Mobile Radio Networks and Weather Radars Dualism: Rainfall Measurement Revolution in Densely Populated Areas

1 Mobile Radio Networks and W eather Radars Dualism: Rainfall Measurement Re v olution in Densely Populated Areas Davide T ornielli Bellini, Graduate Student Member , IEEE, Mario Montopoli, Dario T agliaferri, Member , IEEE, Luca Baldini, Senior Member , IEEE, Elisa Adirosi, Ser gi Duque, Laura Resteghini, Umberto Spagnolini, Senior Member , IEEE Abstract —This study demonstrates, f or the first time, how a network of cellular base stations (BSs)the infrastructure of mobile radio networkscan be used as a distributed opportunistic radar for rainfall remote sensing. By adapting signalprocessing techniques traditionally employed in Doppler weather radar systems, we demonstrate that BS signals can be used to retrie ve typical weather radar products, including r eflectivity factor , mean Doppler velocity , and spectral width. Due to the high spatial density of BS infrastructure in urban en vironments, combined with intrinsic technical features such as electronically steerable antenna arrays and wide receiver bandwidths, the proposed approach achieves unprecedented spatial and temporal resolu- tions, on the order of a few meters and several tens of seconds, respecti vely . Despite limitations related to low transmitted power , limited antenna gain, and other system constraints, a major challenge arises from ground clutter contamination, which is exacerbated by the nearly horizontal orientation of BS antenna beams. This work provides a thorough assessment of clutter impact and demonstrates that, through appropriate processing, the resulting clutter-filter ed radar moments reach a satisfactory level of quality when compar ed with raw observations and with measurements from independent BSs with overlapped field-of- views. The findings highlight a transformative opportunity for urban hydrometeor ology: leveraging existing telecommunications infrastructure to obtain rainfall information with a level of spatial granularity and temporal immediacy like nev er bef ore. Index T erms —Meteorological factors, opportunistic radio propagation signals, radar signal processing . I . I N T RO D U C T I O N Q U ANTIT A TIVE precipitation estimation (QPE) under- pins hydrological modeling, flood and landslide early warning systems, drought assessment, and climate diagnostics. D. T ornielli Bellini, D. T agliaferri and U. Spagnolini are with the Department of Electronics, Information and Bioengineering, Politec- nico di Milano, V ia Ponzio 24/5, 20133 Milano, Italy . e-mail: {da- vide.tornielli,dario.tagliaferri,umberto.spagnolini}@polimi.it S. Duque, is with Huawei T echnologies, Munich Research Center , RiesstraSSe 25, 80992 Munich, Germany . e-mail: ser- gio.duque.biarge@hua wei.com L. Resteghini, is with Milan Research Center, Huawei T echnologies Italia S.r .l., Milan, Italy e-mail: laura.resteghini@huawei.com L. Baldini and E. Adirosi are with National Research Council of Italy , Institute of Atmospheric Science and Climate (CNR-ISAC), via Fosso del cav aliere, 100, 00133, Rome, Italy . e-mail: {luca.baldini,elisa.adirosi}@cnr .it M. Montopoli (corresponding Author) is with the National Research Council of Italy , Institute of Atmospheric Science and Climate (CNR- ISA C), via Fosso del ca valiere, 100, 00133, Rome, Italy , and with Center of Excellence for T elesensing of Environment and Model Prediction of Sev ere events, Univ ersità DellAquila, LAquila, 67100 LAquila, Italy e-mail: mario.montopoli@cnr .it Howe ver , the pronounced spatial and temporal variability of rain fields makes accurate observation intrinsically challeng- ing. Traditional surface networks of rain gauges provide direct measurements of accumulated rainfall but suf fer from sparse, unev en global distribution and point-scale representativeness, especially ov er complex terrain. Optimal rain gauge placement is not always applicable due to logistic issues and integration of gauges with spatially continuous precipitation estimates often carried out [ 1 ]–[ 3 ]. W eather radars offer ov er-land high- resolution spatial snapshots of precipitation at minutes time scale, but they infer surface rain rates through microphysical assumptions and algorithms that are sensiti ve to en vironmental and instrumental effects [3]–[ 5 ]. Satellite remote sensing fills large observational gaps by pro viding quasi-global coverage and nearreal-time precipitation maps. Ho wever , satellite re- triev als remain uncertain for light/shallow precipitation, in particular orographic contexts, and mixed-phase hydrometeors, and typically require ground v alidation and bias correction. These complementary strengths and weaknesses motiv ate inte- grated frameworks that merge satellite, radar, and gauge infor- mation to improv e accuracy and spatiotemporal completeness in QPE for both science and applications [6], [ 7 ]. Recognizing the trade-offs among methods, integrated pre- cipitation estimation merging gauges, radar, and satellite has become a central line of research. Emerging non-traditional opportunistic observations, like those from commercial mi- crow ave links (ground to ground or ground to satellite) , citizen science, v ehicle sensors, and camera-based techniques can complement established systems, but require rigorous quality control before operational adoption [ 7 ], [ 8 ]. Recent advances have en visioned the exploitation of wire- less networks endo wed with integrated sensing capabilities to extract new source of information from the surrounding en vironment [ 9 ]–[12]. The underlying principle is to lev erage these networks, primary designed for interconnecting end- user equipments (e.g., mobile devices), to deli ver services that extend beyond con ventional communication. This can be achiev ed incorporating the base stations (BS), i.e. the network nodes responsible for routing information to end-user de vices such as mobile phones, in a new service able to generate a nov el data stream that bridges en vironmental geophysical variables with the radio-frequency domain. Following this new paradigm, a very preliminary conceptualization of the use of BSs for precipitation sensing was introduced in [13], 2 focusing on antenna beamforming design to maximize the spatial rejection of ground clutter . Howe ver , the authors in [13] employ a BS prototype designed for short-range operation and targeted toward 6G applications, whereas in this work a commercial 5G-Adv anced BS is utilized, which supports communication ov er distances of several kilometers and corre- sponds to a more widely deployed and standardized platform. In addition, the study in [13] does not address the practical challenges associated with integrating precipitation sensing into the standard operation of a BS. These challenges include the analysis of the limited sensitivity of BS system to precipi- tation, the use of a physically based rain scattering models to describe precipitation fields over the resolution v olumes and experimental evidences using actual measurements acquired in both clear sky clutter-only situations as well as during rain precipitation events. Conv ersely , this study demonstrates, for the first time, and with the aid of both physically-based simulations and measured experimental data from operational BS, the feasibility of using BS in weather radar-like mode (BS-WRM) to track extreme precipitation, opening to a new way to look at the opportunistic radio signal observations. The proposed approach le verages the radar-lik e sensing capabilities of BS to monitor rainfall, and, owing to the extensi ve global deployment of BS infrastructure (Figure 1 a), particularly in densely populated areas, this technique exhibits remarkable scalability and considerable operational attractiv eness. If com- pared with the weather radar coverage worldwide in figure 1 b), it can be seen as BS distribution closely follows that of weather radars but with some important differences related to approx 10-times higher spatial resolution and refresh time of fered by BS than custom weather radars. The integration of BS data into QPE frameworks holds significant promise for enhanc- ing multi-source data fusion alongside conv entional ground- based radars, satellite sensors, and rain gauge networks. It is important to note that, unlik e the commercial microw ave link approach, which relies on bistatic radio connections that lev erages the path-inte grated signal’ s attenuation to infer an av erage precipitation intensity , the BS based methodology directly lev erages end-user communication links in a radar-like monostatic scheme, thus enabling range-resolved inference of the precipitation field. The pervasi ve capillarity of BS compared with any other opportunistic sensing tool, makes the themes treated relev ant for improve precipitation field mapping especially in urban areas where there exist an observational gap of precipitation measurements. The paper is or ganized into eight sections. Section II pro- vides a re view of precipitation remote sensing at microwa ve frequencies, in order to contextualize the proof of concept for using BS as a no vel source of local rainfall information. Section III presents an ov erview of BS characteristics, whereas Section IV describes the methodology adopted for processing the BS data. Section V demonstrates rainfall detection from BS using simulated data, and Section VI validates the same concept using actual BS data acquired during dedicated exper - imental campaigns, while Section VII is devoted to discussing the implications of the proposed methodology . Finally , Section VIII presents the conclusions. a) b) Fig. 1: Conceptual visualization of BS distribution reflecting the global coverage trends deri ved from publicly av ailable sources and industry reports [14]–[17]. Y ellow/Orange areas indicate high density (urban regions in North America, Europe, East Asia). Dark green areas show moderate cov erage. Sparse regions represent limited connectivity a); W eather radar coverage at 2019 (with permission from [18]) in b). I I . S T A T E O F T H E A RT O N R E M O T E S E N S I N G O F P R E C I P I T A T I O N This section cov ers a concise overvie w of the state-of- the-art techniques used to monitor atmospheric precipitation worldwide, using sensors working in the microwa ve frequency bands. This is particularly useful for establishing a framework that enables a better interpretation of observations based on the BS approach proposed in this work. A. Satellite active and passive systems Satellite-based active and passi ve microwa ve sensors deliv er complementary insights into global precipitation, distinguished by their spatial resolution and temporal coverage. Activ e sensors onboard low-Earth orbit satellites cap- ture