Threshold detection in correlated non-Gaussian noise fields

Middleton, David

doi:10.1109/18.391244

Cited by 19 publications

(16 citation statements)

References 19 publications

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“…which means that the MSNR solution for the SL is different from the MMSE solution in (14). However, when the optimal thresholds are sufficiently higher than the input standard deviation σ y , the power of the distortion noise is quite low with E{x 2 SL } ≈ k 2 x σ 2 X , which together with (38) means that the two optimal thresholds are very close if k x ≈ 1.…”

Section: Maximum Snr (Msnr) Estimatorsmentioning

confidence: 99%

“…In algorithm A1, ε represents the accuracy that is requested to the approximated solution to stop within n max iterations. Obviously, other iterative numerical approaches can also be used to solve (14), such as the Newton-Rapson method [18] to find the root of F (mse) SL (α) − α = 0. Note that the local convexity of J SL (α) is also confirmed by the MSE plots in Section VIII: thus, it makes sense that for increasing α (starting from 0) the first minimum reached in (11) by the iterative algorithm is also the optimal solution, as confirmed by all the simulation results in Section VIII.…”

Section: Bayesian Soft Limiter Estimator (Sle)mentioning

confidence: 99%

“…To prove the existence of a solution of the fixed point equation (14), it can be observed that the relative minima and maxima of F…”

Section: Appendix B Sle Derivationmentioning

confidence: 99%

See 2 more Smart Citations

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

Banelli

2013

IEEE Signal Process. Lett.

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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).

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Section: Maximum Snr (Msnr) Estimatorsmentioning

confidence: 99%

Section: Bayesian Soft Limiter Estimator (Sle)mentioning

confidence: 99%

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

Banelli

2013

IEEE Signal Process. Lett.

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“…In recent two decades, there has been a tremendous interest in studying the symmetric α ‐stable ( SαS ) distribution which is considered as a generalisation of Gaussian distribution [1–3]. Moreover, it has been tested and found to match the real data with excellent fidelity [8–11], similar to that of the broadly accepted Middleton models [12, 13].…”

Section: Introductionmentioning

confidence: 99%

Near‐optimal detection with constant false alarm ratio in varying impulsive interference

Sun

Wang³

et al. 2013

IET signal process.

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As an important class of non-Gaussian statistic model, α-stable distribution has received much attention because of its generality to represent impulsive interference. Unfortunately, it does not have a closed-form probability density function (PDF) except for a few cases. For this reason, suboptimal zero-memory non-linearity (ZMNL) function has to be used as an approximation in designing locally optimal detector, such as classical Cauchy and Gaussian-tailed ZMNL (GZMNL). To enhance the performance of detectors, the authors first investigate the approximate PDFs for the symmetric α-stable. In particular, a simplified version of Cauchy-Gaussian mixture (CGM) model, called bi-parameter CGM (BCGM) model is detailed. This BCGM model has a concise closed-form, and hence is more tractable than the classical Gaussian mixture model and CGM model. Then based on the preset false alarm ratio (FAR), the test threshold is adaptively evaluated by using BCGM to maintain a constant FAR. The authors further devise an algebraic-tailed ZMNL (AZMNL) with a simplified form. Simulation results show that the detector with AZMNL outperforms the ones with classical Cauchy and GZMNL, and achieves near-optimal performance in varying impulsive interference.

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“…Since we consider the detection of both coherent and incoherent (general and narrowband) signals in the critical limiting threshold régime, where analytical methods are known to exist for predicting performance (see [1], [8]- [9], [20], [23]- [24], [27], [32]- [39]), we must expand the log-likelihood ratio, logA n , about the zero signal (S=0) in order to obtain the optimum receiver in either observation mode. The expansion of logA n in the coherent mode contains a random term 0(S) plus a remainder term and similarly in the incoherent mode the expansion contains a random term 0(S 2 ) plus a remainder term.…”

Section: Approach and Contributionsmentioning

confidence: 99%

Locally Optimum Bayes Signal Detection in Non - Additive Non - Gaussian Noise Backgrounds

Κοκκινοσ¹

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Threshold detection in correlated non-Gaussian noise fields

Cited by 19 publications

References 19 publications

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

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

Near‐optimal detection with constant false alarm ratio in varying impulsive interference

Locally Optimum Bayes Signal Detection in Non - Additive Non - Gaussian Noise Backgrounds

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