Analysis of the LS estimation error on a Rayleigh fading channel

A channel in a wireless communication link is often treated as time invariant over an estimation interval, during which a least squares estimate of the channel is calculated, using training symbols. By a second order Taylor expansion of the channel, the estimation error, due to time variation, can be approximated as a bias and an excess error, which are due to the curvature and linear change of the channel, respectively. Approximate expressions for the variance of the estimation error in a Rayleigh fading channel, are presented here.