Bounds on Channel Parameter Estimation with 1-Bit Quantization and Oversampling

Abstract

In the design of energy-efficient communication systems with very high bandwidths, the analog-to-digital converter (ADC) plays a crucial role, since its energy consumption grows exponentially with the number of quantization bits. However, high resolution in time domain is less difficult to achieve than high resolution in amplitude domain. This motivates for the design of receivers with L-bit quantization and oversampling w.r.t. Nyquist rate. On the downside, standard receiver synchronization algorithms cannot be applied, since L-bit quantization is a highly non-linear function. To understand the channel parameter estimation performance of such a receiver, the Fisher information (FI) is a helpful measure. Since the closed form evaluation of the FI is not possible for correlated Gaussian noise, we give a lower bound that is an extension of a lower bound by Stein et al. to complex valued channel outputs. If the noise is white, the lower bound is tight. Furthermore, we apply the lower bound for the evaluation of the performance of carrier phase estimation of a QPSK based communication system. We show that for any SNR level oversampling reduces the performance loss due to 1-bit quantization. In the mid and low SNR regime, oversampling reduces the performance loss beyond the loss of 2π encountered in case of 1-bit quantization at Nyquist sampling in the low SNR regime.