Long-Term Rain Attenuation Measurement for Short-Range mmWave Fixed Link Using DSD and ITU-R Prediction Models

estimate than the measurements for high attenuation levels. In Schleiss et al. (2013), a link was set up at 38 GHz over 1.85 km with the aim to study the rain attenuation and the wet antenna effect where 2.5 dB maximum wet antenna effect was found. Results in Luini et al. (2018) provide reliable rain attenuation values compared to the DSD at 73, 83, 148, and 156 GHz with a link distance of 325 m. Results in Kim et al. (2013) show a significant Abstract Several millimeter Wave (mmWave) bands, which suffer from rain attenuation, were identified in the World Radiocommunication Conference 2019 (WRC-19) for fifth generation (5G) radio networks. In this paper, long-term attenuation is measured over typical building to building radio links in the built environment, which constitute two 36 m links along a direct link and an indirect side link at 25.84 and 77.54 GHz and a 200 m link at 77.125 GHz. The attenuation was also estimated using precipitation data from a high end accurate disdrometer weather station using the drop size distribution and the International Telecommunication Union (ITU) models. The results indicate that attenuation using Mie theory is in agreement with the ITU model for most of the rainfall events; with higher attenuation being measured than predicted when snow grains and raindrops mix. Raindrops with diameter between 0.1 and 4 mm indicate that the dominant raindrops have considerable influence on the measured attenuation, especially at light and moderate rainfall events. The maximum distance factor restriction of 2.5 in ITU-R P.530-17 is shown not to be suitable for short-range fixed links as it excessively underestimates attenuation. of rainfall intensities are used to investigate rain attenuation: light rainfall ( R ≤ 1 mm/hr), Moderate (1 mm/ hr < R ≤ 4 mm/hr), heavy (4 mm/hr < R ≤ 16 mm/hr), very heavy (16 mm/hr < R ≤ 50 mm/hr), and torrential rainfall ( R > 50 mm/hr).


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difference between the International Telecommunication Union (ITU) model and the measured attenuation with the conclusion that the ITU model is not suitable for rain intensity above 100 mm/hr at 73 and 83 GHz for 500 m links. In Juttula et al. (2019), the scattering effect and attenuation were reported at 100 and 500 m at 60 and 300 GHz where the difference between the DSD and the ITU model reaches 5 dB.
Several works have reported rain attenuation prediction using rain statistics only. In Åsen and Gibbins (2002), a DSD model is used to quantify rain attenuation at 57, 97, 135, and 210 GHz at Chilbolton and Singapore. Their results indicate that the DSD differs with climatic condition levels of pollution. At higher frequencies and high rainfall rate, inconsistency and fluctuations were observed between the ITU model and the DSD attenuation model, with lower attenuation values predicted by the ITU-R model. In Tuhina et al. (2018), rain attenuation measurements were conducted for 22 GHz,23 GHz,and 31.4/30 GHz in a tropical region: Kolkata in India and Belem in Brazil for 2 years. Results show good agreement between the DSD attenuation model and the ITU-R model for rainfall rate below 100 mm/hr, with slight differences below 30 mm/hr. In Saurabh et al. (2010), assuming a log-normal distribution for the DSD, both the DSD model and the ITU-R model gave similar results for frequencies below 30 GHz with a maximum rainfall rate up to 30 mm/hr in a tropical region.
In this paper, precipitation data are collected and used in the prediction models to estimate the rain attenuation in parallel with an mmWave channel sounder, which operates at two frequencies 25.84 GHz (K band) and 77.54 GHz, over two 36 m links: a direct link and an indirect link. Another link with a commercial radio frequency (RF) head is set up for continuous wave (CW) transmission at 77.125 GHz (E band) for attenuation measurements. Measurements are conducted from October to December 2020, and January 2021 for all three links. Since the rainfall rate is insufficient for the prediction of attenuation in the higher frequency bands, more accurate precipitation data are needed which include: rainfall rate, rain drop diameter, DSD, rainfall velocity, particle speed, and water permittivity. Such data can be obtained using a high end disdrometer station as used in the present study. The results of the attenuation prediction and measurement can be applied for regions with similar weather conditions. The ITU-R P.530-17 maximum distance factor restriction of 2.5 for short-range links is also investigated in addition to analyzing the effect of scattering of rain droplets. This paper is organized as follows: the weather measurement system is presented in Section 2 together with rain statistics and raindrop distribution for the measurement period, followed in Section 3 by a description of the fixed link measurement setup for measuring attenuation and the ITU and the DSD prediction models. In Section 4, measurement results using the short-range fixed link data sets and the PWS100 disdrometer precipitation data are presented and compared for discussion; followed by raindrops induced scattering analyses in Section 5. Conclusions and ongoing work are presented in Section 6.

