A broadband radar target energy accumulation method based on transceiver co-design

Abstract

This invention discloses a broadband radar target energy accumulation method based on a combined transmit and receive design. First, by acquiring the radar transmitted signal and the corresponding design requirements of the mismatch filter, an objective function for a broadband radar waveform optimization problem is designed. Then, a broadband radar waveform constraint model and an optimization problem model are established. Finally, the MM algorithm is used to solve the optimization problem and output the optimization result. This method accumulates the energy of a range-extended target exhibiting multiple scattering point characteristics into a single envelope, improving the signal-to-noise ratio of the processed range-extended target. The designed signal is a phase-coded signal; its phase agility, compared to the continuous phase of a linear frequency modulated signal, more effectively improves the signal's anti-sorting capability, while ensuring low intercept performance of the radar transmitted signal while maintaining target detection capability.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a broadband radar target energy accumulation method based on a transceiver joint design. Background Technology

[0002] With the vigorous development of modern electronic countermeasures technologies such as signal interception, the intensity of electronic countermeasures is constantly increasing. The simple, repetitive waveforms emitted by existing radars are easily intercepted, sorted, and identified by the opposing jammers, often facing sophisticated deception and high-power suppression jamming, leading to a sharp decline in radar detection capability. Large time-bandwidth waveforms are a typical low-intercept signal, spreading energy across a large time and bandwidth scale, possessing excellent low-intercept capability. However, large time-bandwidth waveforms are generally achieved through linear frequency modulation, exhibiting obvious time-frequency sorting and identification characteristics, and their high range resolution causes the target to split into multiple scattering points, making them difficult to detect effectively.

[0003] Existing broadband waveform design techniques all rely on prior knowledge of the target. The paper "Radar constant-modulus waveform design with prior information of the extended target and clutter. Sensors, 2016" proposes a constant-modulus waveform design method relying on prior knowledge for the extended range target detection problem. The paper "Fast design algorithm for low peak-to-average power ratio waveforms in broadband cognitive radar. Acta Aeronautica Sinica, 2016" proposes a fast algorithm for low peak-to-average power ratio waveforms to improve the detection performance of broadband cognitive radar systems for extended range targets. However, its design method still depends on the target's impulse response and cannot escape the dependence on prior target information, limiting its application to cognitive radar. All of the above broadband waveform design methods heavily rely on the corresponding prior knowledge; when the prior knowledge is inaccurate or missing, their optimized waveform performance drops sharply. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a broadband radar target energy accumulation method based on a combined transmit and receive design. By designing a mismatch filter between the transmitted waveform and the received waveform of the broadband radar, the range resolution of the broadband radar signal is reduced, and the energy of the range-extended target is concentrated, thereby ensuring both low intercept performance of the radar transmitted signal and target detection capability.

[0005] The technical solution of this invention is: a broadband radar target energy accumulation method based on transceiver joint design, the specific steps of which are as follows:

[0006] S1. Design requirements for acquiring radar transmission signals and corresponding mismatched filters;

[0007] S2. Design the objective function for the broadband radar waveform optimization problem;

[0008] S3. Based on step S2, establish a broadband radar waveform constraint model and an optimization problem model;

[0009] S4. Solve the optimization problem using the MM algorithm and output the optimization results.

[0010] Furthermore, step S1 is specifically as follows:

[0011] Let s(t) be a wideband signal with bandwidth B and time width τ, where t represents time; the discrete form of a radar transmitted signal with length N is... Length is Mismatched filter

[0012] in,(·) T This represents the transpose operator. Represents the field of complex numbers, s N , Represent the Nth and Nth elements of s and w, respectively. 1 element, and

[0013] Furthermore, step S2 is specifically as follows:

[0014] S21. Establish the temporal template matching error function:

[0015] The temporal template matching error function is expressed as:

[0016]

[0017] Where Σ represents the summation operator, (·) p This indicates raising the value to the power of p, and |·| represents the modulo operator. Template for representing cross-correlation function The k-th element, r k (s,w) represents the k-th element of the cross-correlation function r(s,w) of s and w, as follows:

[0018]

[0019] in,(·) H This represents the conjugate transpose operator, and Represents the real number field, I N J represents an N-order identity matrix, and 0 represents a 0 matrix of appropriate size; k The shift matrix is ​​represented as follows:

[0020]

[0021] Among them, Jk (m,n) represents matrix J k The element in the m-th row and n-th column.