vertical profiles via dual-frequency Ku (13.6GHz)- /Ka(35.5GHz)-band radars, resolving hydrometeor vertical structure at ∼ 5 km × 250 m sampling, revisiting the same region ev ery few hours when integrated into an active- passiv e constellation framework [ 6 ]. As demonstrated by the N ASA/J AXA Global Precipitation Measuring Mission (GPM) [ 6 ] and the Chinese Feng Y un 3G (FY -3G) [19] mission, dual-frequency techniques and path inte grated attenuation constraints, yield improvements in rain rate and drop size distribution (DSD) retrieval, including light rain and snowfall, although non-uniform beam filling and complexities in the melting layer remain challenging [20]. Passi ve radiometers operating at 10183 GHz offer wide- swath cov erage with footprints ranging from ∼ 15 km at 3 high frequencies to ∼ 50 km at low frequencies. Bayesian retriev al framew orks (e.g. GPR OF algorithm [ 5 ], [21] and its neural network version: GPROF-NN [22]) have reached a good degree of maturity providing rain-rate estimates over spatial scales of ∼ 1530km. Activ e and passi ve synergy are often used to align high resolution vertical structure from radar with the broader spa- tial sampling of radiometers. These methods help alle viate sampling mismatches and improve retrie v al consistency [20], [23]. Global products like IMERG consolidate the multi-sensor constellation into ∼ 10 km spatial grids at 30-minute intervals, enabling near-real-time hydrological and climatological appli- cations [24], [25]. B. Opportunistic radio signals Opportunistic sensing exploits existing telecommunication infrastructures to infer precipitation from raininduced atten- uation of microwa ve signals. T wo main link types are used: Commercial Microw av e Links (CMLs) in terrestrial cellular backhaul networks and Satellite Micro wave Links (SMLs) such as TVSA T or broadband terminals. Their characteristic spatial and temporal resolutions are summarized in T able I . Operating above 6GHz, both systems experience scattering and absorption by raindrops, making pathintegrated attenuation a proxy for integrated rain rate. As a consequence, neither CMLs nor SMLs resolve the vertical precipitation structure, and geolocating rainfall becomes increasingly uncertain for long link paths. CMLbased rainfall estimation has advanced substantially , enabling highresolution urban monitoring and supporting floodforecasting applications [26]–[31]. SMLs e x- tend this concept to slanted paths, providing broader spatial cov erage and higher temporal sampling [32]–[36]. Despite these dev elopments, important challenges persist: accurate at- tenuationtorain con version requires reliable atmospheric emis- sion models and rainheight information; wetantenna effects; nonuniform rain fields along the path bias; and link hetero- geneity complicates integrated processing. Furthermore, link density remains limited in many regions (T ableII), reducing spatial sampling and hindering homogeneous monitoring. Fu- ture prospects include fusion of CML and SML observations, physicsinformed machinelearning approaches [37], and stan- dardized open datasets to transform communication networks into dense environmental sensing systems for hydrology and climate resilience [38], [39]. Although fiberoptic connections are expected to replace microw ave backhaul on major network backbones, microwa ve links will remain essential where ca- bling is impractical (e.g., rural areas, wetlands), implying that CML a vailability in urban settings will gradually decline. C. Ground based weather radar systems Ground-based weather radars provide high-resolution volu- metric observations of precipitation, typically with radial res- olutions of 100m to 1km and angular resolution of 1 ˇ r, usually resampled, for applications, onto a Cartesian grids at 0.51km. T emporal updates are frequent, with operational weather radar networks such as NEXRAD [45], [46], OPERA [47], [48] and CINRAD [49], [50] in US, Europe and China, respecti vely , deliv ering 5-minute refresh cycles. These characteristics make radars indispensable for monitoring con vecti ve systems and short li ved precipitation extremes. Obviously , weather radars are installed exclusi vely o ver land, which inherently restricts their observational cov erage to terrestrial areas and portions of ocean very close to the coast. T ypical frequencies allocated for weather radars are within S-band ( ∼ 2.7GHz), C-band ( ∼ 5.6GHz) and X-band ( ∼ 9.4GHz) (see table III). The country or continental-wide networks that are mostly built using S- band and/or C-band radars, hav e been designed with the aim of maximizing cov erage while keeping costs lo w , being costs driv en primarily by the number of radars installed. These networks are typically configured to minimize overlap between individual radar cov erage areas. Unav oidably , coverage gaps can occur due to Earth curvature, beam o vershooting beyond 150 km, and beam blockage due to complex terrain or human- made structures. T o fill those gaps, X-band weather radars hav e emerged as a critical component for enhancing precipi- tation monitoring in critical areas. X-band weather radar local networks emer ged with the CASA (Collaborati ve Adaptive Sensing of the Atmosphere) program in the United States [51] and found application in lar ge urban regions like in the DallasFort W orth (DFW) urban testbed [52], and T okyo Metropolitan Area (Japan) [53]. In the latter case, phased array radar antennas are used. Although conv entional weather radar are dominated by system with mechanical moving antennas (i.e. mechanically steered parabolic dish), systems equipped with phased arrays attempt to emerge [54], [55]. Phased array radars (P AR) utilize electronically steered antenna arrays which allow eliminating mechanical inertia. This enables rapid and adaptiv e single or multi-beam scanning, with full-volume updates achiev able in tens of seconds and targeted sector scans in sub-second intervals. Such capability significantly enhances temporal resolution for monitoring rapidly ev olving con vecti ve storms and urban flash-flood hazards. Howev er, P AR systems entail initial higher costs and complexity , require sophisticated calibration to manage beam shape and sidelobes suppression, and remain less widely deployed than con ventional networks. Dual polarization capability is also offering a supplementary advantage over single polarization systems in terms of data quality (e.g. more accurate clutter removal, attenuation effects compensation) and refined quantitative precipitation estimates [56]–[58]. Ho wever , such improvements are conditioned to the av ailability of low noise polarimetric variables. Challenges remain in cost, maintenance, and data fusion, but operational benefits in disaster risk reduction and urban resilience under- score the value of radar networks. I I I . B A S E S TA T I O N S Y S T E M This section describes the usage of base stations of cellular networks as opportunistic weather radars. In cellular communication systems, a BS provides wireless connecti vity between users and the core (wired) communication network. Each BS is responsible for transmitting and recei ving radio- frequency signals within a defined co verage area, commonly referred to as a cell. Hereafter, we will refer to the two BS operating modes as communication standard mode (COM), 4 Link type Frequency band (GHz) Path scale (km) a Native sampling (s) c CML 6–40 ∼ 0 . 2 –10 1–10 (research); (terrestrial backhaul) (typ. 18, 23, 38) (typ. 1–4) 60–900 (operator archives) SML Ku: 10.7–14; ∼ 2 –10 10–60 (typical telemetry); (TV -SA T / do wnlinks) Ka: 18–30 slant path segment up to ∼ 300 Notes. a Length of the path (or effectiv e rainy segment) over which path attenuation is measured. b Nativ e time sampling of recei ved signal level (or SNR) av ailable from operators/terminals; research systems can sample faster than operational archiv es. T ABLE I: Indicativ e spatial and temporal resolution and operating frequency bands for opportunistic precipitation sensing using Commercial Microw ave Links (CMLs) and Satellite Microwa ve Links (SMLs). Ranges are representative of recent deployments; actual values depend on network geometry , sampling strategy , and processing. Region / Corridor CML Density SML Density (links/100 km 2 ) (links/100 km 2 ) W estern Europe 15–25 2–8 Eastern North America 10–20 3–10 W estern North America 6–12 2–6 East Asia 12–22 2–6 South Asia (India) 8–15 1–4 Southeast Asia 10–18 1–3 SE Brazil 8–14 1–3 Southern Africa 5–10 0.5–2 Middle East 6–12 1–3 SE Australia 5–10 1–3 T ABLE II: Indicati ve density ranges of Commercial Micro wave Links (CML) and Satellite Micro wa ve Links (SML) for opportunistic precipitation sensing, expressed as links per 100 km 2 . V alues are conceptual estimates based on published case studies [38], [40], [41], ITU reports ( [42]–[44]), and regional adoption patterns. g =1 g = 2 N g Mobile users Base station Antenna beams a) BS - COM b) BS - WRM Fig. 2: Conceptual figure of a base station (BS) in a typical communication mode (COM) in which BS serves the final mobile users (mobile devices in green) a); and the weather radar mode (WRM) in which BS antenna multi beams (orange lobes) scans a sectorial portion of the cell to intercept rain in the area covered b). which is the primary BS functionality (figure 2 a), and an experimental weather radar mode (WRM), which is the application discussed in the present work 2b). A. Spectrum allocation In typical BS-COM operation (of the 5G or next-generation wireless networks) each group of BSs pertaining to the same operator is allocated with a pre-defined spectrum portion, centered around carrier frequency f 0 and of fix ed bandwidth B . In current 5G standard, regulated by the third generation partnership project (3GPP) and the international telecommuni- cation union (ITU), the allowed carrier frequency f 0 is within the so-called frequency range 1 (FR1, f 0 < 6 GHz) [ 59] while next-generation of wireless networks (6G) will likely extend the operation to frequency range 3 (FR3, 7 ≤ f 0 < 24 GHz). The typical av ailable bandwidth at FR1, which is the operating frequency considered in this work, amounts to B = 100 MHz, while FR3 promises to guarantee much wider bandwidths [60]. On the same bandwidth, each BS is responsible of a different cell, minimizing the mutual interference and ensuring coexistence by suitable spatial reuse of the spectrum [61]. B. Antenna configuration The single BS is typically equipped with three antenna arrays, each cov ering an azimuthal sector of 120 ◦ . Each antenna is made by a uniform rectangular array with N ϕ , N θ patch antennas along the azimuth and ele vation, respectiv ely . The spacing among the patches is optimized to improve the beamwidth for communication