# An Improved Clutter Suppression Method for Weather Radars Using Multiple Pulse Repetition Time Technique

Authors: Yingjie Yu; Yong Li
Journal: Advances in Meteorology
 (2017)

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## Abstract

This paper describes the implementation of an improved clutter suppression method for the multiple pulse repetition time (PRT) technique based on simulated radar data. The suppression method is constructed using maximum likelihood methodology in time domain and is called parametric time domain method (PTDM). The procedure relies on the assumption that precipitation and clutter signal spectra follow a Gaussian functional form. The multiple interleaved pulse repetition frequencies (PRFs) that are used in this work are set to four PRFs (952, 833, 667, and 513 Hz). Based on radar simulation, it is shown that the new method can provide accurate retrieval of Doppler velocity even in the case of strong clutter contamination. The obtained velocity is nearly unbiased for all the range of Nyquist velocity interval. Also, the performance of the method is illustrated on simulated radar data for plan position indicator (PPI) scan. Compared with staggered 2-PRT transmission schemes with PTDM, the proposed method presents better estimation accuracy under certain clutter situations.


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## Body

## 1. Introduction

The velocity and range ambiguity [1] is still one of the major limitations for Doppler weather radar observation. Given a radar wavelength λ, the relationship between the maximum unambiguous range ra and maximum unambiguous velocity va can be presented as vara=cλ/8, where c is the speed of light. With a uniform pulse repetition frequency (PRF) fPRF observation, va can be shown as va=λfPRF/4. That means large maximum unambiguous velocity va can be obtained by increasing the PRF. Along with the increase of maximum unambiguous velocity va comes a decrease in maximum range ra, and vice versa.Various techniques have been proposed to overcome this problem [2–5], like dual-pulse repetition time (PRT) and staggered PRT [3, 6]. The dual-PRT and staggered dual-PRT techniques utilize two PRTs in an n pulses transmission sequence. The dual-PRT method transmits two blocks of uniform PRT pulses with each block at a different PRT (T1,T1,…,T1,T2,T2,…,T2). The optimal velocity estimates can be recovered from the joint analysis of the two Doppler measurements. This method is suitable for the low antenna rotation rate, because the radial velocity remains the same during the n pulse intervals. The staggered PRT method is not restricted by this condition. The PRT alternates between two values (T1,T2,T1,…,T1,T2). The interval of the maximum unambiguous velocity va was well extended and successively adopted for the Next Generation Weather Radar (NEXRAD) network [7]. In order to improve the dealiasing success rate and obtain larger Nyquist velocity, the multiple PRT (M-PRT) technique which utilizes multiple interleaved PRTs was proposed. Tabary et al. [8] presented a triple-PRT scheme implemented on the C-band French Radar Network. This technique works well when spectral width is smaller than 3 m/s and SNR is high. A simultaneous multiple pulse repetition frequency (SMPRT) code [9] was introduced and evaluated. This technique can provide enough information to produce a high-resolution measured spectrum for each range gate. Tahanout et al. [10] proposed an optimal 9-PRT scheme for the suitable shape reproduction of the power spectrum of the radar signal.These techniques which used nonuniform time series make filtering of clutter from the radar signal more complicated. Standard clutter filters cannot be applied directly to the nonuniform sampling scheme. Banjanin and Zrnic [11] developed a scheme which consists of two filters that operate sequentially; the overall filter is time-varying with periodically changing coefficients. Cho and Chornoboy [12] introduced a finite impulse response time-varying filter that is applied to M-PRT transmission. Siggia and Passarelli [13] proposed a Gaussian model adaptive processing (GMAP) algorithm that filters clutter and recovers weather spectrum after notching the spectrum around zero Doppler. Nguyen et al. [14] and Moisseev et al. [15] presented a parametric time domain method (PTDM) for staggered PRT observations, which can accurately estimate the spectral moments of precipitation echoes even with strong clutter.In this work, we extend PTDM toM-PRT observations. This paper is organized as follows. In Section 2, staggered 2-PRT and M-PRT observation techniques are described. The PTDM for clutter suppression and spectral moments estimation is then presented in Section 3. Based on radar data simulations, Section 4 focuses on performance analysis of the proposed method. The error analyses of the proposed method and the staggered 2-PRT technique with PTDM for different noise and clutter scenarios are presented. In order to test the performance of the proposed method, different sample schemes techniques are used for plan position indicator (PPI) observations for comparison. In Section 5, discussions and conclusions are provided.


