Horus—A Fully Digital Polarimetric Phased Array Radar for Next-Generation Weather Observations

Weather radars have become indispensable to meteorologists and the general public for both understanding and awareness of high-impact weather events and as part of the operational warning infrastructure. In the U.S., the operational weather radar network is composed of approximately 160 WSR-88D radars, which are S-band, dish-based, polarimetric Doppler radars. This work reports on the development of a fully digital phased array weather radar that is being used to assess the potential of such technology as a replacement for the WSR-88D radars. The “Horus” radar is a truck-based, S-band, fully digital polarimetric phased array radar. Fully digital systems hold promise for meeting some of the greatest technical challenges facing the meteorological community, such as the effective integration of dual-polarization capability with phased array beam agility. This paper describes the fully digital Horus phased array weather radar that was recently completed by the Advanced Radar Research Center (ARRC) at the University of Oklahoma (OU). An overview of the advantages and challenges facing fully digital arrays for weather observations is provided along with potential mitigation strategies. Initial weather observations with Horus are given with the goal of assessing the radar scanning capabilities and most importantly the polarimetric quality. Finally, a vision for the future of next-generation weather radar operations is given with an eye toward leveraging the scalable design of Horus for high-resolution weather observations.


I. INTRODUCTION
W EATHER radar is the most important tool for observation and warning of increasingly frequent severe weather events. Extreme weather can disrupt communities, negatively impact commerce, civil operations, and cause billions of dollars in damage annually across the globe (e.g., [1]). Unfortunately, current operational weather dish-based radars were not designed to capture rapidly evolving processes that lead to extreme events. Significant improvements in the forecasting of high-impact weather require a new radar design that provides the needed spatial and temporal resolution along with the scanning capabilities afforded by phased array radar (PAR) technology [2], [3], [4], [5], [6], [7].
Polarimetric PAR is emerging as a promising technology for the next generation of weather radars due to its superior capabilities for capturing the microphysics and dynamics of a wide variety of rapidly evolving atmospheric phenomena across scales [2], [8], [9], [10]. Planar PAR antennas with electronic scanning only in elevation (mechanical in azimuth) avoid the issue of tilting the intended polarization axes, i.e., modulation on only one axis of the Poincaré sphere is needed. Such strategies have seen widespread implementation in Japan [11], [12], China [13], [14], and in the U.S. with the nascent Polarimetric Atmospheric Imaging Radar (PAIR) [15]. The Advanced Technology Demonstrator (ATD) [8] is a planar PAR capable of two-dimensional scanning, which requires polarimetric calibration per beamsteering position [16], [17]. A unique cylindrical polarimetric phased array radar (CPPAR) design has also been investigated [18], [19]. It is based on theoretical studies that showed the effectiveness of such designs for maintaining polarization orthogonality, which is needed for accurate polarimetric PAR observations.
The most advanced PAR architecture is a fully digital design, which holds promise for overcoming the challenge of combining polarimetric and PAR technologies [20], [21]. Via element-level control, robust mutual-coupling-based polarimetric "self" calibration is possible, thus having the highest likelihood of attaining accurate rapid-scanning polarimetric observations for long periods without the need for re-calibration. Further, fully digital technology is capable of emulating most other PAR architectures, as virtual subarrays can be defined by appropriately combining digital element-level signals. This feature makes an all-digital architecture useful for the assessment of competing radar designs.
With support from NOAA's National Severe Storms Laboratory (NSSL), the Advanced Radar Research Center (ARRC) at the University of Oklahoma (OU) has developed a fully digital polarimetric rotating PAR system called "Horus" [22], [23], the ancient Egyptian sky god with the all-seeing eye. A photograph of the Horus radar without its radome is shown in Fig. 1. Horus' fully digital architecture will enable rapid (volume scans in seconds) and adaptive scanning. By uniquely obtaining nearly continuous vertical sampling, Horus observations will more accurately capture 4D microphysical processes, including processes key to understanding and predicting the formation of severe hazards (e.g., tornadoes, hail, flooding). Pristine dual-polarization data, achieved by exploiting the alldigital architecture, will improve operational quantitative precipitation estimation as well as understanding of microphysical processes. Horus will operate with minimal attenuation and excellent sensitivity in the S band (2.7-3.1 GHz), which is ideal for atmospheric observations as scattering physics (at that band) are well-understood and the observational range is large. System integration of the Horus radar was recently completed at the ARRC, and initial deployments for polarimetric weather measurements are ongoing.
Here, we motivate the fully digital architecture of Horus for weather observations and give a system overview. Challenges of fully digital PARs and potential solutions are also provided, along with initial polarimetric weather measurements showing a glimpse of the potential of fully digital PARs for highresolution weather observations.

A. High Temporal Resolution and Spatial Sampling
Due to the scattering properties of hydrometeors, operational weather radars in the U.S. operate in the S-band [24], which minimizes attenuation and provides observations that typically hold to the Rayleigh scattering regime [25]. The radar system used in this network is called the Weather Surveillance Radar -1988 Doppler (WSR-88D), sometimes informally referred to as "NEXRAD" (NEXt-generation RADar). Approximately 160 WSR-88Ds make up the operational network in the U.S. The radar was designed to provide quality observations for a variety of meteorological phenomena, from localized intense storms/tornadoes to precipitation events that can cause flooding. The radar also provided improved decision-making for activities such as transportation, aviation, hydrology, and hazardous weather forecasts and warnings.
Severe storms evolve rapidly on timescales of minutes or even seconds in the case of tornadoes [3], [26], [27], [28]. Given the infrequency of tornadoes and other similar phenomena, however, the WSR-88D network was justifiably not designed to provide the temporal resolution that could resolve these rapid-evolving storms. PARs, especially fully digital systems, have the potential of much higher temporal resolution while preserving the required data quality (i.e., bias and standard deviation of radar variables) [29], [30], [31]. This Artist's depiction of example capabilities of a fully digital phased array weather radar. Shown are (a) dense vertical sampling using imaging in a range-height-indicator (RHI) mode, (b) adaptive nulling for interference mitigation (including non-stationary clutter), and (c) symbolic depiction of software reconfigurability for future requirements/missions. potential is realized through a variety of advanced scanning concepts that are described later in this section.
In order to achieve adequate angular resolution with a pencil beam, the WSR-88Ds use an 8.5-m parabolic-reflector antenna and continuously scan in azimuth 360 • at successive elevation angles. Typically, the number of elevation angles is limited in order to provide reasonable volume coverage every few minutes. WSR-88Ds attempt to cover "full" volumes by repositioning the dish to a limited set of elevation angles (typically 5-15 elevation angles). This imposes an inherent trade-off between temporal resolution, spatial coverage, and data quality. In particular, this limited elevation sampling can leave large unobserved gaps in the measurements, especially at farther ranges. As illustrated in Fig. 2a, one often-overlooked advantage of PARs for weather is the ability of extremely dense sampling in elevation, thus minimizing these observational gaps.

