What is perfect and imperfect channel? Often in estimation of the input signal to an unknown channel, the bit error rate is plotted as the performance measure. The curve is compared with an ideal curve labelled as 'Perfect channel'. For example in this paper, http://www.iaeng.org/publication/WCECS2015/WCECS2015_pp668-673.pdf
 although the bit error rate curve is not present, in the introduction the Authors do mention the term perfect channel. One such method of estimation is the Least Squares. 

What is the meaning of a perfect channel? Does a perfect channel mean that there is no noise or does it mean that the pilot symbols are used to estimate the channel?
It's not the channel that is perfect; it is the estimation. So, "perfect channel estimation" means that the receiver knows the fading coefficients perfectly. This is of course only true in a simulation; any actual system  performs imperfect estimation and the estimated channel coefficients are only approximately equal to the actual coefficients.