A centroid correction algorithm in delay-doppler domain based on DFT eigenphase

Abstract

The application relates to a two-step amplitude centroid correction algorithm based on DFT intrinsic phase in a time delay and Doppler domain in a millimeter wave OTFS-ISAC system, the algorithm comprising the following steps: step 1, OTFS modulation is performed on a downlink signal, step 2, a communication model is established, step 3, a sensing model is established, and step 4, amplitude centroid correction is performed, the algorithm has the superior technical effect that: through a new signal model of discrete Fourier transform (DFT) introduced, the challenge of fractional multiple time delay and Doppler estimation is solved, and the probability of sample selection deviation is significantly reduced; through computer simulation, it is shown that the method has better performance than the prior art in terms of sensing accuracy and communication performance without increasing the frame length and bandwidth.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of wireless communication and signal processing, and particularly relates to a two-step amplitude centroid correction algorithm in a time delay and Doppler domain based on DFT intrinsic phase in a millimeter wave OTFS-ISAC system. BACKGROUND

[0002] With the emergence of potential applications such as autonomous driving and unmanned aerial networks in 6G networks, the problem of spectrum resource shortage is becoming increasingly prominent, and the new paradigm of integrated communication and perception has recently received widespread attention. With the development of wireless communication, communication networks and radars are increasingly similar in hardware architecture, general spectrum, channel characteristics, signal processing, and network architecture. The integration of communication and perception aims to achieve trade-offs and mutual benefits between communication and perception through sharing resources, sharing signal processing and protocol stacks, and cross-layer, system information sharing, while greatly reducing hardware and spectrum costs.

[0003] At present, the signal design method of integrating radar and communication can be mainly divided into resource sharing and waveform sharing. The former usually uses two different waveforms to allocate transmission resources supporting communication and radar in time, frequency, and spatial domains in an orthogonal or non-orthogonal manner. The latter designs the same waveform for communication and perception functions, making the two functions more closely integrated. Compared with the resource sharing method, it can usually obtain higher performance gain. In co-wave design, according to the design priority, the current ISAC waveform can be divided into perception-centered design, communication-centered design, and collaborative design of sensing and communication. The perception-centered design method modulates information symbols on radar waveforms represented by frequency modulated continuous wave (FMCW), achieving near-optimal radar performance, but the data rate for communication is usually low. The communication-centered design method captures communication echo signals from targets to obtain sensing parameters of targets using additional hardware and signal processing algorithms.

[0004] As a classic multicarrier transmission scheme, Orthogonal Frequency Division Multiplexing (OFDM) is widely used in LTE and NR uplink and downlink transmission due to its efficient transmission efficiency and strong anti-multipath capability. Therefore, the joint design of integrated waveforms based on OFDM has attracted widespread attention and has shown near-optimal sensing performance for traditional radars in low-mobility scenarios. However, in high-mobility scenarios, severe ICI can cause loss of orthogonality between subcarriers, affecting sensing accuracy and communication performance. In view of the above factors, seeking a new waveform scheme that is robust to high dynamic channels has become a new research topic.

[0005] Orthogonal Time Frequency Space (OTFS) is a new type of multicarrier modulation technology, which shows strong robustness to high dynamic channels. In particular, the error performance of OTFS system in time-varying channel is significantly better than OFDM. In OTFS, information symbols are modulated in a two-dimensional grid of time-delay and Doppler domain, rather than multiplexed in time-frequency domain as OFDM. Each information symbol is mapped to a DD domain basis function through two-dimensional transformation, and these two-dimensional basis functions occupy the entire time-frequency resource, providing the potential of time-frequency full diversity to combat time-selective fading and frequency-selective fading. In addition, the characterization of the channel in the DD domain can be coupled with the geometric properties of the channel reflector, which is usually quasi-time-invariant within a frame (or several frames). Since radar detection is in the form of range (time delay) and velocity (Doppler) groups, OTFS is a natural candidate for ISAC. Due to this unique advantage, research on OTFS-ISAC has received frequent attention. The existing estimation methods include Maximum Likelihood (ML) estimator, Generalized Likelihood Ratio Test (GLRT) estimator and Orthogonal Matching Pursuit (OMP) algorithm, etc. Any one-time estimation of these algorithms needs to traverse the entire dictionary, which increases the complexity and cost of the algorithm. SUMMARY

[0006] In view of the problems of the prior art, the present application provides a two-step amplitude centroid correction algorithm based on DFT intrinsic phase in time-delay and Doppler domain in a millimeter wave OTFS-ISAC system.

