Asymptotic Parameter Tracking Performance with Measurement Data of 1-Bit Resolution

Manuel Stein, Alexander Kurzl, Amine Mezghani, Josef A. Nossek

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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/π-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 □ {2/π}-0.98 dB. By simulating non-linear filtering algorithms for a satellite-based ranging application 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.

Original languageEnglish
Article number7163356
Pages (from-to)6086-6095
Number of pages10
JournalIEEE Transactions on Signal Processing
Issue number22
StatePublished - 15 Nov 2015


  • 1-bit ADC
  • channel estimation
  • hard-limiter
  • parameter estimation
  • ranging
  • tracking


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