  Detecting the presence of subspace signals with unknown clutter (or
interference) is a widely known difficult problem encountered in various signal
processing applications. Traditional methods fails to solve this problem
because they require knowledge of clutter subspace, which has to be learned or
estimated beforehand. In this paper, we propose a novel detector, named
volume-correlation subspace detector, that can detect signal from clutter
without any knowledge of clutter subspace. This detector effectively makes use
of the hidden geometrical connection between the known target signal subspace
to be detected and the subspace constructed from sampled data to ascertain the
existence of target signal. It is derived based upon a mathematical tool, which
basically calculates volume of parallelotope in high-dimensional linear space.
Theoretical analysis show that while the proposed detector is detecting the
known target signal, the unknown clutter signal can be explored and eliminated
simultaneously. This advantage is called "detecting while learning", and
implies perfect performance of this detector in the clutter environment.
Numerical simulation validated our conclusion.
