Variance analysis of unbiased complex-valued ℓ_p-norm minimizer

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 ℓ_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 Cramér-Rao lower bound.