A Method for Resolving Doppler Ambiguity Based on FDA-MIMO Radar

Abstract

The present invention relates to a method for resolving Doppler ambiguity based on FDA-MIMO radar. Aiming at the Doppler ambiguity problem of fast-moving targets in FDA-MIMO radar, a spread-spectrum phase alignment method is proposed, enabling point targets to be focused in the transmit spatial frequency domain. After compensating for the main velocity, the Doppler ambiguity index is estimated by the maximum likelihood method respectively under the conditions of known range ambiguity index and unknown range ambiguity index. The method of the present invention only uses one pulse repetition frequency, and the samples under different pulses are coherent, avoiding coherent processing, greatly improving the efficiency. Moreover, after using Doppler spread alignment, the power spectrum of high-speed targets is refocused, resolving the Doppler ambiguity and greatly enhancing the detection performance of high-speed moving targets.

Description

Technical Field

[0001] The present invention belongs to the technical field of FDA-MIMO radar, and particularly relates to a method for resolving Doppler ambiguity based on an FDA-MIMO radar. Background Art

[0002] In recent years, people have become increasingly interested in the detection of fast-moving targets. However, Doppler ambiguity caused by fast-moving targets is inevitable. For pulsed Doppler radar (PD), when resolving range ambiguity and Doppler ambiguity, there is a conflict in the selection of the pulse repetition frequency (PRF). Since the problem of range ambiguity is relatively difficult to handle, a relatively low PRF is generally selected, which will result in Doppler ambiguity. To handle Doppler ambiguity, multiple pulse repetition frequencies are often required, which makes the samples of different pulses non-coherent, increases the coherent processing time, and also increases the difficulty of subsequent signal processing.

[0003] In recent years, frequency diverse array (FDA) has been widely studied. The frequency diverse array combines FDA with MIMO technology by using a small frequency increment on the transmitting array elements and transmitting orthogonal waveforms. After using matched filtering to separate the transmitted waveforms, the degrees of freedom (DOF) in the range domain can be obtained. Therefore, FDA-MIMO can distinguish the range-ambiguous echoes caused by different equivalent pointing directions of the transmitting beam patterns corresponding to different pulses, because a range-related phase term is introduced between adjacent pulses.

[0004] However, in existing research, the difference in this phase difference between different pulse echoes has only received limited attention. The magnitude of the inter-pulse phase difference is related to the radial velocity of the moving target and the frequency offset. In the case of a slowly moving target or an insufficiently large frequency offset, this phase difference can usually be ignored. The coupling terms of velocity and frequency offset in the FDA-MIMO phase term are ignored. However, this is not negligible for high-speed moving targets and will result in losses in detection, positioning, and tracking performance. At the same time, in the frequency diverse array, for high-speed moving targets, Doppler ambiguity will occur, and the transmitted spatial frequency domain power spectrum becomes extended, affecting target detection and positioning performance. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a method for resolving Doppler ambiguity based on an FDA-MIMO radar. The technical problems to be solved by the present invention are realized through the following technical solutions:

[0006] The present invention provides a method for resolving Doppler ambiguity based on an FDA-MIMO radar, including:

[0007] Step 1: Obtain the target echo data of the FDA-MIMO radar;

[0008] Step 2: Perform Doppler spread spectrum alignment on the target echo data to obtain a vector after Doppler spread spectrum;

[0009] Step 3: Construct a velocity-dependent compensation vector in the transmit spatial frequency domain, and construct a compensation vector in the joint transmit-receive spatial frequency domain according to the velocity-dependent compensation vector;

[0010] Step 4: Perform velocity-dependent compensation on the vector after Doppler spread spectrum according to the compensation vector in the joint transmit-receive spatial frequency domain to obtain a Doppler ambiguity index vector;

[0011] Step 5: Construct a weight vector related to the Doppler ambiguity index according to the Doppler ambiguity index vector, and use the maximum likelihood criterion according to the weight vector and the Doppler ambiguity index vector to obtain an estimated value of the Doppler ambiguity index.

[0012] In an embodiment of the present invention, when the range ambiguity index is known, Step 2 includes:

[0013] Step 21: Construct a target range according to the range ambiguity index

[0014]

[0015] where r0 represents the principal value range determined by the range gate number and the range gate size, p represents the range ambiguity index, and R u represents the maximum unambiguous range;

[0016] Step 22: Construct a joint range-angle cancellation vector according to the target range

[0017]

[0018] where represents a priori known angle, represents the Kronecker product operation, represents the Hadamard product operation, represents the receive steering vector constructed according to the a priori angle, represents the transmit steering vector constructed according to the a priori range, represents the transmit steering vector constructed according to the a priori angle;

[0019] Step 23: Perform Doppler spread spectrum alignment operation on each pulse received signal of the target echo data according to the joint range-angle cancellation vector and obtain a vector x after Doppler spread spectrum after eliminating the remaining phase K-align ,

[0020]

[0021] Wherein, represents the received signal of the k-th pulse, k = 1, 2, …, K, where K represents the total number of pulses, () * represents the conjugate operation, E represents the total transmit power of the signal, M represents the number of transmit units of the FDA-MIMO radar, β0 represents the complex-valued coefficient of the target, j represents the imaginary unit, f0 represents the reference carrier frequency, τ0 represents the common envelope time delay, V represents the radial velocity of the target, c represents the speed of light, T r represents the pulse repetition interval, R0 represents the true target distance, θ0 represents the true angle, b(θ0) represents the true receive steering vector dependent on the angle, a K (R0, V, θ0) represents the true transmit steering vector of the target, x n represents the noise component of the pulse received signal.

