Adaptive digital systems

This chapter discusses the theory of adaptive filters and related systems. An adaptive signal processing system is a system that has the ability to change its processing behavior in a way to maximize a given performance measure. An adaptive system is self-adjusting and is, by its nature, a time varying and non-linear system. A simple example of an adaptive system is the automatic gain control (AGC) in a radio receiver (RX). A generic adaptive signal processing system consists of three parts: the processor, the performance function, and the adaptation algorithm. The processor is the part of the system that is responsible for the actual processing of the input signal, thus generating the output signal. The processor can, for instance, be a digital finite impulse response (FIR) filter. The performance function is a quality measure of the adaptive system. In optimization theory, this function corresponds to the objective function and in control theory it corresponds to the cost function. The task of the adaptation algorithm is to change the parameters of the processor in such a way that the performance is maximized. This chapter also includes example applications of adaptive filters, such as interference canceling, equalizers, and beam-forming systems. Adaptive filters are common in telecommunication applications such as high-speed modems and cell phones.