Outage capacity of a cooperative scheme with binary input and a simple relay

Cooperative communications is a rapidly evolving research area. Most of the cooperative protocols that have appeared in the literature assume slow flat fading channels and Gaussian codebooks. In many cases the relays must fully decode their input. It is well known that cooperation is most effective at low SNR where binary input is optimal. Furthermore, energy and cost effectiveness make simple relays most attractive. Motivated by these two facts, we consider a half-duplex orthogonal cooperation protocol with binary input and relays that simply forward their symbol-by-symbol decisions to the destination which performs algebraic decoding; we call it demodulate-and-forward (DmF). We assume independent slow Rayleigh flat fading channels with full channel state information (CSI) at the destination and compute an upper bound for the outage capacity of the DmF protocol. For low SNR and small outage probability, we derive a simple approximation to this bound. For comparison purposes, we compute the outage capacity of direct binary transmission and a simple low-SNR small-outage-probability approximation. We observe that for very small outage probability the DmF protocol significantly outperforms direct transmission. However, for (relatively) high outage probability, the opposite may happen.