Ultra-low distance-Doppler sidelobe Gray complementary waveform design method

Abstract

The invention discloses an ultra-low distance-Doppler sidelobe Gray complementary waveform design method, and the method comprises the steps: firstly, providing a Pareto effective Golay complementary waveform design framework which carries out the joint optimization of a Doppler elastic receiving and transmitting sequence pair, so as to achieve the balance between SMR and SNR performances; according to the framework, an unconstrained optimization problem with variable weights on the two indexes is considered, a loss function of a series of Pareto multi-objective optimization problems is constructed by utilizing a weighted sum method, and all possible Pareto optimal solutions are solved. Secondly, in order to solve the optimization problem, a model-driven machine learning algorithm is innovatively designed to carry out multi-objective optimization. According to the method, the Doppler sidelobe can be suppressed to the extremely low level of-80.38 dB, but the signal-to-noise ratio loss is small and is only 2.8 dB, and the signal-to-noise ratio loss is improved by 5 dB and 0.3 dB compared with a traditional Doppler elasticity scheme.

Description

Technical Field

[0001] The present invention belongs to the field of radar technology, and particularly relates to a design method for an ultra-low range-Doppler sidelobe Golay complementary waveform. Background Art

[0002] Pulse compression radar can improve the ranging resolution by virtue of large bandwidth and obtain high pulse energy with the help of a pulse matching filter. Since the energy of a single pulse may not be sufficient to detect a target, a specific length sequence can be further modulated on the pulse sequence to construct a transmitted waveform, enabling the receiver to collect sufficient energy, which is usually referred to as phase-coded radar. However, if the coded pulse is reflected by a highly maneuverable target, the output of the pulse compression radar receiver may generate unwanted range sidelobes. Given that the sidelobes of strong targets are likely to suppress the main lobes of weak targets, it may lead to missed detection of weak targets. Therefore, for the multi-target radar detection task with at least one moving target, it is of crucial significance to consider the design of low range sidelobe waveforms with non-zero Doppler.

[0003] The Doppler flexibility technology of Golay complementary waveforms has been widely studied. Such technologies can be roughly divided into two categories. In the first category, the transmitted pulse sequence is optimized based on the assumption of matched filter reception (i.e., conjugate transpose operation). In the second category, the transmit-receive sequence pair is arranged to preferentially reduce the range sidelobes near the zero Doppler axis, but this comes at the cost of signal-to-noise ratio because it does not adopt the matched filter operation on the receiver. Dang et al. proposed a binomial design (BD) of the transmit-receive sequence pair, aiming to reduce the range sidelobes of the ambiguity function within an extended Doppler interval (i.e., reaching -70 dB within the radian interval [-1, 1]). Compared with the PTM technology of the first category, it can achieve higher-order spectral zeros of the pulse sequence ambiguity function, but there is a 5.1 dB loss in signal-to-noise ratio.

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

[0005] Therefore, the single numerical value of the obtained transmit-receive sequence pair can only reflect a certain compromise between these two objectives, which is actually a suboptimal solution for simultaneously minimizing SMR and maximizing SNR. However, in the design of Doppler flexible 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 deficiencies of the prior art, the present invention provides a method for designing an ultra-low range-Doppler sidelobe Golay complementary waveform. First, a Pareto-efficient Golay complementary waveform design framework is proposed. This framework jointly optimizes the Doppler-flexible transceiver sequence pair to achieve a trade-off between SMR and SNR performance. The framework considers an unconstrained optimization problem with variable weights on these two metrics, and uses the weighted sum method to construct a loss function for a series of Pareto multi-objective optimization problems to find all possible Pareto optimal solutions. Secondly, to solve the optimization problem, a model-driven machine learning algorithm is innovatively designed for multi-objective optimization. The method of the present invention can suppress the Doppler sidelobe to an extremely low level of -80.38 dB, but the SNR loss is small, only 2.8 dB, which is 5 dB and 0.3 dB higher than the traditional Doppler-flexible scheme respectively.

