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Compressive sensing methods are used in channel estimation when the channel is thread as sparse where there are zero points in the signal representation. I am in the beginning of the sparse signal processing and trying to understand how to model the sparse channel in the equation below.

Y(k)=H(k)X(k) === > Y(k) received signal in frequency domain

My questions are:

1-What is the presentation of sparse channel h in this equation? 2-How to define the dictionary matrix for sparse channel? 3-For sparse estimation do we need to insert pilot symbols into the transmitted data x(n)? 4-Do you have a reference which explains the sparse channel properties in OFDM systems?

I would appreciate if someone please help on this topic.

Many thanks!

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Are you still there, I've seen this question right now. First let me correct your question,

Y(k)=H(k)X(k) === > Y(k) received signal in frequency domain

That's true, but it's not necessary that signal in frequency domain in order to be used in compressed sensing, it might be in time domain also.

Now, regarding your questions, the representation of h channel can be sparse too but it's not always, it can be also in other forms .. taking an example of multi-path environment, the received signal can be sparse, and h channel can be either sparse or not, that's not important.

how to design the dictionary, that's the goal of the compresses sensing, it's how can you design it, you can check online, you will get many dictionary.

Estimation is different about using compressed sensing. you may use pilot or not, that's different topic.

reference for compresses sensing, is An Introduction to Compressive Sensing Collection Editors: Richard Baraniuk Mark A. Davenport Marco F. Duarte Chinmay Hegde

Thanks

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