## 2.M-PRT Techniques

### 2.1. Uniform PRT

Assuming thatT is the PRT of the traditional uniform PRT technique, the autocorrelation calculated from return signal time series at lag T is R^. The maximum unambiguous velocity is va=λ/4T. The estimated velocity v can be deduced from R^ [1] as(1)v=-λ4πTarg⁡R^,where arg⁡ is argument function.


### 2.2. Staggered 2-PRT

The staggered PRT method applies a pulse transmission sequence that changes intervals betweenT1 and T2. For T2>T1, the maximum unambiguous velocity va will be extended as(2)va=λ4T2-T1.The autocorrelations calculated from return signal time series at lagsT1 and T2 are R^1 and R^2. The Doppler velocities v1 and v2 can be deduced from R^1 and R^2, respectively, with (1).Two approaches have been introduced to deal with the velocity aliasing. One algorithm uses the ratio of autocorrelations [7], given by(3)v=λ4T2-T1arg⁡R^1R^2.If the argument ofR^1/R^2 exceeds the range of (-π,π), the estimated velocity will be ambiguous. The other technique utilizes the maximum unambiguous velocity to revise the aliasing velocity. Suppose va1 and va2 are the maximum unambiguous velocity for uniform PRTs T1 and T2. The dealiased velocity can be shown as(4)v=v1+2Pva1+ε1orv=v2+2Qva2+ε2,where P and Q are the correct Nyquist interval number and ε1 and ε2 are estimate errors.


### 2.3.M-PRT

Mostly,M-PRT technique [9] can be regarded as an extension of the staggered 2-PRT technique. This technique chooses a transmission sequence which has several blocks, and every block is formed of M different PRTs. Its transmitting scheme is [T1,T2,…,TM,T1,T2,…,TM,…]. Similar to the staggered 2-PRT method, the maximum unambiguous velocity can be shown as(5)va=λ4minTi-Tj;i≠j.The relationship between the measured true velocity and the estimated velocitiesv1,v2,…,vM is given by(6)vi=vi+2kivai+εi,i=1,2,…,M.Finding the appropriate integers(k1,k2,…,kM) which minimize the error ε1+ε2+⋯+εM is the way for the measured true velocity retrieval.


## 2.1. Uniform PRT

Assuming thatT is the PRT of the traditional uniform PRT technique, the autocorrelation calculated from return signal time series at lag T is R^. The maximum unambiguous velocity is va=λ/4T. The estimated velocity v can be deduced from R^ [1] as(1)v=-λ4πTarg⁡R^,where arg⁡ is argument function.


## 2.2. Staggered 2-PRT

The staggered PRT method applies a pulse transmission sequence that changes intervals betweenT1 and T2. For T2>T1, the maximum unambiguous velocity va will be extended as(2)va=λ4T2-T1.The autocorrelations calculated from return signal time series at lagsT1 and T2 are R^1 and R^2. The Doppler velocities v1 and v2 can be deduced from R^1 and R^2, respectively, with (1).Two approaches have been introduced to deal with the velocity aliasing. One algorithm uses the ratio of autocorrelations [7], given by(3)v=λ4T2-T1arg⁡R^1R^2.If the argument ofR^1/R^2 exceeds the range of (-π,π), the estimated velocity will be ambiguous. The other technique utilizes the maximum unambiguous velocity to revise the aliasing velocity. Suppose va1 and va2 are the maximum unambiguous velocity for uniform PRTs T1 and T2. The dealiased velocity can be shown as(4)v=v1+2Pva1+ε1orv=v2+2Qva2+ε2,where P and Q are the correct Nyquist interval number and ε1 and ε2 are estimate errors.


