Polar coordinate quantizers that minimize mean-squared error - Scharf, Louis L., author; Voran, Stephen D., author; IEEE, publisher (Colorado State University. Libraries, 1994)
A quantizer for complex data is defined by a partition of the complex plane and a representation point associated with each cell of the partition. A polar coordinate quantizer independently quantizes the magnitude and phase angle of complex data. We derive design equations for minimum mean-squared error polar coordinate quantizers and report some interesting theoretical results on their performance, including performance limits for "phase-only" representations. The results provide a concrete example of a biased estimator whose mean-squared error is smaller than that of any unbiased estimator. Quantizer design examples show the relative importance of magnitude and phase encoding.
Keywords: encoding; approximation theory; analogue-digital conversion