Quantization effects in transform-domain normalized LMS algorithm

The quantization effects of the transform domain normalized least mean square (LMS) algorithm are studied. The discussion is limited to the systems that employ an orthonormal transform to convert the incoming samples to a set of partially uncorrelated components, to be used as actual inputs to an adaptive linear combiner. The quantization effects of the transformation coefficients and the normalized step-sizes are studied separately. The quantization effects of the system variables and its adaptive tap weights are ignored. A performance index is used to derive analytical relations for the performance losses that arise. It is shown that representations of both the normalized step-sizes and the transformation coefficients require fairly low precision. Numerical results that support the development theories are given