Performance analysis for CEM and OSP

We investigate two well-known techniques Constrained Energy Minimization (CEM) and Orthogonal Subspace Projection (OSP) and find out that they can be theoretically treated as equivalent methods when the noise is independent and identically distributed (i.i.d) and its variance is small enough compared to signals, i.e., SNR is large enough. In order to make the condition true, two approaches are applied to modify the OSP technique. One is to estimate the noise covariance matrix and whiten the noise to be i.i.d and unit variance. The other is to estimate sufficient undesired signatures such that the noise approaches i.i.d when the data is projected onto the orthogonal subspace of undesired signatures. The results using simulated and real data demonstrate that our conclusion on the relationship between the OSP and the CEM is correct. It will be instructive to algorithm selection in practical application.