[0022] In an embodiment of the present invention, when the range ambiguity index is known, step 3 includes:

[0023] Step 31: Construct a velocity-dependent compensation vector in the transmit spatial frequency domain as:

[0024]

[0025] Wherein, represents the prior known main velocity, Δf represents the frequency step introduced between the transmit array elements of the FDA-MIMO radar, and T represents the matrix transpose;

[0026] Step 32: Construct a compensation vector g in the joint transmit-receive spatial frequency domain according to the velocity-dependent compensation vector as: K as:

[0027]

[0028] Wherein, 1 N represents an N×1 vector all of whose elements are 1, and N represents the number of receive units of the FDA-MIMO radar.

[0029] In an embodiment of the present invention, when the range ambiguity index is known, step 4 includes:

[0030] Utilize the compensation vector g in the joint transmit-receive spatial frequency domain K , and perform velocity-dependent compensation on the Doppler-spread vector x K-align to obtain the Doppler ambiguity index vector xK-comp is:

[0031]

[0032] In the formula, V u represents the maximum unambiguous velocity, l represents the exponent of the Doppler ambiguity region, L max represents the number of ambiguous Dopplers, r(R0) represents the range-dependent true transmit steering vector, and d(θ0) represents the angle-dependent true transmit steering vector.

[0033] In one embodiment of the present invention, when the range ambiguity exponent is known, step 5 includes:

[0034] Step 51: According to the Doppler ambiguity exponent vector x K-comp , using data-independent beamforming or data-dependent beamforming, construct a corresponding weight vector related to the Doppler ambiguity exponent, and this weight vector is expressed as:

[0035]

[0036] or

[0037] In the formula, () -1 represents the inverse operation, and Q represents the positive definite covariance matrix of the noise component;

[0038] Step 5.2: According to the weight vector and the Doppler ambiguity exponent vector, calculate the estimated value of the Doppler ambiguity exponent according to the following formula:

[0039]

[0040] where represents the estimated value of the Doppler ambiguity exponent, and argmax() represents the independent variable value corresponding to the maximum value of the objective function.

[0041] In one embodiment of the present invention, when the range ambiguity exponent is unknown, step 2 includes:

[0042] Taking the th pulse received signal in the target echo data as a reference, perform Doppler spread spectrum alignment operations on each pulse received signal after the th pulse received signal in the target echo data, and obtain the vector after Doppler spread spectrum

[0043]

[0044]

[0045] In the formula, represents the Hadamard product operation, represents the Kronecker product operation, represents the received signal of the kth pulse, K represents the total number of pulses, () * represents the conjugate operation, E represents the total transmit signal power, M represents the number of transmit units of the FDA - MIMO radar, β0 represents the complex - valued coefficient of the target, j represents the imaginary unit, f0 represents the reference carrier frequency, τ0 represents the common envelope time delay, V represents the radial velocity of the target, c represents the speed of light, T r represents the pulse repetition interval, 1 N represents an N×1 vector of all 1s, N represents the number of receive units of the FDA - MIMO radar, represents the Doppler transmit steering vector of the target, x n represents the noise component of the pulse - received signal.

[0046] In an embodiment of the present invention, when the range ambiguity index is unknown, step 3 includes:

[0047] Step 31': Construct a velocity - dependent compensation vector in the transmit spatial frequency domain as:

[0048]

[0049] In the formula, represents the a priori known main velocity, Δf represents the frequency step introduced between the transmit - end elements of the FDA - MIMO radar, T represents matrix transpose;

[0050] Step 32: According to the velocity - dependent compensation vector construct a compensation vector in the joint transmit - receive spatial frequency domain as:

[0051]

[0052] In an embodiment of the present invention, when the range ambiguity index is unknown, step 4 includes:

[0053] Utilize the compensation vector in the joint transmit - receive spatial frequency domain to perform velocity - dependent compensation on the Doppler - spread vector to obtain the Doppler ambiguity index vector

[0054]

[0055] In the formula, V u represents the maximum unambiguous velocity, and l represents the exponent of the Doppler ambiguity region. L max represents the number of ambiguous Dopplers.

[0056] In an embodiment of the present invention, when the range ambiguity exponent is unknown, the step 5 includes:

[0057] Step 5.1': According to the Doppler ambiguity exponent vector using data-independent beamforming or data-dependent beamforming, a corresponding weight vector related to the Doppler ambiguity exponent is constructed, and this weight vector is expressed as:

[0058] or

[0059] where, () -1 represents the inverse operation, and Q represents the covariance matrix of the noise component;

[0060] Step 5.2': According to the weight vector and the Doppler ambiguity exponent vector, the estimated value of the Doppler ambiguity exponent is calculated according to the following formula as:

[0061]

[0062] where, represents the estimated value of the Doppler ambiguity exponent, and argmax() represents the independent variable value corresponding to the maximum value of the objective function.

