Minimum mean-square error echo cancellation and equalization for digital subscriber line transmission. I. Theory and computation

An integral part of an ISDN (integrated services digital network) is the provision of full-duplex digital transmission capability over voice-grade metallic subscriber lines with all the associated disturbances from echo, intersymbol interference, and crosstalk, among other things. The author presents a theory for analyzing the optimal performance, in the MMSE (minimum-mean-squared error) sense, of full-duplex transceiver structures incorporating echo cancelers and decision-feedback equalizers. The theory augments previously published results by allowing a colored input signal and a fractionally spaced multitap MMSE forward filter in the decision-feedback equalizer. The properties of and efficient ways of calculating the MMSE solutions for various types of line codes, including the precoded partial-response codes and the block codes, are investigated. The author discusses how the MMSE is related to the ubiquitous SNR (signal-to-noise ratio) measure and the concerns associated with using it to gauge the transmission performance