Computation of a useful Cramer-Rao bound for multichannel ARMA parameter estimation

It has been shown earlier that the problem of multichannel autoregressive moving average (ARMA) parameter estimation can be tackled in a computationally efficient way by converting the given process into an equivalent scalar, periodic ARMA process. This correspondence presents methods to compute the Cramer-Rao bound associated with the identification of the scalar ARMA equivalent of a given multichannel ARMA process. The elements of matrix are obtained by a few very simple operations like periodic AR filtering of certain downsampled versions of the input and output sequences and then cross-correlating the filter outputs. The filter is easily obtainable from the model equation and is common for all the parameters. Fig. 4. Curves of probability of resolution versus SNR (in dB) for various null-spectra, / M U ( # ) , /MN(0),/Mu(0)>/min(0)> and / m a x ( 0 ) , when N = 100, L = 10, AT = 2(0i = 15° and 02 = 17°. Each curve was obtained at interval of 2 dB and each point was obtained from 500 trials).