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Algorithms and Applications for Estimating the Standard Deviation of AWGN when Observations are not Signal-Free

Algorithms and Applications for Estimating the Standard Deviation of AWGN when Observations are not Signal-Free,10.4304/jcp.2.7.1-10,Journal of Comput

Algorithms and Applications for Estimating the Standard Deviation of AWGN when Observations are not Signal-Free   (Citations: 5)
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Consider observations where random signals are randomly present or absent in independent and additive white Gaussian noise (AWGN). By using a recently estab- lished limit theorem, we introduce a new estimator for the estimation of the noise standard deviation when the signals are less present than absent and have unknown probability distributions. The bias, the consistency and the minimum attainable mean square estimation error of the estimator we propose are still unknown. However, the experimental results that are presented are very promising. First, when the Minimum- Probability-of-Error decision scheme for the non-coherent detection of modulated sinusoidal carriers in independent AWGN is tuned with the outcome of our estimator instead of the true value of the noise standard deviation, the Binary Error Rate tends to the optimal error probability when the number of observations is large enough. Second, given some speech signal corrupted by independent AWGN, our estimator can be used to estimate the noise standard deviation so as to adjust the standard Wiener filtering of the noisy speech. The objective performance measurements obtained by so proceeding are very close to those achieved when the Wiener filtering is tuned with the true value of the noise standard deviation.
Journal: Journal of Computers - JCP , vol. 2, no. 7, pp. 1-10, 2007
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    • ...MC-ESE is a non parametric estimator that exploits the recent results in statistical decision and est imation theory developed in [1, 2]. The second method, purely dedicated to OFDM signals, exploits the redundancy induced by the cyclic prefix (CP)...
    • ...In order t o analyse to what extent the asymptotic conditions involved by this convergence can be relaxed for applications in radar and speech processing where observations are complex values and signals of interest are mostly less present than absent, the authors in [1, 2] experimentally address the case where d = 2, the upper-bound p is 1/2, r = 1 and s = 0, a rather natural choice with respect to the inequalities above that r and s must ...
    • ...When p ≤ 1/2, d = 2, r = 1 and s = 0, the experimental results in [1, 2] suggest that the asymptotic conditions about the amplitudes of the signals can be relaxed significantly...
    • ...According to these results, an estimate of th e OFDM noise standard deviation can be computed as follows (see [2] for further details):...
    • ...reader is asked to refer to [1, 2] for the computation of the search interval required for this minimisation...

    François-Xavier Socheleauet al. Blind noise variance estimation for OFDMA signals

    • ...Estimators of the noise standard deviation, derived from this theoretical result, are proposed in [11] and [12]...
    • ...According to the theoretical and experimental results presented in [11] and [12], these estimators can be expected to perform well even when many signal coefficients are present among the detail wavelet coefficients...

    Dominique Pastoret al. SPARSITY FROM BINARY HYPOTHESIS TESTING AND APPLICATION TO NON-PARAMET...

    • ...In fact, on the basis of the theoretical background presented in this chapter, applications to speech processing [25], as a continuation of [23], and to orthogonal frequency division multiple access [32]–a promising multiple access technology for new generation wireless networks–have been proposed in [25]...

    Dominique Pastoret al. Wavelet Shrinkage: From Sparsity and Robust Testing to Smooth Adaptati...

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