[0063] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0064] The method for resolving Doppler ambiguity based on FDA-MIMO radar of the present invention, aiming at the Doppler ambiguity problem of fast moving targets of FDA-MIMO radar, proposes a spread spectrum phase alignment method, enabling point targets to be focused in the transmit spatial frequency domain. After compensating for the main velocity, in the cases of known and unknown range ambiguity exponents respectively, the Doppler ambiguity exponent is estimated by the maximum likelihood method. Compared with the need to increase the coherent processing time in the case of multiple pulse repetition frequencies, the method of the present invention only uses one pulse repetition frequency, so that the samples under different pulses are coherent, avoiding coherent processing, greatly improving the efficiency, and after using Doppler spread alignment, the power spectrum of high-speed targets is refocused, solving the Doppler ambiguity and greatly improving the detection performance of high-speed moving targets.

[0065] The above description is only an overview of the technical solution of the present invention. In order to understand the technical means of the present invention more clearly, it can be implemented according to the content of the specification. And in order to make the above and other purposes, features and advantages of the present invention more obvious and understandable, the following specific preferred embodiments are given and described in detail in conjunction with the accompanying drawings as follows. Description of the Drawings

[0066] Figure 1 is a schematic diagram of a method for resolving Doppler ambiguity based on an FDA-MIMO radar provided by an embodiment of the present invention;

[0067] Figures 2a - 2b is a distribution diagram of the target in the spatial frequency domain provided by an embodiment of the present invention;

[0068] Figures 3a - 3b is a spectrum distribution diagram of the received data provided by an embodiment of the present invention;

[0069] Figures 4a - 4b is a schematic diagram of Doppler spread alignment with a known range ambiguity index provided by an embodiment of the present invention;

[0070] Figures 5a - 5b is a schematic diagram of Doppler spread alignment with an unknown range ambiguity index provided by an embodiment of the present invention;

[0071] Figure 6 is a schematic diagram of the Doppler ambiguity index estimation result provided by an embodiment of the present invention;

[0072] Figures 7a - 7b is a schematic diagram of the relationship between the RMSE of the Doppler ambiguity index l and the signal-to-noise ratio and the number of pulses provided by an embodiment of the present invention;

[0073] Figures 8a - 8b is a schematic diagram of the comparison of the CRB at different Δf provided by an embodiment of the present invention. Detailed Embodiment

[0074] In order to further elaborate on the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following provides a detailed description of a method for resolving Doppler ambiguity based on an FDA-MIMO radar proposed according to the present invention in conjunction with the accompanying drawings and specific embodiments.

[0075] The foregoing and other technical contents, features and effects of the present invention can be clearly presented in the following detailed description in conjunction with the accompanying drawings. Through the description of the specific embodiments, a more in-depth and specific understanding of the technical means and effects adopted by the present invention to achieve the predetermined purpose can be obtained. However, the accompanying drawings are only for reference and illustration, and are not used to limit the technical solution of the present invention.

[0076] Embodiment 1

[0077] Please refer to Figure 1 , Figure 1 which is a schematic diagram of a method for resolving Doppler ambiguity based on an FDA-MIMO radar provided by an embodiment of the present invention. As shown in the figure, the method for resolving Doppler ambiguity based on an FDA-MIMO radar in this embodiment includes:

[0078] Step 1: Obtain the target echo data of the FDA-MIMO radar;

[0079] Step 2: Perform Doppler spread spectrum alignment on the target echo data to obtain a vector after Doppler spread spectrum;

[0080] Step 3: Construct a velocity-dependent compensation vector in the transmit spatial frequency domain, and based on the velocity-dependent compensation vector, construct a compensation vector in the joint transmit-receive spatial frequency domain;

[0081] Step 4: Perform velocity-dependent compensation on the vector after Doppler spread spectrum according to the compensation vector in the joint transmit-receive spatial frequency domain to obtain a Doppler ambiguity index vector;

[0082] Step 5: According to the Doppler ambiguity index vector, construct a weight vector related to the Doppler ambiguity index, and based on the weight vector and the Doppler ambiguity index vector, use the maximum likelihood criterion to obtain an estimated value of the Doppler ambiguity index.

[0083] The method for resolving Doppler ambiguity based on an FDA-MIMO radar in this embodiment proposes a spread spectrum phase alignment method for the Doppler ambiguity phenomenon that occurs in fast-moving targets, enables point targets to be focused in the transmit spatial frequency domain, and estimates the Doppler ambiguity index using the maximum likelihood criterion.

[0084] To facilitate the description of the method of the present invention, in this embodiment, a pulsed received signal under a Gaussian interference background is constructed by simulation as the target echo data of the FDA-MIMO radar. Taking the received signal of the k-th pulse of the FDA-MIMO radar as an example, the specific construction method is described as follows.

[0085] Step a: Set the FDA-MIMO radar to be composed of M transmit elements and N receive elements, and the element spacing is d, where M, N, and d are all greater than 0.

[0086] Step b: Since Doppler ambiguity will occur in high-speed moving targets, the radial velocity V of the target is constructed as:

[0087] V = V0 + (l - 1)V u (1),

[0088] In the formula, V0 is the main velocity of the target, and l represents the index of the Doppler ambiguity region,

[0089] L max is the number of ambiguous Dopplers, V u represents the maximum unambiguous velocity.

