Joint optimal power allocation and relay location for decode-and-forward multi-hop relaying over log-normal channel

A joint optimisation of power allocation (PA) and relay location is proposed for decode-and-forward relaying over multi-hop, independent, log-normal fading channels. Optimisation is carried out at high signal-to-noise ratio (SNR) and low SNR scenarios to minimise the outage probability with a constraint on total transmit power and end-to-end relaying distance. End-to-end average bit error rate is also minimised assuming the same constraints. Optimisation is carried out to find optimal PA (OPA) for a given relay location, optimal relay location (ORL) for a given PA and joint OPA and relay location. All the optimisation problems reformulated from the original problems are shown to be convex except relay location optimisation minimising outage probability at low SNR scenario. It is then solved using properties of concave minimisation. Optimal allocation factors do not depend on the instantaneous channel state information. It also does not depend on total available power in the system except allocation factors evaluated by optimising outage at high SNR. It is observed that OPA allocates more power to weaker links and ORL allocates less distance to weaker links. It is also observed that performance improvement increases with increase in link unbalance and distance-based allocation is most effective.