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In Pauluzzi and Beaulieu, various SNR estimation methods are compared. Among the blind methods considered, the $M_2M_4$ estimator seemed to be unambiguously the best. However, it has been shown that the $M_2M_4$ estimator is too high for low SNR, and too low for very high SNR; see here for details. In addition, computing the estimator is kinda like walking through a minefield; there's no guarantee of existence for the system $M_2 = S+N$, $M_4 = k_a S^2 + 6SN + k_w N^2$ for arbitrary positive ${M_2, M_4, k_a, k_w}$ and hence total failure for the method is common.

It has been roughly 20 years since Pauluzzi and Beaulieu's paper. Have any advances in blind SNR estimation been made? What do experts currently regard as the gold standard in blind SNR estimation?

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