purposes, conv entionally using a slanted ( ± 45 deg) polarization. Such arrays ha ve full electronic scanning capabilities and can implement flexible beampatterns according to needs. In typical operation, the BS-COM implements beamforming 1 to maximize the data- rate to/from the users by directional transmission/reception in multiple directions. The minimum half po wer beamwidths (HPBWs) along azimuth ( ∆ ϕ ) and elev ation ( ∆ θ ), is ruled by N ϕ and N θ respectiv ely , with typical array footprints of the order of few de grees and maximum antenna gains that range from 20 to 30 dBi. C. W aveform, frame organization and emitted power The 3GPP standard-compliant BSs operate in half-duplex , alternating downlink (DL) and uplink (UL) communication phases in which the BS is transmitting (serving the users) or receiving information from the users, respectiv ely , in a time division duple xing working mode. The DL and UL time slot, denoted as τ DL and τ U L , are typically interleaved according to predefined patterns in order to operate BS-COM under its nominal operating conditions (see Figure 3 a). The maximum 1 The beamforming is either digital or analog, mainly depending on the car- rier frequency . Digital beamforming allows flexible beam-pattern generation at the expense of a higher hardware and processing cost, especially for analog- to-digital and digital-to-analog components, and it is therefore widespread only at carrier frequencies f 0 < 6 GHz. 5 Parameter Symbols S-Band C-Band X-Band Frequency (GHz) f 0 (2.7, 3.0) ( 2.7 ) (5.4, 5.8) ( 5.6 ) (9.3, 9.6) ( 9.4 ) Peak Input Power (kW) P tx (750, 1000) ( 750 ) (200, 350) ( 200 ) (25, 100) ( 100 ) Noise Figure (dB) F (3, 5) ( 4 ) (3, 5) ( 4 ) (3, 5) ( 4 ) Pulse Length ( µ s) τ tx (0.3, 2.0) ( 0.33 ) (0.3, 2.0) ( 0.33 ) (0.3, 2.0) ( 0.33 ) Antenna Max Gain (dBi) G max (45, 46) ( 43 ) (44, 45) ( 43 ) (43, 44) ( 43 ) HPBW Azimuth ( ◦ ) ∆ ϕ ≈ 1.0 ( 1 ) ≈ 1.0 ( 1 ) (1.0, 1.5) ( 1 ) HPBW Ele vation ( ◦ ) ∆ θ ≈ 1.0 ( 1 ) ≈ 1.0 ( 1 ) (1.0, 1.5) ( 1 ) Polarization Scheme - Dual-pol (H/V) Dual-pol (H/V) Dual-pol (H/V) T ABLE III: T ypical system features of weather radars at S-, C-, and X-bands. Bold numbers in the round brackets refers to values used in the simulations of figure 11 . continuous power emitted by the BS during DL is limited by regulations, implying an emitted power P tx of tens to hundreds of W atts depending on the antenna gains. In both periods (DL and UL), the BS employs orthogonal frequency di vision multiplexing (OFDM). In OFDM, the av ailable bandwidth, B , is divided in N sub subcarriers, each of them at frequency f n = f 0 + nδ f , n = 0 , ..., N sub − 1 , where δ f is the subcarrier spacing, chosen in a pre-defined pool according to the 3GPP numerology [62]. T o simplify , the transmission is organized in symbols, each of duration 1 /δ f so that to allow the orthogonality of the subcarriers and symbols are grouped in frames, whose duration is a flexible parameter that can be optimized by the BS according to the specific context, constrained by the required alternation between DL and UL operation, which tends to follow a regular and periodic or cyclic pattern ov er time (see figure 3 ). D. Differ ences and Similarities Between a BS and a W eather Radar The BS technology strikes an interesting parallelism be- tween a radar-like BS, termed as BS-WRM, and specifically designed weather radars. Differences between the two systems interest antenna technology , transmission hardware and the acquisition schedule. 1) Antenna scan mode and coverage strate gies: Most of weather radars make use of mechanical scans except in few cases that uses phased array technology . The latter is more closely related to that performed by a typical BS-COM that uses arrays of patch antennas to electronically scan the surrounding scene. Aside from the differences in antenna performance (BS-COM has nearly half of the antenna gain of a weather radar with a much wider HPBW up to 6 times higher), another important difference to underline is related to the fact that a weather radar is optimized to detect the surrounding en vironment indiscriminately by performing volumetric scans with at gi ven repetition cycle, whereas the BS-COM is de- signed to guarantee the capacity coverage within the cell, thus in this case multi-beams are directed towards users, and no full scanning is implemented, except for quasi-periodic idle periods in which a BS scans the co verage area to search for new users. 2) Antenna elevation angles: In terms of siting, BSs are typically located at a giv en height from ground (ranging from 5 − 6 m to 20 − 30 m) and tilted downward with elev ation !"#"$%& '()*+,-./01)2345.$#)63%"7)$36"$/10+84"& 9 !" : Downlink ( DL ) time 9 #$ ) : Guard ( gu ) time 9 %" : Uplink ( UL ) time Pulse 0 ( p =0) 𝜏 !" 𝜏 #$ 𝜏 %" 𝜏 &' t Pulse 1 ( p =1) 𝜏 !" 𝜏 #$ 𝜏 %" 𝜏 &' t+ 𝑇 𝑠 Pulse N p - 1 ( p = N p - 1) 𝜏 !" 𝜏 %" 𝜏 &' t+p 𝑇 𝑠 𝑇 ( a) b) '())*2"0+:"4)40%04)63%"7)$36"$/10+84"& 9 &' : T ransmitting ( tx ) time 9 (' : 4 eceiving ( rx ) time 9 )* : idle ( id ) time ; + : <132 ) +.6" ) <06-1.$# interval 𝜏 #$ 𝜏 )* 𝜏 +* 𝜏 )* 𝜏 +* 𝜏 )* 𝜏 +* Fig. 3: Representation of time frame organization a) in the typical BS-COM working mode; b) in the experimental BS-WRM. Note that in panel a), downlink (DL) and uplink (UL) time slots are depicted as separate and contiguous slots for ease of illustration, whereas in practice they interleav e using a more articulated pattern following the 3GPP standard. 6 angle with respect to horizon θ < 0 ◦ , in order to maximize the illumination of the users. In such circumstance, the illuminated scene is dominated by the ground clutter (e.g. b uildings, civil infrastructures, bridges, etc.). Therefore, operate a BS as a weather radar would require the implementation of dedicated de-cluttering methods (see later sections). It is worth noting that, although the BS antenna is typically do wntilted in order to comply with local regulatory requirements and to optimize data transmission performance, dedicated configurations in which the beams are directed upwards are technically feasible and cannot be ruled out for future implementations. 3) Acquisition cycle: As described in section III-C, BS- COM typically operates a pattern scheme of DL transmission and UL reception time slots for τ DL and τ UL , respecti vely (figure 3 a). Such a scheme is typical for a BS in its nativ e COM mode but it can be easily adapted to a typical pulsed WRM. This can be achiev ed by allocating a time period τ tx for transmission and reserving some of the remaining time ( τ rx ) for the reception of the back-scattered radar echoes (figure 3 b). Howe ver , since both COM and WRM must coexist together , only a small fraction ( τ rx ) of the total a vailable time ( T s ) is dedicated to the reception of the meteorological signals. The time τ gu is a sort of guard period that guarantees a clear separation between the transmitted signal and the received one making the latter more easily detectable. As a consequence, a blind zone caused by τ tx + τ gu arises. Howe ver , such blind zone is expected to be of the order of the Inter-Site Distance (ISD). Therefore, the blind zone of one BS could be likely covered by other BSs in the surrounding area. The rest of the av ailable intra-frame time ( τ id ) is an idle period from the point of view of the WRM, whereas it is an activ e UL time for the COM. Indeed, during τ id the BS could continue to operate a DL and UL sequence thus continuing to guarantee the COM service. Having figure 3 b in mind, one of the main difference in the acquisition cycle of BS-WRM, with respect to more customary pulsed weather radar systems, stems on the fact that the acquisition of meteo-signals is not continuous but intermittent in BS-WRM being the sequences of τ tx and τ rx interleav ed by an idle period τ id . The selection of τ tx , τ rx and τ id , is quite flexible but it must comply , in the first instance, to ensure the capacity of the BS-COM service through an adequate time τ id . Secondary , from the standpoint of BS-WRM, τ tx and τ rx should be properly selected to allow a sufficient signal- to-noise-ratio (SNR) and cov erage in range. T oo short τ tx implies lower transmitted energy and consequently lower SNR. On the contrary , too lar ge τ tx can erode τ rx restricting the maximum unambiguous radar range. Howev er, thanks to the OFDM mode, the transmitted signal in τ tx has a bandwidth B much larger than 1 /τ tx resulting in a pulse compression gain B τ tx ≫ 1 which allow to maintain the range resolution high in the presence of longer τ tx [63] (see Section IV for details). For reasons of confidentiality , complete typical v alues of BS- WRM cannot be made publicity av ailable. For what of interest here, order of magnitude of B is around 20 MHz achieving range resolution around 7 m with a slow time sampling interval T s = τ tx + τ gu + τ rx + τ id = 2 . 5 ms. 4) T ransmitted power: One main drawback, of BS-WRM is due to the low power engaged compared to weather radars. For obvious reasons, there is significantly less av ailable peak power (order of 10 − 3 ) in a BS-WRM than in a traditional weather radar, and consequently the ability to detect meteo target at far ranges will be limited (see section V). 