On intraference and its implications in complex-valued signal processing

We introduce the concept of intra-ference in order to quantify the degree to which the integrity of bivariate (or complex) sources is preserved in applications based on matrix decompositions of bivariate data. This is achieved by examining the pseudocovariance matrix of noncircular complex sources, and by recognising that the pseudocovariance is intrinsically complex valued. We illuminate how the existing decompositions such as the strong uncorrelating transform (SUT) not only decorrelate the bivariate sources from one another, but also decorrelate and scatter the data channels within each bivariate source, thus violating source integrity. Examples showing that the intra-ference arises due to the phase ambiguity in the existing matrix decompositions support the approach.