Istituto di Scienza e Tecnologie dell'Informazione     
Chen Y., So H., Kuruoglu E. E. Variance analysis of unbiased complex-valued lp-norm minimizer. In: Signal Processing, vol. 135 (June 2017) pp. 17 - 25. Elsevier, 2017.
Parameter estimation from noisy complex-valued measurements is a significant topic in various areas of science and engineering. In this aspect, an important goal is finding an unbiased estimator with minimum variance. Therefore, variance analysis of an estimator is desirable and of practical interest. In this paper, we concentrate on analyzing the complex-valued "p-norm minimizer with p≥1. Variance formulas for the resultant nonlinear estimators in the presence of three representative bivariate noise distributions, namely, α-stable, Student's t and mixture of generalized Gaussian models, are derived. To guarantee attaining the minimum variance for each noise process, optimum selection of p is studied, in the case of known noise statistics, such as probability density function and corresponding density parameters. All our results are confirmed by simulations and are compared with the Cramr-Rao lower bound.
URL: http://www.sciencedirect.com/science/article/pii/S016516841630370X
DOI: 10.1016/j.sigpro.2016.12.018
Subject lp-norm estimation
Impulsive distributions
Alpha-stable distribution
Generalised Gaussian distribution
Student-t distribution
Complex-valued signals
Variance analysis
G.3 PROBABILITY AND STATISTICS. Distribution functions
52A21 Finite-dimensional Banach spaces
62G05 Estimation
60E07 Infinitely divisible distributions; stable distributions

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