Two weighted selection combining (WSC) schemes are proposed for a differential decode-and-forward relaying system in Rayleigh fading channels. Compared to the conventional selection combining scheme, the decision variable of the relay link is multiplied by a scale factor to combat the error propagation phenomenon. Average bit-error rate (ABER) expressions of the two proposed WSC schemes are derived in closed-form and verified by simulation results. For the second WSC scheme, asymptotic ABER expression and diversity order are derived to gain more insight into this scheme. Moreover, it is demonstrated that both WSC schemes can overcome the extra noise amplification induced by the link adaptive relaying scheme. The first WSC scheme is slightly inferior to the second one, which has a higher complexity. Both proposed WSC schemes outperform the conventional selection combining scheme.
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