Optimization of ARMA(p,q) Models for SISO Multipath Fading Channel Simulation with Arbitrary Correlation

An ARMA(p,q) model parameterization method is outlined and proposed for approximating the Clarke\´s theoretical autocorrelation function. The method uses a strategy that consists of computing the AR coefficients in a preliminary stage and then, in a subsequent stage, computing the MA coefficients. In the first stage it considers a "redesigned" least squares modified Yule Walker equations estimator for determining the AR coefficients, and in the second stage it uses the Durbin\´s method for computing the MA coefficients. An ARMA(7,6) model and an ARMA(14,13) model are obtained for approximating the Clarke\´s theoretical correlation statistics considering a nominal discrete-time maximum Doppler frequency of f_D=0.05. The accuracy of the fitting provided with the two obtained ARMA(p,q) models is compared with results from the literature. Both the ARMA(7,6) and the ARMA(14,13) models provide very good fitting.