On the Equivalence of Maximum SNR and MMSE Estimation: Applications to Additive Non-Gaussian Channels and Quantized Observations

  title={On the Equivalence of Maximum SNR and MMSE Estimation: Applications to Additive Non-Gaussian Channels and Quantized Observations},
  author={Luca Rugini and Paolo Banelli},
  journal={IEEE Transactions on Signal Processing},
  • L. Rugini, P. Banelli
  • Published 19 May 2016
  • Computer Science, Mathematics
  • IEEE Transactions on Signal Processing
The minimum mean-squared error (MMSE) is one of the most popular criteria for Bayesian estimation. Conversely, the signal-to-noise ratio (SNR) is a typical performance criterion in communications, radar, and generally detection theory. In this paper, we first formalize an SNR criterion to design an estimator, and then we prove that there exists an equivalence between MMSE and maximum-SNR estimators, for any statistics. We also extend this equivalence to specific classes of suboptimal estimators… 

Figures and Tables from this paper

Multiple-Threshold Estimators for Impulsive Noise Suppression in Multicarrier Communications
Multicarrier wireless communication systems, which usually operate over frequency-selective fading channels, are practically also impaired by environmental impulsive noise. In order to boost the
GMM-based Symbol Error Rate Prediction for Multicarrier Systems with Impulsive Noise Suppression
Close form expressions for the SER are derived both for non-fading and frequency-selective Rayleigh and Rician fading channels affected by impulsive noise which is represented by GMMs, thus including Bernoulli-Gaussian (BG), Middleton Class-A, as well as (approximated) alpha-stable noise.
Performance of MAP Channel Estimator in Power Line Communication with OFDM under Impulsive Noise
The results show that the MAP estimator which is designed with the assumption of white Gaussian noise has a satisfactory performance even under heavy impulsive noise.
Centralized and Decentralized Channel Estimation in FDD Multi-User Massive MIMO Systems
We design a centralized and a decentralized variational Bayesian learning (Cand D-VBL) algorithms for the base station (BS) of a frequency division duplex massive multiple input multiple output
Adaptive Temporal Matched Filtering for Noise Suppression in Fiber Optic Distributed Acoustic Sensing
The fundamental theory underlying the algorithm, which is based on signal-to-noise ratio (SNR) maximization, is presented, and the efficacy of the algorithm is demonstrated with laboratory experiments and field tests.
Robust Bayesian Beamforming for Sources at Different Distances with Applications in Urban Monitoring
This work proposes an iterative algorithm for spatial filter for localization and separation of acoustic sources that is robust against deviations in manifold model, can deal with sources at different distances and power levels, and does not require an a priori known number of sources.
Pseudorange Measurement Method Based on AIS Signals
The test results show that the pseudorange measurement accuracy was better than 28 m (σ) without any modification of the existing AIS system and the algorithm can greatly improve the accuracy of pseudorange estimation under low signal-to-noise ratio (SNR) conditions.
Speech Enhancement Based on Constrained Low-rank Sparse Matrix Decomposition Integrated with Temporal Continuity Regularisation
This paper develops an alternative optimisation algorithm for noisy spectrogram decomposition by means of TCCLSMD, which can lead to more stable and reasonable results than the existing LSMD algorithm.


Estimation in Gaussian Noise: Properties of the Minimum Mean-Square Error
It is shown that the minimum mean-square error (MMSE) of estimating an arbitrary random variable from its observation contaminated by Gaussian noise is found to be infinitely differentiable at all positive SNR, and in fact a real analytic function in SNR under mild conditions.
On Conditions for Linearity of Optimal Estimation
It is proved that the Gaussian source-channel pair is unique in the sense that it is the only source- channel pair for which the mean square error (MSE) optimal estimator is linear at more than one SNR values.
Mutual information and minimum mean-square error in Gaussian channels
A new formula is shown that connects the input-output mutual information and the minimum mean-square error (MMSE) achievable by optimal estimation of the input given the output, which has an unexpected consequence in continuous-time nonlinear estimation.
On MMSE Estimation: A Linear Model Under Gaussian Mixture Statistics
This paper provides analytical bounds for the minimum mean square error estimator (MMSE), and relates them to the signal-to-noise-ratio (SNR) in a Bayesian linear model.
Bayesian Estimation of a Gaussian Source in Middleton's Class-A Impulsive Noise
  • P. Banelli
  • Computer Science
    IEEE Signal Processing Letters
  • 2013
This letter derives the minimum mean square error (MMSE) Bayesian estimator for a Gaussian source impaired by additive Middleton's Class-A impulsive noise and considers two popular suboptimal estimators, such as the soft-limiter and the blanker, as low-complex alternatives.
Robust parameter estimation of a deterministic signal in impulsive noise
A robust class of estimators for the parameters of a deterministic signal in impulsive noise has the structure of the maximum likelihood estimator (MLE) but has an extra degree of freedom: the choice of a nonlinear function (which is different from the score function suggested by the MLE) that can be adjusted to improve robustness.
Functional Properties of Minimum Mean-Square Error and Mutual Information
It is shown that the minimum mean-square error (MMSE) is a concave functional of the input-output joint distribution and Lipschitz continuous with respect to the quadratic Wasserstein distance for peak-limited inputs.
Adaptive Noise Mitigation in Impulsive Environment: Application to Power-Line Communications
A proposal for impulse statistics estimation under severe conditions (i.e., for very rare impulse events, based on impulse detection over corrupted OFDM symbols) is made and a general scheme of automatic impulse mitigation is proposed, according to the disturbance ratio of the environment.
Mutual Information and Conditional Mean Estimation in Poisson Channels
It is found that, regardless of the statistics of theinput, the derivative of the input-output mutual information with respect to the intensity of the additive dark current can be expressed as the expected difference between the logarithm of the Input/Output Ratio and its noncausal conditional mean estimate.
MIMO radar waveform design based on mutual information and minimum mean-square error estimation
  • Yang Yang, R. Blum
  • Computer Science
    IEEE Transactions on Aerospace and Electronic Systems
  • 2007
This paper addresses the problem of radar waveform design for target identification and classification and presents an asymptotic formulation which requires less knowledge of the statistical model of the target.