Indoor optimization positioning method of MIMO frequency modulation continuous wave radar

Abstract

An indoor optimization positioning method of an MIMO frequency modulation continuous wave radar comprises the following steps: after a data matrix is generated based on an echo signal after analog-to-digital conversion, filtering an environment static target and radio frequency leakage by using a time domain filtering technology, and after the data matrix after the time domain filtering is carried out, carrying out indoor optimization positioning on the MIMO frequency modulation continuous wave radar based on the data matrix after the time domain filtering; the actual distance between the target and the radar is calculated through distance dimension fast Fourier transform, the speed Doppler of the target relative to the radar is calculated through speed fast Fourier transform, so that a distance Doppler spectrum is generated, after the signal-to-noise ratio is increased through multi-channel data incoherent accumulation, the total number of the targets is estimated through a constant false alarm rate (CFAR) algorithm, and the distance Doppler spectrum is obtained. Obtaining distances and speeds corresponding to different target points; and finally, angle estimation is carried out on each point on the CFAR through a super-resolution solution angle algorithm (ESPRIT) to obtain angle information, distance, speed and angle data matching is carried out through digital beam forming (DBF), distance, angle and speed data of a corresponding target are obtained, and a two-dimensional coordinate of the target is correspondingly obtained. According to the invention, the number of human body target point clouds can be increased while human body coordinates, speed and angle information are accurately obtained, and the method has the advantages of high interference resistance, low requirement on the signal-to-noise ratio of data and low dependence degree on the external environment.

Description

Technical Field

[0001] The present invention relates to a technology in the field of millimeter wave radar, and in particular to a method for optimizing the number of effective point clouds and human target positioning for spatial positioning and motion tracking of a multiple-input multiple-output (MIMO) frequency modulated continuous wave millimeter wave radar. Background Art

[0002] The existing millimeter-wave radar-based positioning technology is often interfered by static strong reflection clutter and radio frequency leakage when detecting indoor human targets. The detection results are less reliable and cannot accurately achieve complete matching of angle, speed and distance information. Summary of the invention

[0003] In view of the shortcomings of the prior art that the angle disorder problem cannot be solved and the distance and speed information obtained based on the angle information cannot be matched and combined to form accurate personnel positioning data, the present invention proposes an indoor optimization positioning method of MIMO frequency modulation continuous wave radar, and the time domain filtering technology is used to filter out static targets. While accurately obtaining the coordinates, speed and angle information of the human body, the number of human target point clouds can be increased. The method has the advantages of strong anti-interference, low requirements on data signal-to-noise ratio, and low dependence on the external environment.

[0004] The present invention is achieved through the following technical solutions:

[0005] The present invention relates to an indoor optimization positioning method of a MIMO frequency modulation continuous wave radar, comprising:

[0006] Step 1) After generating a data matrix based on the echo signal after analog-to-digital conversion, the static targets in the environment and the radio frequency leakage are filtered out using time domain filtering technology;

[0007] Step 2) Based on the data matrix after time domain filtering, the actual distance between the target and the radar is calculated using the distance dimension fast Fourier transform, and the speed Doppler of the target relative to the radar is calculated using the speed fast Fourier transform, thereby generating a range Doppler spectrum (RDM);

[0008] Step 3) After the multi-channel data is incoherently accumulated to improve the signal-to-noise ratio, the total number of targets is estimated by a constant false alarm rate (CFAR) algorithm to obtain the distance and speed corresponding to different target points;

[0009] Step 4) The super-resolution angle solution algorithm (ESPRIT) is used to estimate the angle of each point on the CFAR to obtain the angle information, and the distance, speed and angle data are matched through digital beam forming (DBF) to obtain the distance, angle and speed data of the corresponding target, and the corresponding two-dimensional coordinates of the target are obtained. Technical Effects

[0010] The present invention uses a time domain filtering algorithm to filter out static targets and remove radio frequency leakage, which overall solves the problem that the existing technology cannot detect indoor human targets with high precision while outputting more valid point clouds; while obtaining human distance, angle, and speed information, the number of valid point clouds output by human targets can be increased, which is convenient for motion tracking, that is, indoor human target positioning and the number of valid point clouds can be increased. The spatial distance resolution of the present invention can reach 7.5cm, and the super-resolution angle solution algorithm ESPRIT can be used to achieve an angular resolution of 1.4°, while the field of view angle reaches ±45° in azimuth, and the velocity resolution is about 0.16m / s. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a flow chart of the present invention;

