# Atmospheric Effects on OFDM Wireless Links Operating in the Millimeter Wave Regime
## 7 Simulation Results  
The performance of the OFDM wireless link under various weather conditions was studied using the developed model. A single transmitter and receiver (SISO) transmission link was simulated, within bandwidth of 200 MHz, centered at 28 GHz, 39 GHz, or 60 GHz. Typical transmission distance of 200 m is assumed. Simulations were carried out for reference conditions: an ambient temperature of 25 \({}^{\circ}\)C and air pressure of 101 kPa for an urban environment. Using meteorological parameters, the MPM predicts frequency-dependent absorptive and dispersive phenomena, causing distortions in amplitude and phase of propagated waveform.  
Figure 5: Bit Error Rate (BER) Performance of 64 QAM and effect of Phase Distortion Compensator on it at carrier frequencies of **(a,b)** 28, **(c,d)** 39, and **(e,f)** 60 GHz for 200 m wireless link in different rainfall rate.  
In the current work, the presented results are focused on the effect of rain, where the most significant effect on the link budget was identified. The propagation parameters calculated by the MPM model are summarized in Table 3 for the designated 5G bands. The attenuation and phase shift are revealed to increase with the rain rate and with the carrier frequency. These results correspond with experimental climatic wind tunnel results [4].  
At the second stage, the effect of the rain intensity on the quality of waveform reception and OFDM demodulation is examined. The bit error ratio (BER) as function of SNR at carrier frequencies 28, 39, and 60 GHz of a wireless link of 200 m is presented in Figure 4a,c,e for 64-QAM constellation. For each frequency, the BER is found for different rainy scenarios: no rain, 5, 10, and 15 mm/h. It is important to note that the rain plays a different role at different frequency bands. For instance, setting the carrier frequency to 28 GHz, SNR = 25 dB, the resulted BER is increased from \(2\times 10^{-5}\) (no rain) to \(2\times 10^{-4}\) in rainy conditions (when the rain intensity is R = 15 mm/h). However, for 39 GHz carrier frequency, SNR = 25 dB and rain intensity of R = 15 mm/h, the BER further increases to \(2\times 10^{-3}\) (see Figure 5a,c).  
The received signal quality is analyzed by displaying the constellation diagram for each scenario. A contraction of the constellation diagram demonstrates attenuation of the OFDM signal, while rotation of the diagram is a result of phase shift. Figure 4a,c,e shows the effect of rain on 64 QAM constellation diagram at carrier frequencies of 28, 39, and 60 GHz of wireless link of 200 m. The attenuation expressed by \(\alpha(f)\) causes the constellation to \"shrink\". The revealed counterclockwise rotation of the diagram is a result of dispersion of the propagating OFDM signal due to the rain. The rotation angle increases with frequency corresponding to the incremental phase dispersion, given in term of \(\Delta\beta(f)\) in Equation (11). Both effects cause the symbols to change their position in the constellation I/Q domain resulting in misinterpretation by the demodulators and erroneous symbol receptions.  
While constellation diagrams are useful for graphically visualizing signal data, it is also useful to quantify the disparity between received signal waveform and the ideal constellation by calculating the error vector magnitude (EVM). EVM is the scalar distance between the end points of the measured and ideal phasors and is a measure of how well a digital communications system is performing [27]. As is presented in Figure 6, the higher the QAM signaling order is, the resulted constellation rotation angle (Table 4) at the receiver is more expressed. Therefore, the EVM will increase for high modulation orders, resulting in erroneous detected symbols even at relatively low rainfall intensities.  
Figure 6: Comparison of 64 QAM and 256 QAM constellation diagrams at a carrier frequency of 28 GHz for 200 m wireless link for different rainfall rates.