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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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Signal-to-Noise Ratio Aware Minimaxity and Higher-Order Asymptotics
Since its development, the minimax framework has been one of the cornerstones of theoretical statistics, and has contributed to the popularity of many well-known estimators, such as the regularized M-estimators for high-dimensional problems. In this paper, we will first show through the example of sparse Gaussian sequence model, that the theoretical results under the classical minimax framework are insufficient for explaining empirical observations. In particular, both hard and soft thresholding estimators are (asymptotically) minimax, however, in practice they often exhibit sub-optimal performances at various signal-to-noise ratio (SNR) levels. The first contribution of this paper is to demonstrate that this issue can be resolved if the signal-to-noise ratio is taken into account in the construction of the parameter space. We call the resulting minimax framework the signal-to-noise ratio aware minimaxity. The second contribution of this paper is to showcase how one can use higher-order asymptotics to obtain accurate approximations of the SNR-aware minimax risk and discover minimax estimators. The theoretical findings obtained from this refined minimax framework provide new insights and practical guidance for the estimation of sparse signals.
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- PAR ID:
- 10520300
- Publisher / Repository:
- Institute of Electrical and Electronics Engineers (IEEE)
- Date Published:
- Journal Name:
- IEEE Transactions on Information Theory
- Volume:
- 70
- Issue:
- 5
- ISSN:
- 0018-9448
- Page Range / eLocation ID:
- 3538 to 3566
- Subject(s) / Keyword(s):
- Minimaxity signal-to-noise ratio sparsity soft thresholding hard thresholding linear shrinkage higher-order asymptotics Gaussian sequence model.
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/TIT.2023.3347493
