System Identification using LMS based Adaptive Filters

Adaptive filtering techniques are used in a wide range of applications, including echo cancellation, adaptive equalization, adaptive noise cancellation, and adaptive beamforming, while this paper presents the application of adaptive filtering to system identification problem. System identification will help in finding the system characteristics well. System identification approximates an unknown system. System identification finds numerous applications in communications. In the system identification application, the desired signal is the output of the unknown system when excited by a broadband signal, in most cases a white-noise signal. The broadband signal is also used as input for the adaptive filter. When the output MSE is minimized, the adaptive filter represents a model for the unknown system. The earlier methods of system identification use complex numerical and statistical methods by observing the output for different inputs. The present solution to the system identification problem is by the use of so called neural networks or genetic algorithm. Correspondingly adaptive filtering technique best suites the situation. Adaptive algorithms are categorized into a number of types. In this paper a detailed classification of adaptive algorithms is presented. A number of LMS based algorithms are used in the implementation of system identification. The simulation results of these algorithms are shown in the paper.