[0007] The technical solution adopted by the present invention to solve its technical problems is as follows:

[0008] Step 1: Construct a signal model;

[0009] Step 1-1: Define the Golay complementary pair as two single-mode complex sequences of length L, namely x[·] and y[·], and 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 sequence x and 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 ;

[0012] Step 1-2: The Golay complementary waveforms s x (t) and s y (t) are phase-encoded by x and y, that is and where u(t) is the unit energy baseband pulse shape and satisfies T c is the chip length;

[0013] Step 1-3: During transmission, s x (t) and s y(t) is further controlled by the feature binary vector p = [p 0 , p 1 , …, p n , …, p N-1 , T where N represents a positive number, and p n = 1 or -1; when p n = 1, s x (t) is transmitted, and when p n = -1, s y (t) is transmitted; therefore, the P - pulse sequence Z P (t) is defined as:

[0014]

[0015] where T is the pulse repetition interval PRI;

[0016] Step 1 - 4: Let q = [q 0 , q 1 , ···, q N-1 be the coefficient vector of the receiving filter, and the Q - pulse sequence Z Q (t) is defined as:

[0017]

[0018] where represents the complex conjugate of the receiving filter coefficient;

[0019] Step 1 - 5: Let Z P (t) be the transmitted signal and Z Q (t) be the time - domain response of the received signal. Set the input of the receiver matched filter to Z P (t)e jυt , where υ = 2πf d , and f d is the Doppler shift in Hz; Z P (t)e jυt passes through a linear filter with an impulse response of Z * Q (-t). Then the output of the matched filter, i.e., the cross - ambiguity function, is:

[0020]

[0021] This cross - ambiguity function is also the continuous cross - ambiguity function of Z P (t) and Z Q (t);

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

[0023]

[0024] where θ = υT = 2πf d T is the Doppler shift in radians over a pulse repetition interval PRI, due to C x (k)+C y (k) = 2Lδk, and the discrete ambiguity function is further simplified to:

[0025]

[0026] where, when k ≠ 0, it represents the range sidelobes to be suppressed; when k = 0 and θ = 0, it represents the main lobe energy;

[0027] Step 2: Pareto optimization framework;

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

[0029]

[0030] The signal-to-noise ratio is defined as:

[0031]

[0032] where is the power of the target, N 0 is the power spectral density PSD of the receiver white noise, and q represents the coefficient vector of the receive filter;

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

[0034]

[0035] Using the weighted sum method, the objective function is constructed from the weighted sum of all objectives; in the Pareto framework, according to the velocity range of the objectives, 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:

[0036]

[0037] where w 1 and w 2 represent the weight coefficients, and the weight values represent the relative importance of the metrics;

[0038] Step 3: Solving with machine learning algorithms:

[0039] Step 3-1: Use a machine learning-based algorithm to solve the optimization problem, and use the stochastic gradient descent SGD algorithm to learn the model parameters;

[0040] The neural network structure of the machine learning-based algorithm consists 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 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. The weight vector is updated using the Adam optimizer by minimizing the loss function. The bias of the forward propagation is set to zero.

[0041] Step 3-2: Input design:

[0042] Set the input of the model as the phase value vector where θ d is the Doppler shift in radians, randomly selected within the Doppler interval [0, 2πf d T]. The index d represents the number of iterations. After training, the loss is minimized over the entire Doppler interval to suppress sidelobes.

[0043] Step 3-3: Optimization objective:

[0044] To find the optimal transceiver sequence pair {p, q}, train the neural network to minimize the loss function to In the formula represents the loss function, and θ represents the initial input phase within the Doppler interval;

[0045] Step 3-4: Backward propagation module design:

[0046] The backward propagation module updates the feature vector z = [z , z 1 , z 2, ···, z N-1 by minimizing the loss function; 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:

[0047]

[0048] where z n = p n * q n , p n is obtained from the polarity of z n in Equation (12), and q n is defined in Equation (13):

[0049]

[0050] Step 3-5: For the Doppler shift θ, e jnθCalculated using Euler's formula as e jnθ = cos(nθ) + j sin(nθ); for the complex weight vector z, written as 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):

[0051]

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

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

[0054] An electronic device, 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 so that the electronic device executes the above complementary waveform design method.

[0055] A computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the above complementary waveform design method is implemented.

[0056] A chip, comprising: a processor for calling and running a computer program from a memory, so that a device installed with the chip executes the above complementary waveform design method.

[0057] A computer program product, the computer program product comprising a computer storage medium, the computer storage medium storing a computer program, the computer program comprising instructions executable by at least one processor, and when the instructions are executed by the at least one processor, the above complementary waveform design method is implemented.

