### Data PDF of Circular ARMA process

Based on (16.5), (9.9), we may write

 (9.18)

Note that although (9.18) is written in terms of the frequency domain quantity , it is a PDF of and integrates to precicely 1 over in . The circular ARMA process is useful for CR bound analysis and as a way to obtain ML ARMA parameter estimates because it is more tractable than (9.6).

A simplification is possible for large valid for circular ARMA processes. Note that

 (9.19)

Problem 1   Show (9.19). Hint: write the time-domain equivalent of (9.18) (similar to section 9.2.3 but with circulant matrix ), then note that the determinant of is approximated by . From there, deduce the result.

Baggenstoss 2017-05-19