[0012] Figure 2 This is a schematic diagram of human body positioning according to the present invention;

[0013] In the figure: a is the establishment of the human target space model; b is the detection and matching of the moving human target space parameters;

[0014] Figure 3 This is the block diagram of the MIMO FMCW radar system;

[0015] Figure 4 This is a schematic diagram of the 4T8R antenna array;

[0016] Figure 5 It is a schematic diagram of the equivalent virtual array of the 4T8R antenna array;

[0017] Figure 6 This is a schematic diagram of the MIMO radar data processing flow;

[0018] Figure 7 Original map for indoor human body positioning;

[0019] Figure 8 This is the signal enhancement processing diagram of indoor human target;

[0020] Fig. 9 This is the result of enhancing the number of effective point clouds of the human body. Specific implementation methods

[0021] like Figure 3As shown, an indoor optimized positioning system of a MIMO frequency modulated continuous wave millimeter wave radar involved in this embodiment includes: a signal source 1 and a transmitting branch composed of a transmitting power divider 2, a power amplifier 3, and a transmitting antenna array TX respectively connected thereto, and a receiving branch composed of a receiving power divider 4, a low noise amplifier 5, and a receiving antenna array RX connected in sequence, wherein: the output end of the low noise amplifier 5 is provided with a low pass filter 6, an analog-to-digital converter 7 and a signal processing module 8 in sequence, the signal generated by the signal source 1 flows into the signal power amplifier through the signal transmitting power divider 2 for amplification, the transmitting antenna array TX sends the amplified signal, the signal is reflected by the indoor object to be measured to form an echo signal, and then the echo is received by the receiving antenna array RX and enters the low noise amplifier 5 to amplify the received signal, and the signal processing module 8 processes the sampled signal after passing through the low pass filter 9, the mixer 6 and the analog-to-digital conversion unit 7 in sequence.

[0022] The signal processing module 8 includes: a MIMO signal processing unit, a CFAR target number detection unit, an ESPRIT super-resolution angle solution algorithm unit, an information matching unit, and a point cloud information output unit, wherein: the MIMO signal processing unit processes the original signal obtained by radar ADC sampling; the CFAR target number detection unit is used to process the signal obtained by the MIMO signal processing unit and obtain the number of targets and their speed and distance information; the ESPRIT super-resolution angle solution algorithm unit respectively solves the targets detected by the CFAR target number detection unit to obtain angle information and two-dimensional coordinate information; the information matching unit matches the obtained angle information, distance information, and speed information; and the point cloud information output unit outputs the information of the corresponding target to form a point cloud.

[0023] The processing means that the MIMO signal processing unit mixes and down-converts the radio frequency signal received by the radar into an intermediate frequency signal. Specifically, due to the transmitted chirp signal S TX (t) is much larger than the target's speed, and the target does not move beyond the distance resolution during the signal transmission and reception process. Then the intermediate frequency signal s is obtained after receiving the signal and down-converting it. IF (t), a digital signal is obtained by ADC sampling; the CFAR target number detection unit processing refers to using the CFAR algorithm to estimate the number of targets after incoherent accumulation of RDM, detect whether the target really exists and obtain the distance and speed corresponding to the existing target, specifically: chirp signal S TX (t) = exp(j(2πf c t+πSt 2 +φ)), intermediate frequency signal Where: f c is the signal carrier frequency, and the signal period is T c, bandwidth is B, then the modulation slope S = B / T c , φ is the initial phase of the signal, s Tx (t) and s Rx (t) is the received and transmitted signal, A is the signal amplitude, R(τ) is the relative distance between the target and the radar, τ is the “slow time”, and c is the speed of light.

[0024] like Figure 4 As shown, the transmitting antenna array TX and the receiving antenna array RX constitute a 4T8R antenna array, with four transmitting antennas at the upper right corner, namely TX0-TX3, and eight receiving antennas at the lower left corner, namely RX0-RX7.

