Online and Offline Bayesian Cramér–Rao Bounds for Time-Varying Channel Estimation in One-Way Relay Networks

In this paper, we examine the Bayesian Cramér-Rao lower bounds (BCRBs) for the channel estimation in an amplify-and-forward (AF) one-way relay network (OWRN) under the time-selective flat-fading scenario, where the superimposed training is adopted at the relay node in order to achieve the individual channel estimation. We formulate the nonlinear dynamic state space for the individual channels and derive the online/offline BCRBs for the fully data-aided (FDA) channel estimator and the partially data-aided (PDA) estimator. The former estimator has full knowledge about the symbols from both the source and the relay, while the latter one has imperfect statistical information about the data of the source, and possesses full information of the symbols superimposed by the relay. For the FDA scenario, we calculate the closed-form online/offline BCRBs and analyze the effect of the nodes´ mobility on the BCRB performance, while for the PDA case, with the assumption of square QAM constellation set at the source, we design one framework to numerically evaluate online/offline BCRBs and analyze the asymptotic BCRBs at high SNRs particularly for the 4-QAM constellation set. Finally, numerical results are provided to corroborate the proposed studies.