# Atmospheric Effects on OFDM Wireless Links Operating in the Millimeter Wave Regime
## 8 Channel Performance Improvement via Phase Distortion Compensation  
As mentioned in Section 3, the effect of the atmosphere on the communication channel is expressed by the attenuation coefficient \(\alpha(f)\) and by the incremental, frequency dependent phase dispersion \(\Delta\beta(f)\), given in Equations (10) and (11), respectively. Figure 4a,c,e presents the effect of these two parameters on the modulated signal, revealing respective \"shrink\" and \"rotation\" in the constellation. While the effect of the attenuation \(\alpha(f)\) is usually considered in an appropriate design of the link budget, we suggest to neutralize the phase dispersion \(\Delta\beta(f)\) caused by the atmospheric medium by adding a phase compensator in the pre-demodulating stage in the receiver MMW chain (see Figure 7). The frequency dependent phase dispersion coefficient can be estimated by meteorological conditions at the receiver site, including relative humidity \(RH\) [%], suspended liquid water content \(W\) [g/m\({}^{3}\)], and rainfall rate \(R\) [mm/h].  
Figure 4b,d,f shows a positive effect of the Phase Compensator on a distorted 64 QAM constellation diagram for different rainy scenarios: no rain, 5, 10, and 15 mm/h. As it presented, Phase Distortion Compensator completely neutralizes the \"rotation\" effect dramatically. As a result, the receiver demodulator becomes able to reproduce the data almost as in no-rain scenarios (see Figure 5b,d,f).  
Table 5 summarizes the expected performances of the average \(EVM\) and BER when an adaptive phase compensator is installed before the OFDM demodulation. A comparison with the performances attained when no compensating mechanism is applied during rainy conditions demonstrates that the proposed novel approach improves the reliability of the channel, leading to a reduction in the \(EVM\)  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Units** & **No Rain** & **5 mm/h** & **10 mm/h** & **15 mm/h** \\ \hline \multicolumn{6}{c}{**28 GHz**} \\ \hline Attenuation Factor & [dB/km] & 0.3074 & 1.0460 & 1.8501 & 2.6809 \\ \hline Phase Factor & [deg/km] & 1.7740 & 3.9402 & 6.5050 & 9.5047 \\ \hline Attenuation for 200 m & [dB] & 0.0615 & 0.2092 & 0.3700 & 0.5362 \\ \hline Incremental part of phase for 200 m & [deg] & 0.3548 & 0.7880 & 1.3010 & 1.9009 \\ \hline \multicolumn{6}{c}{**39 GHz**} \\ \hline Attenuation Factor & [dB/km] & 0.3310 & 1.7524 & 3.1170 & 4.4610 \\ \hline Phase Factor & [deg/km] & 2.9819 & 2.6178 & 9.0821 & 16.4558 \\ \hline Attenuation for 200 m & [dB] & 0.0662 & 0.3505 & 0.6234 & 0.8922 \\ \hline Incremental part of phase for 200 m & [deg] & 0.5964 & 0.5236 & 1.8164 & 3.2912 \\ \hline \multicolumn{6}{c}{**60 GHz**} \\ \hline Attenuation Factor & [dB/km] & 14.63 & 17.5066 & 19.8636 & 22.0577 \\ \hline Phase Factor & [deg/km] & 3.3368 & 11.9821 & 28.9276 & 47.4929 \\ \hline Attenuation for 200 m & [dB] & 2.926 & 3.5013 & 3.9727 & 4.4115 \\ \hline Incremental part of phase for 200 m & [deg] & 0.6674 & 2.3964 & 5.7855 & 9.4986 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Propagation factors of 28, 39, and 60 GHz for 200 m wireless link.  
Figure 7: Flow chart of millimeter wave (MMW) link including Phase Distortion Compensator in the receiver site.  
and consequently lowering the error rate. A quantitative measure of the improvement is expressed via the average \(EVM\) relative reduction (in [%]):  
\[\frac{EVM_{w/o-comp}-EVM_{w-comp}}{EVM_{w/o-comp}}\cdot 100\% \tag{16}\]