Below is an old article on the prevalence of small-scale fading in radio links that I wrote as a post-doctoral researcher in Japan on the defunct WaveRacer site. I plan on adding a few more of these as part of a retrospective.
In the World of the Blind
by Gregory D. Durgin, www.WaveRacer.com
28 May 2001
This article discusses a famous physics experiment and draws an important physical lesson for the wireless channel.
The Multipath Problem
Do we every really have a true line-of-sight radio channel? By line-of-sight, I mean that one and only one wave arrives at a receiver antenna directly from the transmitter. A true line-of-sight channel can only exist in deep space, where transmitter and receiver antennas operate in the complete absence of scatterers.
If we introduce a single object (a near-by comet, for example), we destroy the line-of-sight channel. The new object creates a second, scattered multipath wave. Add another object (a near-by asteroid, for example) and we create a third scattered wave. We also create an infinite number of higher-order scattering: from asteroid to comet to receiver, from comet to asteroid to receiver, from asteroid to comet to asteroid to receiver, etc. We could play this game forever.
Can you imagine how many interactions there are in a cluttered environment like an office building or a city street? The combinations of interactions are infinite. But engineers take solace in the fact that after a few interactions the waves become heavily attenuated. At some point, quantum mechanics kicks in and they don’t even look like traditional waves anymore … just a slow trickle of photons.
So we usually ignore them. Approximations are the life-blood of engineering, so it’s not a bad thing to do. But consider the following physics experiment as “food for thought”. It might change your perception of the wireless channel.
The Elitzur-Vaidman Experiment
There has been a recent buzz in the quantum physics community in the study of quantum non-locality. Fuel for this excitement came from a pair of researchers, Elitzur and Vaidman, who performed a famous optics experiment at the University of Tel-Aviv.
The layout of the Elitzur-Vaidman experiment.
The experimental setup is pictured to the right. Start with a laser source that shoots a strong laser beam through an optical attenuator. The beam is split by a 50/50 splitter into two equal-power beams. These beams are reflected and brought back together at a second 50/50 splitter. This combination results in two final output beams that terminate at photon-detectors. One photon detector never registers any light (D for Dark) because the beams are set to destructively interfere at this juncture. The other photon detector always registers photons (L for Light) because the beams are set to constructively interfere.
The experiment, in this form, is not that interesting because the results of constructively and destructively interfering waves are well understood. The experiment becomes interesting if you greatly increase that initial attenuation so that the laser beam is reduced to a photonic trickle. That is, the power becomes so low that we no longer observe continuous wavefronts; instead we see just an intermittent trickle of photons.
In this scenario, whenever a single photon strikes a beam-splitter, it decides with 50/50 probability which path through the experiment to take. Since the rate of photon emission is so diminished, there is no way (classically) for a lone photon to “know” whether it constructively or destructively interferes with another branch. Our intuition would tell us that it should then arrive with equal probability at either L or D detector.
But of course that’s not what happens. In such a configuration, the single-file photons all arrive at the light detector. It’s as if each photon is pre-programmed to know that the other potential path exists for constructive and destructive interference.
It gets weirder. When researchers placed an obstruction in one of the paths, the one-by-one photons struck the L and D detectors with 50% probability each. Photons struck the D detector without having traveled down the obstructed path. The implications are a little creepy for conventional science; it is possible to detect objects without a photonic interaction with that object. This is what is meant by quantum non-locality.
What It Means for Wireless Channels
So when the intensity of an electromagnetic wave drops well below its photonic coherence, it still behaves like a wave. (That’s good news, because www.particleracer.com just doesn’t have the same ring to it.) So now let’s re-visit the multiple scatterer problem.
We can no longer say with certainty that small wave interactions are negligible. Sure, multiple scattering interactions are weak, but there are countless numbers of them. Even if they drop below photonic coherence levels, these waves are still capable of constructive and destructive addition. Their contribution to received signal strength, when taken in totality, may be quite significant. The exact amount is an unknown problem in wireless communications.
This problem is not purely scholastic, either. There are many spatial processing algorithms for boosting data rates or removing interference that depend heavily on whether a channel is the result of a few discrete multipath or a diffuse sum of a near-infinite number of waves. About the only conclusion we can definitely draw from the EV experiment is this: we always have a little more diffuse multipath power in our received signal than we think.