Outage minimization with limited feedback for the fading relay channel

In this paper, we consider practical methods to approach the theoretical performance limits in the fading relay channel under different assumptions of transmitter channel knowledge. Specifically, we consider two degrees of transmitter channel knowledge: 1) perfect feedback is available and power control is employed and 2) no channel state knowledge is available at the transmitters and only spatial power allocation is possible. First, when perfect feedback is available, the optimal power control policy determines the ultimate limits of performance for constant rate transmission in the slow fading environment. However, in practice, perfect channel knowledge is not possible at the transmitters due to the finite capacity of the feedback links. We find practical methods to approach this performance limit through the use of power control with finite rate feedback. The finite-rate feedback results are shown for the low-complexity, full-diversity amplify-and-forward (AF) protocol. Interestingly, we see that only a few feedback bits are needed to achieve most of the gains of the optimal perfect feedback power control algorithm. Second, we consider the performance limit when the transmitters have no channel state knowledge and derive the optimal spatial power allocation between the source and relay for a given sum power constraint for the AF protocol. For most practical cases of interest, equal power allocation between the source and relay is shown to be nearly optimal. Our work suggests that there is minimal power savings from using spatial power allocation at the transmitters. To obtain large performance improvements over constant power transmission, it is imperative to have feedback for each realization of the channel state to allow for temporal power control.