Phased-Array Radar System Simulator (PASIM): Development and Simulation Result Assessment

Article Phased-Array Radar System Simulator (PASIM): Development and Simulation Result Assessment

Zhe Li 1,2,*, Sudantha Perera 1,2 , Yan Zhang 1,2, Guifu Zhang 2,3 and Richard Doviak 4

1 School of Electrical and Computer Engineering, University of Oklahoma, Norman, OK 73019, USA; [email protected] (S.P.); [email protected] (Y.Z.) 2 Advanced Radar Research Center, University of Oklahoma, Norman, OK 73019, USA; [email protected] 3 School of Meteorology, University of Oklahoma, Norman, OK 73072, USA 4 NOAA/National Severe Storms Laboratory, Norman, OK 73072, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-405-430-4104

Received: 17 January 2019; Accepted: 14 February 2019; Published: 19 February 2019

Abstract: In this paper, a system-specific phased-array radar system simulator was developed, based on a time-domain modeling and simulation method, mainly for system performance evaluation of the future Spectrum-Efficient National Surveillance Radar (SENSR). The goal of the simulation study was to establish a complete data quality prediction method based on specific radar hardware and electronics designs. The distributed weather targets were modeled using a covariance matrix-based method. The data quality analysis was conducted using Next-Generation Radar (NEXRAD) Level-II data as a basis, in which the impact of various pulse compression waveforms and channel electronic instability on weather radar data quality was evaluated. Two typical weather scenarios were employed to assess the simulator’s performance, including a tornado case and a convective precipitation case. Also, modeling of some demonstration systems was evaluated, including a generic weather radar, a planar polarimetric phased-array radar, and a cylindrical polarimetric phased-array radar. Corresponding error statistics were provided to help multifunction phased-array radar (MPAR) designers perform trade-off studies.

Keywords: phased-array radar; polarimetric weather radar; simulation; data quality

1. Introduction The challenge of evaluating data quality from a ground or airborne phased-array radar (PAR) system, such as multifunction phased-array radar (MPAR)/Spectrum-Efficient National Surveillance Radar (SENSR) [1], posted the need of developing an integrated system that is suitable for both simulation and measurement validations. In weather radar applications, a sub-dB accuracy of weather radar moments may be needed, such as for scattering power measurement. To accurately assess the system performance and data quality of future phased-array weather radars, the requirement for simulation fidelity is high. Various weather radar system simulators were developed before. For example, Zrnić[2] described a procedure for simulating weather-like Doppler spectra and signals, in which time series of single-polarization weather radar was generated. Galati and Pavan [3] extended Zrnić’smethod to dual-polarized Doppler weather radar by generating two random sequences of horizontal and vertical polarization pairs with an assigned autocorrelation coefficient and a cross-correlation coefficient. Torres [4] presented a method for simulating over-sampled dual-polarization radar signals by combining Zrnić’smethod and Galati’s work. Cheong et al. [5] introduced a weather radar simulator which derived time-series signals from the output of a numerical weather prediction (NWP) model. Li et al. [6] presented a Monte Carlo simulation-based approach for airborne weather radars, which investigated the impacts of platform and different microphysical

Remote Sens. 2019, 11, 422; doi:10.3390/rs11040422 www.mdpi.com/journal/remotesensing Remote Sens. 2019, 11, 422 2 of 22 parameters on the polarimetric radar variables. Byrd et al. [7] introduced a polarimetric phased-array weather radar simulator, which evaluated the impacts of cross-polar fields on weather observations and included various transmit modes. Barcaroli et al. [8] presented a validation procedure to assess the ability of a polarimetric weather radar simulator to deal with raindrop-size distributions and outputs generated by NWP models. Recently, Schvartzman et al. [9] introduced a weather radar simulator which uses existing Next-Generation Radar (NEXRAD) measurement as truth, and it was still based on a traditional frequency-domain method for polarimetric time-series generation. Even with the achievements of prior simulations, data quality prediction and analysis for MPAR remain a challenge due to limitations. Firstly, using NWP model outputs as weather truth fields is limited to specific scenarios and events that are not sufficient for a comprehensive and realistic representation for all different operational cases. It is more reasonable to use real measurement fields. Secondly, although antenna patterns are widely included in studies such as Reference [7], the impacts of phased-array radar electronics are as important to data quality in practical applications, and transient response of the radar electronics, thus, needs to be considered. Distortions caused by amplifier nonlinearity, phase shifter quantization, or any instabilities of the array elements were reported to affect the overall system performance and data quality [10,11]. Weather measurements are highly sensitive to such effects. However, none of the current weather radar system simulators take them into account. Thirdly, pulse compression waveforms are increasingly used in weather radars, especially in PARs. To better estimate the data quality based on different PAR waveforms and predict the spectrum compliance of the transmitters, we should be able to precisely simulate the time-domain data sequences. Current simulations ignore the transient behaviors of electronics and weather scatterers. In future multi-function systems, however, longer pulses with wider bandwidth tend to be used. Lastly, for multi-mission PAR, the time-scheduling of radar resources (such as power-aperture dwell time) for adaptive scanning or target tracking functions requires the simulation execution in time steps for better system-level evaluations. The proposed solution, which is called phased-array radar system simulator (PASIM), is a newly developed, time-domain simulation software package that utilizes the operational NEXRAD Level II data as the basis of weather truth fields. Usage of such data is more of an engineering solution rather than of meteorological significance. A covariance matrix-based method is applied for time series simulation. The simulation process employs time-domain system updates and electronic behavior models to address the combined effects of antennas, transmit/receive (T/R) modules, and pulse compression waveforms. By using the functions in the MATLAB Phased-Array System Toolbox and other tools, the software is intrinsically based on time-step simulations. The new simulation approach can address the challenges of large-scale system data quality prediction and adds new insights into the system design validations. Based on the improved simulation methods and tools, a more systematic approach for data quality assessments for future PAR weather surveillance systems is developed. Performance evaluation metrics, including bias and standard deviation of the estimated polarimetric weather radar moments compared to the truth fields, are direct outputs from the simulation system. Furthermore, example radar system configurations are evaluated, including the configurations of array manifolds, waveforms, and processing schemes. As such, we can evaluate how the data quality differs and what design approaches are recommended for the best trade-off under different types of weather. This paper is organized as follows: Section2 details the PAR system simulation methods and techniques used by PASIM. Section3 provides system design examples and data quality analysis based on the system-specific architectures and different weather scenarios. Section4 presents the summary and conclusions. Remote Sens. 2019, 11, 422 3 of 22

