N Plus Normalized Threshold Opportunistic Relay Selection with Outdated Channel State Information

In this paper, we propose a new multiple relay selection scheme with the availability of outdated channel state information (CSI) for decode and forward (DaF) relay systems, namely the N plus normalized threshold opportunistic relay selection (N+NT-ORS). In particular, we first opportunistically select N best relays out of all relays in the decoding subset with respect to relay-to-destination signal-to-noise ratios (SNRs). Then the ratios of the SNRs on the rest of the relays in the decoding subset to that of the N-th highest SNR are tested against a normalized threshold μ ∈ [0,1] and only those relays passing this test are selected in addition to the N best relays. Through the derivation of the moment generating function (MGF) of SNR, together with the relationship between MGF and outage probability, we obtain a closed-form expression for the outage probability. In addition to analyzing the asymptotic diversity order for N+NTS-ORS, we also outline a distributed N+NT ORS selection protocol without the need of global CSI at each relay. Numerical results confirm the correctness of the derivation and show how N+NT-ORS outperforms its existing counterparts.