Asymptotic analysis and design of restricted uniform polar quantizer for Gaussian sources

In this paper, an asymptotically optimal restricted uniform polar quantizer (RUPQ) is designed for a Gaussian source subject to the mean-squared error (MSE) criterion. The asymptotic analysis of the RUPQ, provided in the paper, for the first time includes the overload distortion. This enables derivation of the closed-form formulas for the straightforward design of the asymptotically optimal RUPQ, In particular, the closed-form formulas are derived for the asymptotically optimal support limit of the magnitude quantizer and asymptotically optimal rate allocation between the magnitude and phase quantizers. Moreover, our analysis shows that the overload distortion of the asymptotically optimal RUPQ cannot be neglected for rates R <= 5.5 bit/sample in cases when the relative error in calculating signal to quantization noise ratio (SQNR) due to overload distortion neglecting ranges up to 1%. Further, it is shown that the closed-form SQNR formula derived for the asymptotically optimal RUPQ, useful for performance assessment, is reasonably accurate for rates R > 3.5 bit/sample. Results obtained analytically and verified through simulations show that the proposed RUPQ outperforms existing RUPQs in terms of SQNR. The performances near the optimum along with the simple design of the proposed RUPQ model provide its application in various systems such as cellular systems and ultrasound medical systems, in digital spectrum analyzer and in digital processing of orthogonal frequency division multiplexing (OFDM) modulated signals. (C) 2015 Elsevier Inc. All rights reserved.