On geometric properties of the decorrelator

We discuss the geometric properties of the multiuser decorrelator receiver. In particular we show that the prevalent geometric interpretation of the correlating vectors comprising the decorrelator receiver in terms of orthogonal projections of the signature vectors is incorrect. The correct interpretation established is that the correlating vectors are oblique projections of the signature vectors onto appropriate spaces. Furthermore, we show that each branch of the decorrelator consists of an oblique projection onto the space spanned by the corresponding user's signature vector along the space spanned by the interferers, followed by a correlator with correlating vector equal to the corresponding user's signature vector.