2. PASIM System Design

2.1. Simulation Framework In PASIM, all basic radar subsystems are modeled as system objects, including a waveform generator, transmitter, antenna, platform, weather target, propagation path, receiver, etc. The parameters can be defined flexibly to support system-level trade-off analysis. When a radar scans an area of interest, at each scan angle, radar and target positions can be updated based on their motions. Then, the target (radar resolution cell) angles seen by the radar beams are calculated. After that, a steering vector of the current scan angle is computed, from which a radar beam is formed. During each dwell time, a pulse containing the designed transmit waveform is generated, amplified by the transmitter object and then radiated by the antenna (“radiator”) object. When the radiated electromagnetic (EM) waves interact with the weather targets, they are reflected and collected by the antenna (“collector”) objects. Then, the return signals are amplified by the receiver and beamformed, passed through a matched filter, and stored into a three-dimensional (azimuth × range × pulse) data cube. During this process, if the receiver sampling rate is sufficiently high, the transmitted and received signals can be computed based on time-step evolution from a pulse to the next. Currently, NEXRAD Level II data are used as input into the simulator and sampled as “truth fields”. Note that the NEXRAD data here are not meteorological truth fields, but measured radar moments from NEXRAD. Based on phased-array radar system specifications, modeling parameters, and antenna pattern measurements, an end-to-end system simulation can be conducted, and the in-phase and quadrature time series (I & Q) data can be obtained and saved as a data cube. Subsequently, the data cube is fed into a signal-processing chain to obtain polarimetric moment estimates. Finally, these estimates are compared with NEXRAD Level II data, and error statistics are obtained. In Figure1, the structure of PASIM with its functional blocks, and how these blocks are implemented using different programming languages are depicted. The radar system simulation and the testing scenario are based on NEXRAD Level II data. Additional meteorological data are also obtained through the Advanced Weather Interactive Processing System (AWIPS), which can be used to improve the ground-truth data of the weather scenarios and provide a data quality visualization. The system component (antenna, T/R module, and digital backend) parameters are obtained from available commercial products. The core of the implementation is based on the MATLAB Phased-Array System Toolbox [12,13] and other toolboxes. Customized models include signal-processing modules and electronics models. The output of the simulator is a data quality analysis report. Specifically, in Figure1, the input blocks comprise three parts. The “NEXRAD Moment Data” refer to NEXRAD Level II data available from the National Climatic Data Center, and the data are read by the Python ARM Radar Toolkit (Py-ART), which is an open-source software package widely used in the weather radar community [14,15]. The “Vendor/System Component Test Data/Transient Response Data” refer to the radar component parameters used in a real phased-array radar system, such as the datasheet of an AD9361/9371 radio frequency (RF) transceiver, the nonlinear response curve of a high-power amplifier (HPA), etc. The “Radar Parameters” contain user-specific radar system specifications, including waveform (simple rectangular, pulse compression, etc.), array manifolds (planar, cylindrical, etc.), scanning strategy (plan position indicator (PPI), range height indicator (RHI), volume scan, etc.), and so on. The “Time-Domain System Simulation” block is the core of PASIM, which employs the MATLAB Phased-Array System Toolbox, RF/Communications Toolbox and electronics models to perform end-to-end time-domain radar system simulations, as shown in Figure2a, whose output is time-series data organized in a three-dimensional data cube. The “Weather Radar Data Quality Prediction” block produces the radar data quality analysis report. Figure2b summarizes the overall data flow of weather radar data quality prediction. Time series for all the radar transceiver channels are organized into a data cube, which is fed into the weather radar signal-processing chain to compute spectral moments and polarimetric moments. The moment estimation outputs are compared Remote Sens. 2018, 10, x FOR PEER REVIEW 3 of 22

In PASIM, all basic radar subsystems are modeled as system objects, including a waveform generator, transmitter, antenna, platform, weather target, propagation path, receiver, etc. The parameters can be defined flexibly to support system-level trade-off analysis. When a radar scans an area of interest, at each scan angle, radar and target positions can be updated based on their motions. Then, the target (radar resolution cell) angles seen by the radar beams are calculated. After that, a steering vector of the current scan angle is computed, from which a radar beam is formed. During each dwell time, a pulse containing the designed transmit waveform is generated, amplified by the transmitter object and then radiated by the antenna (“radiator”) object. When the radiated electromagnetic (EM) waves interact with the weather targets, they are reflected and collected by the antenna (“collector”) objects. Then, the return signals are amplified by the receiver and beamformed, passed through a matched filter, and stored into a three-dimensional (azimuth × range × pulse) data cube. During this process, if the receiver sampling rate is sufficiently high, the transmitted and received signals can be computed based on time-step evolution from a pulse to the next. Currently, NEXRAD Level II data are used as input into the simulator and sampled as “truth fields”. Note that the NEXRAD data here are not meteorological truth fields, but measured radar moments from NEXRAD. Based on phased-array radar system specifications, modeling parameters, and antenna pattern measurements, an end-to-end system simulation can be conducted, and the in- phase and quadrature time series (I & Q) data can be obtained and saved as a data cube. Subsequently, the data cube is fed into a signal-processing chain to obtain polarimetric moment estimates. Finally, these estimates are compared with NEXRAD Level II data, and error statistics are obtained. In Figure 1, the structure of PASIM with its functional blocks, and how these blocks are implemented using different programming languages are depicted. The radar system simulation and the testing scenario are based on NEXRAD Level II data. Additional meteorological data are also obtained through the Advanced Weather Interactive Processing System (AWIPS), which can be used Remotet Sens.o improve2019, 11 the, 422 ground-truth data of the weather scenarios and provide a data quality visualization.4 of 22 The system component (antenna, T/R module, and digital backend) parameters are obtained from available commercial products. The core of the implementation is based on the MATLAB Phased- withRemote theArray Sens. NEXRAD S 2018ystem, 10 ,T x Level-IIoolbox FOR PEER [12 data REVIEW,13] to and produce other toolboxes a data quality. Customized report models in the form include of statisticalsignal-processing errors4 of such22 as biasmodules and standard and electronics deviation. models. The output of the simulator is a data quality analysis report. Figure 1. The structure of phased-array radar system simulator (PASIM).

Specifically, in Figure 1, the input blocks comprise three parts. The “NEXRAD Moment Data” refer to NEXRAD Level II data available from the National Climatic Data Center, and the data are read by the Python ARM Radar Toolkit (Py-ART), which is an open-source software package widely used in the weather radar community [14,15]. The “Vendor/System Component Test Data/Transient Response Data” refer to the radar component parameters used in a real phased-array radar system, such as the datasheet of an AD9361/9371 radio frequency (RF) transceiver, the nonlinear response curve of a high-power amplifier (HPA), etc. The “Radar Parameters” contain user-specific radar system specifications, including waveform (simple rectangular, pulse compression, etc.), array manifolds (planar, cylindrical, etc.), scanning strategy (plan position indicator (PPI), range height indicator (RHI), volume scan, etc.), and so on. The “Time-Domain System Simulation” block is the core of PASIM, which employs the MATLAB Phased-Array System Toolbox, RF/Communications Toolbox and electronics models to perform end-to-end time-domain radar system simulations, as shown in Figure 2a, whose output is time-series data organized in a three-dimensional data cube. The “Weather Radar Data Quality Prediction” block produces the radar data quality analysis report. Figure 2b summarizes the overall data flow of weather radar data quality prediction. Time series for all the radar transceiver channels are organized into a data cube, which is fed into the weather radar signal-processing chain to compute spectral moments and polarimetric moments. The moment estimation outputs are compared with the NEXRAD Level-II data to produce a data quality report in

the form of statistical errors such as bias and standard deviation. Figure 1. The structure of phased-array radar system simulator (PASIM).

(a)

(b)

Figure 2. Operations of the key modules of PASIM: (a) time-domain system simulation; (b) weather Figure 2. Operations of the key modules of PASIM: (a) time-domain system simulation; (b) weather radarradar data data quality quality prediction. prediction. 2.2. Subsystems 2.2. Subsystems In this section, key subsystems in PASIM that have major impacts on weather data quality are In this section, key subsystems in PASIM that have major impacts on weather data quality are introduced, which include antennas, T/R modules, and RF transceivers, as well as waveforms. introduced, which include antennas, T/R modules, and RF transceivers, as well as waveforms.