B. Beam Agility and Interference Mitigation
An important capability of fully digital arrays is beamforming flexibility. Since the beamforming weights for each element (and polarization) are realized using software-based digital signal processing (DSP), in contrast to the hardware dependence of analog beamforming systems, it is possible to form multiple arbitrary beams. Examples include spoiled transmit beams with potentially hundreds of simultaneous receive beams (see Fig. 2a). This mode of operation is called "imaging" in the weather radar community [5], [11], [28], [32], [33] and can significantly enhance temporal resolution and vertical coverage at the cost of sensitivity and sidelobe performance. The loss in sensitivity is proportional to the "spoiling factor." For example, if the transmit beam is spoiled by a factor of two, there would be a or the present ponding 3 dB loss in sensitivity. Note that sensitivity may not be an issue in high signal-to-noise ratio (SNR) environments (e.g., intense rainfall, hail, etc.) and can be mitigated through the use of phase-only transmit weights [34], [35], [36], [37]. The two-way sidelobe performance challenge can be addressed by using a "spoiled" transmit beam with multiple lobes spaced in angle [38], [39], rather than a single wide transmit beam. This transmit beam design allows a more effective path to meeting two-way sidelobe requirements since the receive beams are not adjacent in angle.
Of all PAR architectures, fully digital PARs (also referred to as "all-digital PARs") have the most degrees of freedom for adaptive beamforming on receive using methods such as minimum variance distortionless response (MVDR) [40], [41] (see Fig. 2b). These methods are extremely powerful for mitigation of interference, ground clutter, and even non-stationary clutter, such as reflections from wind turbines [42], [43], [44], [45] where the performance of conventional clutter filters is limited. Further generalization of adaptive sensing can be employed through the use of space-time adaptive processing (STAP), which incorporates adaptive waveforms into the beamforming construct [46]. Such adaptive methods intrinsically depend on the received data at each element and are therefore challenged by the need to aggregate the data in a single processing unit for covariance matrix estimation, matrix inversion, etc. Recent work in AI/ML-based methods may hold promise for adaptive beamforming in a computationally efficient manner [47], [48], [49], [50]. Although a burgeoning area, the use of AI/ML methods for a variety of other radar tasks, such as control, scheduling, spectrum sharing, dealiasing, etc. [51], [52], [53], will become extremely important for highly digital PARs.

C. Future Proof -Software Defined Radar
Since each radiating element of a fully digital PAR does not have hardware-based phase shifters and attenuators, such systems are by definition "software-defined radars." In addition to the advantages just mentioned and as illustrated in Fig. 2c, a software-defined radar can more readily be reconfigured for new missions. Examples include array segmentation schemes for multiple missions (e.g., weather radar, air traffic control, communications), implementation of sidelobe canceling channels for improved clutter rejection, or new beam shapes for improved temporal resolution, just to mention a few. In the operational weather radar community, it is envisioned that a replacement of the WSR-88D network will be needed by 2040, with the new system possibly having a lifetime of 30-40 years. It is not possible to predict all the future uses and/or configurations that the radar will have over the coming decades. Therefore, the software reconfigurability allowed by a fully digital PAR is fundamentally important, potentially resulting in substantial savings in maintenance and operations costs over the lifetime of the radar.

III. CHALLENGES AND POTENTIAL SOLUTIONS
As is the case with all new technologies, challenges do exist with fully digital PARs that should be addressed [21]. Many have potential solutions and/or are topics of active research and development. The most important of these challenges are described below.

A. Calibration -Polarimetric Requirements for Weather Observations
In the early 2000s, dual-polarization was being investigated for improved weather observations. After the success of the JPOLE experiment led by NSSL, the WSR-88D radar network was upgraded with dual-polarization capability [54], [55]. This capability has become indispensable to the meteorological community yielding important radar products such as hydrometeor classification [55] and improved accuracy in precipitation rate estimation, a process that is referred to as quantitative precipitation estimation (QPE) [54], [56].
Useful dual-polarization observations are highly dependent on precise calibration. Although challenging, this level of calibration has been achieved with the WSR-88D radar [57]. In the case of dual-polarization on a PAR, however, the challenge is more complex since the array must meet calibration requirements on potentially hundreds of beams with varying characteristics [16]. A dish radar needs this calibration only for a single boresight beam, whereas a PAR requires a beamsteering dependent calibration [6], [58]. For the Horus radar, calibration is performed in three steps. First, utilizing the system's unique digital-at-every element architecture, a novel 'recursive' far-field calibration was applied. In this scheme, array panels are independently calibrated at short-range using a standard gain horn antenna, thereby increasing signal-tonoise ratio and mitigating multipath contamination and resulting in an initially calibrated array (with uniform amplitude and phase excitations). Second, mutual coupling calibration is applied [59] to correct for element-level amplitude/phase differences that may have occurred from the time the recursive calibration was applied to the radar deployment time. Third, after boresight array calibration is conducted, scan-loss correction for the copolar H and copolar V antenna gains are applied as a function of steering angle. These corrections are derived from Horus element-pattern measurements collected in the ARRC's anechoic chamber. Calibration parameters from the combination of these steps are produced on the fly and applied in real time. Equivalently, one could precompute "calibration tables" (one per electronically steered beam position) and apply them in real time. We note that because Doppler measurements depend only on pulse-to-pulse relative phase changes measured, Doppler estimates are insensitive to PAR antenna-induced biases, and the standard error of Doppler velocity estimates only depends on the radar frequency and dwell time [25]. Although ground truth near-field data are unavailable at this time (yet forthcoming), measurements suggest that the technique achieved acceptable polarimetric array calibration levels. A more extensive discussion is provided in Section V.
The weather-derived products which drive the requirements for the accuracy of polarimetric measurements are differential reflectivity (Z DR ), copolar correlation coefficient (ρ hv ), and specific differential phase (K DP ). Z DR is the logarithm of the horizontal (H) to vertical (V) returned powers ratio, ρ hv is the correlation coefficient between the H and V returns, and K DP is the derivative of the differential phase ( DP ) with respect to range; where DP is the phase difference between the returns in H and V polarized waves along a radial up to a specified range. To conduct precise measurements of polarimetric variables, it is crucial that the beams for transmitting the H and V polarized waves are well matched in gain and shape at every scanning direction. To achieve an accurate estimate of rainfall rates, it is recommended that the bias of Z DR estimates is kept within ±0.1 dB for intrinsic Z DR between 0 and 1 dB and less than 0.1×Z DR for larger Z DR values [60]. It should be noted that keeping the bias of Z DR estimates within ±0.1 dB is exceptionally difficult to achieve even in radars with parabolic antennas (e.g., WSR-88D network), and for this reason, the bias accuracy to within ±0.2 dB for Z DR less than 1 dB (and up to 0.2×Z DR for larger Z DR values) has been broadly adopted as a calibration goal. In the case of ρ hv estimates, a bias within ±0.006 is deemed sufficient for "sensing the mixed-phase precipitation and gauging the hail size quantitatively." Large PAR systems are typically calibrated (e.g., phase/amplitude alignment) using a near-field scanner prior to system deployment. Unfortunately, any changes in the array performance in the field often result in a need for dismantling the radar and recalibration in a laboratory setting. Fully digital PARs have the potential of using the inherent mutual coupling among individual elements to realign the array after being deployed [59]. This solution to the calibration challenge is an important advantage of fully digital PARs. Further discussion on the use of this approach for the Horus system appears in Section V. Recent work has also shown that polarimetric performance enhancements can be achieved with a fully digital array using the so-called cross-polar canceller (XPC) technique [61], [62], [63]. This method assigns a small number of elements from the entire array in an attempt to mitigate cross-polar contamination by transmitting the opposite phase from the original signal.

