Attenuation and Dispersion on Terahertz Wireless Channels in Falling Rain

Investigations on wireless channel performance in adverse weathers could be helpful and important for the future applications of terahertz communication technique in outdoor scenarios. However, in most cases only amplitude performance has been studied by using a broadband-pulsed terahertz source or an amplitude modulated data stream, not including phase degradation (temporal dispersion). This limitation may mask important aspects of channel performance with phase modulation schemes, especially for wide bandwidth signals. In this work, we report the amplitude and phase characterizations of a terahertz channel in falling rain by a time-domain spectrometer system. We also demonstrate error rate performance by a 16 quadrature amplitude modulated (16-QAM) terahertz signal at a data rate of 5 gigabits per second. We observe that, besides strong water vapor absorption, the weak water absorption line could also lead to obvious dispersion effects. Our work highlights the importance of new frequency band boundaries for minimum temporal dispersion and optimized digital communications in the terahertz frequency range.


Introduction
Wireless networks operating at terahertz (THz) frequencies have been considered to be a promising candidate to satisfy the demands on large data capacity and high physical layer security 1,2 . However, for outdoor applications, they suffer signi cant signal loss due to atmospheric weather effects 3,4 . Previously, amplitude attenuation and related channel performance degradation on THz channels caused by water fog, dust cloud, rain and snow have been investigated by employing an on-off keying (OOK) modulation method [5][6][7] . Higher order modulation techniques (such as QPSK, QAM etc.) are necessary to update the data rate with information on phase variation (temporal dispersion) required. THz time-domain spectroscopy (THz-TDS) technique could be available for monitoring both the amplitude and phase and has been used for sensing water vapor contained in air 8 . But there is lack of study on their degradation in adverse outdoor weathers due to the di culties for data recording, such as uncontrollable weather condition, long observation time, etc.
In this work, we investigate the in uence of falling rain droplets on THz channel performance by employing a commercial T-Ray 2000™ (Picometrix) THz-TDS system and a 162 GHz wireless channel with 16-QAM modulation scheme. A weather chamber was built in laboratory to emulate stable and controllable falling rain. The lab condition could be reproducible and has been previously demonstrated 9,10 . For the rst time, the dispersion effect caused by falling rain droplets is observed and analyzed, which is usually di cult and even impossible for actual outdoor measurements.

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 signi cantly 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 (A Rain ) and falling rain (A FS ) 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 ΔA Rain = A Rain -A FS , is shown in Fig. 1(b) as blue color. The trend versus frequency is identical to published measurements 11 . 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 THz 13 . 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 previously 14 . 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 model 15 , even though never observed in measurements before.
As the THz-TDS system directly probes the electric eld, 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 (ϕ FS ) and in rain (ϕ Rain ) as Δϕ Rain = ϕ Rain -ϕ FS . As shown in Fig. 2 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 demonstrated 16 . 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 con rmed over a short channel distance of 6.18m 17 .
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 larger 18 and up to π at a rain fall rate of 390 mm/hr. This would de nitely 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 GVD Rain = dϕ Rain /dω in rain and GVD FS = dϕ FS /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 predictions 8 . 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 in uence 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 rst 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 in uence 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 droplets 10 .
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 in uence 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 risks 14 . 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. Methods Experiment setup. For both the pulsed and modulated data stream measurements, we launch the radiated THz beam through a weather chamber which could generate controllable and reproducible falling rain. In the pulsed signal experiment, a commercial T-Ray 2000™ (Picometrix) terahertz time-domain spectrometer (TDS) is used. This is a conventional TDS system. Power specra is obtained from measured time-domain waveforms via numerical Fourier transform. GHz by a subharmonic mixer (110-170GHz) which is driven by a 81GHz reference signal from an ×6 multiplier. Finally, the signal is radiated by a THz antenna.
On the receiver side, a low noise ampli er ampli es the D-band signal captured by another identical THz antenna and sends its output to a subharmonic mixer to obtain the IF signal which can be converted to digital sequence by an ADC (EV10AQ190). A Xilinx XC7VX690T FPGA is used for synchronization processing and demodulation operation. The output binary sequence would be compared with the transmitting binary sequence, and then the Eb/N0 parameter can be derived by calculating the bit error ratio easily.
The weather chamber used in this work is fabricated with 3264 31-gauge needles which are epoxied to produce raindrops. The chamber was lled with distilled water to emulate the actual material for rain. The diameter of the needles is small enough such that when no air pressure is applied on the water in the tank, no raindrops are produced. In the chamber, the generated rainfall rate is related to air pressure and in a linear relationship.
Calculations. The dark blue curve in Fig. 1(b) and Fig. 2(a) was computed using a v-VW theory for the absorption and phase shift due to variation of water vapor in the rain chamber 17,19 . It can be expressed as with A j as the line-strength values obtained from JPL data base 20 . ω j is the water vapor resonance line and Δω j is the FWHM linewidth. D is a factor proportional to the density of water vapor. Values of all these parameters should be found in Grischkowsky's publication 17 .
Simulations. Finite element method (FEM) simulation results were performed using COMSOL Multiphysics 5.6 when a pulse radiation propagates through a spherical rain droplet located in vacuum as shown in Fig. 3(a). In this gure, vacuum is assumed as the background to isolate the in uence of water vapor and other gases. Perfectly matched layers (PML) are used to absorb at the edges. A port boundary is employed for the pulse incidence and another port boundary at right side to detect the pulse.
Triangle elements with an identical size of 0.2 mm are used to mesh the geometry. Figure 1 Amplitude performance of THz frequencies due to falling rain. (a) A broadband-pulsed terahertz source is used to launch a THz pulse into free space and falling rain seperately. The black curve stands for the received signal propagates in free space and the blued one for the signal passing falling rain with a rainfall rate of 466 mm/hr. Inverse fast Fourier transformation was conducted on the measured data. Both curves show three peaks with their frequencies determined by the strong water vapor absorption lines. (b) The three solid lines show the measured power attenuation of the THz signal due to falling rain with falling rates of 390 mm/hr (black), 466 mm/hr (blue), and 700 mm/hr (red). The humidity RH 37% is measured in rain while it is RH 36% in free space without rain. The room temperature is usually kept at 25℃. There are three obvious peaks at 0.56 THz, 0.75 THz and 0.98 THz caused by strong water vapor absorption lines and one absorption peak at 0.235 THz due to weak water absorption line. The dark green curve represents the power attenuation due to the pure water vapor with humidity increasing from RH 36% to RH 37% when the temperature is unchanged. Figure 2 Phase variation of THz frequencies due to falling rain. (a) Phase shift due to falling rain by comparing the unwrapped phase spectra of THz signals after propagating through free space and falling rain. The three solid curves represent the rainfall rate at 126mm/hr (black), 256 mm/hr (blue) and 379 mm/hr (red). The dark green curve represents the phase shift caused by the increasing of humidity from RH 36% to RH 37% with room temperature (25oC) unchanged. (b) variation of group velocity dispersion (GVD) for the THz signals by numerical second order derivative with respect to the angular frequency of the phase spectra as in Fig. 2(a). To our knowledge, this is the rst experimental demonstration of the dispersion on THz channels in falling rain.

