Variance analysis is an important research topic to assess the quality of estimators. In this paper, we analyze the performance of the least ℓp-norm estimator in the presence of mixture of generalized Gaussian (MGG) noise. In the case of known density parameters, the variance expression of the ℓp-norm minimizer is first derived, for the general complex-valued signal model. Since the formula is a function of p, the optimal value of p corresponding to the minimum variance is then investigated. Simulation results show the correctness of our study and the near-optimality of the ℓp-norm minimizer compared with Cramér-Rao lower bound.

This paper discusses a nonlinear function for independent component analysis to process complex-valued signals in frequency-domain blind source separation. Conventionally, nonlinear functions based on the Cartesian coordinates are widely used. However, such functions have a convergence problem. In this paper, we propose a more appropriate nonlinear function that is based on the polar coordinates of a complex number. In addition, we show that the difference between the two types of functions arises from the assumed densities of independent components. Our discussion is supported by several experimental results for separating speech signals, which show that the polar type nonlinear functions behave better than the Cartesian type.