Asymptotic Analysis of Switched Uniform Polar Quantization for Memoryless Gaussian Source

This letter performs an asymptotic analysis of the switched uniform polar quantizer (SUPQ) composed of k asymptotically optimal unrestricted uniform polar quantizers designed for the memoryless Gaussian source. The closed-form formulas are derived for signal to quantization noise ratio (SQNR) and the number of phase levels of the quantizers constituting the SUPQ. It is studied how SQNR depends on the variance mismatch and the number of quantizers k. It is shown that with a log-uniform distribution of the variances for which the quantizers constituting the SUPQ are designed one can reduce the variance range of average-taking of SQNR.