Ergodic Channel Capacity of an Amplify-and-Forward Relay System at Low SNR in a Generic Noise Environment

In this correspondence, the ergodic channel capacity at a low signal-to-noise ratio (SNR) is established for variable-gain and fixed-gain amplify-and-forward (AF) relay systems in a generic noise environment. Long-term path loss and short-term channel fading are considered in evaluating the capacity. Since analytic solutions to the capacity are difficult to obtain, we seek approximations and derive corresponding optimal amplification coefficients and power loadings. Useful insights are revealed for the impact of generic noise and relay locations on the capacity and relay-operating status for both variable-gain and fixed-gain relaying. Simulations are provided to verify the derived results.