2.2.1. Antennas

Remote Sens. 2019, 11, 422 5 of 22

Remote Sens. 2018, 10, x FOR PEER REVIEW 5 of 22 2.2.1. Antennas In PASIM, the phased-array radar is placed on a platform, whose position, velocity, and In PASIM, the phased-array radar is placed on a platform, whose position, velocity, and acceleration can be defined. The orientation axes of the platform can be manipulated by a rotation acceleration can be defined. The orientation axes of the platform can be manipulated by a rotation matrix, making it suitable for both ground-based and airborne applications. Furthermore, effects of matrix, making it suitable for both ground-based and airborne applications. Furthermore, effects of electronic scanning such as beam broadening and scan loss are incorporated. Both the element electronic scanning such as beam broadening and scan loss are incorporated. Both the element radiation radiation pattern and array pattern can be imported from EM simulations or chamber measurements. pattern and array pattern can be imported from EM simulations or chamber measurements. Moreover, Moreover, the antenna element is modeled to have polarization diversity by specifying polarized the antenna element is modeled to have polarization diversity by specifying polarized radiation radiation patterns. For instance, realistic dual-polarized patch and crossed-dipole elements are patterns. For instance, realistic dual-polarized patch and crossed-dipole elements are included, whose included, whose horizontal and vertical polarization components can be transmitted simultaneously horizontal and vertical polarization components can be transmitted simultaneously or alternately to or alternately to measure the target scattering matrix. The array axis can be specified flexibly so that measure the target scattering matrix. The array axis can be specified flexibly so that array elements array elements are located along the selected coordinate system axis. The computation of the array are located along the selected coordinate system axis. The computation of the array factor supports a factor supports a linear array, planar array, circular array, and conformal array, while beam steering linear array, planar array, circular array, and conformal array, while beam steering and beamforming and beamforming are implemented by applying complex weights to the individual elements of the are implemented by applying complex weights to the individual elements of the array. To accelerate array. To accelerate the computations, a full array can be partitioned into one or more subarrays, and the computations, a full array can be partitioned into one or more subarrays, and each subarray can each subarray can be steered independently. As an example, Figure 3a,b show a dual-polarized patch be steered independently. As an example, Figure3a,b show a dual-polarized patch element and its element and its three-dimensional (3D) radiation pattern, Figure 3c shows an 8 × 8 planar subarray three-dimensional (3D) radiation pattern, Figure3c shows an 8 × 8 planar subarray using this antenna using this antenna element, while Figure 3d,e show the azimuth cut and elevation cut for the element, while Figure3d,e show the azimuth cut and elevation cut for the synthesized array pattern synthesized array pattern of an 80 × 80 planar array using PASIM, which is formed from 100 of the 8 of an 80 × 80 planar array using PASIM, which is formed from 100 of the 8 × 8 subarrays. The basic × 8 subarrays. The basic parameters of the antenna element and array are listed in Table 1. parameters of the antenna element and array are listed in Table1.

(a) (b)

Figure 3. Cont.

Remote Sens. 2019, 11, 422 Remote Sens. 2018, 10, x FOR PEER REVIEW 6 of 22 6 of 22

(e)

Figure 3. The antenna radiatingFigure element 3. The and antenna array radiating constructed element in PASIM: and array (a) aconstructed simple patched in PASIM: (a) a simple patched element; (b) three-dimensionalelement; (3D) radiation (b) three pattern-dimensional of the patch (3D element;) radiation (c) an pattern 8 × 8 planarof the subarray; patch element; (c) an 8 × 8 planar (d) azimuth cut for the synthesizedsubarray; radiation (d) azimuth pattern cut of for an the 80 synthesized× 80 planar radiation array; (e) pattern elevation of an cut 80 for × 80 planar array; (e) elevation the synthesized radiation patterncut for of the an 80synthesized× 80 planar radiation array. pattern of an 80×80 planar array.

Table 1. The basic parametersTable of the 1. antenna The basic element parameters and array. of the antenna element and array.

ParameterParameter Value Value TypeType Patch Patch Size 5.24Size× 5.24 cm 5.24 × 5.24 cm Polarization Dual linear polarized TransmitPolarization Yes Dual linear polarized ReceiveTransmit Yes Yes Number of elements in azimuthReceive 80 Yes Number of elements in elevationNumber of elements 80 in azimuth 80 Number of elements in elevation 80 2.2.2. T/R Modules and RF Transceivers 2.2.2. T/R Modules and RF Transceivers For a multi-channel polarimetric radar system, electronic instability from pulse-to-pulse (P2P) and channel-to-channel (C2C) needsFor a tomulti be modeled,-channel includingpolarimetric high-power radar system, amplifier electronic (HPA) instability distortions from pulse-to-pulse (P2P) and instabilities in RF transceiverand channel channels,-to-channel quantization (C2C) error needs of phase to shiftersbe modeled, and attenuators including in high T/R-power amplifier (HPA) modules, imbalance of thedistortions power combiners and inst andabilities splitters in in RF each transceiver channel, fluctuation channels, inquantization receiver noise error of phase shifters and floor, phase variations causedattenuators by local oscillatorin T/R modules, and reference imbalance clock instability, of the power and socombiners on. Among and all splitters in each channel, these factors, HPA complexfluctuation gain (including in receiver amplitude noise floor, and phase) phase variation variations due caused to thermal by local effects, oscillator and reference clock which may reduce the systeminstability, coherency and [so16 ],on. is Among a major sourceall these of factors, electronic HPA instability. complex Accordingly,gain (including amplitude and phase) several mathematical modelsvariation were due developed to thermal to characterize effects, which the may nonlinear reduce behavior the system of HPA, coherency such [16], is a major source of as the Saleh model, Volterraelectronic series model, instability. complex Accordingly, power series severa model,l mathematical and Hammerstein–Wiener models were developed to characterize the model [10]. In this study, thenonlinear Saleh modelbehavior is usedof HPA, as a such simple as two-parameterthe Saleh model, function Volterra to series depict model, the complex power series amplitude-to-amplitude (AM-to-AM)model, and andHammerstein amplitude-to-phase–Wiener model (AM-to-PM) [10]. In characteristics this study, the of Saleh nonlinear model is used as a simple two- amplifiers. Ideally, the inputparame signalter to function the amplifier to depict is expressed the amplitude as [17-to] -amplitude (AM-to-AM) and amplitude-to-phase (AM- to-PM) characteristics of nonlinear amplifiers. Ideally, the input signal to the amplifier is expressed as [17] x(t) = r(t) cos[ω0t + ϕ(t)], (1) 푥(푡) = 푟(푡)cos[휔 푡 + 휑(푡)], where ω0 is carrier frequency, and r(t) and ϕ(t) are the amplitude and phase of0 the modulated signal, (1) respectively. The distorted output of the nonlinear amplifier is where 휔0 is carrier frequency, and 푟(푡) and 휑(푡) are the amplitude and phase of the modulated

signaly(,t respectively) = A[r(t)] cos. The[ω 0distortedt + ϕ(t) + outputΦ[r(t)]] of, the nonlinear amplifier is (2)

푦(푡) = 퐴[푟(푡)] cos[휔0푡 + 휑(푡) + Φ[푟(푡)]], (2)

where 퐴[푟(푡)] refers to AM-to-AM conversion, and Φ[푟(푡)] refers to AM-to-PM conversion. Specifically, these two functions can be expressed as

Remote Sens. 2019, 11, 422 7 of 22 where A[r(t)] refers to AM-to-AM conversion, and Φ[r(t)] refers to AM-to-PM conversion. Speciﬁcally, theseRemote two Sens. functions 2018, 10, x FOR can PEER be expressed REVIEW as 7 of 22

훼 α푟ar 퐴(A푟()r=) = 푎 , , (3)(3) + 2 2 1 +1 훽푎β푟ar 2 훼 푟 2 휙αφr (4) Φ(r() )== 2. Φ r 1 + 훽 푟 2 . (4) 1 +휙βφr

AsAs anan example,example, the the optimum optimum parameters parameters for for a solid a solid-state-state power power amplifier amplifier were were selected selected as 훼푎 as= α2a.1587= 2.1587, 훽푎,=βa1.=15171.1517, 훼휙, α=φ 4=.00334.0033, and, and 훽휙βφ==9.10409.1040. .Figure Figure 44aa shows thethe idealidealand and distorted distorted envelopeenvelope of of a a 60-dB 60-dB Taylor-windowedTaylor-windowed linear linear frequency frequency modulation modulation (LFM) (LFM) waveform, waveform, and and Figure Figure4 b4b comparescompares autocorrelationautocorrelation functionfunction (ACF).(ACF). As As can can be be seen, seen, after after thethe SalehSaleh nonlinearity nonlinearity model model is is incorporatedincorporated into into the the amplifier, amplifier, the the Taylor-windowed Taylor-windowed LFM LFM waveform waveform is is distorted, distorted, and and the the matched matched filterfilter output output shows shows increased increased range range sidelobes sidelobes which which are are undesirable. undesirable.

