A geometrical interpretation of signal detection and estimation (Corresp.)

By introducing an appropriate representation of the observation, detection problems may be interpreted in terms of estimation. The case of the detection of a deterministic signal in Gaussian noise is associated with two orthogonal subspaces: the first is the signal subspace which is generally one dimensional and the second is called a reference noise alone (RNA) space because it contains only the noise component and no signal. The detection problem can then be solved in the signal subspace, while the use of the RNA space is reduced to the estimation of the noise in the signal subspace. This decomposition leads to a very simple interpretation of singular detection, even in the non-Gaussian case, in terms of perfect estimation. The method is also extended to multiple signal detection problems and to some special cases of detection of random signals.