[0090] Step c: Construct the Doppler transmit steering vector v k (V) is:

[0091]

[0092] where Δf represents the frequency step introduced between the transmit array elements of the FDA - MIMO radar, T r represents the pulse repetition interval (PRI), T represents the transpose operation, and c represents the speed of light.

[0093] Step d: Respectively construct the angle - dependent transmit steering vector d(θ0) and the range - dependent transmit steering vector r(R0) as:

[0094]

[0095]

[0096] where λ0 represents the transmit wavelength, d T represents the element spacing of the transmit array, τ0 represents the common envelope time delay, and τ0 = 2R0 / c.

[0097] Step e: Construct the angle - dependent receive steering vector b(θ0) as:

[0098]

[0099] where d R represents the element spacing of the receive array.

[0100] Step f: Use r(R0), d(θ0) and v k (V) to construct the transmit steering vector of the fast - moving target of the FDA - MIMO radar as:

[0101]

[0102] where represents the Hadamard product operation.

[0103] Step g: Use the constructed transmit steering vector of the fast - moving target to construct the output of the nth receive array element in the kth pulse as:

[0104]

[0105] where Let \(E\) denote the total power of the transmitted signal, \(\beta_0\) be the complex-valued coefficient of the target, and \(f_0\) represent the reference carrier frequency.

[0106] Step h: Utilize the output of the \(n\)th receiving array element in the \(k\)th pulse constructed By stacking the outputs of \(N\) receiving array elements, the received signal of the \(k\)th pulse is obtained as:

[0107]

[0108] where \(T\) r denotes the pulse repetition interval (PRI), \(c\) represents the speed of light, denotes the Kronecker product operation.

[0109] Step i: Add the noise component to obtain the received signal in the \(k\)th pulse of the FDA - MIMO radar as where \(x\) n is the noise component with zero mean and positive definite covariance matrix \(Q\).

[0110] Furthermore, in this embodiment, after performing spread - spectrum phase alignment on the echo data through Steps 2 - 5, main velocity compensation is carried out, and then the Doppler ambiguity index is estimated by the maximum likelihood method.

[0111] The method for estimating the Doppler ambiguity index in this embodiment includes two cases: known range ambiguity index and unknown range ambiguity index.

[0112] In the case of a known range ambiguity index, Steps 2 - 5 are specifically described, where Step 2 includes:

[0113] Step 21: Construct the target range according to the range ambiguity index

[0114]

[0115] where \(r_0\) represents the principal value range determined by the range bin number and range bin size, \(p\) represents the range ambiguity index. Optionally, the range ambiguity index can be obtained through main range compensation, and \(R\) u represents the maximum unambiguous range;

[0116] Step 22: Construct the joint range - angle cancellation vector according to the target range as

[0117]

[0118] where represents the prior known angle, denotes the Kronecker product operation and denotes the Hadamard product operation, denotes the received steering vector constructed according to the prior angle, denotes the transmitted steering vector constructed according to the prior distance, denotes the transmitted steering vector constructed according to the prior angle;

[0119] Step 23: According to the joint distance-angle cancellation vector perform the Doppler spread alignment operation on each pulse received signal of the target echo data and obtain the vector x after Doppler spreading and eliminating the remaining phase K-align ,

[0120]

[0121] wherein, denotes the received signal of the k-th pulse, k = 1, 2,, K, and K denotes the total number of pulses, () * denotes the conjugate operation, E denotes the total transmitted signal power, M denotes the number of transmitting units of the FDA-MIMO radar, β0 denotes the complex-valued coefficient of the target, j denotes the imaginary unit, f0 denotes the reference carrier frequency, τ0 denotes the common envelope time delay, V denotes the radial velocity of the target, c denotes the speed of light, T r denotes the pulse repetition interval, R0 denotes the true target distance, θ0 denotes the true angle, b(θ0) denotes the true received steering vector dependent on the angle, a K (R0, V, θ0) denotes the true transmitted steering vector of the target, x n denotes the noise component of the pulse received signal.

[0122] When the range ambiguity index is known, Step 3 includes:

[0123] Step 31: Construct the velocity-dependent compensation vector in the transmitted spatial frequency domain as:

[0124]

[0125] wherein, denotes the prior known main velocity, Δf denotes the frequency step introduced between the transmitting array elements of the FDA-MIMO radar, and T denotes the matrix transpose;

[0126] Step 32: Construct the compensation vector g in the joint transmit-receive spatial frequency domain according to the velocity-dependent compensation vector as: K as:

[0127]

[0128] wherein, 1N Denote an N×1 dimensional vector consisting of all 1s, where N represents the number of receiving units of the FDA-MIMO radar.

[0129] When the range ambiguity index is known, step 4 includes:

[0130] Utilize the compensation vector g in the joint transmit-receive spatial frequency domain K , and perform velocity-dependent compensation on the vector x after Doppler spreading K-align to obtain the Doppler ambiguity index vector x K-comp which is:

[0131]

[0132] wherein, V u represents the maximum unambiguous velocity, l represents the index of the Doppler ambiguity zone, L max represents the number of ambiguous Dopplers, r(R0) represents the true transmit steering vector dependent on range, and d(θ0) represents the true transmit steering vector dependent on angle.

