Detection of constrained subspace signals in additive infinite-dimensional interference and noise

The detection of constrained subspace signals in additive infinite-dimensional interference and noise is motivated by consideration of multipath-Doppler channels subject to interference from partially overlapping frequency bands of other sources. Since the interference lies in an infinite-dimensional subspace, the standard method of projecting onto the subspace containing the signal plus interference does not yield a finite-dimensional detection problem. However, an alternative approach may be used to extract the appropriate finite-dimensional problem. Moreover, an energy constraint may be imposed on the desired signal. The generalized likelihood-ratio receiver for this problem is obtained, and expressions for its average probability of error are given.