Weather Station
A PWS100 Weather Sensor station was installed on the roof of the library at Durham University to record precipitations data as shown in Figure 1a. It is a laser based sensor capable of determining precipitation and visibility parameters (Scientific, 2015). Due to its developed measurement technique, the PWS100 can determine each individual particle type from accurate size and velocity measurements. The technical specifications of the station are listed in Table 1. The PWS100 disdrometer covers a measurement area of 40 cm 2 . The station is controlled remotely to store data through the campus wireless network and the CR1000 data acquisition as shown in the block diagram of the measurement system in Figure 1b over an internet protocol address once every minute. Figure 2a illustrates the rainfall intensity statistics between October 2020 and January 2021, with most of the measured rain intensity being under 20 mm/hr. In the results section, the rainfall intensity in mm/h is mapped against the received signal in dBm to estimate the rain attenuation in (dB) over the measurement period. Five types of rainfall intensities are used to investigate rain attenuation: light rainfall (R ≤ 1 mm/hr), Moderate (1 mm/ hr < R ≤ 4 mm/hr), heavy (4 mm/hr < R ≤ 16 mm/hr), very heavy (16 mm/hr < R ≤ 50 mm/hr), and torrential rainfall (R > 50 mm/hr).

Drop Size Distribution
Raindrop Size Distribution (DSD), noted by N (D), plays a critical role in determining the microphysics of rain (Marshall & Palmer, 1948). It has a significant role in radio propagation performance links. The DSD varies and depends on the location. For a given rainfall type, we could get two different types of DSDs which result in different values of signal attenuation. Using the PWS100 disdrometer, the DSD is recorded with 300 values of the number of drops corresponding to the diameter from 0.1 to 30 mm with 0.1 mm resolution. The DSD can be calculated as: where S = 40 cm 2 is the measurement surface of the laser beam of the PWS100 disdrometer, t = 60 s is the integration time, n(Di, vj) is the number of particles registered within the classes with mean diameter Di(mm) and mean speed vj(m/s), and dDi(mm) is the class width associated with the diameter Di. The PWS100 can determine each individual particle type from accurate size. For each minute, we have the corresponding rain rate and number of drops for each bin and the following steps take place for the average DSD: 1. The integration time intervals of disdrometer measurements are to be categorized according to the desired rain rate classes, for example, 5 and 20 mm/hr. 2. For each long-term mean (i.e., in each rain rate class) the disdrometer bin size classes are to be rearranged according to the bin size classes (0.1, 0.2, and 30 mm).  3. The (long-term mean) drop count in each bin size class is to be divided by the measuring area (of the instrument 40 cm 2 ) and by the column height (integration time multiplied by the mean fall velocity of this bin's mean diameter). Thus the (long-term mean) drop counts per unit volume are obtained. 4. To obtain the required distribution density further in each bin size class the drop counts per unit volume are to be divided by the bin size class width.
Appropriate unit conversions are implemented to deliver the result in (m −3 mm −1 ). Figure 2b reports the measured DSD where the peak DSD occurs at around a raindrop diameter of 0.8-1.2 mm for most of the rain events.

mmWave Fixed Link Channel Sounder Setup
The experimental fixed link setup described in Salous et al.  Figure 3d. The transceiver groups the Orpheus interface board, a NI USB-8451, and an electronic circuit power to supply the module. Once mated, the module can be powered up using standard lab PSUs (−5 V, +2.8 V +3.3 V, and +5.1 V +18 V). For the control of the module, a NI USB-8451 is used with the Filtronic Orpheus GUI software. The 200 m point-to-point link is named figuratively "Filtronic link." The three links are remotely controlled through the campus internet network and data are recorded for each minute, simultaneously with the weather station data. The channel data are recorded for 1 s every minute to relate with the rain rate data. The sampling rate of the RF link is 80 MHz and the attenuation per minute is an average of 1 s, as the baseband signal frequency is at 4, 12, and 31 MHz, respectively.

