Lower bound on the mean-squared error in oversampled quantization of periodic signals using vector quantization analysis

Oversampled analog-to-digital conversion is a technique which permits high conversion resolution using coarse quantization. Classically, by lowpass filtering the quantized oversampled signal, it is possible to reduce the quantization error power in proportion to the oversampling ratio R. In other words, the reconstruction mean-squared error (MSE) is in 𝒪(R^-1). It was recently found that this error reduction is not optimal. Under certain conditions, it was shown on periodic bandlimited signals that an upper bound on the MSE of optimal reconstruction is in 𝒪(R^-2) instead of 𝒪(R ^-1). In the present paper, we prove on the same type of signals that the order 𝒪(R^-2) is the theoretical limit of reconstruction as an MSE lower bound. The proof is based on a vector-quantization approach with an analysis of partition cell density