A finite precision analysis of the block-gradient adaptive data-driven echo canceller

The block-gradient (block LMS) algorithm´s finite precision performance in the data-driven echo canceller application is analyzed. From both the analysis and simulation results, it was found that the block LMS requires significantly less precision than the standard LMS algorithm. The analysis also shows how higher convergence and tracking speeds may be traded for an improvement in precision requirements. The authors derive formulae that can be used to accurately compute echo rejection levels as a function of precision, signal powers, step-size, block length, and echo canceller length. The utility of the formulae is demonstrated by showing performance levels for a typical V.32bis full-duplex voiceband modem operating at a transmission rate of 14.4 kbit/s (7200 Hz sampling rate), and for a high-speed digital subscriber line echo canceller operating at a sampling rate of 400 kHz