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

[0059] 1. Improvement in sidelobe suppression performance and signal-to-noise ratio: Since these sequences are obtained from the Pareto optimal set that simultaneously optimizes the SMR and SNR objectives, this transceiver framework is theoretically optimal. Numerical results show that within the Doppler time interval [0, π], the method of the present invention can suppress the Doppler sidelobes to an extremely low level of -80.38 dB, but 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 the present invention provides a more flexible method for designing Golay waveforms. On the one hand, the priorities of the two sub-goals of SMR and SNR can be flexibly adjusted according to actual needs to design Golay complementary waveforms. On the other hand, waveform parameters, such as the length of the transceiver sequence and the range of Doppler intervals, can be customized in the method of the present invention. Description of the Drawings

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

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

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

[0064] Figure 4 is the ranging result of the ordinary GCP scheme, NS scheme and the proposed multi-objective detection method in the embodiment of the present invention. Detailed Embodiment

[0065] The present invention will be further described below in conjunction with the drawings and embodiments.

[0066] The present invention proposes an ultra-low range-Doppler sidelobe Golay complementary waveform design method to improve the anti-Doppler jitter ability of radar signals. First, a Pareto-efficient Golay complementary waveform design framework is proposed, which jointly optimizes the Doppler-flexible transceiver sequence pair to achieve a trade-off between SMR and SNR performance. This framework considers an unconstrained optimization problem with variable weights on these two metrics, constructs a loss function for a series of Pareto multi-objective optimization problems using the weighted sum method, and obtains all possible Pareto optimal solutions. Secondly, to solve the optimization problem, a model-driven machine learning algorithm is innovatively designed for multi-objective optimization. The overall structural diagram of this method is as Figure 1 shown.

[0067] First, a system and signal model are established. The pulse compression radar combines the energy advantage of ultra-long pulses and the range resolution advantage of ultra-short pulses. The transmitted pulse is modulated by frequency / phase encoding and received by correlating with the transmitted signal.

[0068] At the transmitter, the baseband waveform is phase - encoded using GCP. Due to the bipolar nature of GCP, the pulse phase for each bit duration either remains its initial phase or flips 180 degrees. Then, the received delayed signal is correlated with different delayed pulse sequences transmitted, thereby obtaining the autocorrelation of the Golay complementary waveform. Since GCP has an ideal aperiodic autocorrelation, the peak of the autocorrelation function that appears at zero delay lag is equal to the number of transmitted pulses in units of energy per pulse, and is equal to zero at a delay lag 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 phase rotation on the received Golay complementary waveform. This will destroy the complementary property, generate range - Doppler sidelobes, and bring difficulties to 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 the sum of the values of the autocorrelation function is:

[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, δ k is the Kronecker function, x = [x[0],x[1],…,x[L - 1]] T , y = [y[0],y[1],…,y[L - 1]] T . Under the above GCP, the basic Golay complementary waveforms s x (t) and s y (t) are phase - encoded by x and y, that is and where u(t) is the unit - energy baseband pulse shape and satisfies T c is the chip length. During transmission, s x (t) and s y (t) are further controlled by the binary feature vector p = [p 0 ,p 1 ,…,p N-1 T where N represents a positive number, p n = 1 or - 1. When p​n When p = 1, transmit s x (t), and when p n = -1, transmit s y (t). Therefore, the P - pulse sequence Z P (t) is defined as:

[0073]

[0074] where T is the pulse repetition interval (PRI).

[0075] Let q = [q 0 , q 1 , ···, q N-1 be the coefficient vector of the receiving filter. Therefore, the Q - pulse sequence Z Q (t) is defined as:

[0076]

[0077] Transmit Z P (t), and set the input of the receiver matched filter to Z P (t)e jυt , where υ = 2πf d , f d is the Doppler shift in Hz. Z P (t)e jυt passes through a linear filter with impulse response Z * Q (-t). Then the output of the matched filter, which is the cross - ambiguity function, is:

[0078]

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

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

[0081]

[0082] where θ = υT = 2πf d T is the Doppler shift in radians over one pulse repetition interval (PRI). Since C x [k] + C y [k] = 2Lδk, the discrete ambiguity function can be further simplified to:

[0083]

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

[0085] Therefore, based on the above GCP transmission, the objective of the present invention is to suppress the sidelobes caused by k ≠ 0 in the ambiguity function by carefully designing the values of p n and q. n

[0086] Pareto Optimization Framework Design

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

[0088]

[0089] In addition to SMR, the signal-to-noise ratio (SNR) is also an important performance index of the radar detection system. The signal-to-noise ratio of the system is usually defined as:

[0090]

[0091] where σ b 2 is the power of the target, and N 0 is the power spectral density (PSD) of the receiver white noise.

[0092] Therefore, the signal-to-noise ratio can be optimized by maximizing ‖

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

[0094]

[0095] For simplicity, the constants in the discrete ambiguity function and L are omitted.

