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New trends in deterministic lower bounds and SNR threshold estimation: From derivable bounds to conjectural bounds

It is well known that in non-linear estimation problems the ML estimator exhibits a threshold effect, i.e. a rapid deterioration of estimation accuracy below a certain SNR or number of snapshots. This effect is caused by outliers and is not captured by standard tools such as the Cramér-Rao bound (CRB). The search of the SNR threshold value can be achieved with the help of approximations of the Barankin bound (BB) proposed by many authors. These approximations may result from linear or non-línear transformation (discrete or integral) of the uniform unbiasedness constraint introduced by Barankin. Additionally, the strong analogy between derivations of deterministic bounds and Bayesian bounds of the Weiss-Weinstein family has led us to propose a conjectural bound which outperforms existing ones for SNR threshold prediction.