(a) (b)

FigureFigure 4. 4. TheThe impactimpact ofof thethe SalehSaleh nonlinearitynonlinearity modelmodel onon anan exampleexample ofof aa60-dB 60-dB TaylorTaylor windowed windowed linearlinear frequency frequency modulation modulation (LFM) (LFM waveform) waveform and and autocorrelation autocorrelation function function (ACF): (ACF) (a):distortion (a) distortion of the of waveformthe waveform envelope; envelope (b) ACF; (b) ACF of the of waveform the waveform before before and afterand after nonlinear nonlinear distortion. distortion.

OnOn thethe otherother hand, the the C2C C2C spatial spatial instability instability in in a PAR a PAR can can be beevaluated evaluated in PASIM in PASIM as well. as well. The TheC2C C2C amplitude amplitude instability instability mainly mainly distorts distorts antenna antenna pattern, pattern, while while C2C C2C phase phase instability will will both both distortdistort antenna antenna pattern pattern and and increase increase phase phase noise. noise. Another Another C2C C2C error error comes comes from from T/R T/R modulemodule failure,failure, whichwhich distorts distorts antenna antenna pattern pattern by raising by raising sidelobes sidelobe and reducings and reducing gain. Also, gain. the impact Also, of the quantization impact of errorquantization introduced error by introduced the phase shifter by the and phase the shifter resultant and data the qualityresultant can data also quality be assessed can also using be assessed PASIM. Theseusing errorsPASIM. are These included errors during are included the beamforming during the process.beamforming As an process. example, As a an circular example, array a circular with a ◦ diameterarray with of a 10 diameter m is simulated. of 10 m Ais 90simulated.sector consisting A 90° sector of 156consisting patch elements of 156 patch is excited elements to form is excited a beam to ◦ ofform 1.1 abeamwidth. beam of 1.1 Then,° beamwidth. a Taylor Then tapering, a Taylor is applied tapering to keep is applied the pattern to keep sidelobes the pattern below sidelobe−30 dB,s whichbelow matches −30 dB, thewhich NEXRAD matches requirements the NEXRAD as requirements shown in Section as shown 3.1. The in Section C2C random 3.1. The amplitude C2C random and phaseamplitude errors and are modeled phase error as Gaussians are modeled distribution as Gaussian variables distribution with zero variables mean and with standard zero deviationmean and ◦ ofstandard 0.5 dB and deviation 6 , respectively, of 0.5 dB andand the6°, systemrespectively, has a 5%and probability the system of has element a 5% failures.probability It is of assumed element thatfailures. 5-bit It phase is assumed shifters that are 5- used.bit phase Figure shifter5a showss are used. the arrayFigure patterns 5a shows as the impacts array patterns from the as random impacts amplitudefrom the random and phase amplitude errors, whereas and phase Figure errors5b, showswhereas the Figure array patterns5b shows without the array quantization patterns without error andquantization with quantization error and errors with basedquanti onzation 5-bit error phases based shifters. on 5-bit phase shifters.

RemoteRemote Sens.Sens.2019 2018,,11 10,, 422 x FOR PEER REVIEW 88 of 2222

(a) (b)

FigureFigure 5. 5.Typical Typical array array radiation radiation patterns patterns in PASIM in PASIM by incorporating by incorporating the impact the impact of channel-to-channel of channel-to- (C2C)channel instability: (C2C) instability (a) impacts: (a) ofimpacts the random of the channelrandom amplitude channel amplitude and phase and errors; phase (b )error impactss; (b) of impacts phase shifterof phase quantization shifter quantization error based error on 5-bitbased phase on 5- shifters.bit phase shifters.

2.3.2.3. WaveformsWaveforms InIn PASIM,PASIM, variousvarious pulsepulse compressioncompression waveformswaveforms cancan bebe selected,selected, andand theirtheir impactsimpacts onon weatherweather radarradar datadata qualityquality cancan bebe evaluated.evaluated. AsAs anan example,example, anan LFMLFM waveform,waveform, aa Taylor-windowedTaylor-windowed LFMLFM waveform,waveform, andand anan optimizedoptimized nonlinearnonlinear frequencyfrequency modulationmodulation (NLFM)(NLFM) waveformwaveform areare implementedimplemented andand compared.compared. The The “generic “generic radar” radar” parameters parameters for for this this simulation simulation are areshown shown in S inection Section 3.3.1. 3.3.1 The. Thebandwidth bandwidth of the of NLFM the NLFM waveform waveform is 3.6 isMHz 3.6, MHz,and the and transmit the transmit pulse width pulse is width 50 µs. is Th 50isµ examples. This exampleNLFM waveform NLFM waveform uses Gaussian uses Gaussian function as function a spectral asa density spectral function, density which function, can which achieve can a sidelobe achieve alevel sidelobe below level −70 belowdB without−70 dBamplitude without weighting amplitude ( weightingthus, no loss (thus, of signal no loss-to- ofnoise signal-to-noise ratio (SNR))ratio [18]. (SNR))The windowed [18]. The LFM windowed uses a LFMTaylor uses window a Taylor with window a maximum with a maximumsidelobe level sidelobe of −60 level dB ofbelow−60 dBthe belowmainlobe the peak mainlobe so that peak it can so thatachieve it can a similar achieve level a similar of range level sidelobe of range as sidelobe of the NLFM as of thewaveform. NLFM waveform.Figure 6 plots Figure the6 plots matched the matched filter output filters outputs,, reflectivity reflectivity estimation estimation outputs outputs,, and and scatter scatter plot plot of t ofhe thereflectivity reflectivity estimation estimation (truth (truth vs.vs. estimation) estimation) for for the the three three waveforms waveforms,, from from a simulated a simulated sector sector scan scan of ofa tornado a tornado ca case.se. It Itcan can be be found found that that the the high high range sidelobes (around(around− −1313dB) dB) of of the LFM waveformwaveform exertexert an an obvious obvious impact impact on on reflectivity reflectivity data data quality. quality For. instance, For instance, Figure Figure6b shows 6b thatshow strongers that stronger echoes inechoes nearer in range nearer contaminate range contaminate the relatively the relatively weak echoes weak in echoes the northwest in the northwest corner. This corner is also. This validated is also byvalidated Figure6 byc which Figure shows 6c which a larger show deviations a larger indeviation low-reflectivity in low-reflectivity regions. Also, region errors. Also statistics, error indicatestatistics thatindi thecate standard that the standard deviation deviation of estimated of estimated reflectivity reflectivity compared compared to NEXRAD to NEXRAD reflectivity reflectivity for the LFM for waveformthe LFM waveform reaches 1.19 rea dB,ches which 1.19 dB, does which not meet does the not NEXRAD meet therequirements NEXRAD requirement as showns in as Section shown 3.1 in. ForSection the windowed 3.1. For the LFM windowed waveform, LFM while waveform, it can achieve while lower it can range achieve sidelobe lower levels, range its sidelobe power efficiencylevels, its ispower only 0.35efficiency as a result is only of 0.35 aggressive as a result windowing. of aggressive Due windowing. to reduced transmitDue to reduced power, thetransm estimatesit power, in low-reflectivitythe estimates in regions low-reflectivity have larger region errors,s ashave shown larger in Figure errors,6 f. asMoreover, shown in the Figure standard 6f. Moreover, deviation the of thestandard estimated deviation reflectivity of the is 1.14estima dB,ted which reflectivity still does is not1.14 meet dB, which the NEXRAD still does requirements, not meet the as NEXRAD shown in Sectionrequirement 3.1. Ass, as a comparison, shown in Section for the 3.1 NLFM. As a waveform comparison, whose for powerthe NLFM efficiency waveform is 0.87, whose most powerof the relativelyefficiency weakis 0.87 echoes, most of in the the relatively northwest weak corner echoes can in be the observed northwest in Figure corner6 h,can and be theobserved scatter in plot Figure in Figure6h, and6i indicatesthe scatter that plot the in reflectivity Figure 6i indicates estimates that are consistentthe reflectivity with theestimates NEXRAD are truth.consistent For this with case, the theNEXRAD error statistics truth. For show this that case, the the standard error deviation statistics show of estimated that the reflectivity standard is deviation 0.80 dB, which of estimated meets thereflectivity NEXRAD is data0.80 dB, quality which requirement. meets the NEXRAD data quality requirement.

