Bayesian Estimation of a Gaussian Source in Middleton's Class-A Impulsive Noise

Abstract

The paper focuses on minimum mean square error (MMSE) Bayesian estimation for a Gaussian source impaired by additive Middleton's Class-A impulsive noise. In addition to the optimal Bayesian estimator, the paper considers also the soft-limiter and the blanker, which are two popular suboptimal estimators characterized by very low complexity. The MMSE-optimum thresholds for such suboptimal estimators are obtained by practical iterative algorithms with fast convergence. The paper derives also the optimal thresholds according to a maximum-SNR (MSNR) criterion, and establishes connections with the MMSE criterion. Furthermore, closed form analytical expressions are derived for the MSE and the SNR of all the suboptimal estimators, which perfectly match simulation results. Noteworthy, these results can be applied to characterize the receiving performance of any multicarrier system impaired by a Gaussianmixture noise, such as asymmetric digital subscriber lines (ADSL) and power-line communications (PLC).

Real-Time Generation of Standard-Compliant DVB-T Signals

“…In addition, power allocation algorithms can be exploited without changing the DVB-T receiver. Another possibility is the investigation of the effect of impulsive noise [34], non-Gaussian channels, and quantization errors [35], on the DVB-T received signal. Furthermore, by means of our SDR-based design, the DVB-T signal can first be received by a custom DVB-T receiver and then retransmitted to a single destination by a regenerative relay, nearby to the receiver.…”

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

“…Proof: Using the Sherman-Morrison formula [17], (32) becomes [15] that is different from the MSNR solution [16]. Therefore, the equivalence between MMSE and MSNR estimators can be invalid for non-BEM-based suboptimal estimators.…”

Performance Analysis of Distributed Wireless Sensor Networks for Gaussian Source Estimation in the Presence of Impulsive Noise

“…However, the performance of estimation techniques in the presence of impulsive noise is not widely acknowledged. Recently, the authors in [9] considered the MMSE optimal Bayesian estimation (OBE) for a Gaussian source impaired by Middleton class-A impulsive noise. It is shown that the performance of the proposed MMSE OBE strictly depends on the statistical characteristics of the received signal.…”

“…The obtained results showed that the performance improvement of the optimal MMSE estimator over the linear MMSE (LMMSE) estimator under this condition is substantial. However, the analyses in [9], [10] are restricted to the point-to-point scenario and the effect of channel fading is not considered. To the best of authors knowledge, no result exists for the distributed estimation of Gaussian sources in the presence of impulsive noise under Rayleigh fading.…”

“…Here, we provide a mathematical framework for the performance analysis of distributed estimation of a scalar Gaussian source impaired by Middleton class-A noise. A Middleton class-A process is a simple and effective way to model an impulsive noise channel [5], [9]. Our work is an extension of [9] to the distributed WSN scenario.…”