A Study of Optimization Problem for Amplify-and-Forward Relaying over Weibull Fading Channels with Multiple Antennas

We consider power allocation (PA) and relay positioning in a dual-hop regenerative relaying system with multi-antenna destination node in Weibull fading environment. With the fixed relay location, adaptive PA at the source and relay nodes under joint power constraint and with the aim to minimize the average error probability at high signal-to-noise ratios (SNRs) is presented. Then considering fixed PA, the optimal relay location is derived. Thereafter, we propose to jointly optimize the PA and relay positioning. Numerical simulations are also provided to validate the analytical results, and comparisons between the different optimization schemes and their performance are presented. Results show that optimum PA brings only coding gain, while optimum relay positioning yields diversity gains as well. Also, joint optimization improves both, the diversity gain and the coding gain. Furthermore, results illustrate that the proposed adaptive algorithms outperform uniform schemes.