Remote Sens. 20192018,, 1110,, 422x FOR PEER REVIEW 99 of of 22

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Figure 6. 6. ExamplesExamples of ofPASIM PASIM scan scan outputs, outputs, when when the specific the speciﬁc waveforms waveforms of an LFM, of an a LFM,Taylor a- Taylor-windowedwindowed LFM, and LFM, an andexample an example nonlinear nonlinear frequency frequency modulation modulation (NLFM)(NLFM) waveform waveform are used are to

usedestimate to estimate reflectivity reflectivity (ZH) of (Za Hsector) of a scan sector for scan a tornado for a tornado case: case:(a) m (atcheda) matched filter filteroutput output for LFM for LFM;; (b) (sbimulated) simulated ZH ZforH LFMfor LFM;; (c) Z (cH)Z scatterH scatter plot plotfor LFM for LFM;; (d) m (datched) matched filter filter output output for forwindowed windowed LFM LFM;; (e) (seimulated) simulated ZH ZforH forwindowed windowed LFM LFM;; (f) Z (fH)Z scatterH scatter plot plot for windowed for windowed LFM LFM;; (g) m (gatched) matched filter filter output output for forNLFM NLFM;; (h) (shimulated) simulated ZH for ZH NLFMfor NLFM;; (i) Z (Hi)Z scatterH scatter plot plotfor NLFM. for NLFM.

2.4. Time Time-Series-Series Generation and Signal Processing

2.4.1. Monte Carlo Method 2.4.1. Monte Carlo Method In PASIM, there are two possible ways to model the randomness of weather scatterers in space and In PASIM, there are two possible ways to model the randomness of weather scatterers in space time. The first one is Monte Carlo method. That is, in each resolution volume, the total backscattered and time. The first one is Monte Carlo method. That is, in each resolution volume, the total wave field is calculated by summation of the contributions from each scatterer. To simplify the model, backscattered wave field is calculated by summation of the contributions from each scatterer. To it is assumed that all the scatterers in the resolution volume have the same size. According to the simplify the model, it is assumed that all the scatterers in the resolution volume have the same size. definition of reflectivity [19–21], According to the definition of reflectivity [19–21], 4 4 Z Z 4λ4휆 22 22 Zhh푍 == ∫||s푠hh|| N푁((D퐷)dD푑퐷 = 퐾K ∫|푠|shh|| 푁N((퐷D)푑퐷)dD. .(5) (5) ℎℎ 4 4 2 2 ℎℎ ℎℎ π휋|K|퐾w푤| |

The horizontal scattering amplitude of each scatterer can be obtained as

Remote Sens. 2019, 11, 422 10 of 22

The horizontal scattering amplitude of each scatterer can be obtained as p |shh| = Zhh/K/N, (6) where Zhh is the horizontal reﬂectivity in the linear scale, λ is the wavelength of an electromagnetic wave, D is the drop diameter, N(D) is the drop size distribution, Kw is the dielectric constant factor of water, and N is the number of scatterers in the resolution volume. Accordingly, the vertical scattering amplitude of each scatterer can be calculated as

shh |svv| = √ , (7) Zdr where Zdr is the differential reﬂectivity in the linear scale. At each pulse repetition time (PRT), the scatterers’ position and velocity update according to the Doppler velocity and spectrum width. It is assumed that the copolar correlation coefﬁcient ρhv is −σ2/2 reduced by a factor of e δ due to the random scattering phase difference, where σδ is the standard −σ2/2 deviation of scattering phase difference [19]. That is, ρhv = e δ . As a result, q q 2 2 σδ = −2 ln(ρhv) = σδh + σδv. (8) √ For simplicity, PASIM uses σδh = σδv = σδ/ 2, where σδh and σδv are standard deviations of horizontal backscattering phase ϕh and vertical backscattering phase ϕv, respectively. The complex scattering amplitudes for a scatterer are expressed as

jϕh shh = |shh|·e , (9)

jϕv jφ svv = |svv|·e ·e DP , (10) where φDP is the differential phase. The total complex backscattering amplitudes of the resolution volume are N N S = s ·e−jkd·r = s ·e−j2ki·rl hh ∑ hhl ∑ hhl , (11) l=1 l=1 N N = · −jkd·r = · −j2ki·rl Svv ∑ svvl e ∑ svvl e , (12) l=1 l=1 where N is the total number of scatterers in the volume, and ki and kd are incident and backscattering wave vectors, respectively. Each resolution volume is equivalent to a “single scattering center”. The scattering center is an equivalent point target that produces the same scattering amplitudes as the volume does. Shh and Svv are related to the scattering matrix element of the equivalent scattering center by a scaling factor, and Shh and Svv are updated at each time step (PRT) according to the updated distribution of the hydrometeors’ position and velocity within the resolution volume.

2.4.2. Covariance Matrix Method Generating I/Q time-series data based on the statistical correlation among pulses and polarizations is the second method in PASIM. Firstly, two independent random signals V1 and V2 are generated, which follow Gaussian distribution with zero-mean and their standard deviations are derived from reﬂectivity values. According to Reference [20], the autocorrelation function of the received signals is given by

2 −8( πσvmTs ) −j 4πvmTs R(mTs) = S·e λ ·e λ + N·δm, (13) Remote Sens. 2019, 11, 422 11 of 22

where S is the average signal power, v and σv refer to the mean radial velocity and spectrum width of the radar resolution volume ﬁlled by precipitation, m is the index (“lag”) of the pulse (0 ≤ m ≤ M − 1, where M is the number of pulses in the dwell time), Ts is the pulse repetition time, N is the mean white noise power, and δm is 1 for m = 0 and zero otherwise. Based on Equation (13), a complex covariance matrix C, which is an M-by-M Hermitian positive-deﬁnite matrix, can be constructed. Using Cholesky decomposition, C may be decomposed as

C = P·P∗, (14) where P is an M-by-M upper triangular matrix from the diagonal and upper triangle of covariance matrix C. Then, P is applied to V1 and V2 as

V1 = V1·P, (15)

V2 = V2·P. (16) Next, the complex scattering amplitudes of the resolution volume are generated as

Shh = V1, (17)

q ejφDP 2 √ Svv = ρhv·V1 + 1 − ρhv·V2 · . (18) Zdr As a comparison, both the Monte Carlo method and covariance matrix method are statistical methods. Generally, the Monte Carlo method is more representative of the physical process in the real world, as it assumes that there are multiple scatterers within each resolution volume, but it will take more time to run the simulation, while the covariance matrix method is more computationally efﬁcient. A large number of simulations show that both methods can achieve similar moment estimation accuracy when other radar system parameters are the same. The main radar components, parameters, and models used in the simulations are listed in Table2.

Table 2. Summary of the main radar components, parameters, and models used in the simulations. HPA—high-power ampliﬁer.

Radar Component/Parameter/Model Value Antenna element Dual-polarized patch HPA nonlinearity Saleh model Digital phase shifter 5-bit Waveform Rectangular pulse Weather target model Covariance matrix

3. System-Speciﬁc Examples and Data Quality Predictions

3.1. Requirements PASIM is used as a system trade-off study tool such as for the data quality prediction of MPAR/SENSR radar and spectrum compliance investigations. The requirement of data quality analysis is providing high-level guidance for engineering designers to perform trade-off analysis and risk mitigations in the early stage of system design. For example, analysis can provide a range of error margins of weather radar products for a given waveform design that complies with the National Telecommunications and Information Administration (NTIA) spectrum masking. In this section, solutions and techniques described in Section2 are applied to speciﬁc radar systems. Bias and standard deviation of the main weather radar products are used as the performance metrics [22], as listed in Table3. As this paper mainly focuses on polarimetric moment evaluation, data quality of Doppler moments such as radial velocity and spectrum width are not listed in later sections. To Remote Sens. 2019, 11, 422 12 of 22 evaluate Doppler moments, a different scanning strategy (such as shorter pulse repetition time) needs to be employed to mitigate velocity aliasing, which is different from the conﬁguration of polarimetric moment measurements.

