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In recent years, there has been increased interest in the terahertz waveband for application to ultra-high-speed wireless communications and remote sensing systems. However, atmospheric propagation at these wavelengths has a significant effect on the operational stability of systems using the terahertz waveband, so elucidating the effects of rain on propagation is a topic of high interest. We demonstrate various methods for calculating attenuation due to rain and evaluate these methods through comparison with calculated and experimental values. We find that in the 90 - 225 GHz microwave band, values calculated according to Mie scattering theory using the Best and P-S sleet raindrop size distributions best agree with experimental values. At 313 and 355 GHz terahertz-waveband frequencies, values calculated according to Mie scattering theory using the Weibull distribution and a prediction model following ITU-R recommendations best agree with experimental values. We furthermore find that attenuation due to rain increases in proportion to frequency for microwave-band frequencies below approximately 50 GHz, but that there is a peak at around 100 GHz, above which the degree of attenuation remains steady or decreases. Rain-induced attenuation increases in proportion to the rainfall intensity.

There is interest in ultra-high-speed wireless communications and remote sensing systems in the terahertz waveband [

Conventional methods of predicting rain attenuation in wavebands above the microwave band have been based on Mie scattering theory with various distributions of raindrop particle size [

We verify the fitness of these methods by comparing between calculated and measured values for rain attenuation at rainfall intensities of up to 25 mm/hr at frequencies from 96 to 355 GHz. With the goal of applying these results to the wider wavebands used in the field of wireless communications, we furthermore evaluate changes in rain attenuation over wider ranges of frequency and rainfall intensity.

We applied Mie scattering theory with four types of raindrop size distribution as well as the predictive calculation method recommended by ITU-R for rain attenuation to calculate theoretical values for rain attenuation. Rainfall intensity was set at up to 25 mm/hr, and the following frequencies of 96, 140, 225, 313, and 355 GHz were used.

1) Calculation of rain attenuation

The rain attenuation coefficient A [dB], which represents attenuation due to raindrops after propagation over 1 km, can be calculated from the attenuation cross-section Q_{t}, which is a function of particle diameter, D, the wavelength π, and the complex reflection coefficient of water droplets m and a raindrop size distribution N(D) as

For this, the attenuation cross-section can be obtained by applying Mie scattering theory to attenuation due to spherical particles in plane-wave radiation. Here we use the formula of Hulst [

where a_{n} and b_{n} are the Mie scattering coefficients [

2) Raindrop size distribution used in calculations

We used several raindrop size distributions for calculating rain attenuation by Mie scattering theory: the M-P, Best, P-S (hail, sleet, and snow), and Weibull distributions. These are shown in Equations (3)-(6), respectively.

The M-P distribution proposed in Marshall and Palmer [

In this, D is the diameter in mm, and R is the precipitation rate in mm/hr.

In 1950, Best [

The P-S distribution was described by Litovinov in 1957 [

Here,

Sekine and Lind [

This distribution is still in use for microwave and terahertz applications [

ITU-R P.838-3 [_{R} [dB/km] from rainfall intensity R is calculated from

Here, the values of k and πΌ are determined for a given frequency f in the range 1 to 1000 GHz, and ITU-R P676-6 [

This section presents experimental values for rain attenuation at frequencies of 96, 140, 225, 313, and 355 GHz from previous reports.

Experimental values for rain attenuation at 96, 140, and 225 GHz are taken from results by Nemarich et al. [

Type of Rain | N_{0} m^{β3} mm^{β1} | Ξ mm^{β1} |
---|---|---|

Thawing of Pellets (Hail) | 64,500R^{β0.5} | 4.95R^{β0.27} |

Thawing of Granular Snow (Sleet) | 11,700R^{β0.29} | 4.87R^{β0.2} |

Thawing of Non Granular Snow (Snow) | 2820R^{β0.18} | 4.01R^{β0.19} |

who performed measurements on 26 Jan 1983 at Camp Rilea, Oregon, USA. The measurements were performed. between transmitters and receivers placed 1.3 km apart on flat ground. The maximum rainfall was 10 mm/hr, with rain falling at a similar rate over a long period of time.

The average temperature during the experiment was 8.3ΛC, average humidity was 95.7%, and absolute humidity was 1.4 g/m^{3}. Variation in attenuation due to changes in absolute humidity was reportedly estimated to be less than 0.1 dB, so no correction for absolute humidity was performed. Figures 1(a)-(c) show the experimental values as triangles, and the dashed curves indicate regression curves for the experimental values found from fitting.

1) 313 GHz

Experimental values for rain attenuation at 313 GHz are taken from the results of Babkin et al. [

2) 355 GHz

Values for rain attenuation at 355 GHz are taken from the results of an experiment and evaluation performed by the authors between 10:00 and 16:00 on 28 Apr 2010 on the campus of the National Defense Academy in Yokosuka, Japan [^{3}, with the level of variation in attenuation due to atmospheric absorption below 0.5 dB/km, so experimental values were not corrected for absorption attenuation.

We verified the level of fit between theoretical and experimental values for the microwave-to-terahertz waveband. Verification was performed according to the root mean square error (RMSE) of regression curve values found by fitting calculated and experimental values for each frequency.

Calculations | Frequency [GHz] | ITU-R | Weibull | M-P | Best | P-S Hail | P-S sleet | P-S Snow |
---|---|---|---|---|---|---|---|---|

RMSE | 90 | 1.30 | 1.73 | 3.48 | 0.37 | 2.18 | 0.37 | 1.88 |

140 | 2.10 | 2.14 | 4.64 | 0.31 | 2.57 | 0.18 | 1.67 | |

225 | 0.17 | 0.17 | 0.42 | 0.00 | 0.24 | 0.04 | 0.19 | |

313 | 0.28 | 0.22 | 2.91 | 1.30 | 0.63 | 2.12 | 3.66 | |

355 | 0.26 | 0.43 | 2.81 | 1.32 | 0.80 | 2.20 | 3.71 |

The results suggest that rain attenuation in the 90 - 225 GHz waveband has best fit when using Mie scattering theory with the Best and P-S sleet distributions. At 313 and 355 GHz frequencies, good fit was obtained using Mie scattering theory with the Weibull distribution and by the prediction model according to ITU-R recommendations.

In this section we compare calculated and measured values when holding rainfall intensity constant and varying frequency. We also demonstrate frequency characteristics when rainfall intensity is varied.

Here, we obtained a regression formula using experimental values from Nemarich [

We calculated rain attenuation at frequencies between 8 and 1000 GHz, using the Weibull distribution and the ITU-R prediction model while varying rainfall intensity between 1 and 100 mm/hr.

We verified fitness by comparing calculated and measured values for rain attenuation in the microwave-to-

terahertz frequency waveband. We found that in the 90 - 225 GHz microwave band, calculated values from Mie scattering theory using the Best and P-S sleet raindrop size distributions well agreed with experimental values. At 313 and 355 GHz terahertz-waveband frequencies, calculated values from Mie scattering theory using the Weibull distribution and a prediction model following ITU-R recommendations well agreed with experimental values.

We furthermore found that rain attenuation increased in proportion to frequency for microwave-band frequencies below approximately 50 GHz, but that there was a peak at around 100 GHz, above which attenuation remained steady or decreases. Rain attenuation increased in proportion to the rainfall intensity.

Seishiro Ishii,Masahiro Kinugawa,Shunichiro Wakiyama,Shuji Sayama,Toshihisa Kamei, (2016) Rain Attenuation in the Microwave-to-Terahertz Waveband. Wireless Engineering and Technology,07,59-66. doi: 10.4236/wet.2016.72006