[0025] like Figure 5 As shown in the figure, the equivalent virtual array of the 4T8R antenna array is equivalent to a SIMO antenna array with one transmitting antenna and M×N receiving antennas for a MIMO FMCW radar with M transmitting and N receiving antennas. The 4T8R antenna array generates 32 channels of virtual array elements, where: m The virtual array element represents the mth transmitting unit and the nth receiving unit. A uniform linear array is used in the angle solution process. 12 uniform linear arrays with an array element spacing of 0.5λ are generated in the azimuth direction for angle estimation.

[0026] like Figure 1 As shown, this embodiment relates to an indoor positioning method of a MIMO frequency modulated continuous wave millimeter wave radar based on the above system. Based on the data matrix generated by the echo signal after analog-to-digital conversion, a group of signals are first collected by the radar in the targetless air environment during the radar initialization phase, and the intermediate frequency signal obtained by a chirp signal is recorded as Signal None , used for time domain filtering, and then each intermediate frequency signal when the target is present is subtracted from the empty signal in the time domain, expressed as Signal IF -Signal None, it can effectively filter out static environmental targets and RF leakage, and can achieve the acquisition and accurate elimination of static targets and RF leakage signals without any threshold information. Then, the subtracted data is calculated using the range-dimensional fast Fourier transform (Range-FFT) to obtain the actual distance between the target and the radar. Specifically, the signal spectrum peak is obtained by performing a fast Fourier transform on the single-frequency intermediate frequency signal, that is, the distance between the target and the radar is obtained. The speed Doppler of the target relative to the radar is calculated by using the speed fast Fourier transform (Doppler-FFT). The phase information at the peak frequency of the range spectrum is quickly The phase change frequency is obtained by Fourier transform, and then the speed information of the target is solved to generate the range Doppler spectrum (RDM). After the multi-channel data is incoherently accumulated to improve the signal-to-noise ratio, the total number of targets is estimated by the constant false alarm rate algorithm (CFAR). The super-resolution angle solution algorithm (ESPRIT) is then used to estimate the angle of each point on the CFAR, and then digital beamforming (DBF) is used for data matching. DBF is performed on each angle to obtain the range spectrum at that angle. The peak value is the distance information corresponding to the angle, which can form a match between the angle and the distance, and then the two-dimensional coordinates and speed of the target are obtained.

[0027] The frequency f of the intermediate frequency signal IF =Sτ=2Sd / c, d is the distance between the target and the radar, that is, d=cf IF / 2S.

[0028] like Figure 6 As shown in the figure, the chirp signal and echo signal emitted by the radar and the intermediate frequency signal after mixing are Figure 5 There are 12 virtual array elements in the horizontal direction, and the data of the corresponding array elements are taken out to form the following Figure 6 The data matrix in the middle right figure will be used for angle resolution and CFAR target number detection later.

[0029] The speed fast Fourier transform is specifically: the intermediate frequency signals obtained by two adjacent chirp signals have a phase difference of Δφ≈2πf c t=4πvT c / λ, that is, the target's moving speed is: v = λΔφ / 4πT c .

[0030] like Figure 1 As shown, the distance-dimensional fast Fourier transform performs one-dimensional FFT processing on all sampling points of each channel. After processing, there will be some peaks in the spectrum graph, and their positions are the positions of the target, corresponding to the actual distance R=cf between the target and the radar IF / 2S to get the actual distance of the target, where: f IFis the frequency of the intermediate frequency signal, S is the modulation slope of the Chirp signal, c is the speed of electromagnetic wave propagation in a vacuum, the theoretical resolution of the distance dimension is ΔR=c / 2B, and B is the antenna bandwidth.

[0031] The velocity fast Fourier transform uses all Chirp signals of each channel to perform two-dimensional FFT to obtain the velocity information of the target, corresponding to the velocity of the target relative to the radar u = λω / 4πT c , where: ω is the velocity Doppler frequency of the target, λ is the wavelength corresponding to the starting frequency of the FMCW, T c is the time of one chirp cycle of radar signal. That is, according to the multi-target distance and speed information obtained by solving, the range-doppler (RD) diagram of multiple targets can be obtained.

