Time Varying Channel Estimation for DSTC-Based Relay Networks: Tracking, Smoothing and BCRBs

In this paper, we examine the channel estimation in an amplify-and-forward (AF) one-way relay network (OWRN) under time selective flat fading scenario, where the distributed space-time coding (DSTC) is adopted at relay nodes. Different from most existing works, our target is to estimate and track the individual channels of each relay hop instead of the composite channels. To reduce the number of the channel parameters to be estimated, we apply the polynomial basis-expansion-model (P-BEM) and convert the problem to estimating the channel coefficient-vectors (called in-BEM-CVs) of each relay hop. With the aid of the autoregressive (AR) model, we formulate the dynamic state space for the in-BEM-CV estimation. Specifically, we adopt the unscented Kalman filter (UKF) to track the in-BEM-CV dynamic variations in an forward manner, and utilize the unscented Rauch-Tung-Striebel smoother (URTSS) to smooth the UKF´s estimations in an backward manner. To make the study complete, we also derive Bayesian Cramér lower bounds (BCRBs) for the in-BEM-CV estimation. Finally, numerical results are provided to corroborate the proposed studies.