International Journal of Antennas and Propagation

Volume 2019, Article ID 5937973, 12 pages

https://doi.org/10.1155/2019/5937973

## Theoretical and Experimental Study on Echo Fluctuation Suppression of a Cirrus Cloud by Millimeter Wave MIMO Radar

^{1}Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Key Laboratory for Aerosol-Cloud-Precipitation of China Meteorological Administration, Nanjing University of Information Science and Technology, Nanjing 210044, China^{2}Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science and Technology, Nanjing 210044, China^{3}National Demonstration Center for Experimental Atmospheric Science and Environmental Meteorology Education, Nanjing University of Information Science and Technology, Nanjing 210044, China^{4}Key Laboratory of Middle Atmosphere and Global Environment Observation, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China

Correspondence should be addressed to Jinhu Wang; nc.ude.tsiun@gnawregitdlog

Received 18 April 2018; Revised 25 August 2018; Accepted 27 September 2018; Published 13 January 2019

Academic Editor: Lorenzo Luini

Copyright © 2019 Jinhu Wang et al. 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

The scattering properties of nonspherical particles can be approximately computed by equivalent spherical theory. The scattering properties of ice particles were approximately computed by Rayleigh approximation because the sizes of the ice particles are smaller than the wavelength of millimeter wave radar. Based on the above assumption, the echo fluctuation of moving particles was analyzed by computing the total backscattering field of a cirrus cloud using the classical vector potential technique. The simulation results showed that echo fluctuation influences the accuracy of retrieving the physical parameters of a cloud. To suppress the echo fluctuation of moving ice particles, a video integrator of a millimeter wave cloud radar would be used. However, video integrators lose the rapidly changing information of ice particles and reduce radar range resolution; thus, we propose the pace-diversity technique of MIMO radar to reduce the echo fluctuation, which could be validated by theoretical computation and experimental measurements.

#### 1. Introduction

Cirrus clouds are globally distributed and play an important role in regulating the energy budget in the earth-atmosphere system, but they are still a source of major uncertainties in satellite and climate modeling studies [1–5].

To study macro- and microphysical properties such as cloud height, cloud thickness, and ice water content (IWC), active and passive remote sensing instruments that cover visible, infrared, and millimeter and submillimeter wavelengths have been adopted. These instruments include satellite instruments, such as TRMM (tropical rainfall measuring mission) [6] and CloudSat [7]; airborne-based instruments, such as WCR (U. of Wyoming) [8] and ACR (UMass and NASA) [9]; and ground-based instruments, such as MMCR (ARM millimeter wave cloud radar) [10] and CPRS (cloud profiling radar system) [11]. Among them, millimeter wavelength radars have an advantage in detecting the dynamic and structural properties of cirrus clouds [12]. To retrieve the physical properties of clouds, the interaction between electromagnetic waves and ice particles should be studied.

Before studying the scattering properties, the size and shape of cirrus clouds have to be confirmed. Cirrus clouds are composed of almost nonspherical ice crystals with various sizes and shapes. Some numerical methods have been widely used to calculate the scattering properties of cirrus cloud particles, such as the -matrix [13], the finite difference time domain (FDTD) [14], the discrete dipole approximation (DDA) [15], the finite element method (FEM) [16], and the method of moments (MOM) [17]. However, these ice particles are smaller compared to the wavelength of a millimeter wave and are usually randomly orientated, so the scattering properties of an ice cloud can be approximately calculated by the Rayleigh approximation [18].

At present, few researchers discuss the characteristics of a scattering electromagnetic wave when ice particles are in motion because modern weather radar has been equipped with video integrators, which can obtain the average value of received power by integral calculation [19]. Video integrators can transform the video signal, which can amplify the video signal and conduct analog-to-digital conversion and integration processing. Integration processing consists of calculating the distance integral and azimuth integral. However, video integrators have the disadvantage of reducing the distance resolution and have high average time requirements [20]. The radial resolution of radar has the following relationship with the pulse width and velocity of light : . If we use a video integrator, then the integrated times of distance would be introduced, with which the radial resolution of radar has the following relationship along with the pulse width and velocity of light : . When the pulse width remains unchanged, the video integrator would reduce the resolution of the radar range due to .

