  The problem of signal parameter estimation and tracking with measurement data
of low resolution is considered. In comparison to an ideal receiver with
infinite receive resolution, the performance loss of a simplistic receiver with
1-bit resolution is investigated. For the case where the measurement data is
preprocessed by a symmetric hard-limiting device with 1-bit output, it is
well-understood that the performance for low SNR channel parameter estimation
degrades moderately by 2/pi (-1.96 dB). Here we show that the 1-bit
quantization loss can be significantly smaller if information about the
temporal evolution of the channel parameters is taken into account in the form
of a state-space model. By the analysis of a Bayesian bound for the achievable
tracking performance, we attain the result that the quantization loss in dB is
in general smaller by a factor of two if the channel evolution is slow. For the
low SNR regime, this is equivalent to a reduced loss of sqrt(2/pi) (-0.98 dB).
By simulating non-linear filtering algorithms for a satellite-based ranging
application (GPS) and a UWB channel estimation problem, both with
low-complexity 1-bit analog-to-digital converter (ADC) at the receiver, we
verify that the analytical characterization of the tracking error is accurate.
This shows that the performance loss due to observations with low amplitude
resolution can, in practice, be much less pronounced than indicated by
classical results. Finally, we discuss the implication of the result for medium
SNR applications like channel estimation in the context of mobile wireless
communications.
