There are three causes of fading mainly reflection, diffraction and scattering.
These fading types constitute different types of signal distribution from a receiver's point of view.
In the case of scattering, it causes a signal to show a rayleigh distribution, thus short term fading caused by scattering is called rayleigh fading.
rayleigh fading in simple terms:
1.) if transmitter propagates to an area with a lot of structures that will scatter the signal...
2.) rayleigh fading will occur as direct signal (inverse square law signal) will be mixed with scattered signals towards an observation point.
3.) Scattering will deform the signal and make the signal FADE than expected
4.) deformation will vary from 0 to 2Pi radians (0-180 degrees) thus the characteristic short deep fades of Rayleigh fading
5.) Rayleigh fading is observable when no direct line of sight with the transmitter
6.) Rayleigh fading much more pronounced when receiver is in motion, as motion multiplies the observed scattered signals arriving to the observer.
Relation to Shannon Theorem:
"The Shannon theorem states that given a noisy channel with channel capacity C and information transmitted at a rate R, then if R < C there exist codes that allow the probability of error at the receiver to be made arbitrarily small. This means that, theoretically, it is possible to transmit information nearly without error at any rate below a limiting rate, C."
A communication system and protocol usually an established R/C where C>>R. example GSM 200KHz C can not support better than 100KBps. This R/C ratio is based on optimal conditions of interference and fading values. If rayleigh fading due to macro design goes beyod these established values then R/C will be lower thus in the case of GSM it will not support and aggregate speed of 100KBps at 200KHz bandwidth.
(Curiously there was a system that broke the shanon theorem of C>>R and exhibited R>>C on controlled and strict conditions which is CDMA used in IS-95, CDMA2000 and UMTS WCDMA, however the battery penalty (due to processing) is so high that designers are going back to C>>R designs for LTE).
ON CLT and Rayleigh Distribution wide set of topics
but simply, CLT is a distrubution density with an established variance simply states that a com system with good design will have mean received signal that is dense enough and will have variances that is still good enough to support shannon's theorem design limit (previously established) even with rayleigh fading and other fading types inherent in the environment it supports or sustain.
I think that claim, taken at face value [sound byte'd], is somewhat dubious. Such a claim depends on the application. I also disagree that one inherently more robust in terms of interference immunity. If you are operating in a fixed channel using DSSS and you have a loud interference source in the same channel (could be fixed frequency - but higher power than you) you will loose a higher % of your packets than if you were using a FHSS system that utilized the entire band. But if you are using an FHSS system in an area where a lot of your neighbors are also using FHSS and have the same general set of hop channels then you would be in trouble. I've run into both of these situations. The first was using 900MHz ISM DSSS radios in an area where a local internet provider was using louder licensed (somehow) radios in the same channel as me (they were also using DSSS) - that channel was relatively saturated/highly utilized. The latter case was when using a FHSS radio that only had a small set of channels that it actually hopped to - so it didn't utilize the entire band. If there were other broadcasters in the same part of the band it was in it would loose a higher percentage of packets. In particular - I was jamming myself (or rather some installations of the product I was supporting were installed close together and were jamming each-other).
A poor implementation of either can lead to jamming / excessive packet loss. Also, there is no reason why you can't use a combination of the two together to more uniformly utilize the spectrum. Essentially, utilize DSSS at each FH channel.
There are some obvious decisions you should make when designing a system. For example, if you want to operate in the 2.4GHz ISM band you should pick channels between the WIFI channels if you know your device may operate in an area with multiple wifi networks (e.g. avoid picking something right in the middle of channels 1, 6, and 11 - pick frequencies between channels 2-5, 7-10, 12-14).
This article actually says that DSSS systems do WORSE with multipath / delay spread in large areas. But in enclosed small areas they do alright.
"We shall also conclude that for long distances, point-to-multipoint topologies in reflective
environments such as cellular deployments in a city, DSSS has no chance to survive, leaving
FHSS the absolute winner, based on its famous multipath resistance."
http://sorin-schwartz.com/white_papers/fhvsds.pdf
Best Answer
The coherence bandwidth measures how much a channel is statisticallt flat given a fixed size window through which we watch it.
Imagine a transmitter and a receiver, the transmitted signal being \$x(t)\rightleftharpoons X(f)\$. The receiver ideally gets the same \$x(t)\$ at the antenna, but unfortunately there's the mighty channel \$c(t)\rightleftharpoons C(f)\$. The receiver will then get \$Y(f) =X(f)\ast C(f)\$.
That \$C(f)\$ is ideally 1, i.e. it's perfectly flat for each frequency (please note that \$C(f)\$ is a complex function, i.e. \$C(f) : \mathbb{R} \rightarrow \mathbb{C}\$). That's not what happens in real life. If we measure just \$|C(f)|\$ completaly disregarding the phase, that is fundamental in almost all modulation techniques, we find out that it's everything but flat.
Now just close the math-ish door and let all the engineering folks in. There's already one shouting "Hey, if you look close enough that \$C(f)\$ is flat indeed.". Well, he's right and that's where the coherence bandwidth kicks in: you have the channel transfer function, you look at it close enough, and that becomes flat. The coherence bandwidth tells you how much is close enough: if that's 1kHz, well you've got to magnify your \$x\$ axis to see only a 1kHz portion at a time. If that's 1MHz... Well, you guessed it.
So why is it a statistical parameter? Well, you can't certainly measure all the channels you want to transmit on. Some guys at IEEE one day decided "ok, if you are in a city with tall buildings you should expect a \$B_C\$ of this much, if you are on a flat desert \$B_C\$ would be that much", and so on, and various models were born.
When does the delay spread kick in? Well I see you quite grasp what it is, and as you say \$B_C\$ and \$D\$ are close friend. As you know \$D\$ measures how much delay we should expect between the direct (the most direct) path and the others. That number tells us how long before our signal gets compromised by itself. Well it appears that a nice rule of thumb (read: there's little to no physical meaning associated to the following formula) is \$B_C=\frac{1}{D}\$. And we love to know the \$B_C\$ of a channel because it tells us how much bandwidth our signal can use without using advanced techniques such as an equalizer.
Added after OP request
What is delay spread? Here is what I have in my notes: $$\Delta\overline{\tau}=\sum_{l=1}^Np_l\tau_l$$ Where:
The delay spread hence express something like the delay after what I expect most of the power is arrived at the receiver. Consider the situation with: $$N=3\\ \mathbf{p}=[0.7, 0.2, 0.1] \\ \mathbf{\tau} = [1,2,5]ms$$ You get \$\Delta\overline{\tau}=1.6ms\$
While if: $$N=4\\ \mathbf{p}=[0.3, 0.4, 0.2, 0.1] \\ \mathbf{\tau} = [1,2,4,7]ms$$ You get \$\Delta\overline{\tau}=2.6ms\$
As you can see the delay spread measures when most of the power will arrive, and it's quite useful to appropriately tune the receiving equalizer to get the most out of your signal.