## 2.3.M-PRT

Mostly,M-PRT technique [9] can be regarded as an extension of the staggered 2-PRT technique. This technique chooses a transmission sequence which has several blocks, and every block is formed of M different PRTs. Its transmitting scheme is [T1,T2,…,TM,T1,T2,…,TM,…]. Similar to the staggered 2-PRT method, the maximum unambiguous velocity can be shown as(5)va=λ4minTi-Tj;i≠j.The relationship between the measured true velocity and the estimated velocitiesv1,v2,…,vM is given by(6)vi=vi+2kivai+εi,i=1,2,…,M.Finding the appropriate integers(k1,k2,…,kM) which minimize the error ε1+ε2+⋯+εM is the way for the measured true velocity retrieval.


## 3. Parametric Time Domain Method (PTDM)

Bringi and Chandrasekar [16] have shown that the real and imaginary parts of radar signals follow zero mean normal distribution. Suppose V=[V1,V2,…,Vn]t is n samples of received radar signals in one radar resolution volume with sample time t1,t2,…,tn. Hence, the complex vector can be expressed as the sum of two real Gaussian vectors representing in-phase and quadrature components, respectively, like(7)Vs=Is+jQs;s=1,…,n.The multivariate density function ofV [15] can be represented as(8)fV=1πndet⁡Rexp⁡-V∗tR-1V=1πndet⁡Rexp⁡-trR-1R^V,where R=E[V(V∗)t] is the covariance matrix and R^V=V(V∗)t is the sample covariance matrix. tr is the trace function. det⁡(R) is the determinant of R.Assuming that Doppler spectra of clutter and precipitation obey Gaussian distribution, the observed spectrum of Doppler velocityv can be expressed as the summation of independent spectra coming from precipitation Sr(v), clutter Scl(v), and white noise SN(v), as(9)Sv=Srv+Sclv+SNvSrv=Prσr2πexp⁡-v-v-22σr2Sclv=Pclσcl2πexp⁡-v22σcl2SNv=2σN2Tsλ,where Pr and Pcl are the precipitation signal and clutter power, σr and σcl are the precipitation and clutter spectrum width, respectively, σN2 is the noise power, v- is mean velocity, and Ts is sample time. Then, the covariance function can be obtained by fast Fourier transform (FFT) as(10)RT,θ=Prexp⁡-8π2σr2T2λ2exp⁡-j4πv-Tλ+Pclexp⁡-8π2σcl2T2λ2+σN2δT,where θ is the vector of unknown parameters, θ=[Pr,Pcl,σr,σcl,v-,σN2]. T is the temporal variable.ForM-PRT transmission, the element in the covariance matrix R can be written as(11)Rk,l=Rintl-kMT1+T2+⋯+TM+mam;k,l=1,…,n,where(12)m=modl-k,Ma=a1,a2,…,aM-1=T1,T1+T2,…,T1+T2+⋯+TM-1.Here, int is integral function. mod is the remainder of a division.Using the multivariate density function (8), the log-likelihood estimation of θ is as follows:(13)ln⁡Lθ=-ln⁡det⁡Rθ-trR-1θR^V.The parameter vector θ can be estimated by minimizing min⁡[-ln⁡L(θ)].


## 4. Analysis of the Performance

### 4.1. Simulation of Radar Signal

The main task of this work is to discuss the accuracy of estimated velocity under different clutter conditions. So, different values of mean velocity, signal-to-noise ratio (SNR), and clutter-to-signal ratio (CSR) are chosen to generate the observed Doppler spectra. We select a periodic scheme with 4 different PRTs: 1050, 1200, 1500, and 1950μs. Their greatest common factor is Tu=150μs. The ratio of PRTs is 7/8/10/13. The corresponding PRFs can be written as 952, 833, 667, and 513 Hz. The parameters of the simulated X-band radar signal are shown in Table 1.Table 1
Parameters of the simulated radar signal.
Parameter
Value
Wavelength (m)
0.03
Mean velocity (m/s)
-
v
a
,
-
0.9
v
a
,
…
,
0.9
v
a
,
v
a
CSR (dB)
20, 40
SNR (dB)
20, 40
Precipitation spectrum width (m/s)
4
Clutter spectrum width (m/s)
0.25
Noise power (dB)
20


