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Baseband processing algorithms often require knowledge of the noise power, signal power, or signal-to-noise ratio (SNR). In practice, these parameters are typically unknown and must be estimated. Furthermore, the mean-square error (MSE) is a desirable metric to be minimized in a variety of estimation and signal recovery algorithms. However, the MSE cannot directly be used as it depends on the true signal that is generally unknown to the estimator. In this paper, we propose novel blind estimators for the average noise power, average receive signal power, SNR, and MSE. The proposed estimators can be computed at low complexity and solely rely on the large-dimensional and sparse nature of the processed data. Our estimators can be used (i) to quickly track some of the key system parameters while avoiding additional pilot overhead, (ii) to design low-complexity nonparametric algorithms that require such quantities, and (iii) to accelerate more sophisticated estimation or recovery algorithms. We conduct a theoretical analysis of the proposed estimators for a Bernoulli complex Gaussian (BCG) prior, and we demonstrate their efficacy via synthetic experiments. We also provide three application examples that deviate from the BCG prior in millimeter-wave multi-antenna and cell-free wireless systems for which we develop nonparametric denoising algorithms that improve channel-estimation accuracy with a performance comparable to denoisers that assume perfect knowledge of the system parameters.
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This content will become publicly available on April 29, 2026
Autocovariance function estimation via difference schemes for a semiparametric change point model with m‐dependent errors
We discuss a broad class of difference‐based estimators of the autocovariance function in a semiparametric regression model where the signal consists of the sum of a smooth function and another stepwise function whose number of jumps and locations are unknown (change points) while the errors are stationary and ‐dependent. We establish that the influence of the smooth part of the signal over the bias of our estimators is negligible; this is a general result as it does not depend on the distribution of the errors. We show that the influence of the unknown smooth function is negligible also in the mean squared error (MSE) of our estimators. Although we assumed Gaussian errors to derive the latter result, our finite sample studies suggest that the class of proposed estimators still show small MSE when the errors are not Gaussian. Our simulation study also demonstrates that, when the error process is mis‐specified as an AR instead of an ‐dependent process, our proposed method can estimate autocovariances about as well as some methods specifically designed for the AR(1) case, and sometimes even better than them. We also allow both the number of change points and the magnitude of the largest jump grow with the sample size . In this case, we provide conditions on the interplay between the growth rate of these two quantities as well as the vanishing rate of the modulus of continuity (of the signal's smooth part) that ensure consistency of our autocovariance estimators. As an application, we use our approach to provide a better understanding of the possible autocovariance structure of a time series of global averaged annual temperature anomalies. Finally, the R package dbacf complements this article.
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- Award ID(s):
- 2311103
- PAR ID:
- 10608707
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Australian & New Zealand Journal of Statistics
- ISSN:
- 1369-1473
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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