Performance Comparison Analyses of the $$N$$ N th Best Relay Selection Schemes Over Independent and Non-identically Distributed Nakagami- $$m$$ m Fading Channels

Abstract

In this work, we study the $$N$$ N th best relay selection schemes with the consideration that in some case the best relay is unavailable due to the restriction of practical implementation. With amplify-and-forward relaying protocols, the interested $$N$$ N th best relay schemes are investigated over independent and non-identically distributed (i.ni.d) Nakagami- $$m$$ m fading channels. For such opportunistic relaying schemes, we first obtain the closed-form expressions to the probability density function (PDF) and cumulative distribution function (CDF) of the instantaneous end-to-end signal-to-noise ratio with appropriate mathematical proof. Then, with the obtained CDF and PDF, three main measurements are investigated as well as the corresponding explicit solutions, $$i.e.$$ i . e . , outage probability, average symbol error ratio (SER), and ergodic capacity. At the same time, as a byproduct, the corresponding performance metrics over Rayleigh fading are also derived. Finally, the detailed performance comparison analyses are presented under different values of $$N$$ N and different Nakagami- $$m$$ m channel fading severity parameters. The numerical results show that the increase of $$N$$ N incurs the very severe loss in performance such outage probability, SER, and ergodic capacity. However, the loss in performance can be decreased greatly when the $$N$$ N th systems have bigger fading severity factors. The derivations are of significance because the Nakagami- $$m$$ m fading spans via the fading severity parameters a wide range of fading scenarios that are typical in realistic wireless relay networks.