B. Power Consumption
At a high level, prime power consumption of a PAR system can be segmented into the (1) transmit/receive (TR) modules including the high-powered amplifier (HPA), lownoise amplifier (LNA), and any phase shifters and attenuators, (2) digital transceivers, (3) back-end processors, and (4) offarray computational needs. For a fully digital PAR, every element (and polarization) is digitized and processed, meaning that the digital transceivers and any onboard processing (e.g., FPGAs) dominate the power needs. Of course, onboard processing results in lower power consumption for off-array computations. Furthermore, fully digital arrays require no phase shifters/attenuators in the TR module. Nevertheless, the prime power needs for a fully digital PAR are certainly larger than for a PAR based on analog beamforming. For example, the power needed for the Horus radar discussed in the next section (assuming 1600 radiating elements) would be approximately 50 kW of prime DC power for the array only. This number does not include the radar infrastructure (e.g., chiller, back-end servers, pedestal, etc.), which can be significant but is independent of the PAR architecture. Fortunately, several efforts are underway in industry to design dedicated application-specific integrated circuits (ASICs) for the digital radar market [64]. In addition to providing the flexibility inherent in a digital array, these new ASIC designs will have the capability to reduce overall power consumption.

C. In-Band Interference
Interference is an important issue for any radar or communication system. Mitigation strategies include filtering, of course, with the goal of rejecting sources outside the operating frequency band. In-band interference can also be an issue, with sources from intentional jammers in defense applications to unintentional interference in all application spaces. A major concern with interference is that the A/D converters and/or mixers in the digital transceivers could become saturated resulting in unusable data. Analog beamforming for either the entire array or at the sub-array level enables some level of angular directivity since the array (or sub-array) pattern will be relatively narrow compared to the radiation pattern of a single element. For a fully digital system, there is little spatial directivity since each element is digitized and the element pattern can be ∼40-60 • wide [65].
At least two potential solutions for in-band interference of fully digital PARs exist, and precursor systems to Horus have been used to explore these [66], [67]. First, as will be described in the next section, the Horus radar is based on the Analog Devices AD9371 digital transceiver integrated circuit (IC). The AD9371 is a direct conversion receiver [68], [69]; hence this zero-IF downconversion plan provides baseband in-phase (I) and quadrature (Q) digital signals with 16-bit sampling. The dynamic range afforded by this sampling is sufficient to adequately for signals with moderate levels of interference. Moreover, the overall dynamic range of this digital beamforming radar is increased by a factor of 10 log 10 (N ) compared to an analog beamforming radar that uses the same receiver [70], [71]. For Horus, N>1000, and this is especially useful for civilian applications such as weather observations whose echo strengths can span an 80 dB power range [72]. Second, miniaturized frequency-tunable filters are being investigated that could be embedded into the antenna array [73] with little impact on antenna performance. Other more exotic mitigation strategies have also been investigated, such as element-level angular selectivity based on tunable mutual coupling resonant circuits [74].

D. Data
With a rudimentary calculation based on digitizing each element and polarization of an array made up of thousands of elements, it quickly becomes obvious that the amount of data is a challenge. For example, a 1600-element Horus radar would produce ∼1.5 TB/s at full bandwidth if recording data at each element and polarization and assuming a reasonable received duty cycle. To elaborate, each of Horus' 1600 elements has an independent vertical channel and independent horizontal channel, with each channel possessing its own digital receiver. The AD9371 digital receiver is rated to sample up to 125 MSPS, and each 16-bit sample is mapped into a word of two bytes. Each receiver which produces a unique two-byte in-phase signal and a unique two-byte quadrature signal. Collectively, this produces more than a terabyte of data at full bandwidth, as mentioned above. It should be mentioned that we subsequently govern sample rate of the in-phase and quadrature signals leaving the digital receivers by changing decimation factors and designing decimation filters to produce output data rates that accommodate the next item in our digital chain. On the other hand, analog beamforming systems (and sub-array systems) reduce the number of digitized channels at the expense of flexibility and advanced capabilities. Data reduction on a digital array can be achieved via digital coherent beamforming, which has the advantage of improved SNR since noise from different channels has a lower correlation, while reducing the sheer amount of data for both transport and processing. Various real-time beamforming topologies proposed include systolic schemes and others that will be discussed in the next section. Of course, all methods rely on an efficient data networking system.

IV. HORUS SYSTEM OVERVIEW
The Horus radar, shown in Fig. 1, is an integrated mobile radar system designed to demonstrate the feasibility of fully digital radars and enable research into the opportunities and challenges presented by such designs. As mentioned, the radar system consists of 1600 dual-polarization S-band elements. Each active element is driven by two fully independent radar chains. The high-level specifications of the Horus radar are listed in Table I. To elaborate on this table, conservative loss estimates have been accounted for during the design process, so that the resulting hardware system will perform as expected. For instance, we estimated total transmitter losses of 2 dB, an aperture efficiency of 50 percent, and a TX waveform taper loss of 1 dB; hence, a 6 dB loss on transmit was estimated. On receive, our lab data revealed a receiver noise figure of 3 dB, receive antenna losses (elevation scan angle loss 1.5 dB, elevation beamwidth taper loss 1.4 dB, azimuth scan angle loss 1.5 dB, azimuth beamwidth taper loss 1.4 dB), and RX waveform taper loss of 1 dB. Our maximum pulse compression gain is established by the apex of the system's time bandwidth product, 100e-6 × 100e6 = 10e4, i.e., 40 dB. Next, the following paragraphs and sections continue to build upon the data found in Table I.
The mobile platform is built on an International HV607 medium-duty truck. As mentioned in Section III, one of the challenges with fully digital arrays is power consumption. A power take-off (PTO) generator, driven by the truck engine and capable of providing 150 kW, is integrated into the truck below the chiller on the driver's side. The system is liquidcooled via a 16.7-ton chiller located behind the truck cab. The pedestal provides mechanical pointing of the array in both azimuth and elevation. It can rotate continuously 360 • at 12 RPM in azimuth. The elevation positioning is intended to deploy the array to a configurable elevation tilt and remain at that angle during operations. A rotary assembly is integrated into the pedestal which has an electrical slip-ring, rotary fluid union, and fiber optic rotary joint (FORJ). The pedestal is placed on top of a riser, which elevates the bottom of the array above the chiller when the array is deployed into the operational position. Telescoping outriggers are incorporated into the platform for stability and leveling.
The array and supporting back-end electronics are mounted to the pedestal arms in weatherproof enclosures. The back-end electronics encompass the array AC-DC power supplies, data processing and storage servers, networking, and centralized timing and synchronization electronics. Co-locating the digital array with the back-end electronics simplifies the connections that must be made through the rotary joint and slip rings.