### 4.2. PTDM Implementation

Using the log-likelihood function (13) to retrieve the precipitation and clutter spectral moments, the convergence of a local minimum will lead to wrong estimations in some cases. In order to reduce the estimate errors, we should make sure that the results of minimum (13) come from the convergence of global minimum. According to Moisseev et al. [15], this problem can be solved by selecting the appropriate seed value, especially for mean velocity seed value selection which has the biggest effect on the convergence of the optimization procedure. Similar to Moisseev et al. [15], the search range of unknown parameters is given in Table 2. Stot is the total signal power, and σNsys represents the system noise floor. Using the Nelder-Mead simplex method [17, 18], the estimated values of unknown parameters are retrieved. Figure 1 shows a scatter diagram of estimated velocities for 4-PRT technique using PTDM, when CSR = 20 dB. It can be revealed that the estimated velocities are accurately retrieved using this method. The mean velocities almost coincide with true velocities. The standard deviations and biases are presented in Figure 2. The results show that the standard deviations are less than 0.5 m/s and the biases are near zero without increase.Table 2
Range of unknown parameters.
Parameter
Range
Mean velocity (m/s)
(-va,va)
Clutter power (dB)
(0,Stot+10)
Precipitation power (dB)
(0,Stot+10)
Precipitation spectrum width (m/s)
(1, 5)
Clutter spectrum width (m/s)
(0.1, 0.3)
Noise power (dB)
(σNsys, σNsys+10)Figure 1
The true velocity (solid line) versus estimated velocities (hollow dot) from 30 simulations when CSR = 20 dB and SNR = 40 dB using PTDM. The mean of estimated velocities of each input velocity is shown as a red asterisk character.Figure 2
Standard deviation (solid line with hollow dot) and bias (dotted line with cross) of estimated velocities in Figure1.The noise and clutter environment is complex and variable in radar detection. The simulation can be carried out through two cases. The first one describes the conditions near the radar. The ground clutter echoes have various intensities. The other one considers the situations far away from the radar where ground clutter can be neglected. The simulated data are collected in the Nyquist velocity interval.In the first type of simulation, the CSR changes from −20 dB to 40 dB. SNR is fixed to +40 dB during the computation. Figure3 shows the curves of standard deviation and bias of velocity estimates versus CSR, when applying 2-PRT and M-PRT schemes. The clutter suppression method used in both transmission schemes is PTDM. The biases increase with CSR at a similar rate for the two PRT schemes. The absolute values of biases do not exceed 0.5 m/s. For the range from −20 dB to 20 dB, the standard deviation are smaller than 1 m/s and obviously the 4-PRT schemes provide better estimation accuracy. The estimation error increases with CSR, especially from 20 dB to 30 dB. When CSR > 30 dB, the values tend to be almost steady near 1.8 m/s.Figure 3
Bias (a) and standard deviation (b) of velocity estimates for the 4-PRT (solid line) and 2-PRT (dashed line) with SNR = 40 dB using the PTDM.
(a)
(b)The second simulation is implemented for 0 dB ≤ SNR ≤ 40 dB and CSR = −20 dB. In Figure4, the biases and standard deviations are shown for the PTDM velocity estimates. In the [15 dB, 40 dB] interval, the measured velocities for both PRT schemes are sufficiently accurate. Then, the bias and standard deviation increase with the decrease of SNR and reach the maximum near SNR = 0 dB. For the range from 5 dB to 40 dB, the measured velocities are acceptable for the biases close to zero and the standard deviations are less than 0.6 m/s. The performance of 4-PRT schemes has better precision especially when the noise is strong (from 0 dB to 15 dB).Figure 4
Bias (a) and standard deviation (b) of velocity estimates for the 4-PRT (solid line) and 2-PRT (dashed line) with CSR = −20 dB using the PTDM.
(a)
(b)In order to test the effectiveness of the proposed method, theI and Q data for plan position indicator (PPI) scan were simulated. Choosing a range-azimuth space of 30 km × 60°, the resolution is 150 m and 1°. The radial velocity of each cell in the background is set to one constant. The fan-shape range from the center to 12 km is defined as ground clutter with zero Doppler velocity and spectral width σc=0.25m/s. At the range from 8.5 km to 25 km, a circle region is set to simulate the wind shear in which the velocity field is unstable and changes rapidly in velocity magnitude and direction. The maximum velocity in wind shear field is 10 m/s and spectral width is equal to 4 m/s. From Figure 4, we have already known that the velocities estimates are desirable over a large range of SNR. This simulation is focused on comparing the observation results between different techniques under different CSR scenarios. SNR is fixed to 40 dB. Figures 5(a)–5(c) correspond to a situation with CSR = 10 dB, Figures 5(d)–5(f) to CSR = 20 dB, and Figures 5(g)–5(i) to CSR = 30 dB.Figure 5
Radial velocity estimated from simulatedI and Q radar data sampled at ((a), (d), (g)) unique PRT of 1050 μs, ((b), (e), (h)) 2-PRT (1050 and 1200 μs), and ((c), (f), (i)) 4-PRT (1050, 1200, 1500, and 1950 μs) with SNR = 40 dB and different CSR scenarios: (a)–(c) CSR = 10 dB, (d)–(f) CSR = 20 dB, and (g)–(i) CSR = 30 dB. Note that the data are shown for 30 km × 60° space. The range and azimuth resolutions are 150 m and 1°, respectively. The corresponding unambiguous velocities are 7.14 m/s for unique PRT and 50 m/s for the other two schemes. The pulse pair processing (PPP) method is used in (a), (d), and (g). The PTDM is used in the others.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)Figures5(a), 5(d), and 5(g) illustrate the estimates of radial velocity sampled at single PRT 1050 μs using the pulse pair processing (PPP) method. The corresponding maximum unambiguous velocity is 7.14 m/s. The velocity aliasing can be seen obviously in the region of wind shear field. Because of the ground clutter, the estimation of velocity is highly influenced.Figures5(b), 5(e), 5(h), 5(c), 5(f), and 5(i) show the obtained velocity estimates for the 2-PRT (1050 and 1200 μs) and 4-PRT (1050, 1200, 1500, and 1950 μs) schemes with PTDM, respectively. The maximum unambiguous velocity of both transmission schemes is 50 m/s. The problem of velocity aliasing is well solved. Compared with Figures 5(b) and 5(e), the clutter is filtered out better in Figures 5(c) and 5(f). For the case CSR = 30 dB, the clutter filtering results are almost the same.


