Ben–gurion University of the Negev Faculty of Engineering Sciences

In this thesis, the problem of minimum-variance unbiased (MVU) parameter estimation in low signal-to-noise ratios (SNRs) or few number of samples was studied. Performance lower bounds are commonly used in statistical signal processing for system design and analysis. In most practical problems there exists a threshold SNR below which the performance of the estimators, such as the maximum likelihood estimator (MLE) rapidly degrades. This phenomenon cannot be predicted by the Cramér-Rao bound, therefore, different approximations of the Barankin bound are usually used to find the threshold region. In this work, we show some popular problems in which the uniformly unbiased assumption is too demanding, and in fact no uniformly unbiased estimator exists. In particular, we analytically show that in periodic problems the Barankin bound can go to infinity by taking test-points at specific locations. This proof was extended also to the case of Gaussian models with bounded expectation which carries the information about the unknown parameters of interest. The conclusions of this work are as follows. First, calculation of the Barankin bound is heavily dependent on the chosen test-points, and in some problems it can go to infinity. Accordingly, the Barankin bound in these problems is meaningless. Second, the uniformly unbiasedness constraint is too demanding and may not be satisfied in many practical cases. Therefore, new performance lower bounds with modified unbiasedness constraints should be investigated.