[0032] The ESPRIT algorithm specifically includes:

[0033] 1) For M antenna array elements forming a one-dimensional linear array, the array element spacing is λ / 2, and there are K narrowband signal waves in the space, respectively [s 1 (t), s 2 (t),…,s K (t)], the corresponding spatial wave direction is [θ 1 (t), θ 2 (t),…,θ K (t)], when the first unit is taken as the reference unit, the received signal of each unit is Where: n i (t) represents the additive noise of each antenna unit; the above model is represented by a matrix, that is, X = AS + N, where: X(t) = [x 1 (t), x 2 (t), …, x M (t)] T The array receives the signal, S(t) = [s 1 (t), s 2 (t),…,s M (t)] T is the envelope of the signal, N(t)=[n 1 (t), n 2 (t),…,n M (t)] T is additive noise (stationary Gaussian random process), A=[a(θ 1 ), a(θ 2 ), a(θ K )] is the flow matrix of the signal, is the phase difference vector;

[0034] 2) The signals received by the first M-1 virtual array elements of the uniform linear array are taken as the first subarray, and the second virtual array element to the Mth virtual array element are taken as the second subarray. The received signal X(t) = AS(t) + n x (t), Y(t)=AΦS(t)+n y (t), where: Φ is the rotation invariant factor matrix, which means that the two sub-arrays only differ by a fixed phase, and the received signal matrix is ​​obtained

[0035] 3) Calculate the covariance matrix of the received signal matrix Z(t) Then the covariance matrix R zz Perform eigendecomposition and use the eigenvectors of the largest K eigenvalues ​​as the signal subspace, where K is the target number. The rotation invariant matrix can be obtained through the subspace method, and then the eigendecomposition can be performed to obtain the angle information of each bright spot on the CFAR.

[0036] The data matching means that due to the limitation of ESPRIT algorithm, when solving the angle, the output is not output in the order of input, so DBF is needed to match each incoming wave. Specifically, for the digital beamforming process of a linear array, when the spacing of the equally spaced linear array is d, and the signal is incident at an angle θ to the array normal, the array output signal Y = W T (θ 0 )X, where X is the above received signal, W = [w 0 , w 1 ,…,w N ] is the signal steering vector, w i =2πd i sin(θ 0 / λ), i=1, 2, ..., N, and use the estimated angle to perform digital beamforming, that is, to form a main beam in the direction of the incoming wave, and then perform a range fast Fourier transform to solve the range spectrum in the angle direction to obtain the distance information, thereby matching the distance with the two-dimensional space angle information. In this way, the speed, angle, and distance of the target are matched, and information points are output, which is convenient for the subsequent output of the point cloud.

[0037] In the microwave darkroom and normal office environment settings, with sawtooth modulation, 2GHz sweep bandwidth, center frequency 60GHz, the transceiver antenna configuration is 4 transmitting antennas and 8 receiving antennas, such as Figure 7 and Figure 8 As shown in Figure 1, it is a schematic diagram of effectively removing static clutter and RF leakage interference targets. Figure 7The experimental group shown is: a human body is walking at a distance of 2.5m from the radar, but due to the small RCS of the human body, the human body signal is submerged by DC and other clutter signals, and it is almost impossible to obtain the incoming wave signal of the human body. Figure 7 The target is interfered by RF leakage, and the interference target appears at a position close to 0m, and the target cannot be displayed. After using this filtering method, Figure 8 As shown, Figure 8 As shown in the figure, the target information enhancement data processing result diagram is shown. After time domain filtering and phasor mean cancellation algorithm processing, the human target is highlighted. From the figure, we can see the human wave information at 2.5m. Figure 1 , Figure 8 After processing, point cloud information can be obtained. The target is highlighted, the target information can be clearly obtained, and the accurate matching method is used to obtain the correct point cloud information, which can achieve better personnel positioning and tracking, and avoid the misjudgment and loss of point cloud information caused by the clustering method, thereby increasing the number of effective point clouds.

[0038] like Fig. 9 As shown, the output of the human body point cloud is more than 30, which is twice the output of the 15 point cloud target that can be achieved by the traditional signal processing link.

[0039] Compared with the existing technology, this method uses the DOA super-resolution angle solution algorithm, time domain filtering and incoherent accumulation to perform human body positioning and point cloud formation on the 60GHz MIMO FMCW millimeter wave radar platform, which can accurately locate human targets and generate twice the number of effective point clouds compared to traditional signal processing links, which is helpful for subsequent signal processing, etc. In summary, the present invention combines the acquisition of target spatial positioning information with the generation of target effective point clouds, and completes the groundbreaking indoor human target positioning and point cloud number improvement technology.

