Effects of sampling and quantization on single-tone frequency estimation

Abstract

The effects of sampling and quantization on frequency estimation for a single sinusoid are investigated. Cramér-Rao bound for 1-bit quantization is derived and compared with the limit of infinite quantization. It is found that 1-bit quantization gives a slightly worse performance, however, with a dramatic increase of variance at certain frequencies. This can be avoided by using four times oversampling. The effect of sampling when using nonideal antialiasing lowpass filters is therefore investigated through derivation of the Cramér-Rao lower bounds. Finally, fast estimators for 1-bit quantization, in particular, correlation-based estimators, are derived , and their performance is investigated. The paper is concluded with simulation results for fourtimes oversampled 1-bit quantization.

SNR-Aided Accurate Phase Estimation in 1-Bit Software-Defined Receiver

“…(15b) The mean values of the I-Q channel outputs are the same as (11) and (13), respectively. The variance can be expressed as…”

“…First, the problem of parameter estimation for a single sinusoid was previously investigated in [8]- [11]. In [11], Cramér-Rao bound (CRB) of 1-bit quantization could be derived under the assumption of independence between quantized samples. The effects of 1-bit sampling and quantization were also discussed.…”

Linear prediction approach to oversampling parameter estimation for multiple complex sinusoids

“…Generally, the sampling rate is susceptible to the sampler performance and the special application. For example, in the 1-bit quantization frequency estimation, a sampling rate larger than 4 times the Nyquist frequency is required [9]. It has been proved [18] that the CRLB for angular frequency estimation decreases at the rate of O(N −3 ) asymptotically.…”

“…In signal processing, oversampling is the process of sampling a signal with a sampling frequency significantly higher than the Nyquist frequency of the signal being sampled. In 1-bit quantization spectral estimation [9], it is used to compress the spectrum, and to avoid the singular frequency which incurs high estimation error. In [10], oversampling is utilized to obtain more data in a fixed duration, and is expected to improve the estimation accuracy according to Cramér-Rao lower bound (CRLB) [11] analysis.…”

Statistical results for system identification based on quantized observations

“…For more information on sign quantizers, see for instance Host-Madsen and Händel (2000), where the ml and crlb are calculated for estimating the frequency of a sinusoidal in noise. Second, for multi-level quantization, the log-likelihood is…”