A digital communication system is developed, using moving average matched filter (MAMF) detectors, for environments where the noise is unknown a priori and may change constantly and significantly. A system in which basis vectors representing a signal subspace are transmitted rather than a fixed signal vector is described. At the receiver the transmitted basis-vectors are linearly combined so that the output signal-to-noise ratio (OSNR) of the MAMF is maximized. This linear combination represents an adaptation of the transmitted signal to changes in the noise environment. A system combining the fixed vector and the signal subspace approaches is simulated and shown to potentially outperform either system alone for an arbitrary distribution of narrowband noise center frequencies.