A method and apparatus for designing nonlinear frequency modulation signals for active sonar detection

Abstract

The application provides a nonlinear frequency modulation signal design method and device for active sonar detection, and the method comprises the following steps: an initial NLFM signal is designed by using a phase dwell principle; a target function of an NLFM signal mathematical model is constructed by associating a signal to be optimized with the initial NLFM signal; the NLFM signal mathematical model is solved based on the target function by using a least square error approximation method; and an optimized NLFM signal is obtained by combining an iterative algorithm. The method has high calculation efficiency, and the generated NLFM signal has the characteristics of narrow main lobe and low side lobe, has good imaging quality, and can improve the precision of sonar detection. Due to the phase change of the signal in each iteration in the waveform design, the obtained NFLM signal has good Doppler sensitivity, so that the Doppler frequency shift generated under the high-speed target does not seriously affect the matching filter performance of the receiver, and the designed signal has good Doppler sensitivity, which is beneficial to the measurement of the target speed.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of radio communication, and particularly relates to a nonlinear frequency modulation signal design method and device for active sonar detection. BACKGROUND

[0002] With the increasing demand for ocean exploration accuracy, detection probability, and communication performance, sonar systems have changed from passive to active. An active sonar system includes three parts: sonar signal waveform, sonar channel, and sonar receiver. Waveform design is a very important part of an active sonar system. Research shows that for active sonar, the sonar transmission waveform system determines how the receiving system processes signals and directly affects the system's range resolution, velocity resolution, target detection accuracy, anti-interference ability, and channel matching performance. By designing appropriate sonar transmission signal waveforms, target information can be better obtained, and the detection accuracy and anti-interference ability of underwater exploration can be improved.

[0003] Sonar accuracy and resolution are consistent. To improve the range measurement accuracy and range resolution of sonar, the transmission signal must occupy a large sustained bandwidth in the frequency domain; to improve the speed measurement accuracy and speed resolution of sonar, the signal must occupy a large sustained time width in the time domain. Therefore, the ideal transmission signal requires a wide pulse and a large bandwidth. People usually use pulse compression signals with a large time-width-bandwidth product. In pulse compression technology, commonly used transmission signal waveforms include linear frequency modulation (LFM) signals and nonlinear frequency modulation (NLFM) signals.

[0004] For LFM signals, in multi-target detection, the high sidelobes of LFM signals can easily lead to missed detection and false detection. In order to suppress the sidelobes, weighting processing is often needed, but this can cause the main lobe to spread and result in a loss of signal-to-noise ratio. In addition, LFM signals can produce Doppler coupling time shift phenomena, and cannot simultaneously consider time resolution and frequency resolution to independently provide range and velocity measurement values.

[0005] The concept of NLFM was first proposed by Key, Fowle, and Haggarty in 1959. NLFM signal is a frequency modulation signal, and its modulus function is nonlinear compared with LFM signal. It is designed to overcome the shortcomings of LFM signal, and its outstanding advantage is that direct matched filtering can obtain lower sidelobes without the need for weighting processing, thus avoiding the signal-to-noise ratio loss problem caused by weighting, and obtaining better measurement accuracy and accurately identifying target signals.

[0006] The initial waveform design method derived the phase function of the NLFM signal in the form of a window function, such as an NLFM signal designed based on the phase dwell principle. This method reduces the peak-to-side-lobe ratio, but also results in a wide main lobe, thus obscuring its target information. Alternatively, optimization algorithms based on the FM function are used to find optimal waveforms. For example, Roohollah Ghavamirad et al. obtained the NLFM signal by solving a constrained optimization problem using the Lagrangian method. In their work, this method resulted in a smaller main lobe width and further reduced the peak-to-side-lobe ratio.

[0007] However, the computational complexity leads to slow operation. Currently, no NLFM signal design method can effectively balance these two factors, improving computational efficiency while optimizing performance metrics. Summary of the Invention

[0008] To address the problems of wide main lobe and high side lobe in NLFM signals designed using the traditional phase dwell principle, which affect sonar detection accuracy, the first aspect of this invention provides a nonlinear frequency-modulated signal design method for active sonar detection, comprising the steps of: designing an initial NLFM signal using the phase dwell principle; correlating the signal to be optimized with the initial NLFM signal to construct an objective function for the mathematical model of the NLFM signal; solving the mathematical model of the NLFM signal based on the objective function using the least squares error approximation method; and obtaining the optimized NLFM signal by combining an iterative algorithm.

