Multipath channel estimation in single carrier modulation I think it’s a basic question, but I couldn’t get it’s clear answer. If we have data symbols $x$ vector of length $N$ x $1$ ; it’s convoluted with a multipath channel $h$ of length $L$ x $1$; the resulted signal
$y$ = $h * x$ ;
where $*$ is convolution operation.
if we have $x_{(1:4:N)}$ is the pilot symbols which well-known at the receiver, how can we get $h$ based on $y$?
thank you.
What's missing to answer this is the spectral occupancy of x, specifically the modulated version that is convolved with the channel h. Since the convolution is a linear operation, and h is a linear channel, we will only be able to determine h for those frequencies that are occupied by x, and with a relative accuracy that will be proportional to the power at each frequency (We will be able to make a better estimate of the frequency response of h for those portions of the spectrum with higher SNR).
If x does not sufficiently occupy all the channels of interest, we will not be able to completely estimate the linear channel.