## Origin of frequency division

17.11.2013 18:35

The most basic feature of radio communication, practically since its invention, is the division of the electromagnetic spectrum between different users on the basis of different sine wave frequencies. In fact, the word radio spectrum is basically synonymous with this division and the first question about any kind of radio is usually what frequency it operates on.

After working in the Department of Communication Systems for most of the past two years, I began to wonder what is the original reason behind frequency division. It's one of those fundamental questions that sometimes pop into your head to keep your mind off more depressing topics.

Image by Spigget CC BY-SA 3.0

The classical electromagnetic field theory gives a wave equation in empty space that does not favor the sine wave over any other kind of wave function. Similarly, a wave shared between transmitters can be decomposed into multiple independent channels based on any one out of an infinite set of orthogonal function families. Again, there is no preference to the sine and cosine functions and the Fourier decomposition that is ubiquitous in radio communication theory.

In fact, a lot of recent technologies, for example third-generation GSM, sub-divide their channels using orthogonal functions other than a sine wave. However, this is done only after first filtering the radio signal based on sine wave frequencies.

Electromagnetic field in a practical, Earth-based environment however does favor a division of signals based on sine waves. One classical reason is that objects that appear in the path of radio waves only come in a certain range of sizes. Diffraction and other such phenomena are mostly based on the relationship between wavelength and obstacle size. This means that sine waves with certain frequencies will have more favorable propagation properties than others. Hence it makes sense for instance to use a frequency band that will have better propagation for longer-range applications.

Another reason why it is natural to treat electromagnetic waves as a sum of sine functions is because of quantum mechanics and the fact that the frequency determines the photon energy. Size of energy quanta determines how the field can interact with matter in its path and this again affects atmospheric path loss in different frequency bands.

While physics of radio propagation gives valid reasons why limit a transmission to a particular part of the electromagnetic spectrum, it doesn't explain why use relatively narrow band transmissions. Radio spectrum generally spans from 3 kHz to 300 GHz while most communication technologies will currently top out in the range of 100 MHz per channel.

The historic reason why frequency division was originally used is that the natural response of most electromagnetic and mechanical systems is a harmonic oscillation. Such oscillators can be conveniently used as signal filters to extract a channel in a shared medium.

Modern systems that use other kinds of orthogonal functions for multiplexing use digital processing for signal filtering. Only in recent history has digital processing been able to process signals with significant bandwidth. That left analog filters and the frequency division as the only option for multiplexing in the early days of radio. We are still long way off before 300 GHz of radio spectrum could be processed digitally.

Another problem with purely digital processing is that passive analog filters can have a much higher dynamic range compared to A/D converters or even active analog filters. The range between noise floor and coils melting or quartz crystals shattering is significantly better than the linear range of transistors. The ability to extract a weak signal in the presence of another transmission with a much higher power is crucial in radio technology where it's not unusual to see power differences well over 10 orders of magnitude. That is why even state-of-the-art software defined radios have front-end signal conditioning implemented in analog technology.

The only current technology I know that largely does away with frequency multiplex is Ultra-wideband. It is of course still frequency band limited. Partly because of propagation physics mentioned above and partly artificially, to minimize interference with other technologies that share the same frequency band. However with effective bandwidths in the range of giga-hertz it depends on frequency division much less than conventional technologies. Unfortunately I don't know the details of UWB implementation, so I don't know how it manages to overcome the dynamic range problem and other technological limitations.

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