How sensitive is compute-and-forward to channel estimation errors?

We investigate the sensitivity of Compute-and-Forward (C&F) to channel estimation errors. More specifically, a general formula for the computation rate region of a C&F relay, suffering from imperfect channel estimation, is derived, which is then tightly approximated for Gaussian distributed channel estimation errors. Furthermore, a closed-form expression for the distribution of the C&F rate loss is presented, which can be efficiently used to compute relevant statistical parameters, such as the mean rate loss. Numerical and simulation results highlight the high sensitivity of the overall network performance to channel estimation errors.