[0009] Preferably, the objective function is constructed based on the least squares mean square error, specifically expressed as follows:

[0010]

[0011] Where χ(f) is the signal to be optimized in the frequency domain, and γ(f) is the initial NLFM signal in the frequency domain, i.e.

[0012] γ(f)=|γ(f)|e jθ(f)

[0013] Where |γ(f)| is the corresponding amplitude and θ(f) is the corresponding phase.

[0014] Preferably, before designing the initial NLFM signal using the phase dwell principle, the method further includes: calculating the phase of the initial NLFM signal based on the power spectral density spectrum of the selected signal window type; and optimizing the phase of the NLFM signal using an iterative algorithm to obtain an optimized NLFM signal.

[0015] Preferably, calculating the phase of the initial NLFM signal specifically includes: obtaining the group delay function T by integrating the power spectral density spectrum P(f) of the corresponding window type.g (f); Calculate the inverse group delay function The frequency function f(t) of time is obtained; the phase of the initial NLFM signal is obtained by integrating the frequency function f(t).

[0016] Preferably, the inverse group delay function Solve using numerical methods.

[0017] Preferably, the objective function is discretized by sampling points to obtain a discretized objective function.

[0018] Preferably, solving the NLFM signal mathematical model using the least squares error approximation method specifically includes: obtaining the partial derivatives of the objective function using the least squares error approximation method.

[0019] Preferably, in the iterative algorithm, the number of iterations is the number of iterations required for the objective function to converge.

[0020] A second aspect of the present invention provides a nonlinear frequency-modulated signal design apparatus for active sonar detection, comprising:

[0021] Initial NLFM signal design module, configured to design initial NLFM signals using the phase dwell principle;

[0022] The objective function construction module configures the objective function used to correlate the signal to be optimized with the initial NLFM signal and construct the mathematical model of the NLFM signal.

[0023] The mathematical model solving module is configured to solve the mathematical model of NLFM signals based on the objective function and using the least squares error approximation method.

[0024] The iterative optimization module is configured to combine iterative algorithms to obtain optimized NLFM signals.

[0025] Preferably, the objective function construction module is further configured to: construct an objective function based on the least squares mean square error, specifically expressed as:

[0026]

[0027] Where χ(f) is the signal to be optimized in the frequency domain, and γ(f) is the initial NLFM signal in the frequency domain, i.e.

[0028] γ(f)=|γ(f)|e jθ(f)

[0029] Where |γ(f)| is the corresponding amplitude and θ(f) is the corresponding phase.

[0030] The application discloses a nonlinear frequency modulation signal design method for an underwater active sonar detection system based on least square mean square error. In the underwater active sonar detection system, designing a flexible and efficient waveform generation system is crucial to improving the detection performance of the sonar. The nonlinear frequency modulation (NLFM) signal can obtain good sidelobe suppression performance without weighting in pulse compression, good measurement accuracy, and accurate identification of target signals. The improved NLFM signal design method provided by the application uses the phase dwell principle to design an initial NLFM signal, and then uses the least square error approximation method and an iterative algorithm to continuously optimize the phase of the NLFM signal. After multiple iterations, an optimal optimized phase is obtained, and then an improved NLFM signal is obtained. The method has high calculation efficiency, and the generated NLFM signal has the characteristics of narrow main lobe and low sidelobe, has good imaging quality, and can improve the detection accuracy of the sonar. Due to the change of the signal phase in each iteration in the waveform design, the obtained NFLM signal has good Doppler sensitivity, so that the Doppler frequency shift generated under a high-speed target will not seriously affect the matched filter performance of the receiver. BRIEF DESCRIPTION OF DRAWINGS

[0031] For the sake of description, only parts related to the application are shown in the drawings.

[0032] Figure 1 The figure is a step schematic diagram of the nonlinear frequency modulation signal design method for active sonar detection in an embodiment of the application.

[0033] Figure 2 The figure is a whole flow schematic diagram of the nonlinear frequency modulation signal design method for underwater active sonar detection system based on least square mean square error in another embodiment of the application.