[0007] The method provided by the present application comprises the following steps:

[0008] Step 1, OTFS modulation is performed on the downlink signal;

[0009] Step 2, a communication model is established;

[0010] Step 3, a perception model is established;

[0011] Step 4, the amplitude centroid is calibrated.

[0012] Further, in step 1, OTFS modulation is performed on the downlink signal:

[0013] The OTFS frame structure transmitted to the ith target in the downlink is designed as formula (1) as follows:

[0014]

[0015] wherein, Doppler initial value for pilot frame, delay initial value for pilot frame, k v = [2v max f c NT / c] is the maximum Doppler index, calculated by the maximum speed v max of the sensing target, the symbol number N, the sampling interval T and the speed of light c, l τ = [2r max MΔf / c] is the maximum delay index, calculated by the maximum distance r max of the sensing target, the subcarrier number M, the subcarrier interval Δf and the speed of light c, Doppler interval and delay interval are used to prevent mutual interference between data and pilot caused by fractional multiple Doppler dispersion and delay dispersion, and The size of and is determined by the system's tolerance to interference and the demand for spectral efficiency.

[0016] Further, in step 2, a communication model is established:

[0017] OTFS demodulation is performed on the received signal to obtain the input-output relationship in the downlink DD domain, i.e. the following formula (2):

[0018]

[0019] Wherein, f i represents the matrix of the i-th transmit beam (BF), ρ i represents the complex path gain of the i-th target corresponding to the downlink, f i represents the Doppler shift of the path, the subcarrier interval Δf = 1 / T, and the channel steering vector v i is the two-way radial Doppler shift, θ i is the expected direction angle, l = 0, 1, …, M-1, k = 0, 1, …, N-1, and k' = 0, 1, …, N-1.

[0020] Further, in step 3, a sensing model is established:

[0021] Step 3.1, let θ i be the steering angle of the i-th target vehicle relative to the base station, and consider a uniform linear array (ULA) with an antenna spacing d = λ / 2, λ being the carrier wavelength, and the receive steering vector is represented by the following formula (3):

[0022]

[0023] Step 3.2, the radar echo channel is modeled as follows (4):

[0024]

[0025] where h i represents the two-way channel complex gain including path loss and radar cross section coefficient related to the i-th target, the two-way radial Doppler shift is v i , and the two-way time delay is τ i .

[0026] From the above, the N R dimensional echo signal received by the array antenna is represented as follows (5):

[0027]

[0028] where w is the time-domain additive Gaussian noise vector with variance , represents the transmit beamforming matrix, is a P-dimensional signal composed of the continuous-time signals sent to P targets, s(t) is a multi-dimensional transmission signal on the transmitting array.

[0029] Step 3.3, the time-frequency domain symbol is transformed to the DD domain by SFFT, and the expression of the received pilot response is as follows (6):

[0030]

[0031] where:

[0032]

[0033]

[0034] u i is the i-th row of the receive BF matrix, f i is the i-th column of the transmit BF matrix.

[0035] Further, in step 4, the amplitude centroid is calibrated:

[0036] Step 4.1, assuming that the beam pointing angles of the transceiver are θ i , i.e. f i = a(θ i ) and u i = b H (θ i ), the detection of the amplitude spectrum peak is performed within the pilot detection region Γ i , i.e. as follows (9):

[0037] ​

[0038] where region Γ i includes all Doppler-delay pairs (k, l) satisfying and The Doppler-delay pair (k, l) represents the peak position of the amplitude spectrum. Meanwhile, each sample around the peak is denoted as:

[0039] A[n', m'] = y i [k + n', l + m'] … … (10).

[0040] where n' and m' represent the distance of the sample from the amplitude in Doppler axis and delay axis respectively.

[0041] The index distance of the spectrum peak sample.

[0042] Step 4.2, the fractional Doppler index κ i and delay index i i are calculated using the peak sample and its left / right neighbor samples, i.e. n' ∈ [-1, 0, 1], m' = 0, as follows:

[0043]

[0044]

[0045] Step 4.3, the two-dimensional centroid of the channel response amplitude spectrum is calculated to ensure that the two DFT samples for delay calibration and Doppler calibration are just on both sides of the actual peak, and the selection criterion is used to select the sample by comparing the polarity of the amplitude of the peak sample on both sides, as follows:

[0046]

[0047] and

[0048]

[0049] Step 4.4, the selection method based on the DFT intrinsic phase is as follows:

[0050]

[0051] and

[0052]

