Joint Phase and Timing Estimation With 1-Bit Quantization and Oversampling

Abstract

Digital receivers based on 1-bit quantization and oversampling w.r.t. the transmit signal bandwidth promise lower energy consumption. However, since 1-bit quantization is a highly non-linear operation, standard off the shelf receiver algorithms cannot be applied. In this paper we consider an unknown phase rotation and timing offset and a fully digital receiver. To reduce the non-linear behavior introduced by 1-bit quantization, 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. Based on the least squares objective function we derive a typical digital matched filter receiver with a data- and timing-aided phase estimator and square time recovery based timing estimation. Our main contribution is to show that both estimators are consistent under very general assumptions, e.g., arbitrary colored noise and stationary ergodic transmit symbols. Performance evaluations are done via simulations and are compared against a numerically computable upper bound of the Cramér–Rao lower bound. For low signal-to-noise ratio the estimators perform well but for high signal-to-noise ratio they run into an error floor. The performance loss of the phase estimator due to decision-directed operation or estimated timing information is marginal.