Magnitude/Phase Quantization of Independent Gaussian Variates

The performance of two-dimensional polar quantization of independent Gaussian variates is evaluated as a possible improvement over one-dimensional quantizers. The distortion measure is assumed to be squared error. The quantizers are a generalization of more restrictive polar quantizers analyzed previously, admitting a differing number of phase positions in each magnitude sector. Results are provided for several bit rates up to 2.5 bits/sample. The optimal design always performs as well or better than the restricted polar quantizer, and, in the cases analyzed, slightly outperforms the Max (single-sample) quantizers for a fixed number of levels.