5) P olarization scheme: BS uses slanted linear 45 ◦ slanted linear polarizations both in the transmission and reception side. Although slanted ± 45 ◦ linear polarizations is quite common during transmission in most of commercial weather radar systems, the horizontal symmetry of some meteorological hydrometeors (e.g. liquid drops) and the absence of the hori- zontal and vertical components in reception makes the use of polarimetry trick y for BS-WRM. 6) Carrier frequency: The BS working frequency can be approximately 5.0 GHz, which is in close proximity to the 5.6 GHz band allocated for C-band weather radar services. It should be noted that the BS operating frequency is not standardized globally and may differ across regions. Nonethe- less, for the purposes of simulation and comparative analysis performed, the BS operating frequenc y is fixed at 4.9 GHz in this study . Although at first glance 4.9 GHz and 5.6 GHz frequency difference appears to be not significant, it has some consequences in the BS-WRM derived quantities (see section V). I V . P RO C E S S I N G C H A I N The processing chain stems from the reception of I-Q signal of the BS-WRM. Let us assume that the BS-WRM reserves a periodic time interval in the standard-compliant frame organi- zation in which it implements an activ e beam scanning over a predefined azimuth sector . W e denote with N g the number of beams that the BS-WRM implements, with a single beam pat- tern denoted by f g ( θ , ϕ ; θ g , ϕ g ) in which ( θ g , ϕ g ) indicates the pointing direction of the g -th beam, g = 1 , ..., N g . Hereafter , for sake of clarity we use the subscript g to denote a quantity referred to the g -th beam (e.g., f g ( θ , ϕ ; θ g , ϕ g ) = f g ( θ , ϕ ) ). Follo wing the frame or ganization in figure 3 b, for each beam the BS-WRM transmits a re gular train of pulses identified by the pulse index p , whereby a single pulse comprises the effecti ve duration, τ tx , the switching time from Tx to Rx, τ sw , a receiving interval, τ rx , that enables the BS-WRM to gather the precipitation echoes and an idle interval, τ id , which is needed to separate weather and telecommunication services (see figure 3 b). Consequently , having N ′ p pulses per beam, the total duration of the beam sweeping is T tot = N g N ′ p T s . T tot is periodically repeated ov er fairly long duty cycles (tens of seconds) to monitor and track precipitation. A. Pre-pr ocessing Let us define the Rx complex I-Q signal by the BS-WRM on the g -th beam and p -th pulse as y g ( t, pT s ) . Such signal has duration τ tx and bandwidth B , with time-bandwidth product τ tx B ≫ 1 . It is first sampled at rate ∆ t = 1 /B adc (in verse of the sampling bandwidth of the receiv er analog-to-digital con verter B adc , which is usually larger than the effecti vely employed signal’ s bandwidth B ) and con verted to range di- mension by ∆ r = c ∆ t/ 2 , obtaining a discrete version of y g , that is, y g ( m ∆ r , pT s ) , m = 1 , ..., M , where M is the number 7 of range samples. Ob viously , the quantity M ∆ r corresponds to the radar maximum unambiguous range which is equal to cτ rx / 2 . The first processing step is to compute the cross- correlation between the Rx signal y g ( m ∆ r , pT s ) and the Tx signal s g ( m ∆ r , pT s ) , obtaining the rang e-compressed signal x g ( m ∆ r , pT s ) . Such range-compressed signal has effecti ve range resolution equal to c/ 2 /B ≥ ∆ r , usually larger than the range sampling. B. Doppler spectrum estimation The second processing step is the estimation of the Doppler spectrum from x g ( m ∆ r , pT s ) , operating a windo wing fol- lowed by a periodogram for each m -th range bin. The complex Doppler spectrum is defined as: X g ( m ∆ r , k ∆ f )= F w { x g ( m ∆ r , pT s ) } = T s W N p − 1 X p =0 x g ( m ∆ r , pT s ) w ( pT s ) e − j 2 πk ∆ f pT s (1) where k = − N p / 2 , ...., N p / 2 − 1 denotes the sample index in the Doppler frequenc y domain, and ∆ f = 1 / ( N p T s ) is the Doppler frequency resolution. The term w ( pT s ) denotes the complex weight of the window at the p -th pulse, aimed at reducing the sidelobes in the Doppler spectrum and ease the ground clutter filtering, and W = q P N p − 1 p =0 | w ( pT s ) | 2 is a normalizing factor . A suitable choice is a Blackmann or Blackmann-Nuttal window . Note that the windowing operation is restricted to N p < N ′ p samples in order to obtain multiple Doppler instances of the same scene, which can subsequently be a veraged (figure 5 a,b). The Doppler power spectral density is then calculated by the periodogram technique as: S g ( m ∆ r , k ∆ f ) = | X g ( m ∆ r , k ∆ f ) | 2 (2) Then, the total Rx power on the g -th beam, m -th range bin is the inte gral of the power spectral density: P rx , g ( m ∆ r ) = ∆ f N p 2 − 1 X k = − N p 2 S g ( m ∆ r , k ∆ f ) . (3) Eqs. ( 2 ) and ( 3 ) are the core of the whole processing that follows, and the key quantity from which the radar moments can be derived. C. W eather radar quantities For what follows, it is useful to recall the fundamental equations that govern the operation of a weather radar . Let us consider again a single beam, whose pointing angle is ( θ g , ϕ g ) . The total receiv ed po wer at range r = m ∆ r is e xpressed as [56]: P rx , g ( m ∆ r ) = C g Z g ( m ∆ r ) ( m ∆ r ) 2 L 2 g ( m ∆ r ) (4) where: (i) ( m ∆ r , θ g , ϕ g ) identifies a resolution volume at distance r = m ∆ r for the g -th beam (ii) C g is the radar constant for beam g , which includes all the system parameters that pertain to the measurement system (e.g., emitted po wer, radiation pattern–explicitly dependent on the specific beam– , etc.) and need to be calibrated a-priori in order to enable QPE (see Appendix A for further details), (iii) Z g ( m ∆ r ) is the equiv alent reflectivity factor measured in (mm 6 m − 3 ), (iv) L 2 g ( m ∆ r ) is the integral path loss due to atmospherics effects (eg. water vapor and rain) from the radar site up to distance m ∆ r . 1) Reflectivity factor : In ( 4 ), Z g ( m ∆ r ) depends by scat- tering and microphysical features of hydrometeors detected as follows: Z g ( m ∆ r ) = λ 4 0 π 5 | K w | 2 Z ∞ 0 σ b ( D , χ ) N ( D, m ∆ r, θ g , ϕ g ) dD . (5) In the latter , | K w | 2 is the dielectric factor and it is derived from the electric permittivity of water ( ≈ 0.93 at S-C and X bands), σ b ( D , χ ) is the backscattering cross section (mm 2 ) of the drop with equiv alent diameter D illuminated with polarization χ and N ( D , r , θ g , ϕ g ) is the drop size distri- bution in (m − 3 mm − 1 ) at the resolution volume at position ( m ∆ r , θ g , ϕ g ) . 2) Mean Doppler velocity : The mean Doppler v elocity V D , g at m -th range gate and g -th beam is defined as: V D , g ( m ∆ r ) = 2 λ 0 P N p 2 − 1 k = − N p 2 k ∆ f S g ( m ∆ r , k ∆ f ) P rx , g ( m ∆ r ) | {z } f D , g (6) in which factor 2 λ 0 deriv es from the well known link between Doppler frequency and velocity: f = − 2 v λ 0 , where λ 0 = c/f 0 is the carrier wa velength and S g and P rx , g are defined in ( 2 ) and ( 4 ), respectively . 3) Doppler spread : The Doppler spread ( W D , g ) quantifies the dispersion of Doppler shifts around the mean value and serves as an indicator of turbulence-induced effects: W D , g ( m ∆ r ) = 2 λ 0 v u u u t P N p 2 − 1 k = − N p 2 ( k ∆ f − f D , g ) 2 S g ( m ∆ r , k ∆ f ) P rx , g ( m ∆ r ) . (7) 4) Minimum detectable reflectivity factor : One last quan- tity that needs to be introduced is the minimum detectable reflectivity (MDZ) which is strictly related to the radar system sensitivity (i.e. the e xpected minimum detectable signal in terms of Z g ). MDZ is obtained by in verting ( 4 ) assuming L 2 g = 1 and considering the power lev el from which the signal to noise ratio (SNR) is equal to 1. This corresponds to the minimum useful signal lev el that is theoretically detectable in noise at the receiv er output. Consequently: MDZ g ( m ∆ r ) = P min rx , g C g ( m ∆ r ) 2 (8) In practice, the minimum po wer le vel yielding the MDZ is computed as P min rx , g ( m ∆ r ) = P noise F n SNR min , where P noise is the thermal noise power , F n is the noise factor of the receiv er and SNR min is the minimum SNR required by the user at the recei ver output. T ypically SNR min = 1 and values of Z g below MDZ are not detectable. 8 The main limitation to QPE by weather radars (and by BS-WRM as well) is the presence of ground static clutter , that biases the estimated precipitation and hinders QPE. In the following section we describe the employed processing chain for ground clutter filtering. T o simplify the notation, we drop the beam index g for simplicity , referring to single- beam processing, and we refer to the av ailable datum as x ( m, p ) ≜ x g ( m ∆ r , pT s ) , X ( m, k ) ≜ X g ( m ∆ r , k ∆ ν ) , dropping the sampling intervals as well. D. Ground static clutter (GC) r emoval Separate rain signal from the unwanted ground clutter (GC) is of fundamental importance to achieve reliable QPE results, especially if neg ativ e elev ation angles are used, as with BS- WRM. Following literature (e.g. [64]), there can be two distinct approaches to suppress clutter in weather radar images: 1) a two-step procedure, in which sufficiently long rain-free periods are collected to construct a static clutter map that fa- cilitates clutter identification, followed by the application of a zero-Doppler notch filter to suppress the clutter contribution in precipitation-affected data [56]; or 2) a single-step procedure that exploits the statistical and/or textural differences between clutter and precipitation, which are directly observable in the acquired data, thereby eliminating, or making less decisiv e, the need for a-priori acquisition of no-rain data. Herein, due to the complexity in operating a dual system like BS-WRM, we follow an approach according to the second clutter suppression class although a refinement, which incorporates the collection of no-rain data, is also proposed. The clutter suppression algorithm used in this work, is an improved extension of that proposed in [64]. The algorithm’ s block diagram is shown in figure 4 . The starting point is the range compressed received signal for a giv en g -th beam: x ( m ∆ r, pT s ) (see section IV -A and figure 5 a) which is processed following sev eral steps: 1) Sub-sampling : The objective of the sub-sampling step is to construct two temporal staggered sequences, denoted by x 1 and x 2 , from the original data x ( m, p ) such that, for each range bin m , the follo wing condition holds: x 1 ( m, p ; s, o ) = x ( m, 2 p − 1 + s ) , (9) x 2 ( m, p ; o, s ) = x ( m, 2( p + o ) + s ) (10) for p = 1 , ..., ( N p − o ) / 2 , being N p the number of samples in a giv en window at position s (figure 5 b,c,d). The sequences x 1 and x 2 share a common shift s = n ∆ s with n an index from 0 to N D -1 and N D the maximum number of windows that can be allocated into the original time sequence x with a giv en shift gap ( ∆ s ). Within a generic window , x 2 is offset by a quantity o with respect to x 1 . By setting s = 0 and o = 0 we end up with ev en and odd sequences (compare figure 5 d and e)) used in [64]. 2) Evaluate the differential phase (DP) : the algorithm follows with the definition of the the differential phase in the spectral domain ( ϕ ) as the Hermitian product of the two spectra of the sequences x 1 ( m, p ) and x 2 ( m, p ) (figure 5f), as: ϕ ( m, k ; o, s ) = ∠ ( X 1 ( m, k ; s, o ) X ∗ 2 ( m, k ; o, s )) (11) Sub - sampling on moving window i - th eq.s (9) - (10) Differential phase of staggere d sequences eq. (11) Circular variance eq. (13) Circular variance - driven Clutter mask eq. (14) ! ! ! " Fouri er transform ( " 𝒘 ) Eq.s (12) # ! # " $ % &' $ Input received ra nge compressed signal for beam g - th S ()*+ , &' $ in predominant no - rai n c ondi ti ons Per sis ten cy - driven Clutter mask eq. (15) &' % Output Clutter - Filtered spectra eq. (16) Offset: - Shift : . Circular variance thresho ld : % / Per si ste nc y thresho ld : 0 1 Update time frame loop for N D windows 0 Define Per sis ten cy !23,45 6 7,8 & 9 Fig. 4: Block diagram of the clutter suppression algorithm used in the BS-WRM. T extured-filled boxes indicate input and output quantities, whereas those gray-shaded are the auxiliary input parameters. where: X 1 ( m, k ; s, o ) = F w { x 1 ( m, p ; s, o ) } X 2 ( m, k ; s, o ) = F w { x 2 ( m, p ; s, o ) } (12) denote the complex amplitude Doppler spectra of x 1 ( m, p ; s, o ) and x 2 ( m, p ; o, s ) , respectiv ely , through the F w operator defined in ( 1 ). The DP depends on the rangeDoppler bin ( m, k ) and on the offsetshift pair ( o, s ) . Note that the time series x 1 and x 2 hav e ( N p − o ) / 2 samples each and are sampled at 2 T s instead of T s (figure 5 (ce)). This has the dual effects to reduce the spectral resolution X 1 and X 2 to ∆ f = 1 / [( N p − o ) T s ] with respect to X in ( 1 ) that has ∆ f = 1 / ( N p T s ) as well as, to halving the Doppler frequency unambiguous limits from ± 1 2 T s to ± 1 4 T s , respectiv ely . T o restore the proper frequency resolution of X 1 and X 2 to that of X , a zero padding of o/ 2 samples on both x 1 and x 2 is applied. The final result is to hav e the k index in (11) that varies from 1 to N p / 2 covering the spectral domain within ± 1 4 T s . 