An MSE-based theoretical limit to the performance of linear source extraction and equalization methods in undermodeled scenarios

Abstract

This paper presents a simple and, to a certain extent, surprising result for Source Separation in an underdetermined scenario: without loss of generality, under the restriction that all sources have unit power, the sum of the residual mean-squared errors (MMSE) obtained after the estimation of all the sources is given by the difference between the number of sources and the number of sensors. This result can be extended to the case of single-input single-output (SISO) equalization, in which the obtained limit depends on the relationship between the length of the channel and equalizer impulse responses.