Prediction Models
Rain attenuation affects the Quality of Service of radio links in the millimeter wave bands. It is therefore vital to have accurate and reliable propagation models for predicting rain attenuation using precipitation data such as rainfall rate, DSD, velocity, temperature, and water permittivity. The prediction models used in this study are the ITU-R P.838-3 model and the DSD model, which use frequency parameters, wavelength, water permittivity, and raindrop distributions (Shrestha & Choi, 2017).

ITU-R P.838-3 Model
This model was validated theoretically and experimentally and is recommended for the frequency range from 1 to 1,000 GHz. It is given by: where R is the rainfall rate (mm/h), k and α are model parameters, which depend on the frequency f(GHz), and γ is the specific attenuation in dB/ km. The ITU recommendation provides a look-up table of the values k and α for different frequencies for both the vertical and horizontal polarization (Recommendation ITU-R P. 2005) are noted in Table 2.
The total attenuation for a specific distance depends on the effective path length d eff , between the Tx and Rx antennas as: where the effective path length, d eff , of the link is obtained by multiplying the actual path length d by a distance factor r, from ITU-R P.530-17 as where R 0.01 is the rain rate exceeded for 0.01% of the time (with an integration time of 1 min). In ITU-R P.530-17 it was recommended to use a maximum value of r equal to 2.5 while in the updated recommendation P.530-18, the restriction on the maximum value of r has been removed. For the present study, results with and without the restriction of r = 2.5 are compared with the measured attenuation for our short-range fixed links for both frequency bands.

Drop Size Distribution Model
The attenuation using the DSD model based on Mie theory in Bohren and Huffman (1998) is given as: where γ is the specific attenuation in dB/km, = 2 2 is the extinction cross section (m 2 ) for water drops of diameter D (mm), and N(D) is the measured DSD value (m −3 mm −1 ) at diameter D from the sensor weather station PWS100. The extinction efficiency Q ext can be calculated from Mie scattering or Rayleigh scattering theory depending on the size parameter X = πD/λ, where λ is the wavelength.
For the current rain attenuation prediction, we use the measured DSD from the PSW100 weather station. The disdrometer records only fall velocity and not for each particle; hence, we use Equation 6 given in Atlas and Ulbrich (1977) and Atlas et al. (1973) for the calculation of particle speed. The DSD can also be calculated using theoretical and analytical models such as: the Marshall-Palmer (M-P) distribution (Marshall & Palmer, 1948) and the Weibull distribution (Jürg & Enrico, 1978). In this study, we use the measured raindrop distribution from the PWS100 disdrometer. For comparison, we consider the widely used Gamma distribution, given by Ulbrich (Carlton, 1983) where D (mm) is the rain drop diameter, N 0 is the intercept parameter, μ is the shape parameter, and λ is the slope parameter, and the mean value of μ is 3 (Kumar et al., 2010;Nabangala, 2016). Gamma distribution given in Ulbrich model is applied to fit the rain DSD and used for comparison purpose only. The theoretical relation between the terminal fall velocity and the drop dimension is taken for the DSD calculation because the velocity of each particle is not measured. The type of scattering effect depends on the extinction efficiency which relies on m the complex refractive index of water; which is related to temperature and frequency (Schiebener & Straub, 1990). Throughout the measurement period, an average computation was used on the temperature. The average temperature was 7° and the complex refractive index of water was calculated according to Table 3 for each frequency band. Figure 4 presents the extinction efficiency as a function of size parameter X, where Mie theory calculations have been implemented to calculate the extinction efficiency. It should be noted that X refers to Mie size parameter as a function of diameter D, λ, and π. When the rain drop is much smaller than the wavelength X ≪ 1, D < λ, the probability of scattering increases and the wavelength decreases, that is, Rayleigh scattering. Mie scattering takes place when X ≈ 1, while geometric optics scattering occurs when X ≫ 1.
The high capability measurement of the disdrometer provides for each minute the corresponding rain intensity, number of recorded droplets for each diameter type, the temperature, the fall velocity, and humidity. For each rainfall, the dominant number of drops is extracted. Figure 5 displays the parameters that have significant impact on the attenuation behavior computed from the collected precipitation data throughout the measurement period. At each raindrop diameter, the figure displays the maximum number of drops found from the total rain statistics, its speed in m/s, and the corresponding rain intensity. An exponential variation of particle speed up to 5 mm drop size is observed, beyond which the velocity flattens out. The number of drops is seen to be in the range of 25-250, while most of the raindrops size falls between 0.1 and 2 mm.
Because previous data sets in the paper we published in Huang et al. (2019) revealed a significant wet antenna effect, the present study provides results following extensive updating of the measurement link setup along with longer term measurement campaign than before, which reduces the antenna wetness effect by placing antenna hoods and integrating the IF unit with the RF heads. In addition, long-term measurement disdrometer meteorological data from the PWS100 of 3 years are now available. The data are being submitted and used for the ITU-R Study Group 3 data sets bank.

