# Low-Complexity Blind Parameter Estimation in Wireless Systems with Noisy Sparse Signals

## TL;DR

This paper introduces low-complexity blind estimators for noise power, signal power, SNR, and MSE in wireless systems with sparse signals, enabling improved parameter tracking and signal recovery without additional pilot overhead.

## Contribution

It proposes novel blind estimators leveraging data sparsity, with theoretical analysis and practical applications in millimeter-wave and cell-free wireless systems.

## Key findings

- Estimators accurately track system parameters in noisy, sparse data environments.
- Application examples show improved channel estimation accuracy.
- Estimators operate with low computational complexity.

## Abstract

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.