Design factors for dual-hop AF systems with partial relay selection

In dual-hop AF relaying systems with partial relay selection, a relaying node is selected from N available relays based on a maximum relay-to-destination signal-to-noise ratio (SNR) policy. Exact closed-form expressions are obtained for the probability density function (PDF) and the cumulative distribution function (CDF) of the instantaneous end-to-end SNR of dual-hop amplify-and-forward (AF) relaying systems with partial relay selection, operating over Nakagami-m fading channels. Outage probability and average symbol error probability are calculated using the derived PDF and CDF expressions, and Monte Carlo simulation results are used to verify the results. Exact results permit accurate comparisons of the performances of dual-hop AF relaying systems without relay selection, and dual-hop AF relaying systems with partial relay selection. It is shown that the diversity gain of dual-hop AF systems with partial relay selection is proportional to the minimum of the fading parameter of the source-to-relay link, m₁, and the fading parameter of the relay-to-destination fading link, m₂, multiplied by the selection pool size, N, i.e. min{m₁,N_m2}. It is shown also that although the performance of partial relay selection systems is improved by increasing the selection pool size, a relay selection pool of more than m₁/₂ relays is not of practical benefit.