Optimal Amplify-and-Forward Scheme for Parallel Relay Networks with Correlated Relay Noise

Abstract

This paper studies a parallel relay network where the relays employ an amplify-and-forward (AF) relaying scheme and are subjected to individual power constraints. We consider correlated effective relay noise arising from practical scenarios when the relays are exposed to common interferers. Assuming that the noise covariance and the full channel state information are available, we investigate the problem of finding the optimal AF scheme in terms of maximum end-to-end transmission rate. It is shown that the maximization problem can be equivalently transformed to a convex semi-definite program, which can be efficiently solved. Then an upper bound on the maximum achievable AF rate of this network is provided to further evaluate the performance of the optimal AF scheme. It is proved that the upper bound can be asymptotically achieved in two special regimes when the transmit power of the source node or the relays is sufficiently large. Finally, both theoretical and numerical results are given to show that, on average, noise correlation is beneficial to the transmission ratewhether the relays know the noise covariance matrix or not.

Design of amplify‐and‐forward relaying schemes for layered relay networks

“…Before we go any further, we first reformulate (9) in a more compact matrix form. It can be easily found that treating the scaling factors at the other relays as constants, the network can be regarded as a dual‐hop one [24]. Using more compact matrix formulation, the equivalent channel vector at the first hop is given by and the channel vector at the second hop is given by .…”