Quantization noise effects in the complex LMS adaptive algorithm-linearization using dither

The insertion of dither at the input to a quantizer is a well-known technique for extending the dynamic range of that operation. Employment of this technique requires that some method be used to reduce or eliminate the effects of the dither signal on the system. A common method is to shape the spectrum of the dither so that it will be rejected. In this paper, dither is used to "linearize" the rounding quantizer at each accumulator input of the vector complex LMS adaptation algorithm, and the effects of dither and quantization noise on steady-state mean square error are studied. It is shown that if the dither vector is temporally white, then the increase in steady-state mean square error due to dither is larger than that due to quantization noise, regardless of the spatial properties of the dither vector. However, it is also shown that the affects of dither can be made neglegible compared to that of quantization noise by properly shaping the temporal spectrum of the dither vector.