0
$\begingroup$

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.

$\endgroup$
1
$\begingroup$

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.

$\endgroup$
2
  • $\begingroup$ Do you mean it's not possible to estimate h in that case ? I think it's similar to single carrier (SC) modulation; how can we estimate the channel in case of SC ? $\endgroup$
    – Fatima_Ali
    Sep 26 '20 at 14:09
  • 1
    $\begingroup$ @Fatima_Ali it is also not possible to estimate in SC for the same reason--- For example you can not use a single tone to estimate the channel over its entire bandwidth, you can only measure the phase and amplitude change on that tone, at its one frequency--- how could you possibly know how the channel would distort other frequencies from that? For equalization we typically use sounding waveforms that approximate white noise over the bandwidth of interest. $\endgroup$ Sep 26 '20 at 15:25

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.