In this paper, our aim is to propose a fully distributed adaptive algorithm for learning the parameters of a widely linear autoregressive moving average model by measurements collected by a network. To this end, we consider a connected network where every node uses the augmented complex adaptive infinite impulse response (ACA-IIR) filter as the learning rule. We firstly formulate the learning problem as an optimization problem and resort to stochastic gradient optimization argument to solve it and derive the proposed algorithm, which will be referred to as diffusion ACAIIR (DACA-IIR) algorithm. We also introduce a reduced-complexity version of the DACA-IIR algorithm. We use both synthetic and real-world signals in our simulations where the results show that the proposed cooperative algorithm outperforms the noncooperative solution.
