NDA Timing Estimation with 1-bit Quantization and Oversampling at the Receiver

Abstract

As communication systems require ever higher bandwidths, designing digital receivers based on 1-bit quantization and oversampling w.r.t. the transmit signal bandwidth can reduce circuit complexity and lower the energy consumption. This is due to the fact that high resolution in time domain is less difficult to achieve than high resolution in amplitude domain. However, as 1-bit quantization is a highly non-linear operation, standard channel parameter estimation algorithms for digital receivers cannot be applied. In this paper we consider an unknown phase rotation and an unknown timing offset at the receiver. Furthermore, we assume that the receiver applies uniform phase and sample dithering, which can be implemented by sampling at an irrational normalized intermediate frequency and with an irrational oversampling factor, respectively. Starting from the least squares objective function, we derive a phase independent, non-data aided (NDA) timing estimator. Considering sample dithering, we prove that the estimator is consistent, even if the noise is colored due to oversampling w.r.t. the signal bandwidth. Moreover, we numerically evaluate the variance of the estimator and compare it to the Cramer-Rao lower bound. We find that the qualitative behavior is similar to the Oerder&Meyr estimator that is often used in the unquantized case and that oversampling can significantly improve the performance.