objective nonconvex optimization problem can be expressed as:

[0098]

[0099] Where w1 and w2 represent weight coefficients, and the weight values ​​represent the relative importance of the metric.

[0100] Solving using machine learning algorithms:

[0101] Due to the integer nature of p and the complex value of q, multi-objective optimization problems are actually NP-hard. A machine learning-based algorithm is proposed to solve this problem. The stochastic gradient descent (SGD) algorithm is used to learn the model parameters.

[0102] Machine learning-based algorithm structures such as Figure 2 As shown, it consists of a forward propagation module and a backward propagation module. The forward propagation module calculates the input normalized random phase with Doppler shift in radians. The backward propagation module calculates the loss function according to Equation (10) and then updates the weight vector in the forward propagation module. Here, the weights trained in the neural network are set as the output feature vector z. The weight vector is updated using the Adam optimizer by minimizing the loss function. The bias of the forward propagation is set to zero.

[0103] Input design: Set the model input as a phase value vector. Where θ d For the Doppler frequency shift in radians, within the Doppler interval of interest [0, 2πf]... d θ is randomly selected from [T]. The index d represents the iteration number. After multiple iterations of training, θ d The selection is expected to cover the entire Doppler interval as much as possible. After training, the loss is minimized over the entire Doppler interval to suppress sidelobes, rather than just minimizing the loss on uniformly spaced Doppler shift samples derived from the Doppler Vandermonde matrix when close to null space.

[0104] Optimization objective: To find the optimal transmit / receive sequence pair {p,q}, train the neural network to minimize the loss function. In the formula Let θ represent the loss function, and let θ represent the initial input phase within the Doppler interval.

[0105] Backpropagation module design: Note that 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 Note that the feature vector z is derived from the weight vector of the last layer of the neural network. Loss function It is derived from the objective function in equation (10). For the weighted sum method, the loss function is given by the following equation:

[0106]

[0107] Among them, z n =p n *q n p n From equation (12) z n polarity acquisition, q n Defined in equation (13).

[0108]

[0109] However, since most machine learning models are designed to handle real-valued problems, the complex-valued optimization problem of this invention employs two separate models to handle the real and imaginary components. For the Doppler frequency shift θ, e jnθ It can be calculated as e using Euler's formula. jnθ =cos(nθ)+j sin(nθ). For the 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 Let z represent the imaginary part. Two complex numbers e jnθ The multiplication with z is given by the formula:

[0110]

[0111] Thus, complex multiplication can be performed as a series of real multiplications. The algorithm for the weighted sum method is shown in Algorithm 1 below, which uses the Adam optimizer. Let the number of iterations be D and the learning rate be γ.

[0112]

[0113] The NS scheme has an inherent flaw: the Doppler elastic complementary waveform is achieved by finding the null space of the Doppler Vandermonde matrix, and then decomposing the null space vector into eigenvectors controlling the transmitted waveform and coefficient vectors generating the received code. To ensure the existence of the null space vector, the number of discrete Doppler shift samples must be less than the number of pulses. However, the more Doppler shift samples, the better the desired sidelobe suppression performance, as the loss function on the Doppler shift is minimized for each sample. Therefore, existing Doppler recovery schemes have performance bottlenecks, and there is still significant room for improvement in sidelobe suppression performance.

[0114] In this invention, a random search algorithm is used to sample Doppler frequencies covering the entire Doppler interval. The more iterations the algorithm performs, the more discrete the selected Doppler frequency shift values ​​become, resulting in a finer Doppler frequency shift interval. Therefore, it is desirable to achieve extremely low range-Doppler sidelobe suppression performance throughout the entire Doppler interval.

[0115] Furthermore, unlike existing literature which only proposes one type of Doppler elastic GCP waveform with certain SMR and signal-to-noise ratio performance, this invention proposes a series of GCP waveform generation methods that achieve an optimal trade-off between SMR and signal-to-noise ratio.

[0116] Example:

[0117] 1. Comparison of the distance-Doppler suppression performance between the proposed solution and existing Doppler elastic solutions;

[0118] The examples provide comparison results for different schemes, namely the ordinary GCP scheme, PTM scheme, BD scheme, NS scheme, and the ambiguity function in the Doppler interval [0, π] using the weighted summation method of the present invention. The comparison results are shown in Table 1.

[0119] Table 1 Numerical results for PTM, BD, NS, and the proposed scheme.

[0120]

[0121] The sidelobes of the method of this invention are 5 dB lower than those of the NS scheme, and the receiver signal-to-noise ratio loss is 0.3 dB lower than that of the NS scheme. The maximum tolerance speed for target detection can reach 184.95 km / h, and the corresponding Doppler resistance spacing can reach [20.6, 20.6] kHz.

[0122] 2. Pareto Frontier: Achieving the optimal trade-off between SMR and SNR.

[0123] Simulations were performed using the weighted sum method. Figure 3 The Pareto front in this case was plotted.

