Higher-order Narrow-band Array Processing

This communication deals with narrow-band array processing using higher-order cumulants. A versatile tensor formalism is presented and adopted throughout to handle higher-order statistics of complex multivariates. We essentially focus on the use 4th-order cumulants for source localization in the spirit of the modern "subspace" techniques. We discuss "full cumulant tensor" solutions and their "downsized" versions in matrix form. Higher-order cumulants are usually advocated for in presence of additive Gaussian noise, but other potential advantages often are overlooked : non-Gaussian sensor noise cancellation, "more sources than sensors" ability, blind identification. This is discussed via the notion of fourth-order signal subspace. The paper is not intended as being a review, but other related approaches based on higher-order statistics are briefly reported.