Table 3. Next-Generation Radar (NEXRAD) requirements of data quality for basic weather radar moments.

Radar Variable Bias Standard Deviation Reflectivity 1 dB 1 dB Radial velocity 1 m/s 1 m/s Spectrum width 1 m/s 1 m/s Differential reflectivity 0.1 dB 0.2 dB Correlation coefficient 0.005 0.01 Differential phase 1◦ 2◦

3.2. Configuration of System Examples and Weather Scenarios In addition to a generic radar reference with a similar configuration to NEXRAD, two PAR systems with different array manifolds were used as examples for data quality evaluations. The first system example was the Advanced Technology Demonstrator (ATD) [23,24], which is a planar array being tested by the National Severe Storms Laboratory (NSSL) of the National Oceanic and Atmospheric Administration (NOAA). The other example was the Cylindrical Polarimetric Phased-Array Radar (CPPAR) [25,26], which uses a cylindrical polarimetric array with commutated beams, such that the antenna patterns are invariant with respect to azimuth scan angles. The azimuth-invariant beams can enhance polarimetric pattern isolations. Because the focus of the examples was demonstrating the impact of antenna pattern synthesis, we assumed these systems used the same waveform (1.6 µs rectangular pulse), and the channel electronics used generic parameters as the Saleh model for the amplifier and a 5-bit phase shifter in Section 2.2.2. Two representative weather scenarios were considered. The first scenario was an intense tornado with a large reflectivity gradient in the field of view. The tornado event occurred in Moore, Oklahoma at 8:08 p.m. coordinated universal time (UTC) on 20 May 2013, in which Level-II data from KTLX radar (an operational NEXRAD) were used as weather truth fields. The second case was convective precipitation with a relatively uniform weather field distribution, which was also observed by KTLX radar on 4:33 a.m. UTC on 19 May 2013. In each case, a sector of a PPI scan with 0.5◦ elevation, which mainly consists of precipitation area, was selected for PAR simulations. Since the two events were observed by the same NEXRAD within two consecutive days, the time-variant NEXRAD system drift was small, which is beneficial for consistent data quality evaluations.

3.3. Data Quality Results from PASIM

3.3.1. Generic Radar A generic SENSR radar system was simulated, whose parameters were chosen to match the key system parameters of NEXRAD as listed in Table4. After PASIM generated the I/Q data cubes, the pulse pair processing (PPP) method was employed to estimate the polarimetric weather radar moments. Both the tornado and the convective precipitation cases were used as weather truth ﬁelds. In the tornado case, a northern sector of the PPI image that mainly consisted of precipitation is plotted in Figure7, which shows that all the simulated polarimetric moments were consistent with the truth ﬁelds, and error statistics are provided in Section 3.3.4. The major source of estimation error was found to be the sidelobes of the antenna pattern, which was validated by the fact that, if the sidelobe level was negligible, the standard deviation for estimated ZH and ZDR both reduced to 0.01 dB. Remote Sens. 2019, 11, 422 13 of 22

Table 4. System speciﬁcations of a generic radar. Remote Sens. 2018, 10, x FOR PEER REVIEW 13 of 22 Radar Parameters Values After PASIM generated theFrequency I/Q data cubes, the pulse 2800 pair MHz processing (PPP) method was employed to estimate the polarimetricAntenna weather Gain radar moments 45.5. Both dB the tornado and the convective ◦ precipitation cases were used as weatherBeamwidth truth fields. In the tornado 1.0 case, a northern sector of the PPI First sidelobe −32 dB image that mainly consisted of precipitationWaveform is plotted in Figure Rectangular 7, which pulse shows that all the simulated polarimetric moments were consistentPulse width with the truth fields, 1.6andµ s error statistics are provided in Section 3.3.4. The major sourcePulse repetition of estimation frequency error was found 300 to Hz be the sidelobes of the antenna pattern, which was validatedRange by the resolution fact that, if the sidelobe 250 level m was negligible, the standard Peak power 700 kW deviation for estimated 푍 and 푍 both reduced to 0.01dB. 퐻 Noise퐷푅 ﬁgure 2.7 dB

(a) (b)

Figure 7.7. SimulatedSimulated weatherweather radar radar moments moments from from the the generic generic radar radar example, example, and and comparison comparison with with the Nest-Generationthe Nest-Generation radar radar (NEXRAD) (NEXRAD “truth”) “truth” fields for fields Case for 1: (Casea) reflectivity, 1: (a) reflectivity (b) differential, (b) diffe reflectivity,rential (reflectivityc) correlation, (c) coefficient, correlation ( dcoefficient) differential, (d) phase. differential phase.

◦ For thethe convectiveconvective precipitationprecipitation case, aa largerlarger sectorsector spanningspanning 9090° inin azimuthazimuth comprisingcomprising moremore uniform weather ﬁeldsfields waswas selected. As can be seen in Figure8 8,, the the simulated simulated moments moments were were alsoalso consistentconsistent with NEXRAD truth ﬁelds.fields. E Errorrror statistics are provided in Section 3.3.43.3.4,, whichwhich cancan alsoalso meet thethe requirementsrequirements inin TableTable3 .3.

Remote Sens. 20182019, 1011, x 422 FOR PEER REVIEW 1414 of of 22

(a) (b)

Figure 8. Simulated weatherweather radarradar moments moments from from the the generic generic radar radar example, example, and and comparison comparison with with the theNEXRAD NEXRAD “truth” “truth” fields fields for Case for 2:Case (a) reflectivity, 2: (a) reflectivity, (b) differential (b) differential reflectivity, reflectivity, (c) correlation (c) correlation coefficient, coefficient,(d) differential (d) differential phase. phase.

3.3.2. Advanced Advanced Technology Demonstrator (ATD) To implement a testbed of a larger scale planar polarimetricpolarimetric phased phased-array-array radar radar (PPPAR) (PPPAR) for weather and air air-traffic-traffic observation, ATD, which is an S-bandS-band dual-polarizationdual-polarization active phased phased-array-array radar with 4 4-m-m a apertureperture size size,, wa wass initially deployed in Norman, Oklahoma in 2018 [ 2244]. The The technical technical specificationsspecifications of of ATD ATD,, which are relevant to PASIM, are listed in Table5 5.. Again,Again, bothboth thethe tornadotornado and th thee convective precipitation precipitation case casess we werere simulated, simulated, while while,, for for the the PPPAR PPPAR system, system, the the “ “uniform”uniform” weather fieldsfields inin thethe second second case case provided provided more more insights insights into into the the weather weather radar radar data d quality.ata quality. Note Note that thatPASIM PASIM used used a simplified a simplified dual-polarized dual-polarized patch patch antenna antenna model model as described as described in Section in Section 2.2.1. The 2.2.1. PASIM The outputs of the polarimetric moments and the average Z bias along the azimuth dimension are PASIM outputs of the polarimetric moments and the averageDR 푍퐷푅 bias along the azimuth dimension areshown shown in Figure in Figure9. Error 9. Error statistics statistics for Casefor Case 1 and 1 and Case Case 2 are 2 are provided provided in Sectionin Section 3.3.4 3.3.4, respectively., respectively. As can be seen, simulated moments appear appeareded to be a little bit “ “smeared”smeared” compared to the truth fieldfieldss due to the broader beamwidth of ATD than NEXRAD NEXRAD.. More importantly, as the array beam scanned away from the broadside, the Z bias increased, which is consistent with the two-way power scanned away from the broadside, theDR 푍퐷푅 bias increased, which is consistent with the two-way ratio of horizontal and vertical patterns that is dependent on azimuth. The system Z bias values power ratio of horizontal and vertical patterns that is dependent on azimuth. The systemDR 푍퐷푅 bias valuesmatch match the theoretical the theoretical results result in Referencess in References [27,28 ],[27 which,28], which further further confirms confirms that ATDthat ATD requires requiresZDR calibration at each azimuth radial. 푍퐷푅 calibration at each azimuth radial.