[0053] Step 4.5, the radial Doppler and delay of target i are estimated using the echo signal as follows:

[0054]

[0055] and

[0056]

[0057] The method has the following superior technical effects compared with the prior art in the technical field:

[0058] 1. The method introduces a new signal model of discrete Fourier transform (DFT), solves the challenge of fractional delay and Doppler estimation, and significantly reduces the probability of sample selection bias;

[0059] 2. Computer simulation shows that the method achieves better performance than the prior art in terms of perceptual accuracy and communication performance without increasing frame length and bandwidth. BRIEF DESCRIPTION OF DRAWINGS

[0060] Figure 1 includes Figure 1a and Figure 1b is a schematic diagram of the Doppler spectrum amplitude and phase of the method;

[0061] Figure 2 is a simulation schematic diagram of the relative deviation of CRLB about the number of points used of the method;

[0062] Figure 3 is a schematic diagram of the BER of the method compared with ideal channel estimation and uncalibrated pilot channel estimation;

[0063] Figure 4 is a schematic diagram of the communication performance comparison of channel estimation, equalization, and decision of the method;

[0064] Figure 5 is a simulation schematic diagram of the probability of correctly selecting observation points of the method;

[0065] Figure 6 is a schematic diagram of the speed MSE of the method compared with the speed MSE of the ABC algorithm;

[0066] Figure 7 is a schematic diagram of the comparison of the method with the ML algorithm and the GLRT algorithm. DETAILED DESCRIPTION

[0067] In order to more clearly understand the above-mentioned purposes, features and advantages of the present application, the present application will be further described in detail below in combination with the drawings and specific embodiments.

[0068] The method includes the following steps:

[0069] Step 1, OTFS modulation is performed on the downlink signal:

[0070] The OTFS frame structure transmitted to the ith target in the downlink is designed as:

[0071]

[0072] wherein, is the initial value of the Doppler of the pilot frame, is the initial value of the time delay of the pilot frame, k v = [2υ max f c NT / c] is the maximum Doppler index, calculated from the maximum speed υ max of the perceived target, the symbol number N, the sampling interval T, and the speed of light c, τ = [2r max MΔf / c] is the maximum time delay index, calculated from the maximum distance r max of the perceived target, the subcarrier number M, the subcarrier interval Δf, and the speed of light c; the Doppler interval and the time delay interval are used to prevent mutual interference between data and pilots caused by fractional multiple Doppler dispersion and time delay dispersion, and The size of and is determined by the system's tolerance to interference and the demand for spectral efficiency;

[0073] Step 2, establish a communication model:

[0074] The time-domain signal received by the ith target is represented as:

[0075]

[0076] wherein, n(t) represents the time-domain additive Gaussian noise with a variance of a(θ i ) is the channel transmission steering vector, as shown in the following formula (3):

[0077]

[0078] After OTFS demodulation of the received signal, one frame of data symbols is obtained:

[0079]

[0080] The input-output relationship of the downlink DD domain is obtained, as shown in the following formula:

[0081]

[0082] wherein, f i represents the matrix of the ith transmit beam, ρ if represents the complex path gain of the downlink corresponding to the i-th target. i This represents the Doppler frequency shift of the path, with a subcarrier spacing Δf = 1 / T, and the channel steering vector. v i For the two-way radial Doppler frequency shift, θ i Let l = 0, 1, ..., M-1, k = 0, 1, ..., N-1, k′ = 0, 1, ..., N-1;

[0083] Step 3: Establish a perception model;

[0084] Step 3.1, the transmit and receive steering vectors are respectively:

[0085]

[0086] Step 3.2, model the radar echo channel as follows:

[0087]

[0088] Among them, h i The two-way channel complex gain, including path loss and radar cross-section coefficient, is ν, which is related to the i-th target. The two-way radial Doppler frequency shift is ν. i The two-way delay is τ i ;

[0089] Therefore, the array antenna receives N R The echo signal is expressed as follows (8):

[0090]

[0091] Where w is the variance The time-domain additive Gaussian noise vector, Represents the transmitted beamforming matrix. A P-dimensional signal, consisting of continuous-time signals sent to P targets. Together they form a multidimensional transmission signal on the transmitting array, s(t).

[0092] Step 3.3, the time-frequency domain symbols are transformed to the DD domain using SFFT, as shown in equation (9):

[0093]

[0094] The expression for the received pilot response is:

[0095]

[0096] in:

[0097]

[0098]

[0099] u i is the i-th row of the receive BF matrix. i is the i-th column of the transmit BF matrix.