A. High-Level Architecture
Many decisions and technical compromises must be made when developing a complex system such as the Horus radar. System scalability was a key design constraint for the array electronics. Additionally, maintainability and modularity were important considerations during the design phase of the array electronics to ensure the system could be supported for many years, while also offering opportunities to upgrade various aspects of the system during the course of future research.
The Horus panel electronics provide the scalable building block of the fully digital array. The block diagram of a Horus panel for a row of eight dual-polarization elements within the panel is shown in Fig. 4. The antenna for each Horus panel consists of 64 passive radiating elements connected to the RF electronics via SMP-MAX connectors. The antenna mounts to a continuous ground plane from the front of the array, while the rest of the panel electronics are installed from the rear for accessibility during system maintenance. The Horus array electronics utilize a brick architecture to provide a highly serviceable and modular hardware platform. As a ground-based system, there is space for the depth of a "brick" architecture, rather than being constrained to panelization of the electronics in a tile. Since the electronics are not as tightly integrated as required by a tile architecture, the material stack-up and fabrication design rules for each printed circuit board (PCB) in the panel are individually tailored to improve manufacturability and minimize fabrication costs.
A passive backplane for power distribution, known as the Analog Bridge, is installed inside the panel as seen in the center portion of Fig. 3. Eight OctoBlades and a SuperBlade constitute the brick assemblies that populate the array. An OctoBlade contains the full radar chain from the analog RF radar front-ends through the digital transceivers and processing for eight dual-polarized antenna elements. The SuperBlade is responsible for converting the systemlevel 400 VDC power to 50 VDC and 12 VDC used by panel electronics, as well as, centralized monitoring, control, and signal distribution for each panel. Digital Bridges span the back of two OctoBlades and assist the SuperBlade with distributing timing, synchronization, and control signals to the FPGA boards within the OctoBlades.
The OctoBlade serves as the fundamental building block of the Horus radar. Given the importance of this line-replaceable unit (LRU), the high-level design of the OctoBlade is described next.

B. The OctoBlade
The OctoBlade is the heart of the Horus panel electronics, containing the radar front-end, RF-to-digital transceivers, and radar signal processing FPGAs. A single OctoBlade supports eight dual-polarization antenna elements with its 16 channels of radar electronics. As with other aspects of the system, the OctoBlade is also modular, primarily to facilitate system upgrades, scalability, and design reuse in future projects. Modularity is also beneficial during volume production for PCB yield rates, as it reduces the number of electronics that must be discarded if there is a PCB that does not pass the quality assurance tests and is unable to be repaired. The OctoBlade, as seen in the left panel of Fig. 3, has three main components: the Quad board (OCTO-QUAD), the FPGA board (OCTO-FPGA), and the Heat Transport Duct (HTD). A single blade consists of an HTD in the middle with a mated set of Quad boards and FPGA boards mounted on either side of the HTD, and a pair of metal lids for enclosure (not shown in Fig. 3). The two sets of Quad/FPGA boards on either side of the HTD feed eight RF ports for a single polarization. By feeding the antenna in this fashion, the OctoBlade has the benefit of physically isolating the H and V polarization circuitry, which preserves the inherent polarimetric isolation provided by the antenna by minimizing parasitic couplings. The OctoBlade is hot-swappable and is also symmetric, so the OctoBlade is insensitive to orientation when installed in a panel.
The Quad board is responsible for the analog RF circuitry and the conversion between the RF and digital domains. Each of the eight channels on the Quad board has an independent radar chain with a 10 W GaN high-power amplifier (HPA), a transmit and receive switch (T/R switch), a limiter, and a low noise amplifier (LNA). Since Horus is a fully digital radar, digitally controlled stepped attenuators and phase shifters are not necessary, as that functionality is implemented in the FPGA digital signal processing fabric. An attenuated bypass path around the LNA is implemented to enable high linearity measurements of mutual coupling while transmitting full power out of nearby elements to assist with system calibration. The Analog Devices AD9371 is a dual-channel RF transceiver capable of tuning from 300 MHz to 6 GHz with up to 100 MHz of instantaneous bandwidth. This highly integrated transceiver is utilized on the Quad board to provide the translation layer between the RF radar front-end and the digital interface between the Quad board and the FPGA board. The Quad board also incorporates several supporting circuits, like numerous RF calibration paths between the AD9371 and the radar front-end, external LO distribution to the AD9371, and hot-swap power controllers to protect the Quad board in the event of power issues.
The main processing on the FPGA board is implemented with a pair of Intel Arria 10 GX FPGAs that perform the array signal processing and digital waveform generation. Each Arria 10 is supported by a bank of double data rate version 4 (DDR4) RAM for storing arbitrary waveforms and buffering receive samples prior to digital beamforming. Nowadays, utilization of DDR4 RAM in modern radars that rely on FPGAs [75], [76] is one of the best ways to achieve real-time beamforming and other radar functions at reasonable power and monetary costs. An Intel Cyclone V System-on-a-Chip (SoC) FPGA based daughtercard, running Linux on the hardened ARM processor cores, configures and manages the Arria 10s, the AD9371 transceivers, as well as, performing online diagnostics and ensuring proper operation of the electronics. Four Samtec QRM8-RA connectors provide the JESD20B, SPI and GPIO interfaces for the AD9371 transceivers and for controlling the radar front-end. External LOs for the AD9371s feed through the FPGA board from the Digital Bridge to the Quad board. The data network on Horus is implemented within the Arria 10 FPGAs and exposed via six Samtec ARC6 connectors on the rear of the PCB. These connectors route directly to four high-speed serial transceivers per port on the Arria 10 FPGAs. In addition to the external ports, there is an internal network port between the two Arria 10s routed through the PCB. This implementation is protocol agnostic, enabling the exploration of varying network protocols and architectures. Additional diagnostic interfaces, such as JTAG, I2C and a serial UART console for the Cyclone V SoC, are available to the SuperBlade via the Digital Bridge to support managing and debugging OctoBlades while installed in the radar system.
The HTD is an aluminum cold plate with blind mates to liquid distribution manifolds that are integral to the Horus panel mechanical structure. The internal serpentine fluid path navigates by each of the major heat-producing components on an OctoBlade to move the heat into the coolant. The HTD utilizes Staubli dripless connectors to allow an OctoBlade to be inserted and removed from a panel without leaking, even while fluid is circulating through the rest of the system.

C. Cooling and Structural System
It is important to maintain stable thermal characteristics and minimize temperature gradients across the aperture on phased arrays for system reliability and calibration performance. While the HTD is responsible for removing the heat from an OctoBlade, the Horus system has been designed to appropriately distribute and collect the coolant fluid throughout the array in a practical and scalable manner. When the Horus project first began, air cooling was considered, however, it was determined that while potentially feasible at a single blade level, the necessary amount of airflow and pressures involved were not practical at the system level. As a result, the decision was made to liquid-cool the system.
The fluid distribution for the array is incorporated into the mechanical structure of the panel. The electronics lattice is intentionally reduced compared to the element lattice spacing within the panel, in order to make space for the supporting mechanical frame and fluid distribution. In Fig. 3, one can see the rectangular aluminum columns on either side of a panel that were used during prototyping. Horizontal fluid distribution manifolds are welded between the vertical columns at the top and bottom of each panel. Each horizontal manifold is only open to one of the vertical columns, forcing the fluid to flow through the OctoBlade and SuperBlade HTDs in a panel passing the exhaust fluid through the other horizontal manifold and vertical column. Each horizontal manifold is shared between adjacent panels vertically, alternating the fluid flow direction through HTDs with each panel. Likewise, each vertical column is shared between adjacent panels horizontally across the array. This method of fluid distribution ensures that all HTDs in the system are in parallel and no coolant flows out of one HTD and into another. This results in nearly uniform temperatures across the full array, minimizing thermal impacts on array calibration.

