Splitting the Least-mean-square Algorithm

The least-mean-square (LMS) algorithm is an adaptation scheme widely used in practice due to its simplicity. In some applications the involved signals are continuous-time. Then, usually either a fully analog implementation of the LMS algorithm is applied or the input data are sampled by analog-to-digital (AD) converters to be processed digitally. A purely digital realization is most often the preferred choice, however, it becomes costly for high-frequency input signals since fast AD converters are needed. In this paper we propose a hybrid analog/digital approach allowing the AD conversion rate to be as low as the update-rate of the LMS algorithm. We demonstrate the advantage of this approach applying it to an interference cancellation problem occurring in wireline communications: the sampling rate of the AD converters is reduced by a factor of 250.