[0034] Figure 3 The figure is a calculation flowchart under the iteration cycle of the nonlinear frequency modulation signal design method for underwater active sonar detection system based on least square mean square error in another embodiment of the application.

[0035] Figure 4 The figure is a structure schematic diagram of the nonlinear frequency modulation signal design device for active sonar detection in another embodiment of the application.

[0036] Figure 5 The figure is a comparison diagram of the matched filter output corresponding to the traditional phase dwell principle method under different window types in another embodiment of the application.

[0037] Figure 6 The figure is an imaging index comparison diagram of the designed signal in another embodiment of the application. DETAILED DESCRIPTION

[0038] The application will be described in further detail below with reference to the drawings and embodiments. The specific embodiments described herein are intended for purposes of illustration only and are not intended to limit the claimed application. The embodiments in the present application and the features in the embodiments can be combined with each other without conflict under the condition that they are not mutually exclusive.

[0039] In a specific embodiment, a least square mean error based nonlinear frequency modulation signal design method for an underwater active sonar detection system is provided, comprising the following steps: an initial NLFM signal is designed by using a phase station principle, and then an optimal NLFM signal is obtained by continuously optimizing through a least square error approximation method and in combination with an iterative algorithm, so as to simplify calculation and have good imaging performance. In waveform design, firstly, the NLFM signal designed by using the phase station principle has Doppler robustness, and the improved method in the present application uses an iterative method, so that the designed signal has good Doppler sensitivity, which is more conducive to target speed measurement. Secondly, the improved method is superior to the traditional phase station principle in terms of sidelobe suppression effect of the NLFM signal under the condition of reducing calculation work. The NLFM signal designed by using the improved method has lower sidelobe and sharper main lobe, thereby improving the accuracy of sonar detection.

[0040] Figure 1 For the step schematic diagram of the nonlinear frequency modulation signal design method for active sonar detection in the present embodiment, the method specifically comprises:

[0041] S1, an initial NLFM signal is designed by using a phase station principle. The phase station principle considers that for a time-domain rapidly changing signal, the positive and negative areas of the rest regions can offset each other except for the position where the derivative is zero (station point), and finally the integral result of the function is mainly affected by the station point. Based on the phase station principle, the relationship between the signal phase and the power spectral density (PSD) of the corresponding window type can be gradually derived, so that the signal phase is obtained through the PSD, and thus the initial NLFM signal required by the present application is obtained.

[0042] The designed NLFM signal x(t) is defined as follows:

[0043]

[0044] Wherein, a(t) and are the amplitude and phase corresponding to the signal x(t), and T is the pulse period of x(t). In the present embodiment, its amplitude is considered as a constant.

[0045] In another specific embodiment, the signal designed by using the phase station principle is used as the initial NLFM signal, and specifically comprises the following steps:

[0046] The interval The group delay function T is obtained by integrating the power spectral density P(f) of the corresponding window type g (f):

[0047]

[0048] where B is the signal bandwidth; k1 and k2 are integration constants, depending on T g The boundary conditions of (f) are that and The time-frequency function is then calculated from the inverse group delay function as follows:

[0049]

[0050] In a specific embodiment, for the inverse group delay function that is not easily available, numerical methods can be employed to solve it.

[0051] The signal phase is obtained by integrating the frequency function as shown in equation (4). By substituting (4) into (1), the initial NLFM signal required for the improved method can be obtained.

[0052]

[0053] S2, the target function of the NLFM signal mathematical model is constructed by associating the signal to be optimized with the initial NLFM signal. The target optimization problem-based mathematical model is established by associating the signal to be optimized with the initial NLFM signal designed using the phase residence principle. In order to realize the phase optimization of the signal to be optimized, the initial NLFM signal is associated with the signal to be optimized in this embodiment, and specifically, the best target function is obtained by the sum of squares of the difference between the Fourier transform of the signal to be optimized and the Fourier transform of the initial signal, i.e., the mean square error, to match the target optimization problem. Thus, the mathematical model based on the target optimization problem is established. The target function of the NLFM signal mathematical model based on the mean square error is as follows:

[0054]

[0055] where k(f) is set to the signal to be optimized in the frequency domain. γ(f) is the initial NLFM signal in the frequency domain, i.e., γ(f) = |γ(f)|e jθ(f) ; |γ(f)| is the corresponding amplitude, which is the root of the PSD in S1; θ(f) is the corresponding phase, which is the frequency domain expression of the corresponding phase of the initial signal obtained in S1.

