[Note] I've asked this question at http://dsp.stackexchange.com/questions/1434/capacity-of-channels-with-pilots with NO answers.

Question is about "channel capacity" http://en.wikipedia.org/wiki/Channel_capacity I guess it is pretty elementary for experts, however I have not seen it discussed in e.g. Proakis book or Tse "Fundamentals of Wireless Com".

Question (roughly speaking): is channel capacity known for the fading channel with "pilots" ? (discrete, memoryless channel). "Pilots" - means we transmit on certain positions symbols known to receiver and transmitter both. It is common for all modern telecommunication standards GSM, UMTS, LTE to have "pilots".

Simplest example:

Consider the following signal model ("block" fading), block length $N$, pilot number $k$

$r_{i,l} = h_l s_{i,l} + n_{i,l}$

here $i=1...N$ - index of symbol inside block, $N$ - block length $l=1...infinity$ - index of block

$h_l$ - are random i.i.d, but constant on block i.e. does not depend on "i",

$s_{i,l}$ sent symbols, assume that for $i=1...k$ and all $l$ they are pilots i.e. they are equal to $1$. For other $i$ these sent information signals - assume also i.i.d.

$n_{i,l}$ - noise - random i.i.d.

What is the capacity of this channel ? Assume that distributions of all random variables are given - for simplicity can assume they are Gaussian.

i.i.d. - "independent identically distributed"

Let me explain how pilots are used in the standard algorithms. We do not know $h$ - so first we proceed "channel estimation", we make some estimate of $h$ from known pilots and than estimate data symbols with "known" h.