A Doppler spread compensation method for nonlinear FDA-MIMO radar

Abstract

The present invention discloses a Doppler spread compensation method for a nonlinear FDA-MIMO radar, which belongs to the field of radar signal processing technology. The present invention comprises: constructing a transmitting end array and a receiving end array of a nonlinear frequency-shifted FDA-MIMO radar; calculating the array element transmission signal of the transmitting end array according to a preset frequency increment; and then obtaining the target echo signal of the receiving end array, and obtaining the signal data after pulse compression, and searching for the target speed, performing Doppler spread compensation on the signal data according to the obtained target speed, and then performing target detection. The present invention avoids the problem that the traditional method requires that the carrier frequencies between the array elements of the FDA-MIMO radar cannot differ too much, and realizes the Doppler spread compensation of the nonlinear frequency-shifted FDA-MIMO radar by using a speed search method. Compared with the resampling algorithm based on interpolation filtering, the present invention can more accurately compensate for the Doppler offset of each array element, realize coherent accumulation between array elements, and enable the nonlinear frequency-shifted FDA-MIMO radar to have the ability to detect moving targets under low signal-to-noise ratio conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal processing, and in particular to a nonlinear FDA-MIMO (Frequency Diverse Array-Multiple Input Multiple Output) radar Doppler spread compensation method. Background Art

[0002] The concept of a frequency diversity array (FDA) was first proposed by Antonik and Wicks. This array primarily achieves new system functions by adjusting the carrier frequency differences between array elements. The multi-carrier signals transmitted by a frequency diversity array offer new advantages for target detection and parameter estimation.

[0003] Multiple-Input Multiple-Output (MIMO) technology leverages the advantages of frequency diversity arrays in transmitting multiple carrier signals, enabling precise separation of the transmitted steering vectors at the receiving end. Therefore, the two technologies are often combined to form FDA-MIMO radars.

[0004] For frequency-steering array radars, due to the varying carrier frequencies between array elements, coherent accumulation of signal energy cannot be achieved within a single radar CPI (Coherent Processing Interval). To address this issue, a resampling algorithm based on interpolation filtering can be used to eliminate the Doppler spread caused by frequency offset in FDA-MIMO radar echoes from moving targets. However, this method cannot effectively compensate for Doppler spread when using a frequency-steering array radar with nonlinear frequency offset. Summary of the Invention

[0005] In view of the deficiencies in the prior art, the present invention provides a nonlinear FDA-MIMO radar Doppler spread compensation method.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0007] A nonlinear FDA-MIMO radar Doppler spread compensation method includes the following steps:

[0008] Step S1, constructing a transmitting end array and a receiving end array of a nonlinear frequency offset FDA-MIMO radar;

[0009] Step S2, calculating the element transmission signal of the transmitting end array in step S1 according to the preset frequency increment;

[0010] Step S3: obtaining the target echo signal of the receiving end array according to the array element transmission signal in step S2, and obtaining the signal data after pulse compression;

[0011] Step S4, searching for the target speed according to the signal data obtained in step S3;

[0012] Step S5: Doppler spread compensation is performed on the signal data of step S3 according to the target speed obtained in step S4, and target detection is performed using CFAR (Constant False Alarm Rate) technology.

[0013] Furthermore, step S1 is specifically as follows:

[0014] Preset the number of array elements at the transmitter and receiver of the FDA-MIMO radar, and set the array element spacing between the transmitter and receiver elements according to the center frequency of the transmitted signal:

[0015]

[0016] Among them, d T is the distance between transmitting elements, d R is the receiving array element spacing, wavelength f0 is the center frequency of the transmitted signal, and c is the speed of light.

