Minimum outage probability for the relay channel under individual power constraints

In this letter, minimum outage probability for a fading relay channel is considered for long-term individual power constraints (IPC) at the source and the relay. By utilizing Lagrange multiplier theory, it is shown that solving the IPC problem is equivalent to solving a weighted sum power constrained (wSPC) problem. Opportunistic decode and forward (ODF), and simplified ODF (SODF) protocol performances are investigated and compared with a lower bound on outage probability, under both individual and sum power constraints (SPC). It is shown that, under IPC, the source or the relay does not necessarily deplete its average power constraint, but some power can remain unutilized for ODF or SODF.