[0124] Figure 3 In the diagram, the lines connecting the red triangles represent the Pareto fronts of multi-objective optimization problems with different weighted signal-to-noise ratios (SMRs) and signal-to-noise ratios (SNRs). Different combinations of w1 and w2, with varying priorities for SMR and SNR, are considered. The values ​​of w1 and w2 range from 0 to 1, and the sum of their weights equals 1. It can be seen that the Pareto fronts formed by the non-dominant solutions appear above the points of the traditional schemes NS, BD, PTM, and Plain GCP, indicating that the method of this invention outperforms the traditional schemes in both SMR and SNR performance. Figure 3 As can be seen, even without assigning a weight to the signal-to-noise ratio (SNR) metric, the points w1=1, w2=0 show an SMR gain of 5dB and an SNR gain of 0.3dB compared to the NS scheme. Compared to the PTM scheme, the SMR gain at the points w1=0, w2=1 is 6.5dB.

[0125] 3. Multi-target detection simulation.

[0126] This embodiment simulates the ranging results for multiple targets. It's important to note that a range-Doppler map is generated using a correlation filter, and then the correlation results of multiple pulses are summed to obtain the ranging result. The simulated scenario includes five targets: three strong targets (targets 1-3) with a normalized signal amplitude of 0 dB, and two weak targets (targets 4 and 5) with a normalized signal amplitude of -40 dB. The simulation parameters are shown in Table 2. The positions and velocities of these targets are listed in Table 3.

[0127] Table 2 Simulation Parameters

[0128] carrier frequency 60GHz bandwidth 1.76GHz PRI 2μs GCP length 64 Doppler frequency shift interval [0,π) Pulse count 16,32 Learning rate <![CDATA[10 -5 ]]> Optimization program Adam Number of iterations <![CDATA[2×10 5 ]]>

[0129] Table 3. Positions and velocities of multiple targets

[0130] Target Distance (m) Speed ​​(m / s) Target 1 50 3 Target 2 90 42 Target 3 100 60 Target 4 105 15 Target 5 102 2

[0131] The simulated radar system has a range resolution of 8.5 cm and a maximum unambiguous range of 300 m. Simulations were performed on the ordinary GCP scheme, the NS scheme, and the weighted sum method with w1=1 and w2=0. The ranging results for the three schemes are as follows: Figure 4 As shown.

[0132] like Figure 4 As shown, in high-speed scenarios, the sidelobe suppression performance of the ML-based method is superior to other schemes. For the ordinary GCP scheme, it can be seen that a weak target at 102 meters is overwhelmed by the range sidelobes of a strong target. The results indicate that under high mobility conditions, the simple GCP waveform cannot distinguish between strong and weak targets. The proposed method (represented by the blue line) suppresses the sidelobes of moving targets to an extremely low level, below -100 dB. Compared to the ordinary GCP scheme, the radar detection threshold using this waveform is reduced by nearly 55 dB. Even for targets at relatively close range (targets 3, 4, 5), the method of this invention can easily distinguish between strong and weak targets.

[0133] It can also be observed that the proposed method exhibits greater performance gains than other conventional methods as the speed increases. For target 2 with a speed of 42 m / s, the range sidelobe of the proposed method is as low as -125 dB, nearly 10 dB higher than the NS scheme and 60 dB higher than the ordinary GCP scheme. When the speed increases to 60 m / s (target 3), the range sidelobe of the proposed method is suppressed to -130 dB, 20 dB higher than the NS scheme. Furthermore, the advantages of this method are also evident in the signal-to-noise ratio (SNR) gain. For low-speed targets, there is almost no difference in SNR among the various schemes. For high-speed targets, the target SNR detected by the proposed method is higher than the other two schemes, nearly 0.5 dB higher than the NS scheme and nearly 1 dB higher than the ordinary GCP scheme.

[0134] This invention innovatively designs a Pareto optimization framework for constructing complementary waveforms of low-range Doppler sidelobes and high-signal-intensity Golay. Compared with existing Doppler elastic schemes, a set of globally optimal tradeoff transmit / receive sequence pairs is jointly designed, achieving multi-objective optimization.

[0135] Secondly, for the multi-objective optimization problem of Golay complementary waveforms, an unconstrained optimization problem is proposed. The objective function is constructed using a scalar weighted sum of SMR and SNR indices, and the Pareto optimal sets of transmit-receive sequence pairs are finally obtained, which are then mapped to Pareto fronts. Numerical results verify that the Pareto fronts generated by this framework outperform existing Doppler elastic GCP waveforms in both SMR and SNR performance, demonstrating the effectiveness of the framework.

[0136] Finally, inspired by multi-task learning, a model-driven machine learning approach was designed to solve the aforementioned optimization problem. In the machine learning model, the transmit and receive sequence pairs that determine the coefficient vectors of the phase-coded modulator and the pulse compression filter are considered as hyperparameters that need to be trained.