[0022] S22. Establish the frequency domain modulus matching error function;

[0023] The frequency domain template matching error function is expressed as:

[0024]

[0025] Among them, y l (s), z l Let y(s) represent the signal spectrum sequence that has been oversampled by M times, and spectral template be respectively. The l-th element of the phase sequence z of the spectral template, where l = 1, 2, ..., MN, and z is an introduced auxiliary variable.

[0026] y(s) is specifically represented as:

[0027]

[0028] Wherein, matrix P is an MN×N dimensional matrix, specifically represented as:

[0029]

[0030] It is a Fourier matrix, f l The l-th column vector of matrix F is shown below:

[0031]

[0032] set up Then we can obtain:

[0033]

[0034] in,

[0035] S23. Establish the objective function for the optimization problem;

[0036] From steps S21 and S22, we know that the objective function of the optimization problem can be written as:

[0037]

[0038] Where ξ represents the frequency domain and time domain weighting coefficient, which is a pre-set constant coefficient, and 0 < ξ < 1.

[0039] Furthermore, step S3 is specifically as follows:

[0040] A constant-mode sequence based on phase optimization is selected to constrain the radar transmitted signal s to constant mode:

[0041] |s i |=1,i=1,2,…N

[0042] Among them, s i This represents the i-th element of the transmitted signal.

[0043] Using the phase sequence z of the spectral template as an auxiliary variable, constant modulus constraint is applied:

[0044] |z l |=1,l=1,2,…,MN

[0045] Then, power constraints are applied to the mismatched filter w:

[0046]

[0047] Where ||·||2 represents taking the 2-norm, This represents the square root operator.

[0048] The optimization problem model is then established as follows:

[0049]

[0050] Furthermore, step S4 is specifically as follows:

[0051] S41, the problem It can be broken down into three independent sub-problems;

[0052] Alternating optimization of s, w, and z, the three sub-problems in the (u+1)th iteration optimization process are as follows:

[0053]

[0054]

[0055]

[0056] Among them, s (u) w (u) z (u) Let s, w, and z represent the result of the u-th optimization, where z is the result of the optimization. l(u) Indicate z (u) The l-th element of the optimization result.

[0057] S42, fixed w (u) z (u) Solving the problem Find s (u+1) :

[0058] The temporal template matching part can be approximated as:

[0059]

[0060] in,

[0061]

[0062]

[0063] β k =p|r kt | p-1 -2α k |r kt |

[0064]

[0065] in,(·) p This represents finding the power of p; λ max (A w ) is matrix A w The largest eigenvalue; const represents a pre-defined constant. x (u) =Ts (u) ,(·) * This represents the transpose operator. I N Represents an N-order identity matrix. Represents the real number field.

[0066] The frequency domain template matching part can then be approximated as:

[0067]

[0068] Among them, z (u)l Let represent the l-th element of the result of the u-th optimization of z, and:

[0069] d = c + 2(H - λ) max (H)I N )s

[0070]

[0071]

[0072]

[0073] δ l =p|y lt | p-1 -2γ l |y lt |

[0074]

[0075] Among them, y l =y l (s),

[0076] Merge the frequency domain and time domain template matching error functions:

[0077]

[0078] Subproblem This can be equivalent to:

[0079]

[0080] st|s i |=1,i=1,2,…,N

[0081] Where g = ξb + (1 - ξ)d; then we can obtain:

[0082] s = e jarg(-g)

[0083] That is, s (u+1) , where arg(·) represents the calculation of phase.