3) Calculate the circular variance (CV) : Since a single DP map ϕ ( m, k ; o, s ) may be noisy due to the limited number of pulses used for its computation, we use the circular variance (CV) as a measure of the DP dispersion, to quantify its stability ov er dif ferent shifts ( s = 0 , ..., ( N D − 1)∆ s ). The CV is defined as follows: σ ( m, k ; o ) = 1 −     1 N D ( N D − 1)∆ s X s =0 e j ϕ ( m,k ; o,s )     2 (13) and it yields a more robust measurement of phase stability . When, σ ( m, k ; o ) approaches zero, phase at bin ( m, k ) is stable indicating a stable target (i.e. likely clutter). Otherwise, it implies precipitation or noise. A conceptual representation of CV in (13), is giv en in Figure 6 which allow to better 9 1 1 st window 𝑁 ! 𝑁 " - th window 𝑠 = 𝑛&∆𝑠 i- th window 𝜙 𝑚 , 𝑘 ; 𝑜 , 𝑠 = ∠ ℱ ! ( 𝑥 " ).ℱ ! ( 𝑥 # ) ∗ 1 𝑁 ! 𝑘 𝑁 ! 1 𝑜 𝑁 ! 1 𝑜 2 nd window a) b) c) d) e) f) x 1 x 2 x 𝑁 ! # 𝑇 $ 2𝑇 $ Fig. 5: Representation of differential phase definition , ϕ ( m, k ; o, s ) (f). The initial time sequence x = x g of N ′ p samples for a single g-th beam (a) is then processed separately in N p -wide moving windows each of them spaced by a shift quantity s (b). In a single window the time series of N p samples (c) is then divided in two distinct time series x 1 and x 2 as in eq. ( 9 ) and (10) of staggered samples (d), (e) orange and blue samples respectively , as a function of the offset o . T extured orange and blue samples in d) and e) are those discarded by the effects of the imposed offset. understand the meaning of σ ( m, k ; o ) . In particular , it can be observed that the individual exponential terms in (13) (orange vectors in figure 6 ) may exhibit substantial noise depending on the observed scene, whereas the resulting mean component (green vector), which is strictly related to the definition of CV in (13), still depends on the instability of the DP components, although it is more robust to their random fluctuations. In summary , σ ( m, k ; o ) constitutes a more stable measure of DP variability and is therefore well suited for clutter identification in a more homogeneous manner . Ho wev er, σ ( m, k ; o ) is an ex- plicit function of the relati ve offset between the two sequences, o , which is an external parameter to be tuned according to the specific precipitation e vent. Setting o = 0 , i.e., employing the method in [64], may be inadequate for particular rain ev ents characterized by reduced turbulence, namely a narrow Doppler spectrum, which in turn leads to an higher DP stability similar with that typically observed in the presence of ground clutter . Increase the of fset o > 0 should hav e the effect to rapidly reduce DP stability for rain signature while maintaining it higher for clutter . Therefore, assuming that clutter has a much higher phase stability than precipitation, the optimal value of o would be in versely proportional to the Doppler spread of precipitation W D in the original spectrum (and it would ev entually depend on the range). Figure 7a well clarifies the the beha vior of CV as a function of o in a real case acquired by BS-WRM during a rain event. This figure is obtained using N ′ p = 128 , N p = 64 , ∆ s = 5 . Looking at the left most panel, the clutter is well visible around the zero-Doppler line, while precipitation signature extends over s=0 s=1 s max =(N D - 1) ∆𝑠 rea l Imaginary 𝜙(𝑚 , 𝑘; 𝑜 , 𝑠) s=0 s=1 rea l Imaginary 𝜙(𝑚 , 𝑘; 𝑜 , 𝑠) s max =( N D - 1) ∆𝑠 a) b) Resultant les s than s max Single DP unitar y abs . terms Resultant approach ing s max Single DP unitar y abs terms Clutter - like signature Rain - like signature Fig. 6: Schematization of CV principle. A case of unstable ϕ terms with o = 0 , producing a resultant much more less than unity and consequently σ approaching one a); the complementary case in b). the entire Doppler domain with some folding effects [56]. Howe ver , as the offset increases (from the left to the right panels), a markedly improved separation between clutter and precipitation is achiev ed, although at the expense of an an increasing loss of Doppler resolution due to the usage of a lower number of effecti ve number of samples along time. 4) Determine CV -driven clutter mask ( C M V ) : A clutter mask, denoted as C M ( m, k ) , is a binary map defined ov er the rangeDoppler domain that characterizes the presence or absence of clutter for each range-Doppler bin ( m, k ) . Specifi- cally , the function assumes the value C M = 0 in the presence of clutter and C M = 1 under clutter-free conditions. Starting from CV (as in Figure 7a), the CV -driv en clutter map ( C M V ) is defined as: C M V ( m, k ; o ) = ( 0 σ ( m, k ; o ) ≤ σ for clutter 1 σ ( m, k ; o ) > σ otherwise (14) where the threshold σ can be set either a-priori (e.g., σ = 0 . 1 ) or based on offline statistics of the clutter ev aluated on a purposely collected dataset in which no-rain data dominate. It is worth to highlight that, differently from our procedure, the method in [64] define C M setting a threshold directly on the differential phase in (11) which is much more sensiti ve to noise than σ in (13) (see figure 6 and related main text). The variations of CV as a function of the offset o , (Figure 7a), clearly indicate that o is a key parameter for achieving effecti ve discrimination between clutter and rain. Increasing o reduces phase coherency within those ( m, k ) -bins where rain signature is present, thus CV rapidly con verges to unity ,while 10 Circular Variance (o = 10) -2 0 2 Doppler Velocity [m/s] 4 6 8 10 12 Circular Variance (o = 20) -2 0 2 Doppler Velocity [m/s] 4 6 8 10 12 Circular Variance (o = 30) -2 0 2 Doppler Velocity [m/s] 4 6 8 10 12 0 0.2 0.4 0.6 0.8 1 -2 0 2 Doppler Velocity [m/s] 4 6 8 10 12 Range [km] Circular Variance (o = 0) (a) Example of CV in the range-Doppler domain, with increasing offset shifts starting from o = 0 to o = 30 , from left to right, respectiv ely , for a real BS-WRM acquisition during a rain event.W ith reference to the calculation of the differential phase (figure 5 ), which is at the base of the circular variance definition, the parameters used are: N ′ p = 128 , N p = 64 , ∆ s = 5 . Persistency (o = 0) -2 0 2 Doppler Velocity [m/s] 4 6 8 10 12 Range [km] Persistency (o = 10) -2 0 2 Doppler Velocity [m/s] 4 6 8 10 12 Persistency (o = 20) -2 0 2 Doppler Velocity [m/s] 4 6 8 10 12 Persistency (o = 30) -2 0 2 Doppler Velocity [m/s] 4 6 8 10 12 0 20 40 60 80 100 (b) Example of persistency (%) in the range-Doppler domain over a 5 minute time interval, with increasing offset shifts starting from o = 0 to o = 30 , from left to right, respectively , for a real BS-WRM acquisition during a rain event. Fig. 7: Example of CV σ v arying the offset o (a) and persistency Ψ (b) over the same rain ev ent. Persistency (T obs = 20min) -2 0 2 Doppler Velocity (m/s) 3 4 5 6 7 8 9 10 11 12 0 20 40 60 80 100 Persistency (T obs = 5min) -2 0 2 Doppler Velocity (m/s) 3 4 5 6 7 8 9 10 11 12 Range (km) Fig. 8: As in figure 7b for o = 20 , b ut moving from 5 min to 20 min observation time. leaving that associated to clutter on lower values, as its phase dispersion is low ev en at larger lags o . As a consequence, the CV thresholding in (14), is expected to produce more accurate C M V . Howe ver , increments of o produces a deterioration of Doppler resolution too, leaving also some ov erlap between the rain-clutter classes (compare figure 7a leftmost and rightmost panels). Improv ements of C M V can be achie ved through the implementation of the next step. 5) Determine persistency-driven clutter mask ( C M P ) : Since the clutter mask C M V in (14) is a real-time estimate that depends on the number of processed samples and/or spectra quality , the clutter filtering process may vary over time, with the obvious consequence of yielding a less homogeneous clutter suppression across the temporal dimension. T o address this limitation, a refined clutter mask can be introduced, for- mulated on the basis of the concept of persistence. Persistency ( Ψ( m, k ) ) can be defined as the number of occurrences for which C M V ( m, k ) in (14) equals 0 (i.e. indicating clutter) ov er a predefined temporal interval. This interval is selected such that no-rain conditions prev ail, ensuring that the acquired scenes are mainly dominated by ground clutter . Then, the persistency-dri ven refined clutter mask ( C M P ) can be re- triev ed as: C M P ( m, k ; o ) = ( 0 Ψ( m, k ; o ) > Ψ for clutter 1 Ψ( m, k ; o ) ≤ Ψ otherwise (15) where Ψ is a persistency threshold that can be obtained similarly to the pre vious step by settling a quantile over the persistency map. It should be noted that the construction of 11 Unfiltered [dBW] -5 0 5 4 6 8 10 12 Range (km) -140 -130 -120 -110 -100 GC CV-filtered (o=0) (dBW) -5 0 5 4 6 8 10 12 GC CV-filtered (o=20) (dBW) -5 0 5 Doppler Velocity (m/s) 4 6 8 10 12 Range (km) GC -filtered (o=20) (dBW) -5 0 5 Doppler Velocity (m/s) 4 6 8 10 12 Fig. 9: Example of ground clutter filtering on raw range-Doppler power spectrum (upper-left), obtained using the CV -driven clutter map for o = 0 and o = 20 samples (upper right and bottom left, respectiv ely), and using the persistency-dri ven clutter map (bottom- right). All the quantities plotted refer to powers in dBW . White pixels are those identified as clutter with the selected approach indicated in each panel’ s title. C M P requires the acquisition of multiple instances of C M V so that its availability depends on the capability to collect data predominantly under non-rainy conditions, which is currently not a fully automated process. Similarly to figure 7a for CV , figure 7b shows the persistency , Ψ , as a function of the increasing offset (from left to right panels). As expected, for larger of fsets, the rain-clutter distinction becomes increasingly pronounced. Figure 7b is b uilt considering 5 min acquisitions in mixed rain and no rain conditions. Increasing the acquisition time from 5 min to 20 min (see figure 8 ) has the expected consequence of markedly reducing the rain signature, which by its nature exhibits higher temporal and spatial variability than clutter , the latter tending to persist in a more pronounced and stable manner . Then, the result in figure 8 (bottom right), is a good example on how the final clutter map, C M P , in (15) can be easily obtained by applying a proper threshold on the persistency Ψ . 