## 4.1. Simulation of Radar Signal

The main task of this work is to discuss the accuracy of estimated velocity under different clutter conditions. So, different values of mean velocity, signal-to-noise ratio (SNR), and clutter-to-signal ratio (CSR) are chosen to generate the observed Doppler spectra. We select a periodic scheme with 4 different PRTs: 1050, 1200, 1500, and 1950μs. Their greatest common factor is Tu=150μs. The ratio of PRTs is 7/8/10/13. The corresponding PRFs can be written as 952, 833, 667, and 513 Hz. The parameters of the simulated X-band radar signal are shown in Table 1.Table 1
Parameters of the simulated radar signal.
Parameter
Value
Wavelength (m)
0.03
Mean velocity (m/s)
-
v
a
,
-
0.9
v
a
,
…
,
0.9
v
a
,
v
a
CSR (dB)
20, 40
SNR (dB)
20, 40
Precipitation spectrum width (m/s)
4
Clutter spectrum width (m/s)
0.25
Noise power (dB)
20


## 4.2. PTDM Implementation

Using the log-likelihood function (13) to retrieve the precipitation and clutter spectral moments, the convergence of a local minimum will lead to wrong estimations in some cases. In order to reduce the estimate errors, we should make sure that the results of minimum (13) come from the convergence of global minimum. According to Moisseev et al. [15], this problem can be solved by selecting the appropriate seed value, especially for mean velocity seed value selection which has the biggest effect on the convergence of the optimization procedure. Similar to Moisseev et al. [15], the search range of unknown parameters is given in Table 2. Stot is the total signal power, and σNsys represents the system noise floor. Using the Nelder-Mead simplex method [17, 18], the estimated values of unknown parameters are retrieved. Figure 1 shows a scatter diagram of estimated velocities for 4-PRT technique using PTDM, when CSR = 20 dB. It can be revealed that the estimated velocities are accurately retrieved using this method. The mean velocities almost coincide with true velocities. The standard deviations and biases are presented in Figure 2. The results show that the standard deviations are less than 0.5 m/s and the biases are near zero without increase.Table 2
Range of unknown parameters.
Parameter
Range
Mean velocity (m/s)
(-va,va)
Clutter power (dB)
(0,Stot+10)
Precipitation power (dB)
(0,Stot+10)
Precipitation spectrum width (m/s)
(1, 5)
Clutter spectrum width (m/s)
(0.1, 0.3)
Noise power (dB)
(σNsys, σNsys+10)Figure 1
The true velocity (solid line) versus estimated velocities (hollow dot) from 30 simulations when CSR = 20 dB and SNR = 40 dB using PTDM. The mean of estimated velocities of each input velocity is shown as a red asterisk character.Figure 2
Standard deviation (solid line with hollow dot) and bias (dotted line with cross) of estimated velocities in Figure1.The noise and clutter environment is complex and variable in radar detection. The simulation can be carried out through two cases. The first one describes the conditions near the radar. The ground clutter echoes have various intensities. The other one considers the situations far away from the radar where ground clutter can be neglected. The simulated data are collected in the Nyquist velocity interval.In the first type of simulation, the CSR changes from −20 dB to 40 dB. SNR is fixed to +40 dB during the computation. Figure3 shows the curves of standard deviation and bias of velocity estimates versus CSR, when applying 2-PRT and M-PRT schemes. The clutter suppression method used in both transmission schemes is PTDM. The biases increase with CSR at a similar rate for the two PRT schemes. The absolute values of biases do not exceed 0.5 m/s. For the range from −20 dB to 20 dB, the standard deviation are smaller than 1 m/s and obviously the 4-PRT schemes provide better estimation accuracy. The estimation error increases with CSR, especially from 20 dB to 30 dB. When CSR > 30 dB, the values tend to be almost steady near 1.8 m/s.Figure 3
