  This paper deals with the problem of adaptive multidimensional/multichannel
signal detection in homogeneous Gaussian disturbance with unknown covariance
matrix and structured deterministic interference. The aforementioned problem
corresponds to a generalization of the well-known Generalized Multivariate
Analysis of Variance (GMANOVA). In this first part of the work, we formulate
the considered problem in canonical form and, after identifying a desirable
group of transformations for the considered hypothesis testing, we derive a
Maximal Invariant Statistic (MIS) for the problem at hand. Furthermore, we
provide the MIS distribution in the form of a stochastic representation.
Finally, strong connections to the MIS obtained in the open literature in
simpler scenarios are underlined.
