Let's assume I send a root raised cosine pulse of 1ns at t=0 through a wireless channel. The power measured @ Receiver from t=0 is shown in image.enter image description here

Now from this image, I know that there are multipath components(due to spreading of signal power across time).

I want to know that up to which time do I have to measure the power for a single symbol transmitted and how can I know that after a certain amount of time the second symbol will start. (how can I measure that certain amount of time?)

In this received power I know that(by spreading) that there are multipath components. I want to measure the Gain of those multipath components. So how can I sample it and how do I know about the number of multipath components?

  • $\begingroup$ Where on earth do you find an impulse to apply to a wireless channel? $\endgroup$ – Dilip Sarwate May 8 '19 at 3:14
  • $\begingroup$ Sir, you can assume it to be a pulse of time T(very short duration ) $\endgroup$ – Avinash Baldi May 8 '19 at 3:32

Typically a known sequence is transmitted (often as a preamble) that has properties to aid in determining the channel characteristics (by spreading its energy across all frequencies within your signal bandwidth) and in determining the symbol clock (many transitions at the symbol clock boundary). Both can be accomplished by using pseudo-random sequences which also have the desirable property of an autocorrelation that approximates an impulse function (useful for establishing a timing boundaries under low SNR conditions). When shorter sequences are sufficient for acquisition and channel estimation, Barker codes also have the desirable autocorrelation and signal energy spreading properties mentioned (these go hand in hand: the autocorrelation of white noise is an impulse).

The details on estimating the channel (or equalizing your signal to remove the channel distortions) for single-carrrier modulation schemes are identical to the operations detailed in this post here: Compensating Loudspeaker frequency response in an audio signal

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