Figure 3
Simulation on pulse wave propagation through a rain droplet. (a) A 2D numerical time-domain simulation ( nite element method) of an input wave propagating through a suspended rain droplet marked as a black circle. The total background is set as vacuum to isolate the in uence of water vapor and other gases. The rain droplet is spherical with a diameter of 1.9 mm, which is identical to that we generated by the rain chamber in our laboratory. The inset (left) shows the input pulse and the red arrow indicates its propagation direction. Scattering phenomenon caused by the rain droplet is clearly evident. (b) Simulated power attenuation spectra caused by the rain droplet. There is only water continuum absorption observed here because no water vapor contained in this simulated background. The weak water absorption line de ned in the vV-W-HITRAIN model could not be found here due to the different theoretical model (which doesn't consider that line) used by the COMSOL Multiphysics 5.6. (c) Simulated group velocity dispersion (GVD) in vacuum with and without rain. The black and straight line indicates no dispersion when the pulse wave propagates in vacuum only. The oscillations in the blue curve implies the scattering caused by the rain droplet. after propagating through free space (black) and falling rain (blue) with the detector xed at the optimum position for the carrier at 162 GHz. After through falling rain, the BER values at the received power below -40.3 dBm could not be recorded due to the scattering and absorption by falling rain droplets. The inset shows schematic measurement setup, with one transmitter at 162 GHz, and with the receiver mounted on a linear rail to vary the position of the receiver. (b) Power pattern measured when channel propagates through free space (black) at temperature T =17℃, humidity RH 34% and falling rain (blue) at rainfall rate Rr = 350 mm/hr. (c) BER performance under the power patterns in Fig. 4(b). Error rate of 10-10 could not be achieved in falling rain due to the signal loss. There is no obvious jump observed in the power and BER patterns when the THz channel operates at 162 GHz, which is far away the water and water vapor absorption lines. The temporal dispersion is negligible and the its in uence on the 16-QAM modulated channel is not evident. Implementation of the 162 GHz communication system. A Xilinx Vertix-7 serial FPGA(XC7VX485T) is employed to generate the modulated signal with a data rate up to 5 Gbps at an intermediate frequency (IF) of 1.25GHz. The generated digital sequence from FPGA is converted into an analog signal by a DAC (MD662H) and then mixed with a radio frequency (RF) of 162 GHz by a subharmonic mixer (110-170 GHz) which is driven by 81 GHz reference signal from X6 multiplier. Then the generated THz signal is radiated into rain by a commercial horn antenna from Custom Microwave Inc. On the receiver side, a low noise ampli er ampli es the D-band signal captured by a combination of a Te on lens (focal length 5 cm) and an identical antenna. Its output is launched into a subharmonic mixer to obtain the IF signal which could be converted to a digital sequence by an ADC (EV10AQ190). A Xilinx XC7VX690T FPGA is used to process the synchronization and demodulation operation. The output binary sequence would be compared with the transmitting binary sequence to obtain the bit error ratio (BER).