Discussion of Measurement Results
This section presents the calculated attenuation at 25.84 GHz (K band) and 77.54 GHz (E band) over the two 36 m links between October 2020 and January 2021 and the 77.125 GHz band over the 200 m link from November 2020 to January 2021 adopting the ITU and DSD models for comparison with the measured rain attenuation for which the data availability ratio for direct and side 36 m links is 82.55% and 70.47% for the 200 m link. Vertical to vertical polarization, which is common to all the three links is selected for the two bands over 252 hr of rain data. The attenuation is calculated and referenced using sunny clear sky days before and after the recorded data. We perform the following steps to measure the attenuation: initially, a reference signal is obtained for sunny and clear sky hours chosen before the rainfall event; then subtract from the reference signal the received signal during the rain event. The data are verified each minute to ensure reliability and to avoid loss in the signal due to the measurement system rather than rain. Measurement days where snow occurs are compared to rainy days. The attenuation is mapped against the rain intensity. The effects of raindrop diameter distribution, and diameter of the dominant drops on the measured attenuation are presented. The measurements through this period include some gaps of no rain hours and days while 218 hr of light rainfall data, 32 hr of moderate rainfall data, 3.4 hr of heavy rainfall data, and around 25 min of very heavy rainfall data were recorded. Predominant and frequent rain events were identified for calculation and modeling of the rain attenuation. For accurate and reliable rain attenuation study, minutes corresponding to equipment transient behavior (rising and drop of the received power), the power flatness of the system, atmospheric attenuation, equipment  icing, humidity, and wind are not used in the analysis. For each link, the best measured data sets and the most stable signal strength are used for the estimation of the attenuation.

Predicted Attenuation
The estimated rain attenuation using the disdrometer data is presented for both the ITU and DSD model. The rain attenuation is classified into two categories: (a) physical, which uses the measured radio link data for rain loss calculation to integrate it into the radio channel parameters for link budget calculation and (b) modeled attenuation, which predicts the attenuation using the DSD model based on Mie scattering theory given by Equation 5 using the disdrometer data and the ITU-R prediction model given in Equation 2. When measuring and calculating rain attenuation with rain intensity statistics, raindrop distributions, and particle size, various parameters such as atmospheric conditions (Han & Duan, 2019), scattering and interaction between raindrops, and absorption (Mora Navarro & Costa, 2016; Surco Espejo & Costa, 2017) need to be considered. In this study, it is assumed that the raindrops are spherical for Mie theory and scattering. The interactions between raindrops are negligible. Other climatic conditions such as wind, snow grains, snowflakes, and ice pellets are also not considered for rain attenuation through snow events but will be presented to show their effect on the signal strength. As shown in Figure 4, the size parameter X is 5 and 16 for 26 GHz, and 77 GHz, respectively. At higher frequency, the extinction efficiency approaches 2.5 and the size parameter is greater than 10 (larger raindrops) almost near to geometric cross section area, when Mie theory is applied.
Equations 5 and 2 are given for the specific calculation in dB/km, so the distance factor r should be taken into consideration when converting to the specific path lengths of 36 and 200 m. This factor was mainly derived from long-range measurements. Using the ITU recommended maximum value of 2.5 raises the question regarding its application for short-range links less than 1 km (Budalal et al., 2020;Huang et al., 2019;Olsen et al., 1978). Hence, the suitability of the maximum r factor is further investigated for the current short-range links. Figures 6 and 7 show the calculated attenuation for the K and E bands using the ITU and DSD models for the 36 and 200 m, respectively. The figures indicate good agreement for most of the rain events, whereas during the snow events comparison with the DSD and the ITU is mainly derived from rain drops not snow grain and snowflakes; therefore, the DSD model shows higher attenuation values up to 4 dB than the ITU model since during the snow events the raindrop distribution is formed of a mixture of raindrops and snow particles. Consecutive heavy rainfall events show slightly higher attenuation using the ITU model at the E band for both links with 1.2 and 4 dB recorded for maximum rainfall rate of 5 mm/hr and 20 mm/hr, respectively, for the direct E band link while a maximum of 6 dB loss for 20 mm/hr for the 200 m link.

