Two-way denoise-and-forward network coding opportunistic relaying with jointing adaptive modulation relay selection criterions

To improve the performance of the two-way denoise-and-forward network coding opportunistic relaying systems (TW-DNF-OR), two novel best-relay selection criterions are presented, which are the jointing adaptive modulation max-min criterion (AM-MM) and the jointing adaptive modulation maximum harmonic mean criterion (AM-MHM). In the proposed AM-MM and AM-MHM criterions, the effect of the modulation schemes used at both sources is exploited perfectly by integrating the adaptive modulation with the max-min and maximum harmonic mean criterions. On the basis of the proposed AM-MM and AM-MHM criterions, the authors analyse the symbol error probability (SEP) of the TW-DNF-OR systems under independent and non-identically distributed Rayleigh fading channels, and obtain the analytical expressions to the approximate upper bounds of the overall average SEPs. The comparison analyses show that the average SEP of TW-DNF-OR is improved greatly when the proposed jointing adaptive modulation best relay selection criterions are used. Moreover, in certain channel realisations or signal-to-noise ratio regions, the adaptive modulation non-selection TW-DNF-OR systems outperform the conventional best relay selection systems in which the adaptive modulation is not integrated with the best relay selection criterions.