Sparse Recovery Problem Solution

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S. David
S. David on 27 Jun 2014
Commented: S. David on 30 Jun 2014
Hello all,
I am working on a communication system where I physically have Np triplets {hp,taup,ap}. From these Np triplets I can build the exact channel matrix.
In practice however I need to estimate the channel. To estimate the channel I first build the dictionaries tau of cardinality Nt and a of cardinality Na. From these dictionaries I form the equation Ax=z, where z is the noisy observation vector, A=[Gamma1*Lambda1*s ... Gamma1*LambdaNt*s .... GammaNa*Lambda1*s .... GammaNa*LambdaNt*s] and x=[x(1,1) ...x(1,Nt) .... x(Na,Nt)]=[x1 ... x_NaNt]. s is the known pilot symbols.
Obviously, x is sparse, and I am using the Basis Pursuit (BP) algorithm to find it. The problem is that when solving the problem x contains much more that Np non-zero elements. How can I find Np unique triplets from Ax=z? This means there is no two triplets share the same hp, taup or ap?
S. David
S. David on 30 Jun 2014
Thanks for explanation.
Indeed, just one entry, which is the first entry of the solution, is 1 and the rest are zeros.

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