Measured Attenuation
The results of the measured attenuation as a function of rainfall up to 25 mm/hr are presented. Figures 8, 10, and 11 show the received signal mapped against the rain intensity and snow particles for the three links: direct 36 m, 200 m, and side 36 m, respectively, for the K and E band vertical to vertical polarization. The figures show that the signal strength follows the rainfall trend. During snow events, the signal takes more time to recover to the level following the end of rain/snow event due to antenna icing as can be seen in Figure 9. This effect should be differentiated from the measurement by eliminating from the analysis the icing events. Compared to the predicted-calculated attenuation as shown in Figure 12 (samples of dominant rainfall events through the measurement period and matched attenuation) the measured attenuation for the direct 36 m link during rain events without snow and before mid of December 2020 shows an average of 0.8-1.5 dB higher attenuation for heavy and very heavy rainfall at 26 GHz, while a difference of 0.4-1.3 dB at 77 GHz. However, higher losses up to 9.5 dB are recorded when a mixture between rain and snow occurs. The side link shows somewhat higher attenuation than the direct link 0.5-2.3 dB as the side link depends on non-Line-of-Sight (NLOS) reflected paths to receive the signal. Thus, the measured attenuation is affected by raindrops scattering mechanism. The K band side link exhibits 1.7 dB difference with respect to the predicted rain attenuation for light, moderate, and heavy rainfall events. Measured rain attenuation for the 77 GHz 200 m link agrees well and follows the predicted attenuation for most rainfall events where 6 dB loss has been recorded for a maximum rain intensity of 20 mm/hr. It can also be observed that the measured attenuation values are not all uniform with the rain fall rate and the calculated attenuation using the ITU and the DSD models using the disdrometer data. For instance, two similar rain intensities may result in two different rain attenuation values. As an example 11 mm/hr was recorded on 13 October 2020 at 10:17 and the 31 October 2020 at 12:58 result in 1.56 and 2.28 dB at 77 GHz, respectively. This is also observed in other works (Aydin & Daisley, 2002;Brazda & Fiser, 2015;Sander, 1975; Schönhuber  Townsend et al., 2009). This instantaneous difference between the measured and the DSD/ITU calculated attenuation values could be due to a number of factors: 1. Mie theory assumes that rain drops are spherical, whereas it is not always the case within a real rainfall event since the DSD model uses real disdrometer data, which is subject to severe weather conditions that reduces its collection capability. 2. For light rain rate, the disdrometer might not be able to count small raindrops in higher windy situations. 3. Other factors that may affect the collected radio data are the humidity (Tamošinait et al., 2011) where the humidity continues its existence in the atmosphere in sunny clear days and temperature variability in space and time (Setijadi et al., 2009). In the DSD model estimation, the average monthly value of temperature was used and the humidity was neglected. 4. Successive rain events up to 10 hr (moderate rainfall events). The signal takes more time to recover after this long-term rain event. 5. The former method inherently assuming a constant analytical DSD for the derivation of the k and alpha coefficients in Equation 2.
The raindrops size and rain event distributions are not uniform within space and time due to the variability of raindrop distribution and the particle size, which corresponds to the number of each dominant raindrop diameter, rainfall speed, and particle speed. Mostly, for all rainfall types, raindrops size between 0.1 and 3 mm contribute to the maximum attenuation which is λ/2 at 77 GHz as shown in Figure 16. This indicates that the number of dominant raindrops has a significant influence on the specific attenuation, which can result with up to 2 dB difference at the same rainfall type within two different dates at the range of 0.1-2 mm drop size.

