# Constant Envelope Modulation Techniques for Limited Power Millimeter Wave Links
## 2 Communication Links in Millimeter Waves  
When the electromagnetic radiation in the millimeter wavelengths and terahertz frequencies regime propagates through the atmosphere, it experiences selective molecular absorptions [34; 35; 36; 37; 38; 39; 40]. Several empirical and analytical models have been suggested for estimating the millimeter and sub-millimeter wave transmission of the atmospheric medium. The transmission characteristics of the atmosphere at the EHF band were calculated using the millimeter propagation model (MPM), developed by [PERSON] [41; 42; 43; 44]. The inhomogeneous atmospheric transmission affects the amplitude and phase of the signals transmitted in the millimeter and sub-millimeter wavelengths [45].  
The transmission characteristics of the atmosphere are shown in Figure 1. In this example, graphs are drawn for several values of relative humidity (RH = 0%, 25%, 50%, 75%, and 100%) at sea level, assuming clear skies and no fog or rain. The attenuation factor, \(\alpha(f)\) in dB/km, is drawn in Figure 1a, revealing absorption peaks at 22 and 183 GHz, where the resonance absorption of water (H\({}_{2}\)O) occurs; as well as absorption peaks at 60 and 119 GHz, due to the absorption resonances of oxygen (O\({}_{2}\)) [46; 47; 48].  
A minimum attenuation is obtained at atmospheric transmission \"windows\" in the Ka- (35 GHz) and W-bands (94 GHz), as well in the vicinity of 130 and 220 GHz [37]. The gray bands represent the spectrum allocated for the 5G. In Figure 1b, we show the incremental group delay (in ps/km) caused by the phase variation in the frequency. The atmospheric transfer characteristics can be calculated for any value of the relative humidity (RH).  
When carrying out a link budget, the atmospheric attenuation must be taken into account. In millimeter wave links, the antennas are usually directive, resulting mainly in line-of-sight (LOS) paths. When a transmitter (T; with an effective isotropic radiated power (\(EIRP_{T}\))) and an interferer (I; with \(EIRP_{I}\)) transmit a signal to a receiver in their LOS (see Figure 2), the corresponding power from the transmitting station is as follows:  
\[P_{Signal}=G_{R}\bigg{(}\frac{\lambda}{4\pi d_{TR}}\bigg{)}^{2}\cdot e^{-2 \alpha(f)d_{TR}}\cdot EIRP_{T} \tag{1}\]  
and from the interferer station, it is as follows:  
\[P_{Interference}=G_{R}\bigg{(}\frac{\lambda}{4\pi d_{IR}}\bigg{)}^{2}\cdot e^{ -2\alpha(f)d_{IR}}\cdot EIRP_{I} \tag{2}\]  
where \(G_{R}\) is the receiver antennas gain, \(\lambda=c/f\) is the wavelength of the transmitted signal (c is the speed of light, f is the frequency), \(d_{TR}\) and \(d_{TI}\) are the distances between the transmitter or interferer  
Figure 1: The effect of the atmosphere on (**a**) attenuation, \(\alpha(f)\) in dB/km, and (**b**) group delay increment, \(\Delta\tau_{d}(f)\) in ps/km.  
to the receiver, respectively, and \(2\alpha(f)\) is the power attenuation factor caused by the atmospheric medium. The signal to interference power ratio at the receiver site is given by the following:  
\[SIR=\frac{P_{Transmitter}}{P_{Interference}}=\left(\frac{d_{IR}}{d_{TR}}\right)^{2 }\cdot e^{-2\alpha\cdot\left(d_{TR}-d_{IR}\right)}\cdot\frac{EIRP_{T}}{EIRP_{I}} \tag{3}\]