Risk-unbiased bound for random signal estimation in the presence of unknown deterministic channel

Estimation of a signal transmitted through a communication channel usually involves channel identification. This scenario can be modeled as random parameter estimation in the presence of unknown deterministic parameter. In this paper, we address the question of how accurately one can estimate a random signal intercepted by an array of sensors, subject to an unknown deterministic array response. The commonly used hybrid Cramér-Rao bound (HCRB) is restricted to mean-unbiased estimation of all model parameters with no distinction of their character and leads to optimistic and unachievable performance analysis. Instead, A Bayesian Cramér-Rao (CR)- type bound on the mean-square-error (MSE) is derived for the considered scenario. The bound is based on the risk-unbiased bound (RUB) which assumes risk-unbiased estimation of the signals of interest. Simulations show that the RUB provides a tight and achievable performance analysis for the MSE of conventional hybrid estimators.