On the Effect of Outdated Channel Estimation in Variable Gain Relaying: Error Performance and PAPR

For the conventional three-node amplify-and-forward (AF) relaying setup, we investigate the effect of imperfect channel state information (CSI) at the relay on the overall performance. In particular, we consider variable gain (a.k.a, CSI-assisted) AF relaying and derive expressions for the outage and the error probability for the case where the relay gain is adjusted based on outdated estimates of the source-relay channel, when operating over Nakagami-m fading. For the case of Rayleigh fading in the source-relay link, we show that the results can be extended to the versatile case of imperfect CSI, where the estimation error is caused either by additive white Gaussian noise or by quantization noise. The obtained expressions are functions of the correlation coefficient between the actual source-relay channel and its corresponding estimate. We also optimize the power allocation for minimization of the outage probability under a total transmit power constraint. Numerical results reveal a considerable degradation of the overall performance, when CSI acquisition is not perfect. Moreover, it is shown that the average relay transmit power is affected when the CSI is outdated, a fact which impacts the design of variable gain relaying in practice. Since outdated CSI leads to fluctuations of the relay transmit power, we derive expressions for the complementary cumulative distribution function (CCDF) of the peak-to-average-power ratio (PAPR) at the relay. By comparing the error probability and the CCDF of the PAPR of variable gain relaying with those of fixed gain relaying, we shed some light onto the following question: How reliable has the instantaneous CSI at the relay to be for variable gain relaying to be preferable over fixed gain relaying, which requires only statistical CSI?