Claims

1. A method for designing ultra-low range-Doppler sidelobe Golay complementary waveforms, the method comprising: Comprising the steps of: Step 1: Constructing the signal model; Step 1-1: Define a Golay complementary pair as two single-mode complex sequences of length L, i.e., x[ ] and y[ ], whose autocorrelation functions sum to: (1) where k = 0, 1, 2,..., L - 1 (L 1), (L 2), , 0, , (L 1), C x (k) and C y (k) are the autocorrelation functions of the sequence x and the sequence y at lag k, respectively, δ k is the Kronecker function, x = [x[0], x[1], , x[L 1]] T , y = [y[0], y[1], , y[L 1]] T ; Steps 1-2: Golay complementary waveforms s x (t) and s y (t) are phase coded by x, y, i.e. and where u (t) is a unit-energy baseband pulse shape and satisfies , T c is the chip length; Steps 1-3: At the time of transmission, s x (t) and s y (t) are further defined by the characteristic binary vector p = [p0, p1, , p n ,…,p N 1] T control, where N represents a positive number, p n = 1 or 1; when p n = 1, s x (t) is transmitted, and when p n = -1, s y (t) is transmitted; thus, the P-pulse sequence Z P (t) is defined as: (2) Where T is the pulse repetition interval PRI; Step 1-4: Let q = [q0, q1, ···, q N 1] is the coefficient vector of the receive filter, Q - the sequence of pulses Z Q (t) is defined as: (3) wherein denotes the complex conjugate of the receive filter coefficients; Step 1-5: Let Z P (t) be the transmitted signal, Z Q (t) be the time domain response of the received signal, set the input of the receiver matched filter to be Z P (t) e jυt where υ = 2πf d , f d is the Doppler shift, unit Hz; Z P (t) e jυt Through the impulse response is Z * Q ( t) linear filter, then the output of the matched filter is the cross ambiguity function: (4) The cross ambiguity function is also Z P (t) and the continuous cross ambiguity function of Z Q (t). The discrete cross ambiguity function is written as: (5) where θ = υT = 2πf d T is the Doppler shift in radians over one pulse repetition interval, PRI, due to C x (k) + C y (k) = 2Lδk, the discrete ambiguity function is further simplified to: (6) Where k≠0 represents the range sidelobes that need to be suppressed; when k =0, θ=0, it represents the main lobe energy; Step 2: Pareto optimization framework; Step 2-1: The sidelobe-to-main lobe ratio SMR is defined as: (7) The signal-to-noise ratio is defined as: (8) wherein the power of interest, N0is the power spectral density PSD of the receiver white noise, denotes the coefficient vector of the receive filter; Step 2-2: The multi-objective optimization problem is expressed as: (9) The weighted sum method is adopted, and the objective function is constructed by the weighted sum of all objectives; in the Pareto framework, according to the speed range of the target, a set of transmit-receive sequence pairs {p, q} is searched to minimize the given objective function; the single-objective non-convex optimization problem can be expressed as: (10) wherein w 1 and w 2 represent weight coefficients, the weight values representing the relative importance of the metrics; Step 3: Machine learning algorithm solution: Step 3-1: The machine learning-based algorithm is used to solve the optimization problem, and the stochastic gradient descent SGD algorithm is used to learn the model parameters; The neural network structure of the machine learning-based algorithm is composed of a forward propagation module and a backward propagation module, the forward propagation module calculates the input normalized random phase of the Doppler shift in radian units, the backward propagation module calculates the loss function according to formula (10), and then updates the weight vector in the forward propagation module; the weight trained in the neural network is set as the output feature vector z, the weight vector is updated by minimizing the loss function using the Adam optimizer, and the bias of the forward propagation is set to zero; Step 3-2: Input design: The input of the model is set as a phase value vector φ = [0, θ d , 2θ d ,···,(N 1)θ d ] T , where θ d is the Doppler shift in radians, randomly selected within the Doppler interval [0, 2πf d T], and the index d represents the iteration number; after training, the loss is minimized over the entire Doppler interval to suppress the sidelobes; Step 3-3: Optimization target: To find the optimal pair of transmit and receive sequences {p, q}, the neural network is trained to minimize the loss function as , where represents the loss function, and θ represents the initial input phase within the Doppler interval. Step 3-4: Backward propagation module design: The backpropagation module minimizes the loss function The feature vector z = [z1, z 2 , · · ·, z N 1]; the feature vector z is derived from the weight vector of the last layer of the neural network; the loss function is transformed from the objective function in equation (10); for the weighted sum method, the loss function is given by (11) where z n = p n *q n , p n is obtained from the polarity of z n in equation (12), q n is defined in equation (13): (12) (13) Step 3-5: For Doppler shift θ, e jnθ is calculated using Euler's formula as e jnθ = cos(nθ) + j sin(nθ); for a complex weight vector z, write z = z r + j z i , where z r represents the real part of z, and z i represents the imaginary part of z; the multiplication of two complex numbers e jnθ and z is given by equation (14): (14) Therefore, the complex multiplication is executed as a series of real multiplications.

2. 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 execute the method of claim 1.

3. 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 claim 1.

4. A chip, characterized by Comprising: A processor is used to call and run a computer program from a memory, so that the device installed with the chip executes the method of claim 1.

5. A computer program product, characterised in that, The computer program product comprises a computer storage medium, the computer storage medium stores a computer program, the computer program comprises instructions executable by at least one processor, and when the instructions are executed by the at least one processor, the method of claim 1 is implemented.

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