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In Figure 13 the measured CDFs are compared with the predicted CDFs from the ITU and DSD models. Good agreement between measured and calculated attenuation is obtained at 77 GHz for the direct, side, and Filtronic links. A notable difference occurs at the lower frequency band at 26 GHz between the measured and the theoretical values for the side link where the measured attenuation has larger values.
In addition, mmWave short-range fixed links require accuracy and reliability of prediction. The ITU-R P.530-17 model uses the effective path length for estimating the rain fade and r distance factor which is derived from long range measurements. It is recommended in the model to use a maximum value of r = 2.5 whereas in the updated recommendation, this restriction has been removed. The recommended value of r with and without the restricted value are implemented into the calculation, and thereafter investigated for the three links within its corresponding frequency bands. Figures 14 and 15 show a full and detailed comparison between the measured and ITU predicted rain attenuation using the maximum recommended distance factor and without using it for the E and K bands, respectively, where rain rate and attenuation were measured for each event in an instantaneous manner within 1 min interval. The results indicate that when the r value is restricted to 2.5, the predicted rain attenuation exhibits higher differences with the measurements than when it is not used at both frequency bands for both the 36 m and the 200 m links.
To further examine the impact of other rain parameters on the link, Figure 16 presents samples of measured attenuation versus raindrop diameter from 0.1 to 7 mm which were within different rainfall rates. The calculated attenuation using Mie theory is correlated to the relevant amount and type of droplets collected at that minute, thanks to the disdrometer's recording capabilities. The attenuation rises with the raindrop diameter. The highest attenuation is illustrated for the events where raindrops' diameters range between 2 and 4 mm. The analyzed results indicate that very heavy and moderate rainfall rate lead to higher attenuation values for both frequencies in the presence of large rain drops (above 2 mm). Similar to the analyses in Figure 6 in the previous section and Figure 16, when the particle speed is 9-10 m/s even with a number of particles lower than 20 drops, it results in higher and variable attenuation specially for very heavy rainfall higher than 20 mm/hr where raindrops with the size of 1-3 mm lead up to 4.5 dB higher attenuation. A diameter in the range of 4-7 mm contributes occasionally to the attenuation up to 2 dB for both frequency bands. It should be highlighted that the computed rain attenuation value is matched for each rain rate event thanks to the weather station data measurement features, which include the associated temperature, drop distribution per diameter for each minute, and humidity provided. We can match the rain event to the matching raindrop size, which means that for example, if the event is 5 mm/hr, we can extract the number of drops for each drop size type and then select the dominant drop. This study found that higher rainfall and a greater number of rain droplets of predominant diameter lead to higher attenuation than the theoretical prediction with low rainfall.
Based on the computations, we identify the drop diameter region that contributes the most to overall attenuation. The phrase (maximum attenuation) refers to the maximum value that is obtained with that number of drops.
The next section elaborates raindrops scattering mechanism using the recorded disdrometer data and Mie theory.