D. Antenna Design and Validation
The Horus antenna design was focused on achieving the same or improved performance compared to that of WSR-88D parabolic-reflector antennas. These design specifications are critical, given that the weather mission presents more challenging polarimetric requirements, in terms of accuracy of estimates than those for aircraft surveillance missions. A Horus antenna panel is composed of 64 elements (8×8) configured in a two-dimensional square lattice of 0.5λ spacing. An aperturecoupled microstrip crossed-patch radiating antenna element with independent feed layers for the H-and V-polarizations was adopted for high cross-polarization isolation (>40 dB) across a scan range of 90 • in the principal planes [77]. A parasitic microstrip patch layer was incorporated to have a frequency operation from 2.7-3.1 GHz. The antenna array was fabricated using a standard PCB process. Taconic substrate was used for the driving and parasitic crossed patch antennas, and Rogers 4350B was used for the feeding network. Design aspects of the antenna array and scanning performance are presented in [77]. Fig. 5 shows the setup and laboratory measurements. Multiple factors in the antenna element were investigated during the design and fabrication process of the 8 × 8 array, and these factors include edge diffraction suppression; fabrication tolerances, bandwidth in excess of 15.4% at a central frequency of 2.8 GHz; port-to-port isolation in the element on the order of -50 dB; cross-polarization levels below -40 dB and co-polar mismatch below 0.1 dB at ±45 • and ±10 • for scanning range in the azimuth and elevation planes; and active reflection coefficient of at least -10 dB at ±40 • for scanning range in any plane.

E. Software Architecture
The Horus system is a software-defined radar, which presents many opportunities to develop novel capabilities, along with risks and pitfalls in managing the system complexity and usability. The Horus system is intended to not only be a testbed for advanced fully digital experiments, but also a fieldable system used to routinely collect polarimetric weather data. Significant effort was invested in identifying the most likely deployment scenarios to determine tolerable constraints and assumptions to incorporate into the software, while still enabling many unique capabilities. While this potentially limits certain experiments, the trade-off is rewarded with a substantial improvement in system usability and frees the operator to focus on radar applications rather than radar technology. Since Horus is software-defined, the system will continuously be upgraded to enable new capabilities.
The software is partitioned into four main layers: the deterministic radar signal processing and control in the Arria 10 FPGAs, the embedded software managing the Octo-Blades on the Cyclone V SoCs, back-end data processing on servers and the operator interface running on desktop or laptop computers. Each layer has strengths and weaknesses, progressively trading development ease for performance guarantees as one traverses the layers from the operator interface toward the FPGAs on the array.
The Arria 10 FPGAs define the low-level capabilities of the Horus array, implementing the radar processing chain in fabric. The transmit processing chain in the FPGA encompasses the generation of parametric or arbitrary waveforms, transmit beamforming that applies spatial weights to the generated waveform, transmit alignment calibration to compensate for amplitude and phase offsets between elements, and transmit predistortion to improve system linearity. At the time of this writing, all of these coefficients are non-adaptive; for instance, the predistortion coefficients are computed offline [78]. On receive, the samples pass through a receive alignment calibration block, down-conversion and decimation to select the desired bandwidth; then the samples are buffered into RAM prior to beamforming. The Arria 10s manage scan scheduling, configuring the appropriate settings for each pulse, and deterministic triggering and control of the functions within the FPGA, as well as, the RF hardware on the Quad board.
To make the high volume of data produced across the array manageable, the conventional Horus operating mode digitally beamforms on the array, so that the data processing servers receive fully formed beams. This enables the reuse of algorithms and processing software previously developed for the ARRC's reflector-based radar systems. Horus currently implements a systolic beamforming architecture over a RapidIO network that interconnects all of the OctoBlades in the array. To elaborate, RapidIO is a commercial open standard interface that supports high-bandwidth, low-latency, packet-switched interconnect between multiple DSP processing elements, and between DSP processing elements and bulk memory. For the Horus team, RapidIO is used to transfer highspeed data between FPGAs for scan configuration and receive beamforming. RapidIO helps to form the distributed backend of the radar. When an Arria 10 receives a packet containing beam data, it retrieves the relevant samples from memory, locally beamforms the directly attached channels, and then combines it with the data it received. In brief, each of the four Arria 10 FPGAs form weighted sums of the in-phase (I) and quadrature (Q) baseband data that are produced by the four digitizers that precede each FPGA with a partially completed beams from upstream FPGAs; hence, partial beamforming is achieved to reduce the amount of raw I and Q data that need to be routed. Once the FPGA has contributed its data to the partial beam, a packet is sent to the next FPGA to repeat the process until the beam is fully formed and ingested by a server via a PCIe FPGA card connected to the RapidIO network.
Overall, the Horus radar is controlled by a scheduler that can switch among scan strategies on a coherent processing interval (CPI) basis. Generally, the "scan strategy" refers to the pulse waveform, polarization state, transmit/receive beam weights, PRT, CPI, number of beams, etc. Therefore, volumetric update rate can be readily traded with data quality. From a systemdesign perspective, the Horus software architecture has been designed to provide the user maximum flexibility with the overarching goal of producing the highest temporal resolution possible while maintaining high-quality polarimetric weather radar observations.

V. CALIBRATION
As highlighted in Section III, the technology landscape supporting modern digital arrays has continually maturing tools for establishing and maintaining calibration and alignment as an intimate corollary to their inherent challenges and opportunities, and this concept is explored more broadly in [21] and [79]. For the present work and discussion on calibration, the focus is first and foremost on approaches to maintaining proper alignment, sufficiently low sidelobes, and correcting for polarimetric-measurement errors. For clarity, we cite Patton and Yorinks who describe "alignment" of a phased-array antenna as the process of bringing all of its radiating elements into phase alignment so that their radiated power will add coherently in a given direction [80]. An important note, however, is that the development of this and similar digital array systems allows for the exploration of the practical limitations in digital array calibration that the team has previously studied. This includes quantifying and extending other performance metrics such as dynamic range [67], [81] and spectrum-related interoperability using digital nonlinear equalization (NLEQ) and digital predistortion (DPD) [82], [83] or even intentional decorrelation of spurious products [66] to maximize dynamic range. For example, such relatively low-power spurious products include third order harmonics and intermodulation terms.
Horus has a number of tools from which it can leverage built-in or auxiliary measurements to assess or estimate the element-level amplitudes and phases of the signals on the data converters (ADCs and DACs) relative to what they should be, ideally, if the array is scanning (transmitting or receiving) to or from a particular angle. Horus achieves this with a specific overall aperture window or taper, taking all physical effects into account. The techniques being used and explored all seek to assess these ground truth relations between the element-(and polarization) -specific digital waveform amplitudes and phases and the actual fields that would exist in a clear atmosphere.
For the purposes of discussion, a brief overview of each of the procedures is given next, followed by references to many more fundamental/in-depth explorations.

