Circular ARMA process

Let the circular ARMA process be defined by the AR recursion for intermediate sequence $y_n$

$$y_n = -\sum_{i=1}^P \; a_i \;y_{[n-i]_N} + e_n, \;\;\;\; 0\leq n \leq N-1$$ (10.16)

followed by an MA recusion to generate $x_n$:

$$x_n = \sum_{i=0}^Q \; b_i \; y_{[n-i]_N}, \;\;\;\; 0\leq n \leq N-1$$ (10.17)

where $e_n$ are assumed to be $N(0,\sigma^2)$ iid RVs and $b_0=a_0=1$, and $[n-i]_N$ means modulo-$N$. The frequency-domain PDF for the circular ARMA process is given in (10.9)