On the Properties of 2 × 2 Oblique Projection Operators

Interference-to-signal ratio (ISR) after oblique projection is usually codetermined by the estimated signal and interference, and it is usually different from the ISR after orthogonal projection. In this letter, we present two new properties of 2 × 2 oblique projection operators. The first property is that the ISR after two-dimensional oblique projection is independent of the estimated signal and is only related to the estimated interference. The other property is that the output ISR after two-dimensional oblique projection is equivalent to that after two-dimensional orthogonal projection. These two properties are demonstrated using theoretical derivation, geometrical interpretation, and simulations.