Which cumulants should be selected for steering vector estimation?

Abstract

Cumulants have been successfully applied in the area of narrowband array signal processing. This motivates a performance analysis to find out the strengths and the weaknesses of each new algorithm. Hitherto, most of the known performance analyses are based on the asymptotic covariance of sample cumulants and are therefore called asymptotic performance analyses. Recently, explicit formulas for the finite-sample covariances of second-, third-, and fourth-order sample cumulants for any kind of signal, any kind of noise, any array shape and arbitrary sensors have been derived. These formulas enable a finite-sample performance analysis. In the single source case the steering vector is proportional to a vector built up by a product of second-order cumulants or by fourth-order cumulants. This means that the finite-sample (co)variance of the steering vector can be investigated by using the formulas for the finite-sample covariance of the second- and fourth-order sample cumulant. Hence, the open question "Which cumulants should be selected for steering vector estimation ?"-is addressed in this paper.