6) Clutter filtered spectra : The clutter-filtered spectra X filt can be simply obtained by the following multiplication: X filt ( m, k ; o ) = C M ℓ ( m, k ; o ) X ( m, k ) (16) and it is equal to zero in those pixels identified as clutter by C M ℓ ( m, k ) = 0 where ℓ = V of ℓ = P to select (14) or (15), respecti vely . Note that, since C M ℓ is constructed based on the definition of DP in (11), which contains N p / 2 samples within the frequency interval ± 1 / (4 T s ) , whereas X contains N p samples within the broader frequency interv al ± 1 / (2 T s ) , the values of C M ℓ are constrained to be equal to 1 outside the range ± 1 / (4 T s ) . Consequently , the product in (16) is to be interpreted as an element-wise (Hadamard) multiplication. T o have an idea of the final result achiev able, Figure 9 shows an example of po wer spectrum S = | X | 2 and S filt = | X filt | 2 in (16) for both ℓ = V and ℓ = P and two of fsets o . When the rain is phase-stable as in the selected example, using only CV for GC filtering may be unsatisfactory (see white pixels in the upper right and lower left panels), whereby a long- term persistency (bottom right) yields a more reasonable result filtering the clutter around zero Doppler only . E. Interpolation methodology The clutter-filtered power signal in range and Doppler S filt ( m, k ) = | X filt ( m, k ) | 2 needs interpolation in the missing clutter bins to restore the precipitation values and avoid biases in the QPE. Assuming that the Doppler spectrum of the precipitation at each range bin can be approximated by a Gaussian function [56], we can frame interpolation as the problem of fitting S filt ( m, k ) with a Gaussian function, whose parameters are computed with usual iterativ e techniques. The final po wer spectrum will be e S ( m, k ) = ( S filt ( m, k ) for C M ℓ ( m, k ) = 1 b Ae − ( k − b µ ) 2 2 b Σ 2 for C M ℓ ( m, k ) = 0 (17) and it is used in (3) and ( 5 ) for calculating the received power and the reflectivity factor , respectiv ely , and consequently rain intensity retrie val as detailed in the next subsection. F . Rain intensity r etrieval The retriev al of the rain intensity R g ( m ) at the m -th range gate and g -th pointing beam direction, starts by plugging the clutter-filtered and interpolated power spectral density , e S ( m, k ) in (17), into ( 3 ), yielding the total recei ved power e P rx , g ( m ) , which includes the contrib ution from precipitation particles plus noise. Then, the equiv alent reflectivity factor , Z g ( m ) , is obtained by in verting the radar equation in ( 4 ). R g is finally obtained considering the widely used empirical power- law relation as follo ws: Z g ( m ∆ r ) = aR b g ( m ∆ r ) (18) in which Z g and R g are in (mm 6 m − 3 ) and (mm/h), respec- tiv ely , whereas a and b are the estimation coef ficients. They are generally tuned by matching radar-measured reflecti vity with rainfall accumulations recorded by rain gauges [56]. Howe ver , due to variations of the drop size distrib ution ev en ov er short spatial scales [65], and differences in the sampling volumes of radar and rain gauge instruments, a and b e xhibit substantial variability [66]. A quite consolidated a-priori choice is to assume Marshall and Palmer coef ficients ( a = 200 , b = 1 . 6 ). Howe ver , gi ven the specific setting of BS-WRM with respect to custom weather radars in terms of polarization and working frequency , a new pair of coefficients: a = 92 . 0563 and b = 2 . 1363 , are deriv ed using a large set of 1.4 M of rainy minutes of measured N ( D ) from the Italian Group of Disdrometry , (details in Appendix C). N ( D ) from disdrometers are used into (B.1) and ( 5 ), together with electromagnetic simulations of the drop’ s radar cross section σ b , to reproduce a statistic of R g and Z g in (18) and tune coefficients a and b , accordingly . It is worth nothing that the tuning process of a and b does not explicitly takes into account altitude displacement in R g 12 a) b) d) c) Fig. 10: Simulations of copolar back scattering cross sections (a) for a base station in weather radar mode (BS-WRM) and custom weather radar (WR). WR is assumed to work at 5.6 GHz with horizontal ( h ) polarization scheme whereas BS-WRM works at 4.9 GHz having a 45 ◦ linear slanted polarization scheme for both transmission and reception. Comparisons in terms of reflectivity factor ( Z ) is in b); minimum detectable reflectivity ( M D Z ) for WR at v arious frequencies and BS-WRM is in c). For BS-WRM the minimum detectable rain rate ( M D R = ( 10 M DZ/ 10 a ) 1 /b with tuned coefficients a =92.0563 and b = 2 . 1363 ) is also shown (magenta dashed line). The Z -difference between BS-WRM and WR vs. Z from WR, are in d). and Z g since both these quantities are simulated at the same altitude as well as inhomogeneities in the radar resolution volume caused by non uniform beam filling ef fects. Such arguments are indirectly considered by adding an uncertainty zero mean noise term on Z g (1 dB error standard deviation in our case). It should be borne in mind that for the conv ersion in (18) to be ef fective, Z g has to be well calibrated. This means that the radar constant and attenuation f actor in (A.1) should be known with a suf ficient de gree of accuracy . On the two-way attenuation factor term, L 2 g , it is generally unknown unless the aid of polarimetry which is not used in the current setting of BS-WRM. Howe ver , BS-WRM typically operates in a domain with a maximum range of 20 km and consequently the L 2 g term in (A.2) is not expected to increase considerably . V . R A I N P R E C I P I TA T I O N D E T E C T I O N F RO M B A S E S TA T I O N : R E S U L T S F RO M S I M U L AT E D S C E N A R I O S In this section the opportunity to use BS-WRM is proven from a simulation standpoint. A comparati ve analysis of BS-WRM rain detectability features with respect to those achiev able from typical weather radar (WR) systems is presented. T o this end, a simulation environment is built by implementing eq. ( 5 ). The latter is run considering, σ b from EM simulations performed by a T -matrix code [67], whereas N ( D , r , θ , ϕ ) is obtained by the GID (Gruppo Italiano di Disdrometria) ground disdrometer database [68] composed by 1.4M of rainy (Appendix C). In this case, N ( D , r , θ , ϕ ) = N ( D ) since sparse point measurements Fig. 11: Simulations of radar reflectivity factor (dBZ) for typical S-, C-, X- weather radars (a,c,e) and BS system (g) and corresponding two-way path integrated attenuation (d,d,f,h) from disdrometer alone do not allow to describe the spatial structure of N ( D ) . In the simulation, for the BS-WRM we assumed 4.9 GHz carrier frequency with a +45 ◦ slanted linear polarization used for transmission and reception, whereas for WR we assumed a C-band radar (5.6GHz) with alternate orthogonal polarizations. For both systems, 0 ◦ elev ation angle with respect the horizon is considered. The comparison of BS-WRM vs. WR is shown in figure 10a) in terms of radar cross sections, σ b . As it is clear there are differences in σ b which are more pronounced around 6 mm of equi valent water drop diameter with σ b from BS-WRM constantly lower than that from WR. The same ef fect is visible in terms of Z e (10b) where the underestimation effects from BS-WRM compared to WR is more evident for Z e larger than 35dBZ. The Z domain above 35dBZ will be likely sampled by the BS gi ven the values on which the minimum detectable signal curve is based (10c). The same panel also highlight the difference in terms of sensitivity of BS with respect typical WRs as well as the minimum detectable rain rate (MDR) from BS which remains lo wer 13 than 1 mm/h. The v alues of MDZ are obtained using the values listed in table III (bold values) for WR, whereas for BS-WRM working at f 0 =4.9 GHz, a factor of the order of 10 − 3 , 24 , 0 . 5 and 18 are applied to the bold values of P tx , τ tx , G max and ∆ θ · ∆ ϕ , referred to C-band in III, respectively , and applying them to eq.s (A.3) and ( 8 ). Consequently , MDR is obtained by simply applying the Z − R conv ersion (see section IV -F) imposing Z= MDZ for the BS-WRM case. Finally , the Z difference between BS-WRM and WR, as a function of Z from WR (10d), evidences as for higher Z the BS-WRM is expected to provide underestimates of the order 3.5 dB (on av erage) with peaks that can reach ev en 8 dB. In summary , the analysis of figure 10 indicates as, although BS-WRM configuration is not optimal for rain observations, it is able to detect moderate to extreme events in an area within a maximum radius of 20 km from the BS site. T o visualize this concept, simulations are refined including antenna beam conv olution. In this case, spatial DSD (i.e. N ( D , r, θ , ϕ ) in eq. ( 5 ) are generated using a spatialization procedure [69] that is able to reproduce DSD features on a spatial domain, as those measured by ground disdrometers time series. T o ingest antenna con volution in Z e , N ( D , r , θ , ϕ ) is generated at finer resolution than that of the radar system to be simulated. The simulations are conducted under the same assumptions employed for the generation of figure 10. Simulations results are in figure 11 which shows both Z e and 2-w ay P ath integrated attenuation ( P I A ) and considers the appropriate M D Z lev el (eq. 8 ) for each system. T ypical weather S-, C, X-band radars describe the full cov erage domain similarly to each other (11a,c,e) due to their similar MDZ values. Howe ver , as expected, a different impact in terms of 2-way PIA is noted with increases of path losses as the frequency increases (b,d,f). BS-WRM (g) suffer for limited sensitivity (i.e. higher MDZ as in figure 10c) which implies that a large domain of the precipitation filed is in visible to the BS system with only medium to high Z e surviving. In this case, 2-way PIA (h) is not in general so relev ant gi ven the coverage limitations although in some extreme cases, care must be taken to address this issue adequately . It is worth pointing out that the simulations produced do not take into accounts some important aspects like the ground clutter that is e xpected to be a dominant factor for BS-WRM since it likely operates in a highly antropicised context. This aspect is treated in the next section with the aid of actual measured data. V I . D E T E C T I O N O F P R E C I P I TA T I O N F R O M B A S E S TA T I O N : R E S U L T S F RO M A C T UA L M E A S U R E M E N T S This section presents the results in terms of radar moments deriv ed from the estimation of the spectral density in ( 2 ) and after applying the de-cluttering processing chain described in Section IV to actual BS-WRM acquisitions, obtained during a real data experiment with a commercial 5GA BS in China in 2025. The impact of ground-clutter filtering, the resulting radar moments, and the comparati ve analysis of acquisitions from two closely spaced base stations (site 1 and 2) positioned 30 m a.g.l. in an urban context (figure 12), are examined to demonstrate, from an observ ational standpoint, both the Fig. 12: PPI sectors for two Base Stations (BSs) sites ( ▲ , ■ ) with the indication of beams swiped (green) in a common Cartesian grid domain. potential and the limitations of the proposed new technique. In the results that follow , the two BSs are configured to have a range resolution of 7.5 m and a number of N p samples processed per-beam equal to 128. The beam ele vation angles are fix ed so that there is a tilt offset of 2 . 