Blind second-order identification of FIR channels: forced cyclostationarity and structured subspace method

We address the problem of blind second-order equalization of scalar-valued polynomial channels. When an almost periodic deterministic function modulates the initial symbol sequence, the observation exhibits second-order cyclostationarity. This property is shown to give rise to a structured spectral factorization problem. The identification of the unknown channel is then always possible via a structured version of the subspace method. No assumption on the channel is required, except the knowledge of a lower bound of the order. The estimate is consistent, and this property remains unchanged in the presence of stationary noise and when the symbols are colored.