Linearly constrained minimum-"geometric power" adaptive beamforming using logarithmic moments of data containing heavy-tailed noise of unknown statistics

This letter presents a new adaptive beamforming approach, against arbitrary algebraically tailed impulse noise of otherwise unknown statistics. (This includes all symmetric α -stable noises with infinite variance or even infinite mean.) This new beamformer iteratively minimizes the "geometric power" of the beamformer's output Y, subject to a prespecified set of linear constraints. This geometric power is defined in terms of the logarithmic moment E\{log|Y|}, as an alternative to the customary "fractional lower order moments" (FLOM). This logarithmic-moment beamformer offers these advantages over the FLOM beamformer: 1) simpler computationally in general, 2) needing no prior information nor estimation of the numerical value of the impulse noise's effective characteristic exponent, and 3) applicable to a wider class of heavy-tailed impulse noises.