6 ◦ in the beams of site 1 with respect to site 2 with site 2 beams pointing lower than site 1. The area cov ered for this experiment is limited to a small sector ≈ 60 ◦ wide which is sampled approximately ev ery 3 s. The maximum range of each BS is limited in the figures to approximately 5 km to better highlight radar moments and clutter filtering which is discussed in the next sub sections. Blind zones of less than 2 km from the BS-WRM position are also fostered by the time spent for transmission plus the guard time. It is important to note that the BS-WRM configuration employed in the following results is purely experimental and currently lacks any established standardization. A. Ground Clutter F iltering The algorithm’ s steps described in section IV -D are here applied to actual data acquired in the Plan Position Indicators (PPIs) configuration of figure 12. An example of observed reflectivity factor , Z , is in figure 13a,b for the two BS sites considered. Strong ground clutter (above 50dBZ) is clearly visible on both BS sites whereas less intense clutter mixes with rain signature in the interv al (40dBZ, 50dBZ) is hardly detectable by visual inspections. After the definition of the clutter mask in eq.(15), clutter can be discriminated and isolated as in figure 13c,d. From these panels it is confirmed as the clutter signature is characterized by a large variability in terms of v alues of Z with spatial distribution which depends by the specific urban scene seen by the BS. The urban context in which the BS-WRM operates can be e xtremely variable depending by en vironmental factors then making the clutter filtering procedure a key step to obtain a sufficient lev el of data quality . After clutter filtering, the final results achiev ed is in 14 a) c) b) d) e) f) Fig. 13: Example of PPIs of acquired reflectivity factor , Z , (rain+GC) for an ev ent occurred during the experimental filed campaign (a,b) for the two BS sites as in figure 12 at identical timestamps. Identified GC is in panels (a,b) while rain only after GC filter is in (e,f). All reflectivity v alues are in dBZ. Left column (a,d,e) refer to BS site 1 ( ■ ), while right column (b,d,f) refer to BS site 2 ( ▲ ). The common area seen by both sites is highlighted by the dashed black box. figure 13e,f. which shown the clutter filtered Z-PPIs due to rain only . By comparing the panels (a,b) and (e,f), the improv ement achiev ed in terms of data quality is glaring. B. PPI of W eather Radar Moments An example of the whole set of radar moments, namely: equiv alent reflectivity factor, Z , mean Doppler velocity , V D , and Doppler velocity spread, W D , defined by eqs. ( 5 )-( 7 ), respectiv ely , is shown in figure 14 in terms of GC-filtered PPIs. From Z-PPIs in panels a) it can be appreciated the ability of BS-WRM to detect a clear signature related to some intense conv ective precipitation cells extending ov er few kilometers with peaks reaching 50-55 dBZ for both BS sites (left and right panels). It is notew orthy that, within the ov erlapping region sampled by the two sites (dashed black box), the measured reflectivity factor Z appears to be in versely correlated between the radars. Specifically , locations characterized by relatively high Z values for site 1 tend to exhibit lower v alues for site 2, and vice versa (see, for instance, the area around position (0 , 0) ). These discrepancies 15 can plausibly be attributed to partial beam blockage associated with ground clutter . It should be emphasized that, although the ground clutter filter is effecti ve in removing clutter echoes and thereby restoring physically consistent Z values at the clutter- contaminated range gates, it does not correct for propagation- related ef fects, primarily attenuation, introduced by terrain or obstacles causing the clutter . In the present case, ground clutter is clearly distributed differently for the two sites (see Fig. 13d and c, respectiv ely), and this asymmetric obstruction likely contrib utes to the observed differences in the reflectivity fields deri ved from the two radars. Ho wever , as will be demonstrated belo w , this in verse correlation is not alw ays systematic and likely also depends on the specific spatial and temporal distribution of precipitation over the scene. In terms of mean Doppler velocity , panels b) sho ws a very good consistency to each other through the complementarity of V D lev els indicating that the precipitation system is moving tow ard Site 1 leaving Site 2 whereas the Doppler spread in c) indicates turbulence effects which are more pronounced in the areas of high Z values where con vection likely takes place. As a final result, Fig. 15 a,b presents the 2-hours time series of the GC-filtered range profiles of Z corresponding to the test beam sho wn in pink in Fig. 12, which was selected because it is approximately collinear with BS sites 1 and 2. Then, the displayed range interval is restricted to the region simultaneously illuminated by both sites. White regions correspond to missing data at the corresponding site after timestamp alignment. Overall, the Z-profiles e xhibit a consistent spatio-temporal structure at the two sites (cf. panels a and b), indicating good qualitati ve agreement along the common viewing direction. A more immediate agreement can be appreciated by looking at the time series of the median value of the rain rate, estimated using eq. (18), from each range profile for both BS sites 1 and 2 (panel c). The correlation reached comparing these time trends is 0.83, thus confirming the good agreement between the observations performed by the two sites. Ho wever , it can be noted that the peaks and valle ys from site 1 and 2 sho wn in c) are not alw ays coincident with some v ariable lags that explain such disagreement. W e argued that this phenomena can be attributed to a non perfect synchronization of the beams. The lower trend in the median rain rate for site 2 than 1 in the region of lower rain rates (i.e. ≈ between hours 8:10 and 8:50) could be caused by stronger clutter in site 2 that also foster a more pronounced beam occlusion, which is clearly more evident in situation of small signal to clutter ratio. In conclusion, although the present analysis does not incorporate external reference observ ations (e.g., rain gauge measurements), the fact that two independent BS systems yield broadly consistent signatures for the same precipitation ev ent is an encouraging indication that BS-WRM is, at least qualitativ ely , a valid tool for rain detection. V I I . D I S C U S S I O N T raditional remote sensing techniques for precipitation es- timation can be often constrained by limited spatial and temporal resolution, as well as heterogeneous sampling and blind zones depending by the specific sensor considered. These limitations can become particularly pronounced in regions characterized by complex orography or dense urban en viron- ments, where near-surface retriev als are frequently degraded by environmental interference (eg. ground clutter). Con versely , in-situ instruments such as rain gauges and disdrometers exhibit higher measurement accuracy b ut suffer from poor spatial representativeness. Emerging opportunistic sensing ap- proaches, including commercial and satellite microwa ve links, hav e of fered a promising av enue to bridge the gap left by con ventional remote sensing systems. Howe ver , the relati vely low density of radio links per unit area combined with the absence of profiling capability , imposes significant constraints on the achie vable spatial resolution of deriv ed precipitation products. Given the widespread coverage of mobile networks, BS-WRM approach, is potentially a high-resolution gap filling solution especially in populated areas as urban contexts, where the capillarity of BS is particularly dense (figure 1 a) compared to that of weather radars (figure 1 b). The spatial density of meteorological radars and telecommunication BS exhibits pronounced differences, attributable to their distinct functional objectiv es. Surveillance weather radars, (e.g. NEXRAD in the U.S) are generally spaced several hundred kilometers apart (order of ≈ 200 k m ) to achiev e extensi ve atmospheric surveil- lance. Assuming such a figure, and radar radius cov erage of ≈ 200 k m too, the nominal density of a typical weather radar network is about one radar per 125600 k m 2 , or roughly 8 × 10 − 6 radars per k m 2 [70]. Within each single radar cov erage there are blind zones of v arying size that limit the rain detection closer to the ground. In contrast, due to the disparity related to the fundamentally different design objec- tiv es, telecommunication infrastructure is deployed at much higher densities [71]. Urban base station densities commonly reach 10 to 100 stations per k m 2 (including 3G, 4G and 5G networks, with spatial increasing density e xpected for 6G). Rural base station densities are significantly lower , although still appreciable compared to the spatial extent of precipitation cores, falling in the range of 0.1 to 0.5 stations per k m 2 . From these arguments and the material presented in the previous sections, it is clear that BS-WRM can become a valid solution for gap filling current weather radar networks for intense or extreme rain ev ents. In addition, the dual use of BS technol- ogy pro vides sev eral notable adv antages: (i) continuous 24/7 operational capability; (ii) very low data latency , as precipi- tation measurements are network-nati ve ; (iii) unprecedented temporal and spatial sampling, enabled by relaxed cov erage constraints, receiver bandwidth approximately an order of magnitude larger than that of con ventional weather radars and the multi-beam electronic steering. Howe ver , the BS approach also presents limitations: its relativ ely low sensiti vity , mainly driv en by low antenna gain and engaged power , restricts ap- plicability to moderate-to-intense precipitation ev ents only . In addition, pervasi ve ground clutter fostered by near-horizontal orientation of antenna beams, although effecti vely removed as shown in Sections IV and VIs, could, partially block the BS signal contrib uting to further deteriorating the observ ed rain field. Path attenuation can further contribute to the signal losses increasing the blindness of the BS-WRM. Howe ver , as suggested in [72], multiple overlapped observations from 16 a) b) c)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Fig. 14: As in figure 13 but for a different timestamp and in terms of GC-filtered PPIs of Reflectivity (top), mean Doppler velocity (middle) and Doppler velocity spread (bottom). 