Advances in Meteorology

Volume 2017, Article ID 8173643, 7 pages

https://doi.org/10.1155/2017/8173643

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

School of Electronics and Information, Northwestern Polytechnical University, Xi’an, China

Correspondence should be addressed to Yingjie Yu; moc.621@jyy_ydnas

Received 7 December 2016; Revised 18 March 2017; Accepted 28 March 2017; Published 9 April 2017

Academic Editor: Hiroyuki Hashiguchi

Copyright © 2017 Yingjie Yu and Yong Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### 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.

#### 1. Introduction

The velocity and range ambiguity [1] is still one of the major limitations for Doppler weather radar observation. Given a radar wavelength , the relationship between the maximum unambiguous range and maximum unambiguous velocity can be presented as , where is the speed of light. With a uniform pulse repetition frequency (PRF) observation, can be shown as . That means large maximum unambiguous velocity can be obtained by increasing the PRF. Along with the increase of maximum unambiguous velocity comes a decrease in maximum range , 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 pulses transmission sequence. The dual-PRT method transmits two blocks of uniform PRT pulses with each block at a different PRT . 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 pulse intervals. The staggered PRT method is not restricted by this condition. The PRT alternates between two values . The interval of the maximum unambiguous velocity 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 (-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 -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 to -PRT observations. This paper is organized as follows. In Section 2, staggered 2-PRT and -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. -PRT Techniques

##### 2.1. Uniform PRT

Assuming that is the PRT of the traditional uniform PRT technique, the autocorrelation calculated from return signal time series at lag is . The maximum unambiguous velocity is . The estimated velocity can be deduced from [1] aswhere is argument function.

##### 2.2. Staggered 2-PRT

The staggered PRT method applies a pulse transmission sequence that changes intervals between and . For , the maximum unambiguous velocity will be extended as

The autocorrelations calculated from return signal time series at lags and are and . The Doppler velocities and can be deduced from and , respectively, with (1).

Two approaches have been introduced to deal with the velocity aliasing. One algorithm uses the ratio of autocorrelations [7], given by

If the argument of exceeds the range of , the estimated velocity will be ambiguous. The other technique utilizes the maximum unambiguous velocity to revise the aliasing velocity. Suppose and are the maximum unambiguous velocity for uniform PRTs and . The dealiased velocity can be shown aswhere and are the correct Nyquist interval number and and are estimate errors.

##### 2.3. -PRT

Mostly, -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 different PRTs. Its transmitting scheme is . Similar to the staggered 2-PRT method, the maximum unambiguous velocity can be shown as

The relationship between the measured true velocity and the estimated velocities is given by

Finding the appropriate integers which minimize the error 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 is samples of received radar signals in one radar resolution volume with sample time . Hence, the complex vector can be expressed as the sum of two real Gaussian vectors representing in-phase and quadrature components, respectively, like

The multivariate density function of [15] can be represented aswhere is the covariance matrix and is the sample covariance matrix. is the trace function. is the determinant of .

Assuming that Doppler spectra of clutter and precipitation obey Gaussian distribution, the observed spectrum of Doppler velocity can be expressed as the summation of independent spectra coming from precipitation , clutter , and white noise , aswhere and are the precipitation signal and clutter power, and are the precipitation and clutter spectrum width, respectively, is the noise power, is mean velocity, and is sample time. Then, the covariance function can be obtained by fast Fourier transform (FFT) aswhere is the vector of unknown parameters, . is the temporal variable.

For -PRT transmission, the element in the covariance matrix can be written aswhereHere, is integral function. is the remainder of a division.

Using the multivariate density function (8), the log-likelihood estimation of is as follows:The parameter vector can be estimated by minimizing .

#### 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 1950 . Their greatest common factor is . 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.