[0040] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principle and purpose of the present invention. The protection scope of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. Each implementation scheme within its scope shall be subject to the constraints of the present invention.

Claims

1. A method for indoor optimization positioning of MIMO frequency modulated continuous wave radar, characterized in that: include: Step 1) After generating a data matrix based on the echo signal after analog-to-digital conversion, the static targets in the environment and the radio frequency leakage are filtered out using time domain filtering technology; Step 2) Based on the data matrix after time domain filtering, the actual distance between the target and the radar is calculated using the distance dimension fast Fourier transform, and the speed Doppler of the target relative to the radar is calculated using the speed fast Fourier transform, thereby generating a range Doppler spectrum (RDM); Step 3) After the multi-channel data is incoherently accumulated to improve the signal-to-noise ratio, the total number of targets is estimated by a constant false alarm rate (CFAR) algorithm to obtain the distance and speed corresponding to different target points; Step 4) The super-resolution angle solution algorithm (ESPRIT) is used to estimate the angle of each point on the CFAR to obtain the angle information, and the distance, speed and angle data are matched through digital beam forming (DBF) to obtain the distance, angle and speed data of the corresponding target, and the corresponding two-dimensional coordinates of the target are obtained.

2. The indoor optimization positioning method of the MIMO frequency modulated continuous wave radar according to claim 1, characterized in that: The step 1 is specifically as follows: in the radar initialization stage, a group of signals are collected by using the radar in the air without a target, and the intermediate frequency signal obtained by a chirp signal is recorded as Signal None , used for time domain filtering, and then each intermediate frequency signal when the target is present is subtracted from the empty signal in the time domain, expressed as Signal IF -Signal None , which can effectively filter out static environment targets and RF leakage; the intermediate frequency signals obtained from two adjacent chirp signals have a phase difference of Δφ≈2πf c t=4πvT c / λ, that is, the target's moving speed is: v = λΔφ / 4πT c .

3. The indoor optimization positioning method of the MIMO frequency modulated continuous wave radar according to claim 1, characterized in that: The velocity fast Fourier transform uses all Chirp signals of each channel to perform two-dimensional FFT to obtain the velocity information of the target, corresponding to the velocity of the target relative to the radar v = λω / 4πT c , where: ω is the velocity Doppler frequency of the target, λ is the wavelength corresponding to the starting frequency of the FMCW, T c It is the time of one chirp cycle of the radar signal, that is, according to the multi-target distance and speed information obtained by solving, the range-doppler (RD) diagram of the multi-target can be obtained.

4. The indoor optimization positioning method of MIMO frequency modulated continuous wave radar according to claim 1 is characterized in that: The distance dimension fast Fourier transform described above performs one-dimensional FFT processing on all sampling points of each channel. After processing, there will be some peaks in the spectrum graph, and their positions are the positions of the target, corresponding to the actual distance R=cf between the target and the radar. IF / 2S to get the actual distance of the target, where: f IF is the frequency of the intermediate frequency signal, S is the modulation slope of the Chirp signal, c is the speed of electromagnetic wave propagation in a vacuum, the theoretical resolution of the distance dimension is ΔR=c / 2B, and B is the antenna bandwidth.

5. The indoor optimization positioning method of MIMO frequency modulated continuous wave radar according to claim 1 is characterized in that: The ESPRIT algorithm specifically includes: 1) M antenna elements form a one-dimensional linear array with an element spacing of λ / 2. There are K narrowband signal waves in space, which are [s1(t), s2(t), …, s K (t)], the corresponding spatial wave direction is [θ1(t), θ2(t), …, θ K (t)], when the first unit is taken as the reference unit, the received signal of each unit is Where: n i (t) represents the additive noise of each antenna unit; the above model is represented by a matrix, that is, X = AS + N, where: X(t) = [x1(t), x2(t), ..., x M (t)] T is the array receiving signal, S(t) = [s1(t), s2(t), ..., s M (t)] T is the envelope of the signal, N(t) = [n1(t), n2(t), …, n M (t)] T is additive noise (stationary Gaussian random process), A = [a(θ1), a(θ2), a(θ K )] is the flow matrix of the signal, is the phase difference vector; 2) The signals received by the first M-1 virtual array elements of the uniform linear array are taken as the first subarray, and the second virtual array element to the Mth virtual array element are taken as the second subarray. The received signal X(t) = AS(t) + n x (t), Y(t)=AΦS(t)+n y (t), where: Φ is the rotation invariant factor matrix, which means that the two sub-arrays only differ by a fixed phase, and the received signal matrix is ​​obtained 3) Calculate the covariance matrix of the received signal matrix Z(t) Then the covariance matrix R zz Perform eigendecomposition and use the eigenvectors of the largest K eigenvalues ​​as the signal subspace, where K is the target number. The rotation invariant matrix can be obtained through the subspace method, and then the eigendecomposition can be performed to obtain the angle information of each bright spot on the CFAR.

