SVD vs matched filter

Question

Reading about singular value decomposition (SVD) in the context of signal processing applications, one can separate the signal from the noise into orthogonal subspaces. On the surface this sounds like using the decomposed output of the SVD is more optimal than matched filter (or correlation) for detection, demodulation, timing estimation, etc. Is this true or is there more nuance to this problem?

Marcus Müller · Answer

That's not true, it's not better.
The thing is: the matched filter just implements the projection in the signal vector space, onto the signal vector itself (or a multiple thereof). (You'll find correlation is just an inner product in that space.)
The line through that vector is the signal subspace, the plane to which that vector is normal is the noise space. Matched filtering is a method of linear algebra, and not different than using the SVD to find the subspaces. It's just that for matched filtering, the signal space is known.

SVD vs matched filter

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