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Low-Complexity Blind Estimator of SNR and MSE for mmWave Multi-Antenna Communications

Hanyoung Park, Ji-Woong Choi

TL;DR

The paper addresses the challenge of estimating fundamental communication metrics in mmWave systems under rapid channel fluctuations, where pilot-based methods falter due to overhead and latency. It proposes low-complexity blind estimators that exploit beamspace sparsity to separate signal and noise components, deriving a fast noise power estimator and subsequently estimating the average signal power, SNR, and a SURE-based blind MSE estimator without ground-truth signals. The key contributions are a beamspace-based noise estimator with $\mathcal{O}(M\log M)$ complexity, closed-form blind estimators for $P_x$ and $\rho$, and a single-snapshot MSE estimator integrated with the noise estimator, all avoiding iterative optimization or training. The proposed approach enables real-time, resilient parameter tracking in mmWave multi-antenna systems, with potential applicability to wideband channels via subcarrier-wise estimation and future theoretical performance analysis.

Abstract

To enhance the robustness and resilience of wireless communication and meet performance requirements, various environment-reflecting metrics, such as the signal-to-noise ratio (SNR), are utilized as the system parameter. To obtain these metrics, training signals such as pilot sequences are generally employed. However, the rapid fluctuations of the millimeter-wave (mmWave) propagation channel often degrade the accuracy of such estimations. To address this challenge, various blind estimators that operate without pilot have been considered as potential solutions. However, these algorithms often involve a training phase for machine learning or a large number of iterations, which implies prohibitive computational complexity, making them difficult to employ for real-time services and the system less resilient to dynamic environment variation. In this paper, we propose blind estimators for average noise power, signal power, SNR, and mean-square error (MSE) that do not require knowledge of the ground-truth signal or involve high computational complexity. The proposed algorithm leverages the inherent sparsity of mmWave channel in beamspace domain, which makes the signal and noise power components more distinguishable.

Low-Complexity Blind Estimator of SNR and MSE for mmWave Multi-Antenna Communications

TL;DR

The paper addresses the challenge of estimating fundamental communication metrics in mmWave systems under rapid channel fluctuations, where pilot-based methods falter due to overhead and latency. It proposes low-complexity blind estimators that exploit beamspace sparsity to separate signal and noise components, deriving a fast noise power estimator and subsequently estimating the average signal power, SNR, and a SURE-based blind MSE estimator without ground-truth signals. The key contributions are a beamspace-based noise estimator with complexity, closed-form blind estimators for and , and a single-snapshot MSE estimator integrated with the noise estimator, all avoiding iterative optimization or training. The proposed approach enables real-time, resilient parameter tracking in mmWave multi-antenna systems, with potential applicability to wideband channels via subcarrier-wise estimation and future theoretical performance analysis.

Abstract

To enhance the robustness and resilience of wireless communication and meet performance requirements, various environment-reflecting metrics, such as the signal-to-noise ratio (SNR), are utilized as the system parameter. To obtain these metrics, training signals such as pilot sequences are generally employed. However, the rapid fluctuations of the millimeter-wave (mmWave) propagation channel often degrade the accuracy of such estimations. To address this challenge, various blind estimators that operate without pilot have been considered as potential solutions. However, these algorithms often involve a training phase for machine learning or a large number of iterations, which implies prohibitive computational complexity, making them difficult to employ for real-time services and the system less resilient to dynamic environment variation. In this paper, we propose blind estimators for average noise power, signal power, SNR, and mean-square error (MSE) that do not require knowledge of the ground-truth signal or involve high computational complexity. The proposed algorithm leverages the inherent sparsity of mmWave channel in beamspace domain, which makes the signal and noise power components more distinguishable.
Paper Structure (9 sections, 2 theorems, 22 equations, 5 figures, 1 algorithm)

This paper contains 9 sections, 2 theorems, 22 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Average Noise Power Estimator
  4. Average Signal Power, SNR, and MSE Estimator
  5. Simulation Results
  6. Simulation Configuration
  7. Performance Analysis
  8. Conclusion
  9. Proof of Theorem \ref{['thm:thm1']}

Key Result

Theorem 1

Consider the signal $\mathbf{x}$ and its noisy observation $\mathbf{y}\sim\mathcal{CN}(\mathbf{x}, N_0\mathbf{I}_M)$. Let $\hat{\mathbf{x}}(\mathbf{y})$ be the denoiser function which estimates $\mathbf{x}$ from $\mathbf{y}$ with weak differentiability. Then, is an unbiased estimate of MSE. Thus, $\mathbb{E}[\mathcal{S}]=\varepsilon^2$.

Figures (5)

  • Figure 1: Power of the (a) noisy signal in the beamspace domain and (b) its sorted version, for $M=64$ and $\text{SNR}=3$ dB.
  • Figure 2: Estimated average noise power depending on SNR.
  • Figure 3: Estimated average signal power depending on SNR.
  • Figure 4: Estimated SNR depending on SNR.
  • Figure 5: Estimated MSE depending on SNR.

Theorems & Definitions (7)

  • Theorem 1: SURE
  • proof
  • Remark 1
  • Remark 2
  • Remark 3
  • Lemma 1: Stein's Lemma
  • proof