[0056] In actual sampling, the theory of continuous implementation is more complex. It is a fast and accurate method to design the signal by discretizing the appropriate sampling points. Let where K = 2N. N is the discrete sampling point. The discrete form of the target function (5) is written as follows:

[0057]

[0058] where is the Fourier transform form of the discrete signal x(n) to be optimized, Y(k) is the discrete form of the initial NLFM signal.

[0059] In vector notation, let x = [x(0), x(1),..., x(N-1)] T be an N x 1 vector, is the element expression of the K x N matrix H. Then X(k) is described in vector form, i.e.,

[0060] [X(0), X(1),..., X(K-1)] T = Hx (7)

[0061] and Y(k) is converted to vector form, i.e., Y = [Y(0), Y(1),..., Y(K-1)] T .

[0062] At this time, the discrete form of the objective function (6) is transformed as follows:

[0063] min x F = |Hx - Y| 2 = (Hx - Y) H (Hx - Y) (8)

[0064] The above expression is expanded as x H H H Hx - x H H H Y - Y H Hx + Y H Y, where (*) H is the conjugate operation. Thus, a mathematical model based on the objective optimization problem is established.

[0065] S3, based on the objective function, the least square error approximation method is used to solve the NLFM signal mathematical model. Based on the least square method, the partial derivative of the objective function with respect to the independent variable parameter x in (8) is obtained to obtain the discrete signal x to be optimized. The partial derivative result is shown in (9) to (11). H H The value of H is equal to KE N , because the columns of the matrix H are orthogonal, where E N is an N x N unit matrix.

[0066]

[0067] → x = (H H H) -1 HH Y (10)

[0068] →x=(KE N ) -1 H H Y (11)

[0069] where (KE N ) -1 is the inverse matrix of KE N .

[0070] S4, combined with the iterative algorithm, obtains the optimized NLFM signal. Combined with the iterative algorithm, the optimal optimization phase is found, and then an optimal NLFM signal can be obtained. The discrete signal x to be optimized is decomposed into two parts, that is, Z = (KE N ) -1 H H and Y. The result is optimized to the best position using the iterative algorithm, and the best solution is when the data tends to be flat. Therefore, in the λ th iteration, the (11) of the discrete signal x to be optimized can be expressed as follows:

[0071] x (λ) = ZY (λ-1) (12)

[0072] According to (12), the following formula can be obtained:

[0073] X (λ) = Hx (λ) (13)

[0074] θ (λ) = phase(X (λ) ) (14)

[0075] where θ( λ ) is the phase of X(k) in the λ th iteration.

[0076] The iteration increases to continuously update the output vector Y, that is:

[0077]

[0078] The frequency domain expression of the corresponding phase of the initial signal based on the phase residence principle is used as the value of θ (0) . The optimal signal x (θ) is obtained by the least square iterative algorithm, where θ is the iteration number when the objective function in (8) tends to converge.

[0079] Figure 2This is a schematic diagram illustrating the overall flow of a nonlinear frequency-modulated (NLFM) signal design method for an underwater active sonar detection system based on least squares mean square error (LSME) in a specific embodiment. The purpose of this embodiment is to design an initial NLFM signal using the phase dwelling principle, and then continuously optimize it using the least squares error approximation method combined with an iterative algorithm to obtain the optimal NLFM signal, thereby simplifying calculations and achieving good imaging performance. In waveform design, the NLFM signal designed using the phase dwelling principle exhibits Doppler robustness. This embodiment further improves upon this using an iterative method, resulting in a signal with good Doppler sensitivity, which is more beneficial for target velocity measurement. Secondly, while reducing computational workload, this improved method outperforms the traditional phase dwelling principle in terms of sidelobe suppression of the NLFM signal. The NLFM signal designed using this improved method has lower sidelobes and a sharper main lobe, improving the accuracy of sonar detection.

