Synthesis of Multichannel Autoregressive Random Processes and Ergodicity Considerations

Abstract
In this paper, a method is presented for synthesizing multichannel autogressive random processes. The procedure allows for variable temporal and cross-correlation properties subject to specific constraint conditions for correlation functions. Expressions for the ergodic series are also developed providing a performance measure to specify the sample integration sizes required to achieve a specific variance of the time-averaged correlation function estimates. A unique aspect of this development is the determination of the functional dependence of the ergodic series in terms of the temporal correlation and variances of the processes. As a result, this analysis provides an analytic description which quantitatively assesses the ergodicity of the auto- and cross- correlation functions in terms of these fundamental process parameters. Thus, the variation of the process statistics based on time averages from those based on ensemble averages is given a more quantitative description than previously noted.

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