A. Far-Field Calibration and UAS-Based Measurements
Traditional methods for far-field phased array calibration are extensions of classical far-field measurements [84] to elementlevel amplitude and phase alignment and/or for assessment of dual-polarization performance [85]. Characterizing antenna patterns with high accuracy typically requires the use of specialized indoor or outdoor antenna range facilities. In both cases, the intrinsic properties of the antenna pattern measurements must exclude undesirable reflections, diffraction, and other external sources of contamination that may influence the overall measurement. When the radar system is deployed, the antenna array is mounted on a mechanical pedestal and is surrounded by other elements such as a radome, tower, lightning protection, and RF equipment. Ground irregularities produced by topography, morphology, and environmental conditions (temperature and humidity) that are different for each site have also been proven to negatively impact the overall performance of radars. Nevertheless, the team has leveraged far-field measurements before for array alignment and calibration [19]. For large arrays, such an approach requires a separation between the radar of aperture diameter D and measurement antenna on the order of 2D 2 /λ, which is not practical indoors for S-band weather radar systems.
As an alternative to this traditional far-field measurement, the ARRC team has proposed and demonstrated a novel method to characterize the antenna patterns of Horus and far-field calibration using an unmanned aircraft system (UAS). The proposed UAS RF test system uses a commercial hexacopter UAS platform, implemented with a customized RF transceiver and antenna probe that provides excellent dynamic range polarization performance [86], [87], [88], [89], [90]. The UAS platform dimensions and features were selected to support RF metrology mission for long endurance, position accuracy, stability, and enough payload to carry out an RF transceiver, DGPS system, and RF probe [91], [92], [93]. Fig. 6 illustrates such a UAS-based polarimetric calibration and characterization of the mobile Horus radar. A 12-inch (0.3049 m) diameter metallic sphere tethered to the UAS platform is used to perform a polarimetric radar calibration in the far-field region (>80 m). In this case a separation of 20 m. from the UAS to the metallic sphere is used to minimize the back-scattering contamination from the drone. The UAS in spherical scanning mode is used to characterize antenna patterns in the far field. For antenna pattern characterization, an antenna probe was designed with high polarization isolation (<50 dB) and beamwidth ( <40 • ) to minimize scattering fields induced in the drone [92]. Antenna patterns of the Horus mobile radar are obtained using a spherical scanning mode when the radar is looking up. This test procedure reduces ground and clutter contamination.

B. Near-Field Calibration
For most large arrays, near-field (NF) measurements provide the standard mechanisms to carefully assess the array characteristics. This is especially true for determining sidelobe levels and pointing accuracy, among other important characteristics. If performed carefully, NF measurements can provide an understanding of root causes of any antenna limitations [94], [95]. For the Horus system, the early work reported in [96] and [97] has continued with a summary included here.
As an initial calibration step, one 8 × 8 antenna subarray panel of the Horus array was fully populated with electronics that make up the transmit and receive signal paths. The complete subsystem was mounted in a near-field chamber for testing (see Fig. 7a). The near-field scanner is comprised of two motorized Velmex BiSlide assemblies, one Velmex VXM Stepper Motor Controller, an S-band open-ended rectangular waveguide probe (OEWP), a Newport "optical breadboard" base, and RF absorber. These features enable the measurement of antenna patterns for H and V polarizations.
The current process for Horus near-field calibration uses a park-and-probe technique to measure amplitude and phase at each channel. Then, the alignment weights are generated, applied digitally, and verified. Measurement of a full, dualpolarimetric transmit or receive pattern requires four separate data collections, one for each combination of array polarization and OEWP orientation (0 • or 90 • ). The 8 × 8 panel hardware can receive both polarizations simultaneously and feedback the data separately. Multiple beam angles can be collected simultaneously on receive. Up to 16 beams can be formed sequentially. After applying the park/probe and the backprojection calibration methods [97], [98] on the 8×8 subarray, the near-field patterns were measured and transformed into the far field. Normalized copolar and cross-polar H and V far-field patterns are presented in Figs. 7 (a) and (b). The left column shows broadside beam measurements and the right column shows a beam scanned at 36 • in elevation. Dotted contours on the copolar H and V patterns indicate the half-power beamwidth (-3 dB) whereas dotted contours in the cross-polar patterns indicate the -40 dB level. A qualitative comparison of the broadside patterns shows excellent mainlobe agreement between the H and V polarizations. The sidelobe structure for each polarization appears to be symmetric about the mainlobe for the horizontal and vertical cuts. Cross-polarization levels are below -50 dB at the peak of the corresponding copolar patterns, and generally going from -55 to -45 dB across all angles. Achieving cross-polarization levels below -45 dB was one of the key goals in the design of the Horus antenna, given the importance of minimizing this contamination for accurate polarimetric measurements [56], [60], [99], [100], [101]. A deeper investigation of polarimetric Horus calibration as a function of beamsteering angle is ongoing; research results will be presented once the investigation is complete.

C. Mutual Coupling
The ARRC team has been exploring and using the ability of highly digital arrays to leverage inherent inter-element mutual coupling measurements to provide feedback paths that encompass the individual phase and magnitude errors of the transmit and receive element's electronics. This concept, which has been used since the early days of such systems [102], is useful for initial calibration and alignment (without the use of near-or far-field test equipment) [103] and in-situ realignment and enforcement of new weightings [19] in digital array systems. Recent activities have been summarized in [96].
As part of the current work, an experiment was designed to measure relative performance of reference-based mutual coupling. A calibration horn was placed in the array's nearfield and connected to an optical delay line (ODL) repeater. By transmitting toward the horn from a single array element and receiving time-delayed returns from all array elements, relative alignment was established. Aligning the array using this test setup effectively focuses the array towards a fixed point in space some distance from the array face, and provides a repeatable calibration "target" which can be returned to for validation.  Fig. 8 shows one set of results from these experiments. The upper and lower panels show the array magnitude and phase, respectively, for the 5 × 1 array of panels (320 independent, dual-polarization radiating elements) that were populated with electronics at the time of the experiment. The "True Magnitude" provides the magnitude of the ground-truth alignment weights from the experiment described above. The organized pattern seen in the magnitude data results from the actual antenna pattern of the horn. The "MC Magnitude" provides weights estimated based on inter-element mutual coupling. With the array uncalibrated, mutual coupling calibration was applied targeting the "focused" array state, which produced an accurate estimate of the "True" weights. The difference between the truth and the estimated magnitude is provided in the right panel and has a standard deviation across the array of 0.012 dB. The lower panels are equivalent except for phase across the 320 channels. The standard deviation, in this case, is 0.395 • .
Although just one example, the results in Fig. 8 illustrate how mutual coupling can be used to realign the array to an arbitrary array state. Current work is underway to implement initial array alignment without the need for near-or farfield systems. Such an algorithm would rely on the inherent redundancy in the array geometry and mutual coupling.