[0080] Figure 3 This is a flowchart illustrating the iterative calculation process of a nonlinear frequency-modulated signal design method for underwater active sonar detection systems based on least squares mean square error in another specific embodiment of the present invention. Figure 3 As shown, the optimal phase is found by combining an iterative algorithm, thus obtaining an optimal NLFM signal. Specifically, in each iteration, the output vector Y is updated, and the discrete signal x is calculated according to equations (12-14) in the aforementioned embodiment. (λ) Its Fourier transform form X (λ) and phase θ (λ) The process is iterated until the objective function converges, yielding the optimized discrete signal x. (θ) .

[0081] Figure 4 This is a schematic diagram of a nonlinear frequency-modulated signal design device 400 for active sonar detection in a specific embodiment of the present invention. The device specifically includes:

[0082] Initial NLFM signal design module 401, configured to design an initial NLFM signal using the phase dwell principle;

[0083] Objective function construction module 402 is configured to associate the signal to be optimized with the initial NLFM signal and construct the objective function of the NLFM signal mathematical model.

[0084] Mathematical model solving module 403 is configured to solve the mathematical model of NLFM signal based on the objective function and using the least squares error approximation method.

[0085] Iterative optimization module 404 is configured to combine iterative algorithms to obtain optimized NLFM signals.

[0086] Figure 5Fig. 4 is a comparison chart of the matched filter output corresponding to the traditional phase dwell principle method in different window types in another specific embodiment, wherein the window types are in turn raised cosine, Taylor, Gaussian and Poisson windows. Table 1 is the power spectral density relationship formula of the four types of signals.

[0087] Table 1 is the power spectral density relationship formula of the four types of signals.

[0088]

[0089] In this embodiment, the sampled NLFM signal x is used as the transmitting signal of the sonar, with a bandwidth of 20 kHz, a time width of 10 ms, a pulse repetition period of 25 ms, an oversampling rate of 9, and the sampling point N determined by the signal bandwidth and the oversampling rate. The signal is sent to the target, and then the echo signal reflected from the target is received. The matched filter algorithm in the echo signal is used to extract specific information about the target, such as distance and scattering information. The quality of the transmitting signal is judged equivalent to the judgment of the output vector y. The output vector y is processed by the filter h at the receiving end of the system. The expression of the output vector y is as follows:

[0090] y = Γ(x)h (16)

[0091] where Γ(x) is the Toeplitz matrix generated by the signal vector x, as shown in (17). In the case of the matched filter, h = x is set H , where (*) H is the conjugate operation. The length of h is N.

[0092]

[0093] From the perspective of matched filtering, the signal output by the improved method when iteration is optimal is compared with the signal output using the phase dwell principle, and the results are shown in Fig. 5. Figure 5 It can be found from the comparison curve that, compared with the phase dwell principle, the improved method makes the main lobe width significantly narrower. In addition, the improved method further reduces the sidelobe level. The overall results show that the method has good sidelobe suppression effect. Therefore, the NLFM signal designed according to the present application can improve the accuracy of sonar detection, and more accurately determine the information of the required target without affecting the nearby small targets.

[0094] Figure 6Figures 6, 7 and 8 show the peak sidelobe level, integrated sidelobe ratio and main lobe width of the signals designed according to the method of the present application in another embodiment under four window types at different iterations. They show the imaging indexes of the signals designed according to the method of the present application at iterations from 1 to the best, where the best is the point at which the curves tend to be flat. The imaging indexes of the peak sidelobe level and integrated sidelobe ratio at iteration 0 are obtained based on the phase-stopping principle. It can be seen from the curves that the imaging indexes are gradually improved from the phase-stopping principle to the improved method. The sidelobe level of the proposed method is reduced and tends to be flat, which is sufficient to not affect the information extraction of small targets next to large targets.

[0095] According to the calculation formula of the main lobe width (-3dB width), the main lobe width of the four signals based on the phase-stopping principle is between 42-50us, while the main lobe width based on the improved method can reach 4us or below. The raised cosine and the Chirp remain at about 3.7us. The Gaussian and the Poisson remain between 1.18-1.38us. Compared with the phase-stopping principle, the improved method significantly narrows the main lobe width. According to the calculation formula of the main lobe width, the main lobe width of the improved method is 1 / 3-1 / 5 of that of the phase-stopping principle. Figure 6 The analysis of the imaging indexes of the designed signals, i.e. the peak sidelobe, integrated sidelobe ratio and main lobe width, can prove that the NLFM signal designed using the method of the present application has good imaging quality.