Table 5. System parameters of the simulated advanced technology demonstrator (ATD).

Radar Parameters Values

Remote Sens. 2018, 10, x FOR PEER REVIEW 15 of 22

Frequency 2800 MHz Array size 4 × 4 m Number of subarrays 100 Beamwidth Azimuth 1.8° First sidelobe −30.3 dB Waveform Rectangular pulse Pulse width 1.6 μs Pulse repetition frequency 300 Hz Range resolution 250 m Peak power 768 W per subarray Noise figure 2.7 dB

Remote Sens. 2019, 11, 422 15 of 22

(a) (b)

Remote Sens. 2018, 10, x FOR PEER REVIEW 16 of 22

(e)

Figure 9. Simulated polarimetricFigure 9. radarSimulated moments polarimetric generated radar from moments the advanced generated technology from the advanced technology demonstrator (ATD) modeldemonstrator of PASIM, and (ATD comparison) model of withPASIM the, and “truth” comparison weather with fields the for “truth” Case 2:weather fields for Case 2: (a) (a) reflectivity, (b) differentialreflectivity, reflectivity, (b ()c differential) correlation reflectivity, coefficient, (dc)) correlation differential coefficient, phase, (e) averaged (d) differential phase, (e) averaged differential reflectivity biasdifferential along azimuth reflectivity from − 45bias◦ to along 45◦. azimuth from −45° to 45°.

3.3.3. Cylindrical Polarimetric Phased-Array Radar (CPPAR) System As the second specific system example, PASIM was configured to simulate S-band CPPAR systems with various diameters. There were two purposes for this simulation. Firstly, we wanted to justify the data quality of CPPAR based on commutative scanning. Secondly, we wanted to guide the selection of CPPAR diameters that can achieve acceptable data quality. The following example shows the PPI scans from a simulated 2-m-diameter CPPAR demonstrator, which is populated by 96 columns of the generic dual-polarized patch elements and uses a 90° sector (24 columns) to form a commutated beam with a beamwidth of 5.2° and the first sidelobe of −30.1 dB. The technical specifications of the simulated CPPAR demonstrator are listed in

Table 6. The simulation results of polarimetric moments and the average 푍퐷푅 bias along all azimuth angles for the convective precipitation case are shown in Figure 10. Error statistics for Case 1 and Case 2 are provided in Section 3.3.4, respectively.

(a) (b)

Remote Sens. 2019, 11, 422 16 of 22

Table 5. System parameters of the simulated advanced technology demonstrator (ATD).

Radar Parameters Values Frequency 2800 MHz Array size 4 × 4 m Number of subarrays 100 Beamwidth Azimuth 1.8◦ First sidelobe −30.3 dB Waveform Rectangular pulse Pulse width 1.6 µs Pulse repetition frequency 300 Hz Range resolution 250 m Peak power 768 W per subarray Noise ﬁgure 2.7 dB

3.3.3. Cylindrical Polarimetric Phased-Array Radar (CPPAR) System As the second specific system example, PASIM was configured to simulate S-band CPPAR systems with various diameters. There were two purposes for this simulation. Firstly, we wanted to justify the data quality of CPPAR based on commutative scanning. Secondly, we wanted to guide the selection of CPPAR diameters that can achieve acceptable data quality. The following example shows the PPI scans from a simulated 2-m-diameter CPPAR demonstrator, which is populated by 96 columns of the generic dual-polarized patch elements and uses a 90◦ sector (24 columns) to form a commutated beam with a beamwidth of 5.2◦ and the first sidelobe of −30.1 dB. The technical specifications of the simulated CPPAR demonstrator are listed in Table6. The simulation results of polarimetric moments and the average ZDR bias along all azimuth angles for the convective precipitation case are shown in Figure 10. Error statistics for Case 1 and Case 2 are provided in Section 3.3.4, respectively.

Table 6. System parameters of the simulated cylindrical polarimetric phased-array radar (CPPAR).

Values for Values for Radar Parameters 2-m CPPAR 10-m CPPAR Frequency 2800 MHz 2800 MHz Array size 2 m diameter 10 m diameter Number of excited columns 24 156 Beamwidth Azimuth 5.2◦ Azimuth 1.1◦ First sidelobe −30.1 dB −30.5 dB Waveform Rectangular pulse Rectangular pulse Pulse width 1.6 µs 1.6 µs Pulse repetition frequency 300 Hz 300 Hz Range resolution 250 m 250 m Peak power 80 W per column 80 W per column Noise ﬁgure 2.7 dB 2.7 dB

From Figure 10, we can find that all the simulated radar moments were smeared obviously compared with NEXRAD truth fields, as a result of the much broader beamwidth of the 2-m-diameter CPPAR, whose data quality cannot meet the NEXRAD requirements. Moreover, the system ZDR bias fluctuated a lot around the two-way power pattern ratio at different azimuth directions, which was mainly caused by a beam smoothing effect. Remote Sens. 2018, 10, x FOR PEER REVIEW 16 of 22

(e)

Figure 9. Simulated polarimetric radar moments generated from the advanced technology demonstrator (ATD) model of PASIM, and comparison with the “truth” weather fields for Case 2: (a) reflectivity, (b) differential reflectivity, (c) correlation coefficient, (d) differential phase, (e) averaged differential reflectivity bias along azimuth from −45° to 45°.

RemoteCase Sens.2 are2019 provided, 11, 422 in Section 3.3.4, respectively. 17 of 22

Remote Sens. 2018, 10, x FOR PEER REVIEW 17 of 22 (a) (b)

(e)

FigureFigure 10. 10. Simulated polarimetric radar moments generated generated from from the the 2-m-diameter 2-m-diameter cylindricalcylindrical polarimetricpolarimetric phased-arrayphased-array radarradar (CPPAR)(CPPAR) modelmodel ofof PASIM,PASIM, and and comparisoncomparison withwith thethe “truth”“truth” weatherweather fieldsfields forfor CaseCase 2:2: ((aa)) reflectivity,reflectivity, ((bb)) differentialdifferential reflectivity,reflectivity, ((cc)) correlationcorrelation coefficient,coefficient, ((dd)) differentialdifferential phase,phase, ((ee)) averagedaveraged differentialdifferential reflectivityreflectivity bias bias along along azimuth azimuth fromfrom− −45◦° to 45◦°.

FromThe other Figure example 10, we shows can find the PPIthat scan all the data simulated from a “full-size” radar moments (10-m-diameter) were smeared CPPAR, obviously which iscompared populated with by NEXRAD 624 columns truth of fields, the generic as a result dual-polarized of the much patch broader elements beamwidth and uses of the a 90 2◦-msector-diameter (156 ◦ columns)CPPAR, whose to form data a commutated quality cannot beam meet with the NEXRAD a beamwidth requireme of 1.1 nts.andMoreover, the ﬁrst sidelobe the system of − 푍30.5퐷푅 bias dB. Thefluctuate technicald a lot speciﬁcations around the two of the-way simulated power pattern full-size ratio CPPAR at different are listed azimuth in Table directions,6. The simulation which was mainly caused by a beam smoothing effect. The other example shows the PPI scan data from a “full-size” (10-m-diameter) CPPAR, which is populated by 624 columns of the generic dual-polarized patch elements and uses a 90° sector (156 columns) to form a commutated beam with a beamwidth of 1.1° and the first sidelobe of −30.5 dB. The technical specifications of the simulated full-size CPPAR are listed in Table 6. The simulation results of polarimetric moments and the average 푍퐷푅 bias along all azimuth angles for the convective precipitation case are shown in Figure 11. Error statistics for Case 1 and Case 2 are provided in Section 3.3.4, respectively.

