The term "millimeter wave" derives its name from the fact that the freespace wavelength at frequencies of operation is on the order of millimeters. At 86 GHz, the highest frequency of operation for this proposal, the wavelength is approximately 3.5 mm. This becomes significant when considering the effects of atmospheric particles on propagation, as these particles can approach significant fractions of a wavelength. Furthermore, absorption by oxygen, nitrogen, and water vapor can create large losses at certain frequencies. These effects were researched in order to create an estimate for atmospheric losses. Since the proposal only requires link budget calculations for clear day conditions, the effects of rain attenuation were not calculated. It can be said, though, that rainfall can dramatically degrade a millimeter wave link, and could potentially be a limiting problem for such a communication system.
The International Telecommunications Union (ITU) has done extensive research on this topic, and has found that the sea level attenuation under standard conditions is approximately 0.45 dB/km at frequencies between 71 and 86 GHz [2]. It can be seen in Figure 2 that there is a significant increase in attenuation in the range of 60 GHz, which is the location of the water vapor peak. Luckily, the E-band frequencies all lie in the local minimum adjacent to this peak, and thus experience significantly less path loss. In order to calculate the total path loss due to atmospheric effects, more than the sea level attenuation values must be known. The ITU document details how to calculate values for higher altitudes, but the method relies on a number of initial conditions and parameters that were deemed unnecessary for this proposal. Instead, approximations were done based on sea level attenuation and attenuation at an altitude of 4 km, using Figure 3. From this graph, the attenuation was determined to be 0.45 dB/km at sea level and 0.15 dB/km at 4 km altitude [3]. The troposphere, which contains approximately 80% of the total mass of the atmosphere, ranges from sea level to 20 km. It was assumed that most of the atmospheric losses would occur in this region.
In order to determine the total atmospheric attenuation, assumptions have to be made based on the given data points. It was assumed that the atmospheric attenuation function has the form:
Where A0 is the sea level attenuation, a is the decay constant, and h is the height above sea level. Using the given data points, A0 is found to be 0.45 and a is 0.275. Using (1), and noting that the attenuation has to be divided by the sine of the elevation angle, theta, the total attenuation can be found by:
In this case, the integral can be bounded at infinity and the result will not be affected. Using a value of 47 degrees for theta, Atotal is found to be 2.24 dB. This highlights another benefit of the E-band, as its attenuation effects are minimized since the frequency range is in a low loss part of the spectrum. It was discussed in [1] that fog and clouds have little to no effect on E-band propagation, along with airborne dust. With this knowledge, it can be assumed that water vapor absorption and absorption by atmospheric gases contribute most of the attenuation.
Figure 2: Sea level atmospheric attenuation over millimeter wave range [2].
Figure 3: Atmospheric attenuation at sea level (line A) and 4 km (line B) [3].
[1] F. Versluis. "Millimetre wave radio technology." Microwave Engineering Europe. November 2008.
[2] ITU-R, P.676-6. "Attenuation by Atmospheric Gases," 2012.
[3] "Weather Applications and Products Enabled through Vehicle Infrastructure Integration (VII)." Internet: http://ops.fhwa.dot.gov/publications/viirpt/sec5.htm. April 25, 2007 (November 21, 2012).