VI. INITIAL WEATHER OBSERVATIONS WITH HORUS A. Meteorological Conditions
During the afternoon of 23 March 2023, a mesoscale convective system formed along a cold front moving West to East over the southern US Plains. Forecast soundings suggested favorable deep shear for supercells (i.e., tornado-producing storms), with intense (25-35 m/s) winds in the 400-mb layer contributing to effective-shear magnitudes in the 30 m/s range. Temperatures changed throughout the day from ∼10 • C to ∼20 • C, with similar changes in dewpoint, producing convective available potential energies (CAPE) around 2000 J/kg in central OK. This environment resulted in several storms that produced damaging winds, lightning, hail, and heavy rain from NW Texas into central Oklahoma, as reported by the U.S. National Weather Service (NWS). 1 Many severe thunderstorm and flash flood warnings were issued by the NWS forecasters throughout the event. Fig. 9 shows the radar reflectivity and Doppler velocity fields of data collected by the operational KTLX WSR-88D in Twin Lakes, OK, at 20:35:06 Z. Data are from a plan-position indicator (PPI) scan at the 0.5 • elevation. Polarimetric weather data were collected with the Horus radar simultaneously to evaluate initial polarimetric calibration and system performance. The radar was deployed at the Radar

B. Experimental Radar Configuration
Due to the availability of tested OctoBlades, these initial weather observations were conducted with only a partial array of one complete column of panels, forming a 5 × 1 array of panels (320 independent, dual-polarization radiating elements). The half-power beamwidth of this configuration is approximately 13 • in azimuth by 3.1 • in elevation. The radar was configured to scan in the range-height indicator (RHI) mode from 0.5 • to 32.5 • with 0.5 • sampling. A pulse-repetition time (PRT) of 1 ms with 64 samples per dwell was used, resulting in a scan time of 4.096 s. Pulse compression waveforms with non-linear frequency modulation were used, with a pulse width of 80 µs and a bandwidth of 5 MHz [104], resulting in a range resolution of 30 m. The progressive pulse compression technique [105], [106] was implemented to mitigate the pulsecompression blind range. Range-time samples were produced at a rate of 15.625 MSPS, resulting in a range sampling interval of approximately 10 m. Data were collected for a range from 0.5-100 km for approximately 10 minutes pointing the antenna broadside to 205 • azimuth, scanning the evolving storm cells as they moved toward the radar.
A single beam was formed by the real-time digital beamforming network and the time-series in-phase and quadrature (I/Q) data were processed. The weather signal processor includes several methods to improve data quality, like, spectral-based noise estimation [107], electromagnetic interference filter [108], ground-clutter filtering [109], and multi-lag estimation [110], [111]. Fields of radar-variable estimates resulting from processing the data from the scan at 20:35:03 Z are presented in Fig. 10.

C. Data Quality Discussion
A qualitative evaluation of fields in Fig. 10 indicates that data were coherently received and processed, since they are relatively smooth and have realistic values. First, the Z h field shows smooth transitions from lower reflectivities of ∼20 dBZ around the edges of the storm, to reflectivities of up to ∼55-60 dBZ at certain convective cores within the storm. This follows a conceptual model of the physics of storms, whereby stronger updrafts near the core produce larger concentration and size of hydrometeors increasing the overall reflectivity. Next, the field of v r shows smooth variation with outbound velocities (red colors) near the surface, and relatively high inbound velocities (green colors) aloft. The transition in Doppler velocity estimates at approximately ∼500 m going from outbound to inbound through an iso-Doppler level (grey tones) indicates a smooth change in the direction of the wind field. This is typical in convective storms and represents a change in storm advection direction. Doppler spectra from a location with weather returns of high signal-to-noise ratio (SNR) is presented in Fig. 11, showing the approximately Gaussian shapes of the H and V spectra [25]. Further, the spectra have similar shapes implying good matching of H/V beam patterns, and indicates reasonable polarimetric calibration.
The fields of Z DR and ρ hv in Fig. 10 present relatively smooth changes and plausible values. Specifically, Z DR values are mostly between 0-3.5 dB. Lower values (near 0 dB) are expected at the higher levels of the storm or in regions Fig. 11.
Doppler spectra from a location with weather returns of high signal-to-noise ratio (SNR). Note that the spectra have similar shapes, which implies good matching of H/V beam patterns, and indicates reasonable polarimetric calibration. with low Z h , indicating presence of small nearly-spherical raindrops, or small, randomly oriented ice particles (e.g., crystals, snow) when above the atmospheric melting layer. At lower heights, Z DR is larger as the process of collision/coalescence [112] increases raindrop size and due to air drag force raindrops become oblate as they are falling. This increases the Z DR , which explains the larger values (1-3.5 dB) at lower altitudes. Certain regions of high Z DR coincide with regions of high Z h , typically observed in the storm updrafts' region where larger (and more oblate) raindrops are present, (c) and (d) are histograms derived using the first ten scans, whereby weather data from the first five scans are averaged and subtracted from averaged weather data from the 6th to 10th scans, and censoring data with SNR ≤ 15 dB. for example, that approximately along the 30 km range and 3 km height.
The magnitude of the correlation coefficient between the horizontally and vertically polarized returns, ρ hv is a key parameter defining the quality of polarimetric radar measurements [113]. The ρ hv field in the bottom left panel of Fig. 10 shows relatively high values (∼0.9-1) as expected from hydrometeors [54]. Most values are approximately 0.99, representing pure water raindrops. The standard errors of the estimates of polarimetric variables are significantly reduced if the maximum ρ hv of the weather signals exceeds 0.99 -a basic requirement for polarimetric weather radars. A region of lower ρ hv is observed at approximately between 40 and 46 km range, where a vertical column with ρ hv ≈ 0.92 is present. This may indicate presence of mixed-phase precipitation, possibly a combination of raindrops and small hailstones, coupled with some signal attenuation (likely higher in the H polarization) as the has beam propagated through strong precipitation cores. Although this was not confirmed by in-situ instrumentation, it is consistent with the conceptual model of deep convective storm cells. We note that several hail reports were received by the NWS and are available online.
The ρ hv is defined as the normalized absolute lag-0 cross-correlation estimate, i.e., |R hv (0)|/ Ŝ hŜv . At low SNR regions, estimates have high standard deviation, therefore, the geometric mean of signal power estimates may be larger than the lag-0 cross-correlation, i.e., Ŝ hŜv > |R hv (0)|, which results in ρ hv > 1. Notice thatŜ h andŜ v are also estimates that depend on the noise power estimate. Correlation coefficient estimates larger than one are typically present on the edges of the precipitation, far from the radar where the SNR is low and are considered invalid. This is commonly observed on ρ hv estimates from any polarimetric weather radar, including those from the operational WSR-88D [114].
Accurate measurements of ρ hv are crucial for polarimetric detection of the melting layer and determination of its height [115] and for identification of the areas with hail and quantification of its size [116]. Therefore, the requirements for the ρ hv measurements in the design of the radars for weather observations are very strict and important. A more detailed evaluation of the impacts of the Horus antenna on ρ hv estimates can be found in [101].
Data from a sequence of 352 scans were analyzed and these showed a smooth evolution of the discussed fields. The scan time series exhibited natural meteorological features consistent with storm evolution and advection, indicating that the Horus data appear accurate and therefore a fully digital PAR technology may be suitable for polarimetric weather observations. To quantify the quality of polarimetric Horus data, we produce histograms of Z h and ρ hv , as well as histograms of differences between fields of Z h and ρ hv . These are shown in Fig. 12. Histograms of Z h and ρ hv are computed using data from the first 60 scans (∼4 min) and include approximately 10 million points. Data censoring is applied using SNR thresholds of 5 dB for Z h and 15 dB for ρ hv [117] to reduce the impact of measurement noise on polarimetric-variable estimators.
A qualitative analysis of Fig. 12(a) shows that reflectivity values measured were between approximately -2 dBZ up to 55 dBZ. The histogram looks smooth reflecting the expected dependence of returns from precipitation systems (i.e., these usually do not have sharp gradients). The ρ hv histogram in Fig. 12(b) shows that most values are concentrated between about 0.97 and 1, with the peak at approximately 0.994. This is a key indicator of the quality of polarimetric calibration and beam matching, and indicates that Horus can measure the correlation coefficient of raindrops with accuracy exceeding the requirements. Histograms in Fig. 12(c) and Fig. 12(d) are derived using the first ten scans, whereby data from the first five scans are averaged and subtracted from averaged data from the 6th to 10th scans, and censored with an SNR ≤ of 15 dB. Resulting difference histograms have zeromean approximately Gaussian distribution, which is expected, and with relatively narrow standard deviations. The standard deviation of Z h difference histograms is 0.7824 dBZ and the one for the ρ hv difference histograms is 0.0057. These are within the NOAA/NWS functional requirements for the future operational U.S. weather radar [118], which are 1 dBZ for Z h and 0.006 for ρ hv .