[0096] In (9), the two objectives conflict with each other, and the improvement of one objective often leads to the deterioration of the other objective. The optimal solution of this multi-objective optimization is usually not a single one, but a set of trade-off solutions. The present invention constructs a Pareto framework to generate a set of solutions that achieve Pareto-optimal trade-offs between SMR and SNR. To transform the multi-objective optimization problem, scalarization techniques are used to combine multiple objectives into one objective.

[0097] ​​The scalarization method used in this invention is the weighted sum method, and the objective function is constructed by the weighted sum of all objectives. In the Pareto framework, according to the velocity range of the objectives, 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:

[0098]

[0099] where w 1 and w 2 represent the weight coefficients, and the weight values represent the relative importance of the metrics.

[0100] Solving by machine learning algorithms:

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

[0102] The structure of the machine learning-based algorithm is as Figure 2 shown, consisting 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 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. By minimizing the loss function, the weight vector is updated using the Adam optimizer. The bias of the forward propagation is set to zero.

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

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

[0105] Backward propagation module design: Note that the product of p and q is regarded as a single parameter z. In Figure 2In it, the backpropagation module updates the feature vector z = [z , z 1 , ···, z 2 by minimizing the loss function N-1 . Note that 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:

[0106]

[0107] where z n = p n * q n , p n is obtained from the polarity of z n in Equation (12), and q n is defined in Equation (13).

[0108]

[0109] However, since most machine learning models are designed to handle real number problems, the complex value optimization problem of the present invention is solved by using two models to handle its real part and imaginary part respectively. For the Doppler frequency shift θ, e jnθ can be calculated by Euler's formula as e jnθ = cos(nθ) + j sin(nθ). For the complex weight vector z, it can be written as 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:

[0110]

[0111] In this way, complex number multiplication can be performed as a series of real number multiplications. The algorithm of the weighted sum method is shown in Algorithm 1 below, where the Adam optimizer is used. The number of iterations is set to D, and the learning rate is set to γ.

[0112]

[0113] The NS scheme has an inherent defect. That is, the Doppler elastic complementary waveform is realized by finding the null space of the Doppler Vandermonde matrix, and then the null space vector is decomposed into the eigenvector for controlling the transmitted waveform and the coefficient vector for generating the received code respectively. To ensure the existence of the null space vector, the number of discrete Doppler frequency shift samplings must be less than the number of pulses. However, the more the number of Doppler frequency shift samplings, the better the expected sidelobe suppression performance because the loss function on the Doppler frequency shift for each sampling is minimized. Therefore, there is a performance bottleneck in the existing Doppler recovery schemes, and there is still a great room for improvement in the sidelobe suppression performance.

[0114] In the present invention, the Doppler frequency sampling covering the entire Doppler interval is realized through a random search algorithm. The more the number of iterations of the algorithm, the more discrete the selected Doppler frequency shift values are, and the finer the obtained Doppler frequency shift interval is. Therefore, it is expected to achieve extremely low range-Doppler sidelobe suppression performance within the entire Doppler interval.

[0115] In addition, different from only proposing a Doppler elastic GCP waveform with certain SMR and signal-to-noise ratio performance in the existing literature, the present invention proposes a method for generating a series of GCP waveforms for optimal trade-off between SMR and signal-to-noise ratio.

[0116] Embodiment:

[0117] 1. Comparison results of the range-Doppler suppression performance between the scheme proposed in the present invention and the existing Doppler elastic schemes;

[0118] The embodiment gives the comparison results of different schemes, that is, the ambiguity functions of the ordinary GCP scheme, the PTM scheme, the BD scheme, the NS scheme and the method of the present invention using weighted sum within the Doppler interval [0, π]. The comparison results are shown in Table 1.

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

[0120]

[0121] The sidelobe of the method of the present invention is 5 dB lower than that 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 tolerable speed of the detected target can reach 184.95 km / h, and the corresponding Doppler resistance interval can reach [20.6, 20.6] kHz.

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

[0123] Simulations were carried out in the case of the weighted sum method, Figure 3 and the Pareto frontier in this case was plotted.