[0133] When the range ambiguity index is known, step 5 includes:

[0134] Step 51: According to the Doppler ambiguity index vector x K-comp , utilize data-independent beamforming or data-dependent beamforming to construct the corresponding weight vector related to the Doppler ambiguity index, and this weight vector is expressed as:

[0135]

[0136] or

[0137] wherein, () -1 represents the inverse operation, and Q represents the positive definite covariance matrix of the noise component;

[0138] Step 5.2: According to the weight vector and the Doppler ambiguity index vector, calculate the estimated value of the Doppler ambiguity index according to the following formula as:

[0139]

[0140] wherein, represents the estimated value of the Doppler ambiguity index, and argmax() represents the independent variable value corresponding to the maximum value of the objective function.

[0141] In this embodiment, that is, taking as the objective function, solve for the value of l corresponding to the maximum value of this objective function, and take it as the estimated value of the Doppler ambiguity index.

[0142] In the case where the range ambiguity index is unknown, steps 2 to 5 are specifically described. Among them, step 2 includes:

[0143] Taking the th pulse received signal in the target echo data as a reference, perform Doppler spread spectrum alignment operations on each pulse received signal after the th pulse received signal in the target echo data, and obtain the vector after Doppler spread spectrum

[0144]

[0145]

[0146] In the formula, represents the Hadamard product operation, represents the Kronecker product operation, represents the received signal of the kth pulse, K represents the total number of pulses, () * represents the conjugate operation, E represents the total transmit signal power, M represents the number of transmit units of the FDA-MIMO radar, β0 represents the complex-valued coefficient of the target, j represents the imaginary unit, f0 represents the reference carrier frequency, τ0 represents the common envelope time delay, V represents the radial velocity of the target, c represents the speed of light, T r represents the pulse repetition interval, 1 N represents an N×1 vector of all 1s, and N represents the number of receive units of the FDA-MIMO radar, represents the Doppler transmit steering vector of the target, x n represents the noise component of the pulse received signal.

[0147] In the case where the range ambiguity index is unknown, step 3 includes:

[0148] Step 31': Construct a velocity-dependent compensation vector in the transmit spatial frequency domain as:

[0149]

[0150] In the formula, represents the a priori known main velocity, Δf represents the frequency step introduced between the transmit array elements of the FDA-MIMO radar, and T represents the matrix transpose;

[0151] Step 32: Construct a compensation vector in the joint transmit-receive spatial frequency domain according to the velocity-dependent compensation vector as:

[0152] ​

[0153] When the range ambiguity index is unknown, step 4 includes:

[0154] Using the compensation vector in the joint transmit-receive spatial frequency domain to perform velocity-dependent compensation on the vector after Doppler spreading to obtain the Doppler ambiguity index vector which is:

[0155]

[0156] In the formula, V u represents the maximum unambiguous velocity, l represents the index of the Doppler ambiguity region, L max represents the number of ambiguous Dopplers.

[0157] When the range ambiguity index is unknown, step 5 includes:

[0158] Step 5.1': According to the Doppler ambiguity index vector using data-independent beamforming or data-dependent beamforming to construct the corresponding weight vector related to the Doppler ambiguity index, and this weight vector is expressed as:

[0159] or

[0160] In the formula, () -1 represents the inverse operation, and Q represents the covariance matrix of the noise component;

[0161] Step 5.2': According to the weight vector and the Doppler ambiguity index vector, calculate the estimated value of the Doppler ambiguity index according to the following formula as:

[0162]

[0163] where represents the estimated value of the Doppler ambiguity index, and argmax() represents the independent variable value corresponding to the maximum value of the objective function.

[0164] In this embodiment, that is, taking as the objective function, solving for the value of l corresponding to the maximum value of this objective function, and taking it as the estimated value of the Doppler ambiguity index.

[0165] The method for resolving Doppler ambiguity based on FDA-MIMO radar of the present invention proposes a spread-spectrum phase alignment method to align the extended Doppler frequencies of different transmitted pulses and eliminate the remaining phase, so that point targets can be refocused in the transmitted spatial frequency domain. After compensating for the main velocity, the Doppler ambiguity index is estimated by the maximum likelihood method in the cases of known and unknown range ambiguity indices respectively. Compared with the need to increase the coherent processing time in the case of multiple pulse repetition frequencies, the method of the present invention only uses one pulse repetition frequency in the FDA-MIMO system, so that the samples under different pulses are coherent, avoiding coherent processing and facilitating subsequent coherent processing, greatly improving the efficiency. Moreover, after using Doppler spread alignment, the power spectrum of high-speed targets is refocused, solving the Doppler ambiguity and greatly enhancing the detection performance of high-speed moving targets.

[0166] Embodiment 2

[0167] This embodiment illustrates the effect of the method for resolving Doppler ambiguity based on FDA-MIMO radar in Embodiment 1 through simulation experiments.

[0168] Simulation 1: Spectral analysis of Doppler ambiguity

[0169] The simulation parameters and target parameters are shown in Tables 1 and 2.

