Performance Lower Bounds of Blind System Identification Techniques in the Presence of Channel Order Estimation Error

In this paper, we derive two performance lower bounds for blind system identification in the presence of channel order estimation error. The first bound deals with models where both the channel and unknown symbols are deterministic, and obtained via the constrained misspecified Cramer-Rao bound (MCRB). When transmitted symbols are unknown random variables i.i.d. drawn from a stochastic Gaussian process, variance of any unbiased estimators is always higher than the second MCRB bound. Both proposed MCRB bounds reduce to the classical Cramer-Rao bounds when the channel order is known or accurately estimated. Besides, the stochastic MCRB is lower than the deterministic bound, especially at high SNRs.