Linearly constrained minimum-‘normalised variance’ beamforming against heavy-tailed impulsive noise of unknown statistics

A new beamforming approach to combat the arbitrary unknown heavy-tailed impulsive noises including all α-stable noises with infinite variance or infinite mean is presented. The new approach, termed as linearly constrained minimum-‘normalized variance’ beamformer (LCMNV), is formulated as one to minimise the normalised variance of the beamformer's output, subject to a pre-specified set of linear constraints. The normalised variance is defined as a pseudo-correlation function of the instantaneously adaptive, infinity-norm snapshot-normalised data, as an alternative to the customary ‘fractional lower-order moments’ (FLOM) for heavy-tailed impulsive noise environments. The proposed beamformer is in essence second-order statistics based, and produces an instantaneously scaled beamformer output. The LCMNV beamformer outperforms the FLOM beamformer with the following advantages: (i) computationally simpler with a closed-form solution, (ii) requiring no prior information or estimation of the effective characteristic exponents of the impulsive noises, (iii) applicable to a wider class of heavy-tailed impulsive noises and (iv) offering better interference-rejection ability.