[0084] S43, Fixed S (u+1) z (u) Solving subproblems Request w (u+1) ;

[0085] Subproblems The objective function can be approximated as:

[0086]

[0087] in,

[0088]

[0089]

[0090]

[0091]

[0092] in, λ max (A s ) represents matrix A s The largest eigenvalue.

[0093] Subproblem This can be equivalent to:

[0094]

[0095]

[0096] We can obtain:

[0097]

[0098] That is, w (u+1) .

[0099] S44, Fixed S (u+1) w (u+1) Solving subproblems Find z (u+1) ;

[0100] Subproblems The objective function can be approximated as:

[0101]

[0102] in,

[0103]

[0104] ρ l =p|z lt | p-1 -2η l |z lt |

[0105] in, Indicate z l . conjugate.

[0106] Subproblem Can be written as:

[0107]

[0108] st|z l |=1,l=1,2,…,MN

[0109] in,

[0110]

[0111] Subproblem It can be equivalent to:

[0112]

[0113] st|z l |=1,l=1,2,…,MN

[0114] in,

[0115] q = [q1, q2, ..., q l ,...,q MN ] H

[0116] We can obtain:

[0117] z = e jarg(-q)

[0118] That is, z (u+1) .

[0119] Finally, the three subproblems in step S4 are solved iteratively until the convergence condition ||f(s) is met. (u+1) ,w (u+1) ,z (u+1) )-f(s (u) ,w (u) ,z (u) Until ||≤ε, output the optimized results s and w, transmit broadband radar signals, and receive and process radar echo signals.

[0120] Where ε represents a pre-defined constant.

[0121] The beneficial effects of this invention are as follows: The method of this invention first obtains the radar transmitted signal and the corresponding design requirements of the mismatch filter, designs the objective function of the broadband radar waveform optimization problem, then establishes a broadband radar waveform constraint model and an optimization problem model, and finally uses the MM algorithm to solve the optimization problem and output the optimization result. This invention's method accumulates the energy of a range-extended target exhibiting multiple scattering point characteristics into a single envelope, improving the signal-to-noise ratio of the processed range-extended target. The designed signal is a phase-coded signal; due to its phase agility characteristics, it can more effectively improve the signal's anti-sorting capability compared to the continuous phase of a linear frequency modulated signal, while ensuring low intercept performance of the radar transmitted signal while also considering target detection capability. Attached Figure Description

[0122] Figure 1 This is a flowchart of a broadband radar target energy accumulation method based on a transceiver joint design according to the present invention.

[0123] Figure 2 This is a flowchart illustrating the optimization problem-solving process in an embodiment of the present invention.

[0124] Figure 3 The phase codeword for the transmitted signal designed according to the method of the present invention in this embodiment of the invention.

[0125] Figure 4 The graphs show the autocorrelation function of the transmitted signal and the cross-correlation function between the transmitted signal and the mismatch filter designed according to the method of the present invention in this embodiment.

[0126] Figure 5This is a frequency domain comparison diagram of the transmitted signal and the 50MHz bandwidth phase-coded signal designed by the method of the present invention in an embodiment of the present invention.

[0127] Figure 6 This is a schematic diagram of the RCS distribution of each scattering point of the target in an embodiment of the present invention.

[0128] Figure 7 This is a simulation result diagram of target accumulation at multiple scattering points within a pulse, as shown in this embodiment of the invention.

[0129] Figure 8 The images shown are the MTD result diagram and the XY plane projection diagram of the matched filter in this embodiment of the invention.

[0130] Figure 9 The diagram shows the mismatched filtering MTD result and the XY plane projection diagram in this embodiment of the invention. Detailed Implementation

[0131] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0132] like Figure 1 The flowchart of a broadband radar target energy accumulation method based on transceiver joint design of the present invention is shown below. The specific steps are as follows:

[0133] S1. Design requirements for acquiring radar transmission signals and corresponding mismatched filters;

[0134] S2. Design the objective function for the broadband radar waveform optimization problem;

[0135] S3. Based on step S2, establish a broadband radar waveform constraint model and an optimization problem model;

[0136] S4. Solve the optimization problem using the MM algorithm and output the optimization results.