[0170] Table 1. Simulation parameters of FDA-MIMO radar

[0171]

[0172]

[0173] Table 2. Parameters of three targets

[0174] Parameter Target 1 Target 2 Target 3 Distance (km) 12 12 12 Radial velocity (m / s) 0 100 800 Angle (°) 30 0 -30 SNR (dB) 20 20 20

[0175] It should be noted that in order to improve the robustness of Doppler ambiguity resolution, the frequency offset needs to be appropriately designed. In order to utilize the coupling term between the target velocity and the frequency offset to resolve Doppler ambiguity, a method for expanding the term related to the Doppler spread frequency is proposed. The scheme for designing the frequency offset includes the following steps:

[0176] D1: When the maximum phase caused by Doppler spread exceeds π / 4, it cannot be ignored, that is

[0177]

[0178] D2: Assuming that the Doppler spread frequency is unambiguous, considering the periodicity of the Doppler spread phase, the following conditions can be obtained:

[0179]

[0180] D3: Simplify the conditional expression of formula (26) to obtain the selection region of frequency offset: Δf min <Δf<Δf max , where

[0181]

[0182]

[0183] Please refer to Figures 2a - 2b the distribution diagram of the target in the spatial frequency domain provided by the embodiment of the present invention shown in the figure, where the radial velocities of the three targets are V1 = 0 m / s, V2 = 100 m / s, and V3 = 800 m / s respectively, Figure 2a where Δf1 = 2.5 MHz in Figure 2b and Δf2 = 203.75 kHz in min . Target 1 and target 2 are stationary and slow, and target 3 is a high-speed moving target. Considering two different frequency offsets Δf1 ∈ [Δf max , Δf2<Δf min , the Capon spectra of the three targets in the spatial frequency domain. It can be seen that due to the radial velocity of 0, the spectrum of the stationary target 1 is focused on Δf1 or Δf2. Moreover, as the radial velocity increases, due to the extended Doppler frequency, the transmitted spatial frequency gradually expands and is proportional to the velocity. In particular, it can be observed from Figure 2a that the spectrum of target 2 is slightly expanded in the transmitted spatial frequency domain, and the maximum power is slightly reduced by 5.9 dB. However, it can be seen from Figure 2b that the power spectrum of target 2 is still focused on Δf2. For the fast moving target 3, the velocity has a great influence on the spectral distribution of the target. In the transmitted spatial domain, the spectrum is severely expanded, and the maximum power is reduced by approximately 14.8 dB. In contrast, when Δf2 is small, the diffusion range in the transmitted spatial domain is greatly reduced, and the power loss is less than 4 dB. This performance loss can be alleviated by some robust methods.

[0184] To prove the superiority of the method of the present invention in solving Doppler ambiguity, the case of five targets is further considered. The parameter settings of the five targets are shown in Table 3.

[0185] Table 3. Parameters of five targets

[0186] Parameter Target 1 Target 2 Target 3 Target 4 Target 5 Doppler ambiguity index -2 -1 0 2 4 Principal velocity (m / s) 75 75 75 75 75 Distance (km) 26.5 26 25 27.5 27 Angle (°) 30 30 30 30 30 SNR (dB) 20 20 20 20 20

[0187] Here, the Doppler ambiguity index Assume that Target 1 and Target 2 are moving away from the radar platform, and the Doppler ambiguity index is negative; while Target 3, 4, and 5 are approaching the radar, and the Doppler ambiguity index is positive. All targets are assumed to have the same main velocity, i.e., V0 = 75 m / s. At the same time, all targets have the same angle and range ambiguity index, i.e., the angle is 30°, and the range ambiguity index p is 1.

[0188] Please refer to Figures 3a - 3b the spectrum distribution diagram of the received data provided by the embodiment of the present invention shown in, where Figure 3a is the transmit-receive two-dimensional spatial domain, Figure 3b the transmit spatial domain of is one-dimensional. The Capon spectrum of the original received signal is as Figure 3a shown. Since the angle and range ambiguity regions are the same, it is difficult to distinguish targets with different radial velocities within the received spatial frequency. As can be seen from Figure 3b , in the transmit spatial frequency domain, there is only one peak for Target 3, i.e., the slow-moving target, and the maximum sidelobe is about 8 dB, resulting in a decrease in estimation performance.

[0189] In addition, to solve the Doppler ambiguity problem, the spread-spectrum phase alignment (SPA) method is adopted. First, let's consider the case where the range ambiguity index is known.

[0190] Please refer to Figures 4a - 4b the schematic diagram of Doppler spread alignment with a known range ambiguity index provided by the embodiment of the present invention shown in, where Figure 4a is the transmit-receive two-dimensional spatial domain, Figure 4b the transmit spatial domain of is one-dimensional. As shown in Figure 4a , after Doppler frequency alignment in the joint transmit-receive spatial frequency domain, the five targets have the resolvability of five peaks. In addition, as shown in Figure 4b , the transmit spatial frequency of the peak corresponds exactly to the target. It should be noted that due to the range-angle dependence and periodicity of the transmit spatial frequency, the spatial frequency corresponding to Target 5 is negative.

[0191] Please refer to the schematic diagram of Doppler spread alignment with an unknown range ambiguity index provided by the embodiment of the present invention shown in 5a - 5b, where Figure 5a is the transmit-receive two-dimensional spatial domain, Figure 5b the transmit spatial domain of is one-dimensional. Note that in Figure 5a , the received spatial frequencies of all targets are zero, which is because the aligned data is independent of range and angle. And the transmit spatial frequency shifts with the radial velocity of the target. As shown in Figure 5b , by comparing with the transmit spatial frequency in Figure 4b which contains range, angle, and velocity, the transmit spatial frequency in Figure 5b is only related to velocity.