[0017] Furthermore, step S2 specifically includes:

[0018] S21. Calculate the carrier frequency of each transmitting element of the transmitting array according to the preset frequency offset Δf:

[0019] f m =f0+m 2 Δf

[0020] Among them, f m is the carrier frequency of the mth element in the transmitting array, Δf is the frequency deviation, and m = 0, ..., M T -1,M T is the total number of elements in the transmitting array;

[0021] S22, according to the array element carrier frequency f of each transmitting array element m Calculate the transmitted signal of the transmitting array element:

[0022] s m (t) = φ m (t)exp(j2πf m t)

[0023] Among them, s m (t) is the transmission signal of the mth array element at the transmitting end, φ m(t) is the baseband signal transmitted by the mth array element at the transmitting end, and its expression is:

[0024]

[0025] Where j is an imaginary number, π is a constant, t is a time variable, B is the bandwidth of the transmitted baseband signal, T p is the pulse width, Indicates pulse width is T p rectangular pulse.

[0026] Furthermore, step S3 specifically includes:

[0027] Step S31: Calculate the target echo signal y of the nth receiving element according to the array element transmission signal n (t):

[0028] y n (t) = (F(t-τ) r )⊙A t (θ)⊙A r (θ) T V(v)Ψ(t)

[0029] Where n = 0, ..., M R -1,M R is the total number of elements in the receiving array, τ r is the time delay of the radiation signal from the transmitting array element to the receiving array element after being reflected by the target, θ is the azimuth angle of the target, Ψ(t) represents the echo envelope vector, and ⊙ represents the Hadamard product;

[0030] F(t) is the vector composed of the array element carrier frequency of the transmitting array element, and its expression is:

[0031] F(t)=[exp(j2πf0t)exp(j2πf1t)…exp(j2πf M-1 t)] T

[0032] A t (θ) represents the transmitting array steering vector, which is expressed as:

[0033]

[0034] A r represents the receiving array steering vector, which is expressed as:

[0035]

[0036] V(v) represents the coupling matrix between the carrier frequency of the transmitting array element and the target velocity, and its expression is:

[0037]

[0038] Where v is the target speed, T pr is the pulse repetition interval, K is the number of pulses;

[0039] S32, target echo signal y n (t) performing multi-channel frequency mixing and pulse compression to obtain an echo signal after pulse compression;

[0040] Furthermore, step S4 specifically includes:

[0041] S41. Take out the output vector of the mth channel of the nth receiving array element after being processed by the receiver within one coherent processing time:

[0042]

[0043] Among them, A nm (θ) represents the joint guidance vector of the transmitting and receiving arrays, r represents the target distance, k represents the pulse number, It represents the signal data after the transmitted signal pulse is compressed, and its expression is:

[0044]

[0045] Step S42: Set the compensation function to:

[0046]

[0047] Among them, v s Indicates the speed to be searched;

[0048] Step S43: According to the formula Predict target speed, where represents target velocity estimation, FT[·] represents fast Fourier transform, and |·| represents modulo.

[0049] Furthermore, step S5 is specifically as follows:

[0050] Step S51: Estimate the target speed Substitute into the compensation function to get the compensation value Combine it with the result obtained in step S41 Multiply them to get the signal data after Doppler spread compensation;

[0051] Step S52: Perform fast Fourier transform along the slow time dimension on the Doppler spread compensated signal data obtained in step S51 to achieve coherent accumulation; then perform target detection on the coherent accumulation results based on CFAR (constant false alarm rate) technology.

[0052] The technical solution provided by the present invention brings at least the following beneficial effects:

[0053] This invention overcomes the traditional requirement that carrier frequencies between FDA-MIMO radar elements must not differ significantly. Instead, it utilizes a velocity search approach to achieve Doppler spread compensation for nonlinear frequency-shifted FDA-MIMO radars. Compared to resampling algorithms based on interpolation filtering, this invention can more accurately compensate for the Doppler shift of each element, achieving coherent accumulation between elements. This enables nonlinear frequency-shifted FDA-MIMO radars to detect moving targets even under low signal-to-noise ratio conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0055] Figure 1 A processing flow chart of a nonlinear FDA-MIMO radar Doppler spread compensation method provided by an embodiment of the present invention;

