Adaptive signal processing

(communications) The design of adaptive systems for signal-processing applications.

Signal processing deals with the extraction of information from signals. The devices that perform this task can be physical hardware devices, specialized software codes, or combinations of both. Some notable applications, in areas ranging from biomedical engineering to wireless communications, include the suppression of interference arising from noisy measurement sensors, the elimination of distortions introduced when signals travel through transmission channels, and the recovery of signals embedded in a multitude of echoes created by multipath effects in mobile communications.

Statistically based systems

Any functional system is expected to meet certain performance specifications. The requirements, as well as the design methodology, vary according to the nature of the end application. One distinctive design methodology, which dominated much of the earlier work in the information sciences, especially in the 1950s and 1960s, is based on statistical considerations. This framework assumes the availability of information in advance about the statistical nature of the signals involved, and then proceeds to design systems that optimize some statistical criterion. The resulting optimal designs are, in general, complex to implement. Only in special, yet important cases have they led to successful breakthroughs culminating with the Wiener and Kalman filters.

Moreover, in many situations a design that is motivated by statistical considerations may not be immediately feasible, because complete knowledge of the necessary statistical information may not be available. It may even happen that the statistical conditions vary with time. It therefore may be expected, in these scenarios, that the performance of any statistically based optimal design will degrade as the real physical application deviates from the modeling assumptions.

Adaptive systems

Adaptive systems are devices that adjust themselves to an ever-changing environment; the structure of an adaptive system changes in such a way that its performance improves through a continuing interaction with its surroundings. Its superior performance in nonstationary environments results from its ability to track slow variations in the statistics of the signals and to continually seek optimal designs.

Adaptive signal processing deals with the design of adaptive systems for signal-processing applications. Related issues arise in control design, where the objective is to alter the behavior of a system, and lead to the study of adaptive control strategies; the main issue is the stability of the system under feedback. See also Adaptive control.

Operation

The operation of an adaptive system can be illustrated with a classical example in system identification. The illustration shows a plant (or system) whose input-output behavior is unknown and may even be time variant. The objective is to design an adaptive system that provides a good approximation to the input-output map of the plant. For this purpose, the plant is excited by a known input signal, and the response is taken as a reference signal. Moreover, a structure is chosen for the adaptive system, say a finite-impulse response structure of adequate length, and it is excited by the same input signal as the plant. At each time instant the output of the finite-impulse response system is compared with the reference signal, and the resulting error signal is used to change the coefficients of the finite-impulse response configuration. This learning process is continued over time, and the output of the adaptive system is expected to provide better tracking of the plant output as time progresses, especially when the structure of the plant is time invariant or varies only slowly with time.

Adaptive system identification.