[0100] Step 4, amplitude centroid calibration is performed.

[0101] Step 4.1, assume that the beam pointing angles of the transceiver are both θ i , i.e., f i = a(θ i ) and u i = b H (θ i ), use the set θ i = {τ i , v i} to represent the two-way delay τ i and two-way Doppler shift v i of target i, the two-way delay τ i and two-way Doppler shift v i of target i satisfy the following mapping relationship with the actual distance and radial velocity between target i and the base station:

[0102] τ i = 2r i / c, v i = 2v i f c / c …… (13),

[0103] Use the index value on the delay-Doppler grid to represent the delay τ i and Doppler v i of the detected target i, i.e., the following formula (14):

[0104] l i + i i = τ i MΔf, k i + k i = v i NT …… (14),

[0105] wherein, represents the integer multiple delay index closest to the actual delay index that can be observed, represents the integer multiple Doppler index closest to the actual Doppler index;

[0106] Perform detection of the amplitude spectrum peak within the pilot detection region Γ i , i.e.:

[0107]

[0108] where region Γ i includes all Doppler-delay pairs (k, l) that satisfy and The Doppler-delay pair (χ, ε) represents the peak position of the amplitude spectrum. Meanwhile, each sample around the peak is denoted as:

[0109] A[n', m'] = y i [χ + n', ε + m'] …… (16).

[0110] where n' and m' represent the sample distance from the amplitude in the Doppler axis and the delay axis, respectively.

[0111] Step 4.2, in the Doppler axis where the peak sample is located, the estimation of the fractional Doppler index κ i is calculated using the peak sample and its left / right neighbor samples (n' ∈ [-1, 0, 1], m' = 0) as follows (17):

[0112]

[0113] In the delay axis where the peak sample is located, the estimation of the fractional delay index λ i is calculated using the peak sample and its left / right neighbor samples as follows (18):

[0114]

[0115] Step 4.3, the two-dimensional centroid of the channel response amplitude spectrum is calculated to ensure that the two DFT samples used for delay calibration and Doppler calibration are just on both sides of the actual peak, as shown in Figure 1, which is a Doppler calibration example in a noiseless environment. In this embodiment, the amplitude spectrum peak position of the received sample is detected as Doppler index χ = 64. According to the continuous channel response amplitude spectrum shape, in order to correctly calculate the two-dimensional centroid of the amplitude spectrum, two samples at k = 64 and k = 65 are selected to calculate

[0116] The selection criterion of the polarity of comparing the amplitudes of the samples on both sides of the peak is used to select the samples, i.e., the following (19)-(20):

[0117]

[0118] and

[0119]

[0120] The peak value and the neighbor sample with a phase difference of about 180° from the peak value are selected to ensure that the two selected sample points are distributed on both sides of the real peak value, thereby reducing the probability of selection bias, and the selection method based on the DFT intrinsic phase is in accordance with the following formula (21), (22):

[0121]

[0122] and

[0123]

[0124] Step 4.4, the echo signal is used to estimate the radial Doppler and time delay of the target i, respectively as follows (23), (24):

[0125]

[0126] and

[0127]

[0128] In order to verify the technical performance of the two-step amplitude centroid correction algorithm in the embodiment, the application is further illustrated by the following experiments:

[0129] 1. Theoretical performance:

[0130] 1) Sample selection bias probability:

[0131] The probability of selecting correctly can be expressed as follows:

[0132]

[0133] 2) The expectation and variance of DE-BC, the performance of the DE-BC estimator is evaluated by verifying the statistical characteristics. The estimator of DE-BC is obtained by calculation:

[0134]

[0135]

[0136] 3) Cramer-Rao bound (CRLB):

[0137] The estimated parameters are defined as α = [r0, v0], and the CRLB of each estimated parameter is the diagonal element of the Fisher information matrix , that is:

[0138]

[0139] The Fisher information matrix is calculated as:

[0140] ​

[0141] Figure 2 The relationship of CRLB with respect to the number of samples used for measurement under different fractional index is shown, it can be seen that the error bound of the method using a small number of samples for estimation and the full ML method is not too different, although the gap increases as the fractional index decreases, but it can still be found that when k = 0.1, the lower bound of MSE of the two-point estimation method is only less than one time of the lower bound of MSE of 64-point estimation, and when k = 0.5, there is almost no difference between the two, which strongly confirms the attractiveness of the two-point calibration method.