[0124] Figure 3Among them, the line connecting the red triangle markers represents the Pareto front of the multi-objective optimization problem with different weighted signal-to-noise ratios and signal-to-noise ratios. In this figure, w 1 and w 2 with different combinations are considered, and they have different priorities for SMR and SNR. The value ranges of w 1 and w 2 are from 0 to 1, and the sum of these two weights is equal to 1. It can be seen that the Pareto front formed by the non-dominated solutions appears above the points of the traditional schemes NS, BD, PTM, and Plain GCP schemes, indicating that the method of the present invention is superior to the traditional schemes in both SMR and signal-to-noise ratio performance. As can be seen from Figure 3 , even without assigning a weight to the signal-to-noise ratio index, the point where w 1 = 1 and w 2 = 0 also shows an SMR gain of 5 dB and an SNR gain of 0.3 dB compared with the NS scheme. Compared with the PTM scheme, the SMR gain at the point where w 1 = 0 and w 2 = 1 is 6.5 dB.

[0125] 3. Multi-objective detection simulation.

[0126] In this embodiment, the ranging results of multiple targets are simulated. It should be noted that the range-Doppler map is generated using a correlation filter, and then the correlation results of multiple pulses are added to obtain the ranging result. The simulated scenario contains 5 targets, among which 3 strong targets (Targets 1-3) have a normalized signal amplitude of 0 dB, and 2 weak targets (Targets 4 and 5) have 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 60 GHz Bandwidth 1.76 GHz PRI 2 μs GCP length 64 Doppler frequency shift interval [0,π) Number of pulses 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] Objective Distance (m) Velocity (m / s) Target 1 50 3 Target 2 90 42 Target 3 100 60 Target 4 105 15 Target 5 102 2

[0131] The range resolution of the simulated radar system is 8.5 cm, and the maximum unambiguous range is 300 m. Simulations are carried out for the ordinary GCP scheme, the NS scheme, and the weighted sum method with w 1 = 1 and w 2 = 0. The ranging results of the three schemes are as shown in Figure 4 .

[0132] As shown in Figure 4As shown, in the scenario of high moving speed, the sidelobe suppression performance based on the ML method is superior to other solutions. For the ordinary GCP solution, it can be seen that the weak target at 102 meters is submerged by the range sidelobes of the strong target. The results show that in the case of high mobility, the simple GCP waveform cannot distinguish between strong and weak targets. The proposed method (indicated by the blue line) suppresses the sidelobes of moving targets to an extremely low level, lower than -100 dB. Compared with the ordinary GCP solution, the radar detection threshold using this waveform is reduced by nearly 55 dB. Even for targets at relatively close distances (Targets 3, 4, 5), the method of the present invention can easily distinguish between strong and weak targets.

[0133] It can also be observed that as the speed increases, the method proposed in the present invention has a greater performance gain than other traditional methods. For Target 2 with a speed of 42 m / s, the range sidelobe of the method of the present invention is as low as -125 dB, which is nearly 10 dB higher than the NS solution and 60 dB higher than the ordinary GCP solution. When the speed increases to 60 m / s (Target 3), the range sidelobe of the method of the present invention is suppressed to -130 dB, which is 20 dB higher than the NS solution. In addition, the advantages of this method can also be seen from the aspect of signal-to-noise ratio gain. For low-speed targets, there is almost no difference in the signal-to-noise ratio of each solution. For high-speed targets, the signal-to-noise ratio of the targets detected by the method of the present invention is higher than that of the other two solutions, nearly 0.5 dB higher than the NS solution and nearly 1 dB higher than the ordinary GCP solution.

[0134] The present invention innovatively designs a Pareto optimization framework for constructing low range-Doppler sidelobes and high signal intensity Golay complementary waveforms. Compared with the existing Doppler elasticity solutions, a set of globally optimal trade-off transceiver sequence pairs are jointly designed to achieve multi-objective optimization.

[0135] Secondly, aiming at the multi-objective optimization problem of Golay complementary waveforms, an unconstrained optimization problem is proposed. The objective function is constructed by the scalar weighted sum of the SMR and SNR metrics, and finally the Pareto optimal set of the transmit-receive sequence pairs is obtained, and these optimal sets are mapped into the Pareto front. The numerical results verify that the Pareto front wave of this framework is superior to the existing Doppler elasticity GCP waveforms in terms of both SMR and SNR performance, indicating the effectiveness of this framework.

[0136] Finally, inspired by multi-task learning, a model-driven machine learning method is designed to solve the above optimal problem. In the machine learning model, the transmit-receive sequence pairs that determine the phase encoding modulator and pulse compression filter coefficient vectors are regarded as hyperparameters to be trained.

