The impact of unknown correlated Rayleigh fading on the information rates of dual-hop amplify and forward relay channels

We consider a dual-hop amplify-and-forward relaying system where the channel state is unknown to both the transmitter and the receiver. Our objective is to derive the penalty of the information rate due to the unknown channel state information. We focus on determining the compound effects of fixed-gain relaying and unknown time-varying channels on the achievable information rates of the system. We show that penalty of the information rate due to the unknown channels decays with block length and signal-to-noise ratio while it increases with normalized Doppler shift. We also derive a closed-form expression for the information penalty when the block length is large (asymptotic behavior). This derivation shows that the penalty of not knowing the mobile-fixed-mobile dual-hop relay channel can be equal to or higher than that in the direct mobile-to-mobile source-destination transmission. The additional uncertainty should be taken into account when designing cooperative systems with many relays.