[0142] 2. Simulation condition setting and comparison of simulation results:

[0143] (1) Communication performance:

[0144] In a LoS dominant Rician channel, the maximum speed of the target is 150km / h, the K factor is 13.3dB, the angle of arrival of the RSU and the target obeys the uniform distribution of [0, 2π], the BER of the ABC auxiliary pilot channel estimation is compared with the ideal channel estimation and the uncalibrated pilot channel estimation;

[0145] As shown in Figure 3 , the traditional pilot estimation is severely limited by the phase difference, which is manifested as the difficulty in reaching the decline speed of the ideal estimation with the increase of SNR, after compensation using the estimated phase, only in the case of SNR p = 25dB, and at BER = 10 -2 , about 3dB of SNR gain is provided, and when SNR p = 40dB, both of the phase-compensated channel estimations reach the performance close to the ideal estimation;

[0146] The semantic capacity is used to measure the overall performance of communication including channel estimation, equalization, and decision, which is defined as:

[0147]

[0148] Where x k is any element of the constellation set, H is the information amount, and V(x k ) is the output result of the linear equalizer. Therefore, I PC is an index to measure the achievable rate;

[0149] In a LoS dominant Rician channel, the transmitter sends 4QAM symbols, and after different channel estimations, the receiver uses LMMSE for equalization. The simulation diagram of Figure 4 is obtained, and it can be seen from Figure 4 that with the increase of SNR, I PCRise and reach a steady rate.

[0150] (2) Sensing performance:

[0151] Monte Carlo simulation is performed in a LoS dominant Rician channel, with N = 64 system symbols and a subcarrier bandwidth of Δf = 30 kHz. By comparing the sample selection probability of the simulation and the theoretical results, we obtain Figure 5 As shown in Figure 5 , as κ decreases, the probability of selection bias increases, which is due to smaller κ meaning less spectral leakage. The small sidelobes are easily buried in the noise, making it difficult to select the correct sample. In addition, the curve drawn according to Figure 5 is basically consistent with the simulation results, indicating that the proposed selection scheme can greatly increase the probability of selecting the correct observation point.

[0152] Simulation is performed in a LoS dominant Rician channel with a fractional Doppler index of κ = 0.2. The invention studies the selection bias that often occurs in the polar selection criterion, as shown in Figure 6 , the velocity estimation using the ABC and DE-AB methods maintains a high MSE before SNR p = 10 dB, at which time the peak is completely submerged in the noise. When the threshold is exceeded, the MSE curve shows a waterfall-like downward trend. Different from the ABC method, the DE-AB method suddenly slows down the rate of decline at SNR p = 15 dB, which is mainly affected by the probability of selection bias. The probability of selection bias becomes negligible at SNR p = 35 dB, and the MSE begins to decrease linearly with SNR p . In contrast, it can be clearly seen that the selection method mentioned in DE-AB basically solves the selection bias problem at SNR p = 20 dB, making the MSE begin to decrease linearly. The pilot signal-to-noise ratio is in the interval [15, 35], and DE-AB will enjoy the performance gain brought by the selection method, which shows that DE-AB has the ability to reach the performance limit of two-point estimation.

[0153] Next, to further verify the sensing performance of DE-AB, the invention compares the DE-AB algorithm with the ML algorithm and the GLRT algorithm. To ensure fairness in the comparison, the ML algorithm, the GLRT algorithm, the ABC algorithm, and the DE-AB algorithm are all implemented in the same frame, subjected to the same LoS dominant channel, with a target maximum speed of 150 km / h, an arrival angle uniformly distributed in [0, 2π], and a carrier frequency of 27 GHz. The simulation results are as follows Figure 7As shown, the MSE of each scheme decreases approximately linearly with the increase of pilot SNR, while the ML scheme and the GLRT scheme tend to level off eventually because the receiver can never exhaustively search, and the level off will be reached at a larger SNR as Δk decreases. In contrast, the true value estimation of the present application does not exhibit this phenomenon. The ABC algorithm using the original selection method maintains a high level of MSE due to the selection bias problem, and the performance of the ABC algorithm exceeds the estimation performance of the ML algorithm and the GLRT algorithm with a granularity Δk = 0.1 when the pilot SNR is greater than 36 dB. The DE-AB algorithm obtains a SNR gain of about 10 dB compared to the ABC algorithm, and approaches and exceeds the performance of the ML algorithm and the GLRT algorithm with a granularity Δk = 0.01. This advantage comes from the use of the received pilot phase, which enables the ABC algorithm to function to the greatest extent without being harmed by the selection bias problem.