A. Perspective on Fully Digital Arrays
The authors have attempted to convey the potential of fully digital phased array radars, in general, and more specifically for weather observations. The high temporal resolution afforded by phased arrays is necessary to unravel processes in severe storms, tornadoes, and other high-impact events. In addition to rapid beam steering, fully digital arrays are highly agile in terms of angular sampling and general beam shaping. For example, these sophisticated radars have the potential of creating adaptive nulls on receive with unprecedented degrees of freedom for interference and clutter mitigation. This application is particularly important for moving clutter, such as that caused by wind turbines. As previously emphasized, fully digital arrays are uniquely designed as "software-defined radars," and therefore minimize obsolescence concerns with the ability to reconfigure the array for future and yet-to-be-defined missions. This quality of being "future proof" has the potential to reap a significant reduction of overall operation and maintenance costs over the lifetime of these sophisticated instruments. Although a digital-at-everyelement architecture offers extreme flexibility, several disadvantages were noted in Section III. Examples include power consumption of analog-to-digital converters at every element; a significant amount of digital data that needs to be routed; clock synchronization at each data converter must be carefully maintained, and high cost that is sometimes mitigated by subarraying.
In collaboration with NOAA's NSSL, the ARRC has developed the fully digital Horus phased array weather radar. This polarimetric, S-band radar became operational in late 2022 with the goal of demonstrating the potential of fully digital arrays for weather applications. Of particular note for weather observations is the strict requirement for polarimetric quality similar to the WSR-88D dish-based weather radars operated by the U.S. NWS. It is well understood that the combination of radar polarimetry with phased arrays is arguably the most difficult challenge presented by the technology. Fortunately, the Horus system has been shown to meet this challenge through advanced mutual-coupling-based calibration methods, which should be emphasized are unique to fully digital arrays. For the first time ever, fully digital phased array weather radar data were obtained in December 2022, when the Horus system was deployed near Norman, OK. These initial experiments have shown promising results from a polarimetric quality and beam agility standpoint.

B. Future R&D
Without question, the near-term priority for the Horus radar will be extensive observations with a complete array of electronics. The initial measurements are promising but did not exercise the full capabilities of the Horus radar. For example, only electronic steering in elevation has been attempted thus far. Future experiments will emphasize atmospheric phenomena under a variety of weather conditions, from winter precipitation to deep convection in the spring storm season, utilizing the full capabilities of Horus and showing the potential for scientific novelty. Other non-weather targets of interest include wind farms, wildfires, space debris, aerial biota, and various aircraft (e.g., airplanes, drones, etc.). Convergent research through combined Horus measurements with data from other observation platforms such as rapid-scan satellite radar data will be explored for the study of atmospheric phenomena with multi-frequency and multi-viewing angle observations from ground and space. For example, fast scanning is essential to maximize the collection of matched space-ground precipitation observations for structure and microphysics studies with the Ku/Ka-band PAR radar onboard the Global Precipitation Measurement mission. The future INCUS (Investigation of Convective Updrafts mission) mission will target convective storms and associated fluxes with quickly repeated Ka-band radar measurements that can be compared with their groundbased counterpart to address 2017 Earth Science Decadal Survey key objectives laid out by the National Academies of Sciences, Engineering, and Medicine. The EarthCARE (Earth Clouds Aerosol Radiation Explorer) mission will also carry a W-band Doppler radar that will provide highly complementary observations of precipitation fluxes to Horus. When appropriate, data sharing will be emphasized, especially when engaging the scientific community.
High-quality polarimetric weather measurements rely on accurate and robust array calibration. In early 2023, the ARRC will be finalizing the installation of a large near-field scanner that can be used for array alignment and calibration. These "ground-truth" data will allow accurate beam steering and polarimetric measurements. They will also allow a full-scale demonstration of mutual-coupling realignment, which is vital when considering larger systems. Other important demonstrations will include data throughput capacity, susceptibility to in-band interference, and power consumption measurements. In these cases, theoretical studies have already been performed but validation measurements are prudent.
Other longer-term concepts exploiting the fully digital Horus radar include adaptive beamforming on receive, based on traditional methods and potentially on AI/ML algorithms. In addition, the authors have extensive interest and experience in passive, multi-static measurements for atmospheric observations [119]. To date, these measurements have relied on the WSR-88D radar as the transmitter of opportunity. Certain advantages of using PARs as the transmitter (e.g., mitigation of two-way sidelobes) have been theorized in the past, but not yet demonstrated [120]. Data reduction ideas, such as sparse arrays and various compression methods will also be considered and demonstrated.
Finally, the inherent panel-level scalability of the Horus radar should and must be exploited in the future. Given the S-band wavelength of Horus, even a fairly large array (e.g., 1600 radiating elements for the current system) presents an unacceptable beamwidth for operational radar networks and research applications. By creating a larger array superstructure, tower, power source, etc., a fully digital, S-band, phased array weather radar can be created with the required angular resolution (∼1 • ) based on the scalable Horus design. Such a system would likely have ∼10,000 radiating elements. Since the total transmit power scales with the array size, the sensitivity of the system would rival that of the WSR-88D radar, but with all the advantages of the fully digital Horus weather radar. The outlook is bright for fully digital phased array radars and Horus stands as just one example of what is possible for the future of weather monitoring.