These factors led to an important question: how can we suppress echo fluctuation (RCS fluctuation) without reducing the distance resolution? To solve this problem, first, the echo fluctuation phenomenon of the moving spherical particles was simulated by using the vector potential method under the Rayleigh approximation. Second, we studied the reason why video integrators would reduce the resolution of the radar range and easily lose changed information and we suggested that the best way to suppress echo fluctuation is MIMO radar. To validate the suppression effect of MIMO radar, the RCS values of horizontally orientated hexagonal columns, ellipsoids, and spherical particles were simulated theoretically by HFSS software and compared with the results of detecting moving particles with vertically pointing radar. To experimentally validate the echo fluctuation suppression ability of MIMO radar, the RCS values of cuboid candles based on MIMO spatial diversity were measured in a microwave anechoic chamber at Nanjing University of Information Science and Technology.

#### 2. Analysis of Echo Fluctuation

When the radar transmitter transmits an electromagnetic pulse, an accurate timer is started to measure the time between the starting transmitting pulse and the received echo signal, which is scattered by atmospheric particles. The distance between the radar and the atmospheric particle can be deduced from the consumed time and the speed of light. The atmospheric particles are randomly distributed in space. The magnitude and phase of the electromagnetic waves scattered by atmospheric particles are randomly changed with the enhancement and attenuation of the interference. Atmospheric particles are not fixed at a certain position: assuming the amplitude of the electromagnetic wave scattered to the radar is , the fluctuating distribution follows the Rayleigh probability distribution, which leads to probability distributions of backscattered power in the forms of , and then, average processing would be used in order to retrieve the parameters of particles, which are proportional to the backscattering cross section of all particles in the unit volume [21].

To analyze the echo fluctuation of moving ice particles, the scattering properties of moving ice particles must first be computed. Mie theory [22] can be used to compute the scattering properties of ice particles because an ice cloud can be made of approximately spherical particles. Logan has reviewed the early history of light scattering [23], and the book written by Stratton has outlined this theory in terms of spherical vector wave functions. Professor Shanjie Zhang discussed the plane electromagnetic wave scattering of spherical particles using vector potential [24]. Rayleigh approximation is a special case of Mie scattering that describes the elastic scattering of light by spherical particles, which is much smaller than the wavelength of incident electromagnetic waves [25]. The monographs written by Van de Hulst and Bohren and Huffman have provided a concrete derivation [26, 27]. The vector potential technique was used, and the phenomenon of echo fluctuation produced by moving particles is studied in this paper. Because the ensembles of ice particles are sparse, the mutual interaction would not be considered.

According to Maxwell equations in a linear, isotropic, homogeneous medium, the charge density and current density are and , respectively, and the time-harmonic electromagnetic fields (, ) will satisfy the wave equation; thus, the scattering electric field intensity of the spherical particles in the spherical coordinate system can be obtained by the vector potential technique [24]: where is the amplitude of an incident electromagnetic wave, is the wave number of the incident electromagnetic wave, and are the dielectric constant and magnetic permeability (usually air) outside the sphere, respectively, is the distance between the center of sphere and the scattering observation point, is the radius of the spherical particle, is the azimuth angle in the spherical coordinate system, and and are the relative permittivity and permeability of the spherical particles, respectively.

Whether they are “-plane” or “-plane,” the total scattering electromagnetic field can be expressed as follows:

The received radar power is proportional to the scattering electromagnetic fields or , and can be obtained by [19]. To compute more conveniently, taking two rotating particles as an example and assuming an incident electromagnetic field is kV/m, the frequency of the millimeter wave radar is 94 GHz, and the equivalent dielectric constant of the particle is [28]. The radii of spherical particles and are 10 *μ*m and 8 *μ*m, respectively, the distance between and is 0.8 m, and the distance between the radar antenna and the center of the ensembles of ice particles is 6000 m, which can be found in Figure 1.