[0056] Figure 2 A schematic diagram of the FDA-MIMO radar structure provided in an embodiment of the present invention;

[0057] Figure 3 A schematic diagram of the structure of an FDA-MIMO radar receiver provided in an embodiment of the present invention;

[0058] Figure 4 This is a signal-to-noise ratio-detection probability curve provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0059] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0060] like Figure 1 As shown, an embodiment of the present invention provides a nonlinear FDA-MIMO radar Doppler spread compensation method, comprising the following steps:

[0061] Step S1, constructing a transmitting end array and a receiving end array of a nonlinear frequency offset FDA-MIMO radar;

[0062] In this embodiment, step S1 is specifically as follows:

[0063] The number of array elements in the transmitting and receiving ends of the FDA-MIMO radar is preset, and the array element spacing between the transmitting and receiving elements is set according to the center frequency of the transmitted signal. The array element spacing is expressed as:

[0064]

[0065] Among them, d T is the distance between transmitting elements, d R is the receiving array element spacing, wavelength f0 is the center frequency of the transmitted signal, and c is the speed of light.

[0066] In practice, the FDA-MIMO radar structure is obtained by constructing the transmitting end array and the receiving end array of the FDA-MIMO radar, such as Figure 2 shown.

[0067] Step S2, calculating the element transmission signal of the transmitting end array in step S1 according to the preset frequency increment;

[0068] In the embodiment of the present invention, step S2 specifically includes the following sub-steps:

[0069] Step S21: Calculate the element carrier frequency of the transmitting array in step S1 according to the preset frequency offset Δf. The calculation formula is expressed as:

[0070] f m =f0+m 2 Δf

[0071] Among them, f m is the carrier frequency of the mth element in the transmitting array, and m=0,…,M T -1,M T represents the total number of elements in the transmitting array, Δf is the frequency deviation;

[0072] Step S22: Calculate the transmitting signal of the transmitting element according to the array element carrier frequency in step S21. The calculation formula is expressed as:

[0073] s m (t) = φ m (t)exp(j2πf m t)

[0074] Among them, s m (t) is the transmission signal of the mth array element at the transmitting end, φ m (t) is the baseband signal transmitted by the mth array element at the transmitting end, and its expression is:

[0075]

[0076] Where j is an imaginary number, π is a constant, t is a time variable, and B is the bandwidth of the transmitted baseband signal. Indicates pulse width is T p rectangular pulse.

[0077] In practice, the signal transmitted by each transmitting element is a pulse train signal with a pulse repetition period of T pr.

[0078] Step S3: obtaining the target echo signal of the receiving end array according to the array element transmission signal in step S2, and obtaining the signal data after pulse compression;

[0079] In the embodiment of the present invention, step S3 specifically includes the following sub-steps:

[0080] Step S31: Calculate the target echo signal of the nth receiving element according to the element transmission signal in step S2, expressed as:

[0081] y n (t) = (F(t-2τ) r )⊙A t (θ)⊙A r (θ) T V(v)Ψ(t)

[0082] Among them, τ r is the time delay of the radiation signal from the transmitting array element to the receiving array element after being reflected by the target, θ is the azimuth angle of the target, and F(t) is the vector composed of the transmitting carrier frequency. Its expression is:

[0083]

[0084] Ψ(t) represents the echo envelope vector, A t (θ) represents the transmitting array steering vector, M T is the total number of transmitting array elements, and its expression is:

[0085]

[0086] A r (θ) represents the receiving array steering vector, M R is the total number of receiving array elements, and its expression is:

[0087]

[0088] V(v) represents the coupling matrix between the transmitting carrier frequency and the target speed, and its expression is:

[0089]

[0090] Where v represents the target speed, T pr represents the pulse repetition interval, K represents the number of pulses, and ⊙ represents the Hadamard product.