6. The indoor optimization positioning method of MIMO frequency modulated continuous wave radar according to claim 5 is characterized in that: The data matching means that due to the limitation of ESPRIT algorithm, when solving the angle, the output is not output in the order of input, so DBF is needed to match each incoming wave. Specifically, for the digital beamforming process of a linear array, when the spacing of the equally spaced linear array is d, and the signal is incident at an angle θ to the array normal, the array output signal Y = W T (θ0)X, where X is the above received signal, W = [w0, w1, ..., w N ] is the signal steering vector, w i =2πd i sin(θ0 / λ), i=1, 2, ..., N, and use the estimated angle for digital beamforming, that is, forming the main beam in the direction of the incoming wave, and then performing a distance fast Fourier transform to solve the distance spectrum in the angle direction to obtain the distance information, thereby matching the distance with the two-dimensional space angle information, thereby matching the speed, angle, and distance of the target, and outputting the information point.

7. An indoor optimized positioning system for implementing the method described in any one of claims 1 to 6, characterized in that: include: A signal source and a transmitting branch consisting of a transmitting power divider, a power amplifier, and a transmitting antenna array TX respectively connected thereto, and a receiving branch consisting of a receiving power divider, a low noise amplifier, and a receiving antenna array RX connected thereto in sequence, wherein: the output end of the low noise amplifier is provided with a low pass filter, an analog-to-digital converter, and a signal processing module in sequence, the signal generated by the signal source flows into the signal power amplifier through the signal transmitting power divider for amplification, the transmitting antenna array TX sends out the amplified signal, the signal is reflected by the indoor object to be measured to form an echo signal, and then the echo is received by the receiving antenna array RX and enters the low noise amplifier to amplify the received signal, and the signal processing module processes the sampled signal after passing through the low pass filter, the mixer, and the analog-to-digital conversion unit in sequence.

8. The indoor optimal positioning system according to claim 7, characterized in that: The signal processing module includes: a MIMO signal processing unit, a CFAR target number detection unit, an ESPRIT super-resolution angle solution algorithm unit, an information matching unit, and a point cloud information output unit, wherein: the MIMO signal processing unit processes the original signal obtained by radar ADC sampling; the CFAR target number detection unit is used to process the signal obtained by the MIMO signal processing unit and obtain the number of targets and their speed and distance information; the ESPRIT super-resolution angle solution algorithm unit respectively solves the targets detected by the CFAR target number detection unit to obtain angle information and two-dimensional coordinate information; the information matching unit matches the obtained angle information, distance information, and speed information; the point cloud information output unit outputs the information of the corresponding target to form a point cloud; The processing means that the MIMO signal processing unit mixes and down-converts the radio frequency signal received by the radar into an intermediate frequency signal. Specifically, due to the transmitted chirp signal S TX (t) is much larger than the target's speed, and the target does not move beyond the distance resolution during the signal transmission and reception process. Then the intermediate frequency signal s is obtained after receiving the signal and down-converting it. IF (t), a digital signal is obtained by ADC sampling; the CFAR target number detection unit processing refers to using the CFAR algorithm to estimate the number of targets after incoherent accumulation of RDM, detect whether the target really exists and obtain the distance and speed corresponding to the existing target, specifically: chirp signal S TX (t) = exp(j(2πf c t+πSt 2 +φ)), intermediate frequency signal Where: f c is the signal carrier frequency, and the signal period is T c , bandwidth is B, then the modulation slope S = B / T c , φ is the initial phase of the signal, s Tx (t) and s Rx (t) is the received and transmitted signal, A is the signal amplitude, R(τ) is the relative distance between the target and the radar, τ is the "slow time", and c is the speed of light.

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