Claims

1. A method for designing ultra-low range-Doppler sidelobe Gray complementary waveform, characterized in that: The steps include: Step 1: Build a signal model; Step 1-1: Define the Golay complementary pair as two single-mode complex sequences of length L, namely x[·] and y[·]. The sum of the autocorrelation function is: C x (k)+C y (k)=2Lδ k (1) Where k = -(L-1), -(L-2), ..., 0, ..., (L-1), C x (k) and C y (k) are the autocorrelation functions of sequence x and sequence y at lag k, δ k is the Kronecker function, x=[x[0],x[1],…,x[L-1]] T , y=[y[0],y[1],…,y[L-1]] T ; Step 1-2: Golay complementary waveforms x (t) and s y (t) is phase-encoded by x and y, that is, and Where u(t) is the unit energy baseband pulse shape and satisfies T c is the chip length; Step 1-3: During transmission, s x (t) and s y (t) is further formed 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, transmission s x (t), when p n = -1, transmission s y (t); therefore, the P-pulse sequence Z P (t) is defined as: Where T is the pulse repetition interval PRI; Step 1-4: Let q = [q0,q1, ···,q N-1 ] is the coefficient vector of the receiving filter, Q-pulse sequence Z Q (t) is defined as: in, represents the complex conjugate of the receive filter coefficient; Step 1-5: Set Z P (t) is the transmitted signal, Z Q (t) is the time domain response of the received signal, and the input of the receiver matched filter is set to Z P (t)e jυt , where υ=2πf d , f d is the Doppler frequency shift, in Hz; Z P (t)e jυt The impulse response is Z * Q (-t) linear filter, the output of the matched filter, that is, the cross ambiguity function, is: The cross ambiguity function is also Z P (t) and Z Q (t) continuous cross fuzzy function; The discrete cross fuzzy function is written as: Where, θ = υT = 2πf d T 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: Where, when k≠0, it indicates the range of side lobes that need to be suppressed; when k=0,θ=0, it indicates the main lobe energy; Step 2: Pareto optimization framework; Step 2-1: The sidelobe to mainlobe ratio SMR is defined as: The signal-to-noise ratio is defined as: in is the power of the target, N0 is the power spectral density PSD of the receiver white noise, and q represents the coefficient vector of the receiving filter; Step 2-2: The multi-objective optimization problem is expressed as: Using the weighted sum method, 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: Where w1 and w2 represent weight coefficients, and the weight value represents the relative importance of the metric; Step 3: Machine learning algorithm solution: Step 3-1: Use a machine learning-based algorithm to solve the optimization problem and use the stochastic gradient descent SGD algorithm to learn the model parameters; The neural network structure of the algorithm based on machine learning consists of a forward propagation module and a backward propagation module. The forward propagation module calculates the input normalized random phase of the Doppler frequency shift in radians. The backward propagation module calculates the loss function according to formula (10) and then updates the weight vector in the forward propagation module. The trained weights in the neural network are set to the output feature vector z. The Adam optimizer is used to update the weight vector by minimizing the loss function, and the bias of the forward propagation is set to zero. Step 3-2: Input Design: Set the input of the model to be a vector of phase values where θ d is the Doppler frequency shift in radians, in the Doppler interval [0,2πf d T], the index d represents the number of iterations; after training, the loss is minimized over the entire Doppler interval to suppress the side lobes; Step 3-3: Optimization goal: In order to find the optimal transmit and receive sequence pair {p,q}, the neural network is trained to minimize the loss function In the formula represents the loss function, θ represents the initial input phase within the Doppler interval; Step 3-4: Backward propagation module design: The backpropagation module minimizes the loss function Update 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 It is transformed from the objective function in formula (10); for the weighted sum method, the loss function is given by the following formula: Among them, z n =p n *q n , p n From formula (12), z n The polarity of q n Defined in formula (13): Step 3-5: For the Doppler shift θ, e jnθ Calculated using Euler's formula as e jnθ = cos(nθ) + j sin(nθ); for the complex weight vector z, write z = z r +jz i , where z r represents the real part of z, z i represents the imaginary part of z; two complex numbers e jnθ The multiplication with z is given by equation (14): Thus, complex multiplication is performed as a series of real multiplications.

2. A computer program, characterized in that The computer program enables a computer to execute the method as claimed in claim 1.

3. An electronic device, characterized in that: include: Processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device executes the method as claimed in claim 1.

4. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method as claimed in claim 1 is implemented.

5. A chip, characterized in that: include: A processor, used to call and run a computer program from a memory, so that a device equipped with the chip executes the method as claimed in claim 1.

6. A computer program product, characterized in that The computer program product comprises a computer storage medium storing a computer program, wherein 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 according to claim 1 is implemented.

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