[0091] In practice, for a target with an azimuth angle of θ and a distance of r, which approaches the radar at a uniform radial speed of v, the echo signal received by the receiving array is calculated;

[0092] Step S32: performing multi-channel mixing and pulse compression on the target echo signal in step S31 to obtain a pulse-compressed echo signal;

[0093] In practice, the echo signal received by the receiver Perform multi-channel mixing and pulse compression to obtain the multi-channel processing signal corresponding to each receiving array element. For example, for the 0th receiving array element, the corresponding processing signal is The structure of the receiver is as follows: Figure 3 shown.

[0094] Step S4, searching for the target speed according to the signal data obtained in step S3;

[0095] In the embodiment of the present invention, step S4 specifically includes the following steps:

[0096] Step S41: Take out the output vector of the mth channel of the nth receiving array element after being processed by the receiver within one coherent processing time:

[0097]

[0098] Among them, k represents the pulse number, A nm (θ) represents the joint steering vector of the transmit and receive arrays, It represents the result of pulse compression of the transmitted signal, and its expression is:

[0099]

[0100] Step S42: Set the compensation function to:

[0101]

[0102] Among them, v s Indicates the speed to be searched;

[0103] Then multiply the compensation function by the result of step S41;

[0104] Step S43: Select the result of step S42, perform fast Fourier transform on it, and then take the frequency corresponding to the maximum value of the spectrum to calculate the predicted speed, that is, the target speed is expressed as:

[0105]

[0106] in, v s , FT[·] represents fast Fourier transform, and |·| represents modulo.

[0107] In practice, a one-dimensional search is generally used to determine the target speed, and the search accuracy is generally set to one percent of the search range.

[0108] Step S5: Target speed obtained in step S4 Doppler spread compensation is performed on the data of step S3, and target detection is performed using CFAR (Constant False Alarm Rate) technology;

[0109] In the embodiment of the present invention, step S5 is specifically as follows:

[0110] Step S51: Get the target speed from step S43 Substitute the result into the compensation function set in step S42 and multiply the result by the signal vector in step S41;

[0111] Step S52: Perform fast Fourier transform on the result of S51 along the slow time dimension to achieve coherent accumulation.

[0112] S53: Use CFAR to perform target detection on the result of step S52.

[0113] In practice, CA-CFAR (cell-averaged constant false alarm rate) is used as the specific detection method, where the protection unit length is set to 3 and the training unit length is set to 7.

[0114] In the embodiment of the present invention, further explanation is given by the following simulation experiment. The simulation parameters shown in Table 1 are preset, the spacing between the array elements of the transmitting and receiving arrays is preset to half a wavelength, and additive white Gaussian noise is added.

[0115] Table 1 Simulation parameters

[0116]

[0117] In the simulation experiment, the target speed is limited to 347.45m / s, the target distance is 20km, and the number of pulses is 512. The simulation results are as follows: Figure 4 As shown in the figure, since the frequency offset increases quadratically, it results in a significantly larger Doppler shift than a linear frequency offset. Using a resampling algorithm based on interpolation filtering makes it difficult to accurately compensate for each element. However, the method provided by the present invention can accurately compensate for the Doppler spread caused by nonlinear frequency offset. Compared to a resampling algorithm based on interpolation filtering, the method provided by the present invention can achieve accurate target detection under lower signal-to-noise ratio conditions.

[0118] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

[0119] The above are only some embodiments of the present invention. For those skilled in the art, several modifications and improvements can be made without departing from the inventive concept of the present invention, which all fall within the scope of protection of the present invention.

