Experimental characterization using broadband THz pulses
We have recorded a propagated THz pulse in free space and in falling rain, separately, at temperature 25 ℃9. The measurement in rain was repeated three times at an identical rainfall rate of 390 mm/hr. The total channel distance here is only 4 m due to the laboratory limitation, but we could increase the rainfall rate (Rr) to be 700 mm/hr, which is significantly larger than that for a typical heavy rain condition in nature. Then obvious channel degradation could be observed. When collecting THz waveforms for measuring the averaged signal performance, the system was set to a rapid scan mode with 1000 averages.
The amplitude spectra of the pulses passing free space (ARain) and falling rain (AFS) are shown in Fig. 1(a) with a rainfall rate (Rr) of 466 mm/hr. Strong water vapor absorption lines at 0.56 THz, 0.75 THz and 0.98 THz are clearly observable for both curves. Their difference, i.e. power attenuation due to rain ΔARain = ARain - AFS, is shown in Fig. 1(b) as blue color. The trend versus frequency is identical to published measurements11. The power absorption due to the increasing of pure humidity (from RH 36% in free space to RH 37% in falling rain) is estimated by employing the equation and database of the International Telecommunication Union Recommendation (ITU-R) P.676 − 12 (08/2019)12. The result is shown as the dark green curve in Fig. 1(b). For this model, there is a discrepancy of 10 dB/km when compared with measurements (RH 40%) at frequencies between 0.8-1 THz13. Such difference is much smaller than the power attenuation as in Fig. 1(b). Thus we would attribute the attenuation to the falling rain droplets instead of the increasing of water vapor (or humidity). And also, the absorption by rain droplets (i.e. water continnum absorption) should be more responsible for that than the scattering loss as demonstrated previously14. It should be noted that there is a weak absorption peak at 0.235 THz as marked by the blue arrow. We attribute this to a weak water absorption line, which has been predicted by a vV-W-HITRAN model15, even though never observed in measurements before.
As the THz-TDS system directly probes the electric field, we could also obtain the unwrapped phase spectra corresponding to Fig. 1(a). The phase shift due to falling rain, could be obtained by comparing the phase spectra in free space (ϕFS) and in rain (ϕRain) as ΔϕRain = ϕRain - ϕFS. As shown in Fig. 2(a), there are three obvious jumps corresponding the strong absorption lines of water vapor. This phenomenon has been indicated by the Kramers-Kronig relations and excellent agreement has been demonstrated16. One tiny jump at 0.235 THz could also be observed and we attribute it the weak water line as in Fig. 1(b). We also calculate the phase shift caused by the increasing of water vapor only (dark green curve in Fig. 2(a)). When the humidity changes from RH 36% to RH 37%, the continuum phase shift is small and negligible. In other words, the water vapor would not lead to obvious phase shift except at the peak absorption line frequencies. This has ever been confirmed over a short channel distance of 6.18m17.
We can conclude that the difference in phase shift between the measurement and calculation should be attributed to the falling rain droplets, even though it is smaller than 0.05 π and negligible over a propagation distance of 4 m in this work. However, for a much longer channel path, such as 80 m, the phase shift could be much larger18 and up to π at a rain fall rate of 390 mm/hr. This would definitely degrade data transmission. However, such weather conditions could not be possible in nature and the absorption by falling rain would fail the THz channel before that happens.
We obtain the group velocity dispersion (GVD) for the channel by taking numerical second order derivative with respect to angular frequency (ω) of the phase spectra as GVDRain = dϕRain /dω in rain and GVDFS = dϕFS /dωin free space. The difference between both (ΔGVD) is calculated and shown in Fig. 2(b). The jumps located at 0.56 THz, 0.75 THz and 0.98 THz represent large and unstable GVD caused by water vapor, which is consistent with theoretical predictions8. There is one more jump located at around 0.235 THz due to the water absorption line. All these four frequencies should be avoided to reduce both attenuation and dispersion for future THz wireless communications. At other frequencies, the ΔGVD value is much smaller and more stable, which means the falling rain droplets have negligible influence on the phase performance of the channel.
Simulation characterization using broadband THz pulses
A 2-dimensional numerical simulation in Fig. 3(a) illustrates the propagation of a pulsed THz wave through a suspended rain droplet. The pulse incidence first propagates from the left side and then is detected at the right side with a red arrow indicating its propagation direction. The rain droplet is spherical with a diameter of 1.9 mm, which is identical to the average raindrop size we generated. There are many ripples in the vacuum space when the pulse wave propagated through the droplet, which indicates the generation of scattering components.
Experimental characterization using a data stream
To see the influence of the falling rain on higher order modulation techniques, a 16-QAM THz channel is built with its schematic diagram shown in Fig. 4. More details on the setup should be found in the Methods part.
When a 162 GHz channel propagates through the falling rain at a rainfall rate of 350 mm/hr, a power attenuation of around 0.5 dB is observed. The variation of bit-error-ratio (BER) value with respect to transmitted THz power is recorded and shown in Fig. 4(a). An obvious BER degradation in rain could be observed. The difference between both curves should be attributed to the absorption and scattering effects caused by falling rain droplets10.
When we mount the receiver on a movable rail which permits it to translate along an axis perpendicular to the incoming beam’s propagation direction. By scanning the detector along this line, we map the spatial distribution of the beam arriving at the receiver side. A power loss of 0.5 dB due to rain is observed again in Fig. 4(b) and the corresponding BER degradation is shown in Fig. 4(c). there is no obvious jump observed in the power and BER evolution curves, which means the temporal dispersion caused by falling rain is so small that it has negligible influence on the 16 QAM modulated THz channel over a transmission distance of 0.5 m.
In summary, the amplitude attenuation and temporal dispersion suffered by THz channels passing through falling rain are measured, calculated and analyzed. Obvious temporal dispersion is observed at the frequencies corresponding to water vapor absorption peaks. This makes more cautious considerations required for short range THz wireless communication scenarios, which would lead to serious compromising emissions away the line-of-sight (LOS) channel path and higher eavesdropping risks14. Besides this, the weak water absorption line would cause an extra temporal dispersion at 0.235 THz, which should also be considered carefully to identify possible THz transmission windows in falling rain. We believe this work would not only contribute to the optimization of THz wireless channel performance in falling rain, but also help for the reduction of signal leakage in adverse weather conditions.