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 timedomain 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
20170519