Optimal Signal Selection for FIR Matched Filtering in Pole-Only Noise

With duration-limited signals there is the opportunity for perfect matched filtering by a suitable FIR filter whenever the accompanying noise has pole-only coloration. The maximal SNR value obtainable via matched filtering is itself sensitive to the signal pulse shape initially given. In some signaling situations (e.g. radar) we are unilaterally free to choose signal shape, and with this come prospects of further SNR improvement. Four distinct perspectives on optimizing signal selection are pursued, including a new single-frequency toneburst windowing approach that becomes a very good approximation for large signal sizes. Three of the approaches are capable of near-optimal SNR performance, but the whitener eigenvalue method introduced is recommended as the best possible way of selecting signals. Discussion is included of special multi-tonality issues which arise for smaller signals and for multiple maximum whitener eigenvalues.