[0137] In this embodiment, step S1 is specifically as follows:

[0138] Let s(t) be a wideband signal with bandwidth B and time width τ, where t represents time; the discrete form of a radar transmitted signal with length N is... Length is Mismatched filter

[0139] in,(·) T This represents the transpose operator. Represents the field of complex numbers, s N , Represent the Nth and Nth elements of s and w, respectively. 1 element, and

[0140] In this embodiment, step S2 is specifically as follows:

[0141] S21. Establish the temporal template matching error function:

[0142] The temporal template matching error function is expressed as:

[0143]

[0144] Where Σ represents the summation operator, (·) p This indicates raising the value to the power of p, and |·| represents the modulo operator. Template for representing cross-correlation function The k-th element, r k (s,w) represents the k-th element of the cross-correlation function r(s,w) of s and w, as follows:

[0145]

[0146] in,(·) H This represents the conjugate transpose operator, and Represents the real number field, I N J represents an N-order identity matrix, and 0 represents a 0 matrix of appropriate size; k The shift matrix is ​​represented as follows:

[0147]

[0148] Among them, J k (m,n) represents matrix J k The element in the m-th row and n-th column.

[0149] S22. Establish the frequency domain template matching error function;

[0150] The frequency domain template matching error function is expressed as:

[0151]

[0152] Among them, y l (s), z l Let y(s) represent the signal spectrum sequence that has been oversampled by M times, and spectral template be respectively. The l-th element of the phase sequence z of the spectral template, where l = 1, 2, ..., MN, and z is also an introduced auxiliary variable.

[0153] y(s) is specifically represented as:

[0154]

[0155] Wherein, matrix P is an MN×N dimensional matrix, specifically represented as:

[0156]

[0157] It is a Fourier matrix, f l The l-th column vector of matrix F is shown below:

[0158]

[0159] set up Then we can obtain:

[0160]

[0161] in, S23. Establish the objective function for the optimization problem;

[0162] From steps S21 and S22, we know that the objective function of the optimization problem can be written as:

[0163]

[0164] Where ξ represents the frequency domain and time domain weighting coefficient, which is a pre-set constant coefficient, and 0 < ξ < 1.

[0165] In this embodiment, step S3 is specifically as follows:

[0166] A constant-mode sequence based on phase optimization is selected to constrain the radar transmitted signal s to constant mode:

[0167] |s i |=1,i=1,2,…N

[0168] Among them, s i This represents the i-th element of the transmitted signal.

[0169] Using the phase sequence z of the spectral template as an auxiliary variable, constant modulus constraint is applied:

[0170] |z l |=1,l=1,2,…,MN

[0171] The sequence z here is a phase sequence, which is an auxiliary variable, so it is a constant modulus sequence.

[0172] Then, power constraints are applied to the mismatched filter w:

[0173]

[0174] Where ||·||2 represents taking the 2-norm, This represents the square root operator.

[0175] The optimization problem model is then established as follows:

[0176]

[0177] like Figure 2 As shown, in this embodiment, step S4 is specifically as follows:

[0178] S41, the problem It can be broken down into three independent sub-problems;

[0179] Alternating optimization of s, w, and z, the three sub-problems in the (u+1)th iteration optimization process are as follows:

[0180]

[0181]

[0182]

[0183] Among them, s (u) w (u) z (u) Let s, w, and z represent the result of the u-th optimization, where z is the result of the optimization. l(u) Indicate z (u) The l-th element of the optimization result.