Bias (a) and standard deviation (b) of velocity estimates for the 4-PRT (solid line) and 2-PRT (dashed line) with SNR = 40 dB using the PTDM.
(a)
(b)The second simulation is implemented for 0 dB ≤ SNR ≤ 40 dB and CSR = −20 dB. In Figure4, the biases and standard deviations are shown for the PTDM velocity estimates. In the [15 dB, 40 dB] interval, the measured velocities for both PRT schemes are sufficiently accurate. Then, the bias and standard deviation increase with the decrease of SNR and reach the maximum near SNR = 0 dB. For the range from 5 dB to 40 dB, the measured velocities are acceptable for the biases close to zero and the standard deviations are less than 0.6 m/s. The performance of 4-PRT schemes has better precision especially when the noise is strong (from 0 dB to 15 dB).Figure 4
Bias (a) and standard deviation (b) of velocity estimates for the 4-PRT (solid line) and 2-PRT (dashed line) with CSR = −20 dB using the PTDM.
(a)
(b)In order to test the effectiveness of the proposed method, theI and Q data for plan position indicator (PPI) scan were simulated. Choosing a range-azimuth space of 30 km × 60°, the resolution is 150 m and 1°. The radial velocity of each cell in the background is set to one constant. The fan-shape range from the center to 12 km is defined as ground clutter with zero Doppler velocity and spectral width σc=0.25m/s. At the range from 8.5 km to 25 km, a circle region is set to simulate the wind shear in which the velocity field is unstable and changes rapidly in velocity magnitude and direction. The maximum velocity in wind shear field is 10 m/s and spectral width is equal to 4 m/s. From Figure 4, we have already known that the velocities estimates are desirable over a large range of SNR. This simulation is focused on comparing the observation results between different techniques under different CSR scenarios. SNR is fixed to 40 dB. Figures 5(a)–5(c) correspond to a situation with CSR = 10 dB, Figures 5(d)–5(f) to CSR = 20 dB, and Figures 5(g)–5(i) to CSR = 30 dB.Figure 5
Radial velocity estimated from simulatedI and Q radar data sampled at ((a), (d), (g)) unique PRT of 1050 μs, ((b), (e), (h)) 2-PRT (1050 and 1200 μs), and ((c), (f), (i)) 4-PRT (1050, 1200, 1500, and 1950 μs) with SNR = 40 dB and different CSR scenarios: (a)–(c) CSR = 10 dB, (d)–(f) CSR = 20 dB, and (g)–(i) CSR = 30 dB. Note that the data are shown for 30 km × 60° space. The range and azimuth resolutions are 150 m and 1°, respectively. The corresponding unambiguous velocities are 7.14 m/s for unique PRT and 50 m/s for the other two schemes. The pulse pair processing (PPP) method is used in (a), (d), and (g). The PTDM is used in the others.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)Figures5(a), 5(d), and 5(g) illustrate the estimates of radial velocity sampled at single PRT 1050 μs using the pulse pair processing (PPP) method. The corresponding maximum unambiguous velocity is 7.14 m/s. The velocity aliasing can be seen obviously in the region of wind shear field. Because of the ground clutter, the estimation of velocity is highly influenced.Figures5(b), 5(e), 5(h), 5(c), 5(f), and 5(i) show the obtained velocity estimates for the 2-PRT (1050 and 1200 μs) and 4-PRT (1050, 1200, 1500, and 1950 μs) schemes with PTDM, respectively. The maximum unambiguous velocity of both transmission schemes is 50 m/s. The problem of velocity aliasing is well solved. Compared with Figures 5(b) and 5(e), the clutter is filtered out better in Figures 5(c) and 5(f). For the case CSR = 30 dB, the clutter filtering results are almost the same.