[0192] Simulation 2: Performance of Doppler ambiguity index estimation

[0193] Considering known and unknown range ambiguity indices, for a single target, the performance of Doppler ambiguity index estimation based on the extended frequency alignment method is evaluated. To evaluate the estimation performance, 200 Monte Carlo trials are conducted. Assuming the main velocity of the moving target is 75 m / s, the Doppler ambiguity index is randomly selected within the range of [-2, 2]. In addition, the total number of received pulses is 200 and the signal-to-noise ratio is 0 dB.

[0194] Please refer to Figure 6 the schematic diagram of the Doppler ambiguity index estimation results provided by the embodiment of the present invention shown in the figure. It can be observed from the figure that in both cases, the estimated Doppler ambiguity index is exactly equal to their true values.

[0195] In addition, to further evaluate the performance of the proposed extended frequency alignment (SPA) method, the root mean square errors (RMSEs) of the estimated values of the input signal-to-noise ratio and the number of received pulses are obtained. Please refer to Figures 7a - 7b the schematic diagram of the relationship between the RMSE of the Doppler ambiguity index l provided by the embodiment of the present invention shown in the figure and the signal-to-noise ratio and the number of pulses, where Figure 7a is the relationship diagram of the estimation performance and the signal-to-noise ratio, Figure 7b is the relationship diagram of the estimation performance and the number of pulses.

[0196] Figure 7a the number of pulses is set to 200 and 2000 Monte Carlo experiments are conducted. From Figure 7a the test shows that in both cases, the RMSE of the proposed method decreases as the input signal-to-noise ratio increases. In addition, the RMSE and CRB under the condition of known range ambiguity index p are lower than those under the condition of unknown ambiguity index p. Specifically, as the input signal-to-noise ratio increases, the Doppler ambiguity index can be accurately determined, and its RMSE is even less than the corresponding CRB.

[0197] Figure 7b the signal-to-noise ratio in is -10 dB and 2000 Monte Carlo experiments are conducted. It can be seen that when the number of pulses is greater than 400, the Doppler ambiguity index can be accurately estimated using the range ambiguity index.

[0198] Please refer to Figures 8a - 8b the schematic diagram of the comparison of CRB at different Δf provided by the embodiment of the present invention shown in the figure, where Figure 8a is the variation diagram of CRB with the input signal-to-noise ratio, Figure 8b is the variation diagram of CRB with the number of pulses.

[0199] Figures 8a - 8bThe relationship between the CRB and the input signal-to-noise ratio and the number of pulses for different Δf is compared, where three different Δf are considered, including Δf max > Δf min > Δf3 = 25 kHz. It can be observed that the estimation performance in both cases improves with the increase of the frequency increment. Specifically, when Δf3 = 25 kHz, even with a high input signal-to-noise ratio and a large number of pulses, the CRB performance is poor, indicating that the propagation spatial frequency can be ignored when the frequency increment is very small and cannot be used to estimate the Doppler ambiguity index.

[0200] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "including", "comprising" or any other variant are intended to cover non-exclusive inclusion, so that an article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed. Without further limitation, an element defined by the statement "including a..." does not exclude the presence of another identical element in the article or device including the said element. Words such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect.

[0201] The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A method for resolving Doppler ambiguity based on FDA-MIMO radar, characterized in that, Including: Step 1: Obtain the target echo data of the FDA-MIMO radar; Step 2: Respectively, under the conditions where the range ambiguity index is known and unknown, perform Doppler spread spectrum alignment on the target echo data to obtain the vector after Doppler spread spectrum; Step 3: Construct a velocity-dependent compensation vector in the transmit spatial frequency domain, and based on the velocity-dependent compensation vector, construct a compensation vector in the joint transmit-receive spatial frequency domain; Step 4: According to the compensation vector in the joint transmit-receive spatial frequency domain, perform velocity-dependent compensation on the vector after Doppler spread spectrum to obtain the Doppler ambiguity index vector; Step 5: According to the Doppler ambiguity index vector, construct a weight vector related to the Doppler ambiguity index, and based on the weight vector and the Doppler ambiguity index vector, use the maximum likelihood criterion to obtain the estimated value of the Doppler ambiguity index.

2. The method for resolving Doppler ambiguity based on FDA-MIMO radar according to claim 1, characterized in that, When the range ambiguity index is known, Step 2 includes: Step 21: Construct a target distance based on the distance ambiguity index wherein, r0 represents the principal value distance determined by the range bin number and the range bin size, p represents the range ambiguity index, and R u represents the maximum unambiguous range; Step 22: According to the target distance Construct a combined distance-angle cancellation vector In the formula, represents a priori known angle, represents the Kronecker product operation, and ⊙ represents the Hadamard product operation, represents the received steering vector constructed according to the a priori angle, represents the transmitted steering vector constructed according to the a priori distance, represents the transmitted steering vector constructed according to the a priori angle; Step 23: According to the combined range-angle cancellation vector perform a Doppler spread spectrum alignment operation on each pulse received signal of the target echo data and obtain a vector x after Doppler spread spectrum after eliminating the remaining phase K-align , In the formula, represents the received signal of the k-th pulse, where k = 1, 2, ..., K, and K represents the total number of pulses, () * represents the conjugate operation, E represents the total transmit power of the signal, M represents the number of transmit units of the FDA-MIMO radar, β0 represents the complex-valued coefficient of the target, j represents the imaginary unit, f0 represents the reference carrier frequency, τ0 represents the common envelope time delay, V represents the radial velocity of the target, c represents the speed of light, T r represents the pulse repetition interval, R0 represents the true target range, θ0 represents the true angle, b(θ0) represents the true received steering vector dependent on the angle, a K (R0, V, θ0) represents the true transmit steering vector of the target, x n represents the noise component of the pulse received signal.