[0184] S42, fixed w (u) z (u) Solving the problem Find s (u+1) :

[0185] The temporal template matching part can be approximated as:

[0186]

[0187] in,

[0188]

[0189]

[0190] β k =p|r kt | p-1 -2α k |r kt |

[0191]

[0192] in,(·) p This represents finding the power of p; λ max (A w ) is matrix A w The largest eigenvalue; const represents a pre-defined constant. x (u) =Ts (u) ,(·) * This represents the transpose operator. I N Represents an N-order identity matrix. Represents the real number field.

[0193] The frequency domain template matching part can then be approximated as:

[0194]

[0195] Among them, z (u)l Let represent the l-th element of the result of the u-th optimization of z, and:

[0196] d = c + 2(H - λ) max (H)I N )s (u)

[0197]

[0198]

[0199]

[0200] δ l =p|y lt | p-1 -2γ l |y lt |

[0201]

[0202] Among them, y l =y l (s), ||·|| p This indicates that we are looking for the p-norm.

[0203] Merge the frequency domain and time domain template matching error functions:

[0204]

[0205] Subproblem This can be equivalent to:

[0206]

[0207] st|s i |=1,i=1,2,…,N

[0208] Where g = ξb + (1 - ξ)d; then we can obtain:

[0209] s = e jarg(-g )

[0210] That is, s (u+1) , where arg(·) represents the calculation of phase.

[0211] S43, Fixed S (u+1) z (u) Solving subproblems Request w (u+1) ;

[0212] Subproblems The objective function can be approximated as:

[0213]

[0214] in,

[0215]

[0216]

[0217]

[0218]

[0219] in, λ max (A s ) represents matrix A s The largest eigenvalue.

[0220] Subproblem This can be equivalent to:

[0221]

[0222]

[0223] We can obtain:

[0224]

[0225] That is, w (u+1) .

[0226] S44, Fixed S (u+1) w (u+1) Solving subproblems Find z (u+1) ;

[0227] Subproblems The objective function can be approximated as:

[0228]

[0229] in,

[0230]

[0231] ρ l =p|z lt | p-1 -2η l |z lt |

[0232] in, Indicate z l . conjugate.

[0233] Subproblem Can be written as:

[0234]

[0235] st|z l |=1,l=1,2,…,MN

[0236] in,

[0237]

[0238] Subproblem It can be equivalent to:

[0239]

[0240] st|z l |=1,l=1,2,…,MN

[0241] in,

[0242] q = [q1, q2, ..., q l ,...,q MN ] H

[0243] We can obtain:

[0244] z = e jarg(-q)

[0245] That is, z (u+1) .

[0246] Finally, the three subproblems in step S4 are solved iteratively until the convergence condition ||f(s) is met. (u+1) ,w (u+1) ,z (u+1) )-f(s (u) ,w (u) ,z (u) Until ||≤ε, output the optimized results s and w, transmit broadband radar signals, receive and process radar echo signals, where ε represents a pre-set constant.

[0247] This embodiment further illustrates the invention through the following simulation.

[0248] like Figure 3 , 4 As shown in Figure 5, this embodiment verifies the feasibility of the joint design method of intra-pulse waveform and mismatch filter through broadband low intercept waveform design, as detailed below:

[0249] The design signal bandwidth is B = 50MHz, pulse width τ = 4μs, and the main lobe is widened by 5 times.

[0250] from Figure 3 It can be seen that the phase codeword of the transmitted signal designed by the method of this invention has pseudo-random and agile characteristics, which can increase the difficulty of enemy sorting and identification, thereby improving the low-interception capability of broadband waveforms. From Figure 4 It can be seen that compared to phase-coded waveforms of the same bandwidth, the waveform designed by the method of this invention has a wider main lobe width, i.e., lower range resolution, and better ability to accumulate extended target energy; at the same time, the SNR loss after mismatch filter processing is nearly 2dB. From Figure 5 It can be seen that the spectrum of the waveform designed by the method of the present invention matches the spectrum of the 50MHz random phase-coded waveform, and the bandwidth is close to 50MHz.

