Variance Mismatch Analysis of Unrestricted Polar Quantization for Gaussian Source

In this letter, asymptotic formulas are derived for signal to quantization noise ratio (SQNR) of two unrestricted polar quantizers (UPQs) for the case where designed-for and applied-to Gaussian sources have different variances. It is shown that the limitation in the variance mismatch analysis observed in one of the UPQs can be overcome by the constrained application of asymptotic approximations and by optimizing the last magnitude reconstruction level subsequently. The derived formulas are a useful analytical tool for determining the effect of variance mismatch on SQNR in unrestricted polar quantization for Gaussian source.