## 5. Conclusions

In this paper, a technique applying the parametric time domain method to theM-PRT transmission schemes is proposed. Based on the assumption that the Doppler spectra of clutter and precipitation follow Gaussian shape, simulation studies are carried out using a case of M-PRT schemes.It is shown that the proposed method can effectively estimate Doppler velocity. Two cases are simulated to analyze the standard deviation and bias of measured velocities, which can help to compare the proposed method with 2-PRT transmission schemes with PTDM. The first one describes a situation where SNR is fixed to 40 dB and CSR varies. The biases are nearly the same for both of the methods. As long as CSR is lower than 20 dB, the standard deviation of measured velocity using the proposed method are almost three times less than the 2-PRT transmission schemes with PTDM. The second type of simulation is performed for CSR = −20 dB and 0 dB ≤ SNR ≤ 40 dB. The estimation error of measured velocities using the 4-PRT schemes is much better than that given by the 2-PRT schemes.The PPI scan of measured velocity is built on simulated radar data with SNR = 40 dB and different CSRs. The results confirm that the proposed method not only solves Doppler velocity aliasing but also performs better in clutter suppression than 2-PRT schemes with PTDM especially when CSR < 30 dB.The future works will focus on finding the optimalM-PRT schemes which minimize the estimation error and its applications to real air observation. The method to improve the computing efficiency is also the next emphasis of our research.



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*Source: 8173643-2017-04-09.xml*