Splitting the recursive least-squares algorithm

Exponentially weighted recursive least-squares (RLS) algorithms are commonly used for fast adaptation, in many cases the input signals are continuous-time. Then either a fully analog implementation of the RLS algorithm is applied or the input data are sampled by analog-to-digital (AD) converters to be processed digitally. Although a digital realization is usually the preferred choice, it becomes unfeasible for high-frequency input signals since fast AD converters are needed. This paper proposes a hybrid analog/digital approach essentially allowing the AD conversion rate to be as low as the update-rate of the RLS algorithm. This is basically accomplished by sampling exponentially weighted correlation products instead of the input signals. Furthermore, we propose a mixed-signal filter exactly realizing the exponential weighting according to the cost function. Applying this approach to an interference cancelling problem demonstrates its performance and attractiveness regarding implementation.