[0096] The above embodiments design the non-linear frequency modulation signal by the method provided by the present application, and the analysis of the imaging performance of the signal, such as the peak sidelobe, integrated sidelobe ratio and main lobe width, proves that the optimized NLFM signal of the present application has good imaging quality and improves the precision of sonar detection.

[0097] Although the content of the present application is specifically shown and introduced in combination with the preferred embodiments, those skilled in the art should understand that various changes can be made to the present application in form and details without creative labor, without departing from the spirit and scope of the present application defined by the appended claims.

Claims

1. A method for designing a nonlinear frequency modulation signal for active sonar detection, characterized in that, The method comprises the steps of: designing an initial NLFM signal by using a phase dwell principle; Correlate the to-be-optimized signal with the initial NLFM signal, construct a target function of the NLFM signal mathematical model, the target function is constructed based on the least square mean square error, the target function is discretized by sampling points, a discretized target function is obtained, and the target function is converted by vector representation to obtain wherein the to-be-optimized discrete signal vector is a vector form of the to-be-optimized discrete signal , is a matrix, is a vector form of a discrete form of the initial NLFM signal , wherein K = 2N, and N is a discrete sampling point. Based on the objective function, a least square error approximation method is used to solve the NLFM signal mathematical model, and a partial derivative of the objective function is obtained by using the least square error approximation method to obtain the discrete signal vector to be optimized ; in combination with an iterative algorithm that optimizes the phase of the NLFM signal, the discrete signal vector to be optimized is optimized to tend to be flat, the optimal optimized phase is found, and the optimized NLFM signal is obtained.

2. The method of claim 1, wherein, the target function is constructed based on a least square mean square error, and is specifically represented as: ； wherein, is the signal to be optimized in the frequency domain, B is the signal bandwidth, is the initial NLFM signal in the frequency domain, i.e. ; wherein is the corresponding amplitude, is the corresponding phase.

3. The method of claim 1, wherein, Before the step of designing the initial NLFM signal by using the phase dwell principle, the method further comprises the step of calculating a phase of the initial NLFM signal according to a power spectral density spectrum of a selected signal window type.

4. The method of claim 3, wherein, The step of calculating the phase of the initial NLFM signal specifically comprises: The group delay function is obtained by integrating the power spectral density spectrum P(f) for the corresponding window type ; Computing inverse group delay function Obtaining time frequency function ; Integrating the frequency function yields the phase of the initial NLFM signal.

5. The method of claim 4, wherein, The inverse group delay function Solved by numerical methods.

6. The method of claim 1, wherein, in the iterative algorithm, the number of iterations is the number of iterations when the target function tends to converge.

7. A device for nonlinear frequency modulation signal design for active sonar detection, characterized in that, The method comprises the steps of: an initial NLFM signal design module configured to design an initial NLFM signal by using a phase dwell principle; The target function construction module is configured to associate the signal to be optimized with the initial NLFM signal, construct a target function of the NLFM signal mathematical model, and perform sampling point discretization processing on the target function to obtain a discretized target function, and convert the discretized target function through a vector representation method to obtain wherein the discrete signal vector to be optimized is a vector form of the discrete signal to be optimized , is a matrix, is a vector form of a discrete form of the initial NLFM signal , wherein K = 2N, and N is a discrete sampling point. The mathematical model solving module is configured to solve the NLFM signal mathematical model based on the target function by using a least square error approximation method, and obtain the partial derivative of the target function by using the least square error approximation method to obtain the discrete signal vector to be optimized ; an iterative optimization module configured for combining an iterative algorithm that optimizes the phase of the NLFM signal, the discrete signal vector to be optimized optimization to tend to be flat, find the optimal optimized phase, get the optimized NLFM signal.

8. The apparatus for designing a nonlinear frequency modulated signal for active sonar detection of claim 7, wherein, the target function construction module is further configured to be constructed based on a least square mean square error, and is specifically represented as ； wherein, is the signal to be optimized in the frequency domain, B is the signal bandwidth, is the initial NLFM signal in the frequency domain, i.e. ; wherein is the corresponding amplitude, is the corresponding phase.

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