Table 6. System parameters of the simulated cylindrical polarimetric phased-array radar (CPPAR).

Values for Values for Radar Parameters 2-m CPPAR 10-m CPPAR Frequency 2800 MHz 2800 MHz Array size 2 m diameter 10 m diameter Remote Sens. 2018, 10, x FOR PEER REVIEW 18 of 22

Number of excited columns 24 156 Beamwidth Azimuth 5.2° Azimuth 1.1° First sidelobe −30.1 dB −30.5 dB Waveform Rectangular pulse Rectangular pulse Pulse width 1.6 μs 1.6 μs Remote Sens. 2019, 11, 422 18 of 22 Pulse repetition frequency 300 Hz 300 Hz Range resolution 250 m 250 m results of polarimetricPeak power moments and the average80 WZ perDR biascolumn along all azimuth angles80 W for per the column convective precipitationNoise case figure are shown in Figure 11. Error2.7 statistics dB for Case 1 and Case 22.7 are dB provided in Section 3.3.4, respectively.

(a) (b)

(e)

FigureFigure 11. 11Simulated. Simulated polarimetric polarimetric radar radar moments moments generated generated from from the the 10-m-diameter 10-m-diameter CPPARCPPAR model model ofof PASIM, PASIM, and and comparison comparison with with the the “truth” “truth” weather weather fields fields forfor Case Case 2: 2 (: a()a) reflectivity, reflectivity, (b ()b differential) differential reflectivity, (c) correlation coefficient, (d) differential phase, (e) averaged differential reflectivity bias along azimuth from −45◦ to 45◦.

We can observe from Figure 11 that the 10-m-diameter CPPAR is likely to achieve the data quality that meets the NEXRAD requirements, and the system ZDR bias was low for different azimuth Remote Sens. 2019, 11, 422 19 of 22 directions, which exhibits its advantage compared to the results from the ATD system example. The random ﬂuctuation of ZDR bias curve around the two-way power pattern ratio was mainly caused by sampling error and reﬂectivity gradient.

3.3.4. Discussion Tables7 and8 summarize the PASIM basic data quality evaluation results for the three example systems. Here, standard deviation is used as an error statistic, as bias can be eliminated by the calibration process. We can see from the comparison of the results that, in terms of overall data quality, a full-size CPPAR is expected to obtain the results closest to the generic radar example. As comparisons, ATD and 2-m-diameter CPPAR cannot meet NEXRAD requirements, mainly due to their broader beamwidth. On the other hand, data quality results are also closely related to the weather scenarios; for example, a larger reﬂectivity gradient will lead to degraded data quality due to its contamination through sidelobes of antenna patterns.

Table 7. Summary of error statistics for the tornado scenario (Case 1).

Radar Variable Generic Radar ATD 2-m-diameter CPPAR 10-m-diameter CPPAR

ZH 0.81 dB 1.66 dB 3.79 dB 0.82 dB ZDR 0.18 dB 0.39 dB 0.98 dB 0.21 dB ρhv 0.008 0.01 0.016 0.008 ◦ ◦ ◦ ◦ φDP 1.19 2.65 5.66 1.35

Table 8. Summary of error statistics for the convective precipitation scenario (Case 2).

Radar Variable Generic Radar ATD 2-m-diameter CPPAR 10-m-diameter CPPAR

ZH 0.78 dB 1.42 dB 2.84 dB 0.79 dB ZDR 0.17 dB 0.36 dB 0.87 dB 0.19 dB ρhv 0.006 0.007 0.014 0.006 ◦ ◦ ◦ ◦ φDP 1.12 2.41 4.58 1.22

These data quality evaluation results may provide useful guidance for PAR designs. For example, antenna elements should be designed with special care to reduce sidelobes of the array pattern, which is especially important to ensure acceptable data quality in strong convective weather with a large reflectivity gradient. Low cross-polarization levels, matched co-polarization beam patterns, and stable phase difference for horizontal and vertical polarizations are required for accurate measurements of polarimetric moments. NLFM waveform may be an option for SENSR-type radar systems, which can achieve both low range sidelobes and good power efficiency, while special attention should be paid to the increased phase noise levels if a direct digital waveform synthesizer is used. Currently, there are still some limitations of the PASIM simulations. Firstly, for simplicity, uniform drop size was assumed in weather target modeling. However, to characterize the microphysical properties of precipitation, a more realistic drop size distribution model such as Gamma distribution may be used. Secondly, for the radar transceiver nonlinearity model, only the simple Saleh model was used in the current simulation, while a more accurate model for solid-state transceivers will be incorporated in the future, based on specific hardware designs and their laboratory characterizations.

4. Conclusions and Future Work In this paper, an end-to-end PAR system simulator called PASIM, which was developed for predicting the data quality of future weather radars, was described. Based on the novel concept of time-domain, electronics-incorporated models, we demonstrated the example usages of PASIM, such as the impact of various pulse compression waveforms, the effect of the instability of channel electronics, nonlinear distortion, random amplitude and phase errors in array channels, and the quantization error of array phase shifters. Weather radar moment data qualities for multiple specific radar designs were Remote Sens. 2019, 11, 422 20 of 22 evaluated, including a generic radar, a planar array radar, and cylindrical array radars with various sizes in the context of two different weather scenarios. PASIM simulation results further confirm the following: (1) Antenna elements should have low sidelobes and cross-polarization levels, matched co-polarization beam patterns, and stable phase difference between horizontal and vertical polarizations to achieve accurate measurements of polarimetric radar moments. (2) The NLFM waveform may be an option to meet the MPAR requirements, which can achieve both low range sidelobe levels favorable to convective weather observation, and good power efficiency favorable to weak echo observation. (3) As an example of channel electronic instability, HPA nonlinearity will distort waveform, resulting in increased range sidelobes. Random amplitude and phase errors in array channels, and the quantization error of phase shifters will distort the antenna pattern by raising sidelobes and reducing gain. All of these will cause measurement errors in weather scenarios having a large reflectivity gradient. (4) Array manifolds and sizes have large impacts on polarimetric radar measurement. A planar array will induce differential reflectivity bias as its beam steers away from its broadside, while a 10-m-diameter cylindrical array is likely to achieve data quality comparable to NEXRAD. Better modeling of array channel-to-channel couplings will be developed for the next step. Improved RF transceiver models will be studied. Moreover, to model the interactions between pulse compression waveforms and distributed weather scatterers in the time domain, impulse response (IR) will be added in PASIM to improve the transient system simulations. Such innovation may reveal certain characteristics in the scattered electric field from weather resolution volumes, which may have an impact on the return signals [29–31]. For weather target modeling, a more realistic drop size distribution model will be included in the next step to characterize the microphysical properties of precipitation. Further validation of PASIM using measured weather data by actual phased-array radar testbeds, once they are available, is anticipated.

Author Contributions: Z.L.: Designed and implemented the PASIM software, obtained system data quality evaluation results, and prepared most of the manuscript. S.P.: Established the original idea and initial studies of the system simulation with phased array electronics modeling. Y.Z.: Established the original concepts of PASIM and architecture-specific system modeling. G.Z.: Provided important guidance of the fundamental models and algorithms for weather radar signal processing. R.D.: Provided funding support and collaboration from US government research team, NEXRAD radar information, and guidance of the simulation verifications. Funding: The work was supported by NOAA/NSSL through Grant # NA16OAR4320115. Acknowledgments: We thank Ramesh Nepal from the Intelligent Aerospace Radar Team (IART) of School of Electrical and Computer Engineering, the University of Oklahoma as the initial user of the MATLAB Phased-Array System Toolbox for weather radar simulations at OU, who gave numerous discussions regarding PASIM implementation. We deeply thank Honglei Chen from MathWorks Inc., who provided important guidance and support to the weather radar signal statistical modeling and MATLAB tool. Conflicts of Interest: The authors declare no conflicts of interest.

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