Higher order cumulants-based least squares for nonminimum-phase systems identification

A third-order cumulants based adaptive recursive least-squares (CRLS) algorithm for the identification of time-invariant nonminimum phase systems, as well as time-variant nonminimum phase systems, has been successfully developed. As higher order cumulants preserve both the magnitude and the phase information of received signals, they have been considered as powerful signal processing tools for nonminimum phase systems. In this paper, the development of the CRLS algorithm is described and examined. A cost function based on the third-order cumulant and the third-order cross cumulant is defined for the development of the CRLS system identification algorithm. The CRLS algorithm is then applied to different moving average (MA) and autoregressive moving average (ARMA) models. In the case of identifying the parameters of an MA model, a direct application of the CRLS algorithm is adequate. When dealing with an ARMA model, the poles and the zeros are estimated separately. In estimating the zeros of the ARMA model, the construction of a residual time-series sequence for the MA part is required. Simulation results indicate that the CRLS algorithm is capable of identifying nonminimum phase and time-varying systems. In addition, because of the third-order cumulant properties, the CRLS algorithm can suppress Gaussian noise and is capable of providing an unbiased estimate in a noisy environment.