Training slot allocation for mitigating estimation error propagation in a two-hop relaying system

This paper analyzes a channel estimation error propagation problem for a two-hop amplify-and-forward (AF) relaying system using two-phase. Channel estimator in each phase is obtained by the linear minimum mean squared error (LMMSE) method. The inaccuracy of estimation of the relay-to-destination (RtD) channel in the first phase affects the estimation of the source-to-relay (StR) channel in the second phase, making it more erroneous than the first phase. We derive an close-form expression for the averaged Bayesian mean-square estimation error (ABMSE) of both phases in terms of the length of source and relay training slots, based on which an iterative searching algorithm is then proposed which optimally allocates the training slots to each phase such that the estimation errors are balanced for both phases. Analysis shows how the ABMSE of StD channel estimation varies with the length of relay training slots, the length of source training slots, the relay amplification gain, and the channel prior information respectively. This scheme is shown to be substantially better than a random allocation scheme.