Least Squares Phase Estimation of 1-bit Quantized Signals with Phase Dithering

Abstract

When designing digital receivers for terabit communication systems, it is beneficial in terms of energy efficiency to switch from high amplitude resolution to high time resolution, i.e., using 1-bit quantization and oversampling w.r.t. the transmit signal bandwidth. However, standard receiver synchronization algorithms cannot be applied, since 1-bit quantization is a highly non-linear function. In this paper we consider a known timing offset and an unknown phase rotation at the receiver that applies 1-bit quantization, oversampling, and uniform phase dithering. We consider the cases of white and colored noise, where white noise is obtained by adapting the receive filter bandwidth to the sampling rate. Moreover, we show that the least squares estimator of the phase has a simple closed form solution and is consistent due to uniform phase dithering. Furthermore, we compare its performance to the Cramer-Rao lower bound (CRLB) and show that it asymptotically attains the CRLB at low SNR. In case the noise is white, the least squares estimator can be made asymptotically efficient for high SNR by increasing the oversampling factor. In case of colored noise, a more sophisticated estimator is required to achieve asymptotic efficiency for high SNR.