17 Fig. 15: T ime-range reflectivity factor profiles acquired by different BS sites 1 (a) and 2 (b) along collinear beams (pink region in figure 12). The median rain rates extracted for each range profiles at the av ailable timestamps for BS site 1 (blue) and 2 (red) is in c). ± standard deviation confidence interval is indicated by the colored bars. networked BS could help to alleviate such issue in the future. As a final consideration, it is worth to highlight as the expected amount of data that BS technology can deli ver will be massive opening to machine learning approaches of hight resolution nowcasting of fast ev olving precipitation extremes. Forecast from numerical weather prediction models will also benefit from BS data offering a floor for unconv entional data assimilation at urban scales. V I I I . C O N C L U S I O N S This study proposed an unprecedented methodology for rainfall observation, exploiting radio signals from BS, tradi- tionally dedicated to mobile communications, as a completely new source of information. By applying a processing strategy analogous to that used in weather radar systems, this approach enables precipitation detection at significantly finer spatial and temporal scales than previously achiev able. With the aid of an EM simulation tool, it has been demonstrated that BS system, although it is not optimized for rain observation, is able track medium to high precipitation intensities within 20 km distance from each BS site. An experiment with actual measured data in rainy conditions confirmed the simulation outcomes. Special emphasis has been put ground clutter remov al from Doppler spectrum acquired by BS which represent one of the main limitation of BS for weather applications. A clutter filtering technique, borrowed from those applied to weather radars, has been adapted to BS characteristic and successfully applied to BS acquisitions. The outcomes achiev ed clearly open to validation campaigns and massive use of BS in a networking way and vast areas. A P P E N D I X A R A DA R E Q U A T I O N In this appendix the ke y parameters driving the radar equation for distributed tar gets are discussed. The weather radar equation for the g -th beam ( 4 ) is here reported for an easier reading: P rx ( r , θ g , ϕ g ) = C g Z ( r, θ g , ϕ g ) r 2 L 2 ( r , θ g , ϕ g ) (A.1) in which ( r , θ g , ϕ g ) is the position of a radar resolution cell at distance r from the radar for the g -th antenna beam boresight, whereas P rx and Z are the received av erage po wer and the equiv alent reflectivity factor . In the following, without loss of generality , we simplify the notation by assuming a single beam and dropping the beam index g : P rx ( r ) = P rx , g ( r ) = P rx ( r , θ g , ϕ g ) , C = C g , Z ( r ) = Z g ( r ) = Z ( r , θ g , ϕ g ) , L ( r ) = L g ( r ) = L ( r, θ g , ϕ g ) . The dependence on polarization χ is also dropped. A. P ath integr ated attenuation The term L 2 is the two-way atmospheric path loss factor that is expressed as: L 2 ( r ) = exp h − 2 · PIA( r ) i = exp " − 2 Z r 0 Z ∞ 0 σ e ( D , χ ) N ( D ) dD ! | {z } Specific attenuation: k e ( r, θ , ϕ ) dr # . (A.2) L depends on the extinction radar cross section of the drops ( σ e ) (mm 2 ) and the drop size distrib ution N ( D ) in (mm − 1 m − 3 ), which in turn depends on the specific resolution volume, thus it is N ( D ) ≜ N ( D , r , θ g , ϕ g ) . The integral along the diameter D giv es the specific attenuation ( k e ) in (m − 1 ), while the integral over the range r yields the one-way path integrated attenuation (PIA). B. Radar constant The radar constant ( C ) is di vided into se veral terms, in- corporating all the known system factors contributing to P rx . The expression of the radar constant is shown in (A.3), in which 10 − 18 is a units conv ersion term to ha ve, in (A.1) the power expressed in W atts when Z is in (mm 6 m − 3 ), r is in ( m ), P tx is the transmitted peak power in ( W ), G max is the one way antenna maximum power gain (in linear units), λ 0 is the carrier wavelength in ( m ), | K w | 2 is related to the dielectric constant of water ( ≈ 0.93 at S, C and X bands). The resolution volume is function of the HPBW along azimuth and ele vation at boresight ( ϕ = ϕ g , θ = θ g ) ∆ ϕ , ∆ θ and of the sampling interval along range (defined in Section IV -A) ∆ r = c/ (2 · B adc ) . The term B τ tx (with B adc > B ) is the product of the duration of the Tx wav eform and its bandwidth and it represents the matched filter power gain after range compression at the receiv er end. Since weather radar equation typically assumes pencil Gaussian beam whose main lobe is characterized by standard de viations ∆ ϕ √ 8 ln 2 and ∆ θ √ 8 ln 2 along azimuth and elev ation, respectively , an antenna correction factor ( F ) has to be introduced in C to account for the non- Gaussian pattern of the specific antenna used by the radar/BS (i.e. the antenna array of the BS). 18 C = 10 − 18 · P tx G 2 max λ 2 0 (4 π ) 3 | {z } Trasmission term · π 5 | K w | 2 λ 4 0 | {z } Rayleigh scattering · π ∆ ϕ ∆ θ 8 log 2 ∆ r | {z } Resolution volume · F |{z} Antenna correction factor · B τ tx | {z } Range compression gain (A.3) F = 8 log 2 π ∆ ϕ ∆ θ Z π/ 2 − π / 2 Z π/ 2 − π / 2 f 2 ( ϕ − ϕ g , θ − θ g ) cos ϕ dϕ dθ (A.4) In the latter , f is the normalized power radiation pattern of the radar/BS antenna so that its maximum value is f ( ϕ g , θ g ) = 1 . The square factor in (A.4) is due to the monostatic radar con- figuration (i.e. same antenna for transmission and reception). It is important to remark that F , as well as, the maximum antenna power gain, G max , are generally beam specific, as the radiation pattern f ( ϕ − ϕ g , θ − θ g ) changes as a function of the g -th beam. A P P E N D I X B R A I N I N T E N S I T Y D E FI N I T I O N Rain intensity at altitude h abov e the sea le vel (asl.) is defined as a statistical moment of the drop size distribution ( N ( D ) ) as follows: R ( h ) = 6 π 10 − 4 Z D max D min v ( D, h ) N ( D ) D 3 dD (B.1) where v ( D, h ) is the terminal fall velocity in still air of a liquid drop of equiv alent size D at altitude h asl. R in (B.1) is in (mm/h) when D is in (mm) and v is in (m/s). The terminal drop’ s velocity can be modeled as in [73] with modification to take into account the altitude h [74], [75]: v ( D, h ) = (9 . 65 − 10 . 3 e − 0 . 6 D ) | {z } v 0 ( D )  ρ 0 ρ h  (0 . 375+0 . 025 D ) (B.2) In (B.2), v 0 is the terminal drop’ s fall speed at sea le vel whereas ρ h and ρ 0 , both in (kg/m − 3 ) are the air density at sea and h level, respectiv ely . R ( h ) in (B.1) can be easily modeled knowing the N ( D ) term which is typically deriv ed by disdrometers and the air density profile which can be derived by radiosoundings (i.e. temperature, pressure and humidity sensors on balloons) or considering the international standard atmosphere model as follows: ρ h = ρ 0 (1 − α h ) β (B.3) with ρ 0 = 1 . 225 ( k g · m − 3 ), α = 2 . 2558 · 10 − 5 and β = 4 . 256 . A P P E N D I X C D I S D RO M E T E R D A T A BA S E Disdrometer are non-captati ve instruments able to quantify the particle size distribution (i.e. number of hydrometeros, N corresponding to size equiv alent diameter D ) passing through the sensing area of the instrument in real time. Due to the ability in providing N ( D ) , which drives Z and R in eq.s, ( 5 ) and (B.1), disdrometers are more and more often a key elements to built ad-hoc Z − R relationships as done in section IV -F. The disdrometers used are those collected in Italy by the Italian Group of Disdrometry (GID) network (https://www . gid- net.it/). GID was borne in 2021 thanks to a spontaneous collaboration of different Italian institutions (including re- search centers, univ ersities, and en vironmental regional agen- cies) that manage disdrometers ov er the Italian peninsula. The GID network coordinates field campaigns, data sharing, and intercomparison acti vities across Italy , aiming to improve the accuracy and consistency of rainfall measurements. Nowadays the GID networks consists of 27 disdrometers distributed across Italy , although due to technical issues it is possible that data from some de vices are not av ailable continuously . All the disdrometers of the GID network are laser disdrometer , most of them are Laser Precipitation Monitoring (LPM) of Thies Clima GmbH, ho wever there are also some P arsiv el2 of OTT GmbH. The longest time series of DSD data was the one collected in Rome that consists of more than 13 years of data (i.e. from September 2012 to December 2025). There are 3 disdrometers located at high altitude (i.e. more than 1000 m above sea lev el) that can likely collect sno w or solid hydrometeors although this is not of interest for the present work. All disdrometers in the GID network use a uniform data-processing workflow so that their output (i.e time series of 1-minute DSDs) is provided in a standardized format. This harmonization is key to enabling cross-site comparisons and aggregated analyses. More information on the processing of the raw data adopted by GID to retriev e quality control DSDs is reported in [68]. The GID database is made freely av ailable under a CC BY 4.0 licence by Zenodo ad it is updated yearly (the last version used in this study is updated to 2024 and it is av ailable here [76]). Such a v ersion consists of DSDs of almost 1.4 million rainy minutes. A C K N O W L E D G M E N T This research has been carried out in the frame work of the Joint Lab between Huawei and Politecnico di Milano. The authors would like to thank Mr . Liu Peixi from Huawei T echnologies for the fruitful discussions about BS calibration and the collection of IQ data from the experimental BS-WRM presented. R E F E R E N C E S [1] A. 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