[0251] like Figure 6 , 7 As shown in the figure, this embodiment simulates the accumulation of targets at multiple scattering points within a pulse, as detailed below:

[0252] The broadband radar signal has a bandwidth of B = 50MHz, a transmit pulse duration of τ = 4μs, and is a phase-coded signal with an amplitude of 1. The signal sampling frequency f... s =2GHz. The noise level is set to Gaussian white noise with a mean of 0 and a power of 1. The radar carrier frequency is f. c =10GHz.

[0253] Set the target echo signal-to-noise ratio (SNR) r =5dB, the target has 16 scattering points, such as Figure 6 As shown, the distance between each scattering point is 1.2m, with strong scattering points at 10000m, 10006m, 10012m, and 10018m, all with an RCS of 0.8m. 2 The sum of the areas of these four scattering points accounts for 60% of the total RCS of the range-extended target; the areas of the other scattering points are random, and their sum accounts for 40% of the total RCS of the range-extended target; the target echo signal-to-noise ratio (SNR) r =5dB.

[0254] from Figure 7It can be seen that the pulse compression result obtained through mismatch filtering has only one envelope at the target, while the pulse compression result obtained through matched filtering has four peaks at the target. Calculations show that the signal-to-noise ratio (SNR) of the pulse compression result obtained through matched filtering is 25.2 dB, while that obtained through mismatch filtering is 33.4 dB. The results indicate that, compared to wideband waveform matched filtering, the wideband waveform and mismatch filter designed in this invention can accumulate the target energy into a single detection peak.

[0255] like Figure 6 , 8 As shown in Figure 9, this embodiment simulates the accumulation of targets at multiple scattering points between pulses, as detailed below:

[0256] The transmitted signal is a linear frequency modulated signal with a bandwidth B = 50MHz, a pulse width τ = 4μs, and an amplitude of 1. The signal sampling frequency f... s =2GHz. The noise level is set to Gaussian white noise with a mean of 0 and a power of 1. The radar carrier frequency is f. c =10GHz. The number of pulses is 128.

[0257] Set the target echo signal-to-noise ratio (SNR) r =5dB, the target has 16 scattering points, such as Figure 6 As shown, the distance between each scattering point is 1.2m, with strong scattering points at 10000m, 10006m, 10012m, and 10018m, all with an RCS of 0.8m. 2 The sum of the areas of these four scattering points accounts for 60% of the total RCS of the range-extended target; the areas of the other scattering points are random, and their sum accounts for 40% of the total RCS of the range-extended target; the target echo signal-to-noise ratio (SNR) r =5dB.

[0258] from Figure 8 (a) Figure 8 (b) It can be seen that the target echo signal-to-noise ratio (SNR) is... r In the case of 5dB, the multi-pulse matched filter MTD result shows four obvious spikes at the target location; from Figure 9 (a) Figure 8 (b) It can be seen that the multi-pulse matched filter (MTD) result contains only one envelope at the target location. Therefore, the mismatch filter proposed in this invention does not affect the inter-pulse Doppler phase characteristics of the target, and thus can also achieve the accumulation of multiple pulses.

[0259] In summary, addressing the issue of existing broadband radars having excellent low-intercept performance but poor target detection capability, the method of this invention reduces the range resolution of the broadband radar signal by designing a mismatch filter between the transmitted waveform and the received waveform. This concentrates the energy of range-extended targets, thus ensuring both low-intercept performance of the radar transmitted signal and target detection capability. The method of this invention accumulates the energy of range-extended targets exhibiting multiple scattering point characteristics into a single envelope, improving the signal-to-noise ratio of the processed range-extended targets. The designed signal is a phase-coded signal, whose phase agility, compared to the continuous phase of a linear frequency modulated signal, more effectively enhances the signal's anti-sorting capability.