[0154] The present application is not limited to the above-mentioned embodiments, and the above-mentioned embodiments and descriptions are only to illustrate the principles of the present application. Without departing from the spirit and scope of the present application, various changes and improvements can be made to the present application, and these changes and improvements all fall within the scope of the present application.

Claims

1. A two-step amplitude centroid correction algorithm based on DFT intrinsic phase and Doppler domain in a millimeter-wave OTFS-ISAC system, characterized in that... include: Step 1: Perform OTFS modulation on the downlink signal: The OTFS frame structure transmitted to the i-th target in the downlink is designed as follows (1): in, The initial Doppler values ​​for the pilot frame. Let k be the initial value of the pilot frame delay. v =[2v max f c [NT / c] is the maximum Doppler index, derived from the maximum velocity v of the perceived target. max The number of symbols N, the sampling interval T, and the speed of light c are used to calculate l. τ =[2r max [MΔf / c] is the maximum time delay index, derived from the maximum distance r of the perceived target. max The Doppler interval is calculated from the number of subcarriers M, the subcarrier spacing Δf, and the speed of light c. and delay interval These are used to prevent mutual interference between data and pilot signals caused by fractional-Doppler dispersion and time-delay dispersion, respectively. and The magnitude is determined by the system's tolerance to interference and its spectral efficiency requirements; Step 2, establish the communication model: The received signal is demodulated using OTFS to obtain the downlink DD domain input-output relationship, i.e., the following equation (2): in, f i The matrix ρ represents the i-th transmitted beam (BF). i Let f represent the complex path gain of the downlink corresponding to the i-th target. i This represents the Doppler frequency shift of the path, with a subcarrier spacing Δf = 1 / T, and the channel steering vector. v i For the two-way radial Doppler frequency shift, θ i Let l = 0, 1, ..., M-1, k = 0, 1, ..., N-1, and k′ = 0, 1, ..., N-1. Step 3, Establish a perception model: Step 3.1, let θ i Let be the steering angle of the i-th target vehicle relative to the base station, and consider a uniform linear array (ULA) with an antenna spacing of d = λ / 2, where λ is the carrier wavelength. The receiving steering vector is expressed as follows (3): Step 3.2, model the radar echo channel as follows (4): Among them, h i The two-way channel complex gain, including path loss and radar cross-section coefficient, associated with the i-th target is given by v, where v is the two-way radial Doppler frequency shift. i The two-way delay is τ i ; From the above, the N received by the array antenna R The echo signal is expressed as follows (5): Where w is the variance The time-domain additive Gaussian noise vector, Represents the transmitted beamforming matrix. A P-dimensional signal, consisting of continuous-time signals sent to P targets. Together they form a multidimensional transmission signal on the transmitting array; Step 3.3: Transform the time-frequency domain symbols into the DD domain using SFFT. The expression for the received pilot response is as follows (6): in: u i To receive the i-th row of the BF matrix, f i The i-th column of the BF matrix is ​​sent; Step 4: Calibrate the amplitude centroid: Step 4.1, set the beam pointing angle of both the transmitter and receiver to θ. i That is, f i =a(θ) i ) and u i =b H (θ i ), in the pilot detection region Γ i The detection of the peak value of the internal amplitude spectrum is expressed by the following equation (9): Among them, region Γ i Including all that meet and The Doppler-time delay pairs (k,l) and (χ,ε) represent the Doppler-time delay pairs at the peak position of the amplitude spectrum, and the sampling points near the peak are denoted as: A[n′,m′]=y i [x+n′,e+m′]……(10); Where n′ and m′ represent the distance magnitude of the sample on the Doppler axis and the time delay axis, respectively, and the index distance of the spectral peak sample; Step 4.2: Calculate the fractional-Doppler index κ using the peak sample and its left / right neighbor samples, i.e., n′∈[-1, 0, 1], m′=0. i The estimated value is as follows (11): Using the peak sample and its left / right neighbor samples, calculate the fractional delay index ι. i The estimated value is as follows (12): Step 4.3: Calculate the two-dimensional centroid of the channel response amplitude spectrum to ensure that the two DFT samples used for delay calibration and Doppler calibration are exactly on both sides of the actual peak. Select samples by comparing the polarity of the sample amplitudes on both sides of the peak, as shown in equations (13)-(14): and Step 4.4, the selection method based on DFT eigenphase is based on the following equations (15)-(16): and Step 4.5, using the echo signal, the radial Doppler and time delay of target i are estimated as follows (17)-(18): and

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