# Capacity of channels with pilots?

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 is 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".

What is the literature where it is discussed ?

More precisely let us consider the following signal model ("block" fading)

$$r_i = h s_i + n_i,$$

where $$i=1...N$$ , h - is random, but constant on Block, $$n_i$$ is gaussian noise. (its variance can be 1) known to us 2) uknown to us) Assume we have K-"pilots" i.e. we send symbols $$s_1=1$$ ... $$s_K=1$$.

• Why would the channel capacity change with or without a pilot? Commented Feb 13, 2012 at 18:54
• @JimClay 1. On one hand sending know sequences(pilots), makes you transmit less unknown information, so for a given bandwidth and SNR you would have a smaller capacity(you send less unknown data). 2. BUT, and this is a BIG but, based on the recieved pilots you can filter the received data and gain a higher SNR. So the pilots can help you improve SNR and indirectly increase channel capacity. Commented May 20, 2012 at 12:47
• Channel capacity is independent of the information actually sent through the channel. What the pilots can be used for is to better estimate the current channel capacity. Never can the actual capacity be influenced by whatever is transmitted through the channel. But by having a better estimate of the channel, one can get a higher data rate, closer to the capacity.
– Max
Commented Mar 16, 2018 at 11:27