[0260] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A broadband radar target energy accumulation method based on transceiver joint design, the specific steps of which are as follows: S1. Design requirements for acquiring radar transmission signals and corresponding mismatched filters; S2. Design the objective function for the broadband radar waveform optimization problem; S3. Based on step S2, establish a broadband radar waveform constraint model and an optimization problem model; S4. Solve the optimization problem using the MM algorithm and output the optimization results; The specific steps of S1 are as follows: Set a bandwidth as Time width is The broadband signal is , Indicates time; length is The discrete form of the radar transmitted signal is ; length is Mismatched filter ; in, This represents the transpose operator. Represents the field of complex numbers. , They represent and The The and the first 1 element, and ; Step S2 is as follows: S21. Establish the temporal template matching error function: The temporal template matching error function is expressed as: ； in, This represents the summation operator. This means to find the power of p. This represents the modulo operator. Template for representing cross-correlation function The kth element, express cross-correlation function The The elements are as follows: ； in, This represents the conjugate transpose operator, and , , Represents the real number field. Represents an N-order identity matrix. Represents a 0 matrix of appropriate size; The shift matrix is ​​represented as follows: ； in, Representation matrix The Okay, number Column elements; S22. Establish the frequency domain modulus matching error function; The frequency domain template matching error function is expressed as: ； in, , , These represent the signal spectrum sequences that have been oversampled by M times. Spectrum template Spectrum template phase sequence The l-th element, and , Auxiliary variables introduced; Specifically, it is expressed as follows: ； in, The matrix is A 3D matrix, specifically represented as: ； It is a Fourier matrix. Representation matrix The Column vectors, specifically as follows: ； set up Then we can obtain: ； in, ; S23. Establish the objective function for the optimization problem; From steps S21 and S22, we can see that the objective function for the optimization problem is written as follows: ； in, The frequency-domain and time-domain weighting coefficients are pre-set constant coefficients, and .

2. The broadband radar target energy accumulation method based on transceiver joint design according to claim 1, characterized in that, Step S3 is as follows: Select a constant mode sequence based on phase optimization for the radar transmitted signal. Apply constant modulus constraints: ； in, The number of transmitted signals One element; Spectrum template phase sequence As an auxiliary variable, constant modulus constraints are applied: ； Then the mismatch filter Apply power constraints: ； in, This indicates taking the 2-norm. Represents the square root operator; The optimization problem model is then established as follows: 。 3. The broadband radar target energy accumulation method based on transceiver joint design according to claim 2, characterized in that, Step S4 is as follows: S41, the problem It can be broken down into three independent sub-problems; right , , Perform alternating optimization, in the first... The three sub-problems in the next iteration of optimization are as follows: ； ； ； in, , , express , , No. The result of the second optimization express The optimization result of the first One element; S42, Fixed , Solving the problem beg : The temporal template matching part is approximated as: ； in, ； ； ； ； in, This means to find the power of p. It is a matrix The largest eigenvalue; This represents a pre-defined constant. , , , This represents the transpose operator. , Represents an N-order identity matrix. Represents the real number field; The frequency domain template matching part is then approximated as: ； in, express No. The result of the optimization is the first There are elements, and: ； ； ； ； ； ； in, , , , ; Merge the frequency domain and time domain template matching error functions: ； Subproblem Equivalent to: ； in, Then we can obtain: ； That is ,in, Indicates the calculation of phase; S43, Fixed , Solving subproblems beg ; Subproblems The objective function is approximated as: ； in, ； ； ； ； in, , , , Representation matrix The largest eigenvalue; Subproblem Equivalent to: ； We can obtain: ； That is ; S44, Fixed , Solving subproblems beg ; Subproblems The objective function is approximated as: ； in, ； ； in, , express Conjugate; Subproblem writing: ； in, ； Subproblem Equivalent to: ； in, ； We can obtain: ； That is ; Finally, the three subproblems in step S4 are solved iteratively until the convergence condition is met. Output the optimization results. , It transmits broadband radar signals and receives and processes radar echo signals. in, This represents a pre-defined constant.

Images