Data selection for detection of known signals: the restricted-length matched filter

Data selection algorithms, in detection, search for a small subset of the available data that is sufficient for making an accurate decision. This paper considers data selection for detection of a known signal in colored Gaussian noise. In our model, the performance of the matched filter detector for a specific subset is parameterized by a quadratic form. Selection of the best subset leads to a combinatorial optimization problem using the quadratic form as the objective function. Simulations show that heuristic search algorithms often find good solutions for the selected subset. Additionally, if the noise has a banded covariance matrix, a dynamic programming algorithm finds the optimal solution for any subset size.