Multiple-channel detection of signals having known rank

Bayesian and generalized likelihood ratio tests are derived for detection of a common unknown signal of known rank K in M > K independent channels of white gaussian noise. The cases of known and unknown noise variance are both treated. These derivations encompass the development of explicit expressions for an invariant measure on the grassmannian manifold of K-dimensional subspaces of complex N-dimensional space and parameterization of this manifold to enable the calculation of the necessary marginalization integrals. Performance of the detectors is compared by simulation.