3. The method for resolving Doppler ambiguity based on FDA-MIMO radar according to claim 2, characterized in that, Step 3 includes: Step 31: Construct a velocity-dependent compensation vector in the emission spatial frequency domain which is In the formula, represents the prior known main velocity, Δf represents the frequency step introduced between the transmitting array elements of the FDA-MIMO radar, and T represents matrix transpose; Step 32: According to the speed-dependent compensation vector Construct a compensation vector g in the joint transceiver space-frequency domain K as follows: In the formula, 1 N represents an N×1 dimensional vector consisting entirely of 1s, and N represents the number of receiving units of the FDA-MIMO radar.

4. The method for resolving Doppler ambiguity based on FDA-MIMO radar according to claim 3, wherein Step 4 includes: Utilize the compensation vector g in the combined transceiver spatial frequency domain K , and perform velocity-dependent compensation on the vector x after Doppler spreading K-align to obtain the Doppler ambiguity index vector x K-comp as follows: In the formula, V u represents the maximum unambiguous velocity, l represents the exponent of the Doppler ambiguity region, L max represents the number of ambiguous Dopplers, r(R0) represents the range-dependent true transmit steering vector, and d(θ0) represents the angle-dependent true transmit steering vector.

5. The method for resolving Doppler ambiguity based on FDA-MIMO radar according to claim 4, wherein Step 5 includes: Step 51: According to the Doppler ambiguity index vector x K-comp , use data-independent beamforming or data-dependent beamforming to construct a corresponding weight vector related to the Doppler ambiguity index, and this weight vector is expressed as: or In the formula, () -1 represents the inverse operation, and Q represents the positive definite covariance matrix of the noise component; Step 5.2: According to the weight vector and the Doppler ambiguity index vector, calculate the estimated value of the Doppler ambiguity index according to the following formula: Among them, represents the estimated value of the Doppler ambiguity index, and argmax() represents the independent variable value corresponding to the maximum value of the objective function.

6. The method for resolving Doppler ambiguity based on FDA-MIMO radar according to claim 1, wherein When the range ambiguity index is unknown, Step 2 includes: Using the th pulse received signal in the target echo data as a reference, perform a Doppler spread spectrum alignment operation on each pulse received signal after the th pulse received signal in the target echo data to obtain a vector after Doppler spread spectrum where, ⊙ represents the Hadamard product operation, represents the Kronecker product operation, represents the received signal of the k-th pulse, K represents the total number of pulses, () * represents the conjugate operation, E represents the total transmit power of the transmit signal, M represents the number of transmit units of the FDA-MIMO radar, β0 represents the complex-valued coefficient of the target, j represents the imaginary unit, f0 represents the reference carrier frequency, τ0 represents the common envelope time delay, V represents the radial velocity of the target, c represents the speed of light, T r represents the pulse repetition interval, 1 N represents an N×1 vector of all 1s, N represents the number of receive units of the FDA-MIMO radar, represents the Doppler transmit steering vector of the target, x n represents the noise component of the pulse received signal.

7. The method for resolving Doppler ambiguity based on FDA-MIMO radar according to claim 6, wherein Step 3 includes: Step 31': Construct a velocity-dependent compensation vector in the emission spatial frequency domain It is as follows: In the formula, represents the prior known main velocity, Δf represents the frequency step introduced between the transmitting array elements of the FDA-MIMO radar, and T represents matrix transpose; Step 32: According to the speed-dependent compensation vector Construct a compensation vector in the joint transceiver spatial frequency domain as follows:

8. The method for resolving Doppler ambiguity based on FDA-MIMO radar according to claim 7, characterized in that, Step 4 includes: Using the compensation vector in the combined transceiver spatial frequency domain for the vector after Doppler spreading to perform velocity-dependent compensation, obtaining a Doppler ambiguity index vector as follows: In the formula, V u represents the maximum unambiguous velocity, and l represents the exponent of the Doppler ambiguity region. L max represents the number of ambiguous Dopplers.

9. The method for resolving Doppler ambiguity based on FDA-MIMO radar according to claim 8, characterized in that, Step 5 includes: Step 5.1': According to the Doppler ambiguity index vector Use data-independent beamforming or data-dependent beamforming to construct a corresponding weight vector related to the Doppler ambiguity index, and this weight vector is expressed as: or wherein, () -1 represents an inverse operation, and Q represents the covariance matrix of the noise component; Step 5.2’: According to the weight vector and the Doppler ambiguity index vector, calculate the estimated value of the Doppler ambiguity index according to the following formula: wherein, represents an estimated value of the Doppler ambiguity index, and argmax() represents the independent variable value corresponding to the maximum value of the objective function.

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