Computational noise effects on adaptive filter algorithms

Finite word length arithmetic roundoff noise in adaptive filter algorithms results in statistical variations in the filter weight vector about the infinite precision arithmetic weight vector. These roundoff errors may be modeled as a statistically non stationary driving noise affecting weight mean and covariance convergence. Mean and covariance expressions and bounds are desired for word lengths in fixed-point arithmetic by making use of multiplication roundoff error models. The adaptive filter algorithms consist of the LMS algorithm, the Widrow-Hoff LMS algorithm, pilot-vector algorithm and clipped vector algorithm. All of these algorithms can be implemented on-line and real-time. However, only the behavior of the LMS algorithm is reported here. The implementation of the adaptive filter algorithms in finite word length arithmetic is most evident in minicomputer, microprocessor, and dedicated digital signal processors for on-line real-time signal identification and parameter estimation in many disciplines. Radar signal processing, adaptive beam forming, acoustic signal identification, communication channel enhancement have a definite need for advanced filtering concepts. Our adaptive algorithms are typically employed in these filter configurations. These filters can also be employed in phase distortion equalizers. A particular advantage of these filters is that they can be trained to equalize a variety of distortions. Should a particular distortion scenario change in time, the filters can be made to easily adapt to the new problem.