Claims

1. A nonlinear FDA-MIMO radar Doppler spread compensation method, characterized in that: The following steps are involved: Step S1, constructing a transmitting end array and a receiving end array of a nonlinear frequency offset FDA-MIMO radar; Step S2, calculating the element transmission signal of the transmitting end array in step S1 according to the preset frequency increment; Step S3: obtaining the target echo signal of the receiving end array according to the array element transmission signal in step S2, and obtaining the signal data after pulse compression; Step S4, searching for the target speed according to the signal data obtained in step S3; Step S5: Doppler spread compensation is performed on the signal data of step S3 according to the target speed obtained in step S4, and target detection is performed using a constant false alarm rate technique.

2. The method according to claim 1, wherein Step S1 is specifically as follows: Preset the number of array elements at the transmitter and receiver of the FDA-MIMO radar, and set the array element spacing between the transmitter and receiver elements according to the center frequency of the transmitted signal: Among them, d T is the distance between transmitting elements, d R is the receiving array element spacing, wavelength f0 is the center frequency of the transmitted signal, and c is the speed of light.

3. The method according to claim 1, wherein Step S2 specifically includes: S21. Calculate the carrier frequency of each transmitting element of the transmitting array according to the preset frequency offset Δf: f m =f0+m 2 Δf Among them, f m is the carrier frequency of the mth element in the transmitting array, Δf is the frequency deviation, and m = 0, ..., M T -1,M T is the total number of elements in the transmitting array; S22, according to the array element carrier frequency f of each transmitting array element m Calculate the transmitted signal of the transmitting array element: s m (t)=φ m (t)exp(j2πf m t) Among them, s m (t) is the transmission signal of the mth array element at the transmitting end, φ m (t) is the baseband signal transmitted by the mth array element at the transmitting end, and its expression is: Where j is an imaginary number, t is a time variable, B is the bandwidth of the transmitted baseband signal, T p is the pulse width, Indicates pulse width is T p rectangular pulse.

4. The method according to claim 3, wherein Step S3 specifically includes: Step S31: Calculate the target echo signal y of the nth receiving element according to the array element transmission signal n (t): y n (t)=(F(t-τ r )⊙A t (θ)⊙A r (i)) T V(v)Ψ(t) Where n = 0, ..., M R -1,M R is the total number of elements in the receiving array, τ r is the time delay of the radiation signal from the transmitting array element to the receiving array element after being reflected by the target, θ is the azimuth angle of the target, Ψ(t) represents the echo envelope vector, and ⊙ represents the Hadamard product; F(t) is the vector composed of the array element carrier frequency of the transmitting array element, and its expression is: A t (θ) represents the transmitting array steering vector, which is expressed as: Among them, d T is the distance between transmitting elements, d R is the receiving array element spacing, λ0 is the wavelength; A r represents the receiving array steering vector, which is expressed as: V(v) represents the coupling matrix between the carrier frequency of the transmitting array element and the target velocity, and its expression is: Where v is the target speed, T pr is the pulse repetition interval, K is the number of pulses; S32, target echo signal y n (t) Perform multi-channel mixing and pulse compression to obtain the echo signal after pulse compression.

5. The method according to claim 4, wherein Step S4 specifically includes: S41. Take out the output vector of the mth channel of the nth receiving array element after being processed by the receiver within one coherent processing time: Among them, A nm (θ) represents the joint guidance vector of the transmitting and receiving arrays, r represents the target distance, k represents the pulse number, It represents the signal data after the transmitted signal pulse is compressed, and its expression is: Step S42: Set the compensation function to: Among them, v s Indicates the speed to be searched; Step S43: According to the formula Predict target speed, where represents target velocity estimation, FT[·] represents fast Fourier transform, and |·| represents modulo.

6. The method according to claim 5, wherein Step S5 is specifically as follows: Step S51: Estimate the target speed Substitute into the compensation function to get the compensation value Combine it with the result obtained in step S41 Multiply them to get the signal data after Doppler spread compensation; Step S52: Perform fast Fourier transform along the slow time dimension on the Doppler spread compensated signal data obtained in step S51 to achieve coherent accumulation; and then perform target detection on the coherent accumulation results based on the constant false alarm rate technology.

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