Raindrops Induced Scattering
Scattering due to raindrops has a significant effect because rain scattering is considered one of the main sources of attenuation and interference (Olsen et al., 1993). Scattering can be governed as a function of wavelength (λ) of the incident radiation, the size of the scattering particle, usually expressed as the nondimensional size parameter, X, and the particle optical properties relative to the surrounding medium: the complex refractive index which   depends on frequency and temperature. These parameters identify the scattering modeling which can be divided into single-scattering or multiple-scattering. Single scattering considers one interaction between the incident wave and the precipitation field. When the density of scatterers or the scattering cross section increases multiple scattering occurs. In the current analysis, the most common first order rain scattering approach is adopted. The regular model which is considered widely to cause interference between fixed links (Capsoni et al., 2010) is presented in Figure 17.
Spherical raindrops, Mie theory, and bistatic radar equation given in Capsoni et al. (2010) and Capsoni and D'Amico (1991) are considered for scattering functions calculations. The following functions are derived from Mie theory and describe wave scattering through a common raindrops geometry: 1. Mie scattering amplitude function is given by: the functions π n (cosθ) and τ n (cosθ) describe the angular scattering patterns. a n and b n are Mie coefficients complex functions of drop diameter, refractive index, and wavelength. 2. Scattering cross section. It gives a conjectural definition of how much area is blocked out by the target during the raindrops scattering event. It is given by: Figure 18 shows the calculated scattering cross section as a function of scattering angle. The scattering cross section reaches a value of 1.04 × 10 −4 (m 2 /m 3 ) for a scattering angle of 0° at very heavy rainfall. Operating at higher rain intensity will introduce superior scattering for both bands. 3. Bistatic scattering cross section η per unit volume which is a function of frequency and scattering geometry of raindrops θ s is the scattering angle, N(D) is the measured raindrops distribution. One significant element that defines the prospect distribution of the scattered wave direction is the scattering phase function P(D, θ s ) defined by: where S1(θ) and S2(θ) terms are elements of the scattering amplitude matrix given by the Mie theory. Figure 19 shows the scattering phase function versus the scattering angle for predefined raindrops diameter dominant in the disdrometer measurements. It is noticed from the figure that the 77 GHz band is considerably forward oriented pattern while at 26 GHz it is more inclined to Rayleigh, which explains the difference between the measured and predicted attenuation for the K band side link presented in the previous section when Mie theory was applied for all the calculations of both bands. Figure 20 displays the behavior of the bistatic scattering cross section for the E band versus the scattering angle for the two different rainfall rates: 16 and 39 mm/hr. The rain-induced scattering is due to the beam angle falling below 60°. It is the region where it is having significant effect but confined only to rainfall events higher than 10 mm/hr and considerable raindrops diameter above 1 mm.

Conclusions
Rain attenuation for millimeter wave 5G fixed link applications was investigated using long-term rain statistics and radio data collected over three fixed links at Durham University. For most rain events, the signal level tends to follow the trend of rainfall, and rain attenuation rises as the rain intensity increases. Predicted attenuation values from the DSD and the ITU models have been analyzed and compared to measured data at 22.84 and 77.54 GHz for a direct and a side link over 36 m together with a 200 m point to point link at 77.125 GHz. The DSD proves that rainfall rates are insufficient to estimate rain attenuation values as other factors are involved such as the raindrops shape and distribution, number of dominant drops, diameter, and velocity. The drops diameter in the range of 0.1-2 mm contributes to the overall attenuation within all frequencies for particle speeds in the range between 1 and 5 m/s. Larger raindrops contribute irregularly to the attenuation when the rainfall velocity and particle speed is in the range of (5-10 m/s). Measurement results using the long-term measurements over the short-range fixed links indicate that using recommendation ITU-R P.530-18 without the restricted distance factor recommended in P.530-17 gives attenuation values closer to the measured values. In future work, further measurements will be analyzed to better investigate the path reduction factor value with specific consideration of the spatial homogeneity of precipitation along the path and of any additional effects inducing supplementary attenuation on the link such as wet antenna and/or due to the system, which, as the path length decreases, are expected to be critical for  the isolation of the impact solely due to rain. In this paper a simplified approach of raindrops induced scattering was introduced to minimize the calculation complexity. Data indicate that the scattering cross section varies over a wide range between 0° and 180° and symmetrically to 360°. Further work is ongoing to study the interference between cross-polarization links, along with an evaluation of other precipitation effects such as snow grains, snowflakes, hail, ice pellets, graupel, wind, and humidity on rain attenuation and scattering.

Data Availability Statement
The data that support the findings of this study will be submitted to the ITU-R Study Group 3 data bank (DBSG-3) and availability is subject to ITU-R policy: https://www.itu.int/en/ITU-R/study-groups/rsg3/Pages/dtbank-dbsg3.aspx.