Error performance of multi-hopping half-duplex relay networks

We derive a compact description of error performance of a multi-hopping half-duplex relay network, where each relay performs decoding. For this, we introduce the event of consecutive error which describes that a decoding error might not be corrected by chance at a subsequent relay node. Furthermore, two tight upper bounds are derived. The first one is based on the union bound method and the second one describes the probability that there occurs at least one decoding error in the network. General expressions on error probability in slow, flat fading Rayleigh channels are developed as well and adopted to the chosen transmission scenarios to ensure fair comparison with respect to the amount of transmitted data and system energy. It is shown and evaluated by simulations that relaying achieves better results on error performance even if no spatial diversity is employed. Gains are evaluated by a new metric called asymptotic probability gain.