The topics of matrix spectral factorization (MSF) in conjunction with results from realization theory are applied here in simulating a stationary multi-input/multi-output (MIMO) linear system from a specified power sp...
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The topics of matrix spectral factorization (MSF) in conjunction with results from realization theory are applied here in simulating a stationary multi-input/multi-output (MIMO) linear system from a specified power spectral density matrix. MSF provides the appropriate transfer function matrix and Realization Theory specifies the corresponding parameters of a linear system having this transfer function. This approach can be used to correctly capture the cross correlations that exist in a multichannel vector random process (representing a particular radar target signature). Aspects of the solution to this problem are illustrated using an original representative example problem with a closed-form answer. Existing software programs for accomplishing MSF are identified and one has been successfully validated using the known closed-form solution mentioned above. A streamlined realization algorithm (offered here as the primary theoretical contribution) can be used along with the MSF computer program and can now be applied to actual radar data. Besides multichannel spectral estimation, several other important applications (some old, some new) of this same MSF solution methodology are summarized in Appendix B including extending applicability to the complex case (to handle radar polarization issues related to coherent phase processing), and finally in reexpressing second order statistics of a multichannel autoregressive moving average (ARMA) process as those of a simpler but mathematically equivalent autoregressive (AR) process of slightly higher dimensions (as another original application of the same major result offered here).
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