Signal-to-Noise ratio requirements for wireless relay networks

We develop and analyze expressions on the required instantaneous signal-to-noise ratios for wireless relay networks in this paper. Two basic schemes are studied, namely the one-relay case and the two-relay case. The latter can further be divided into a two-phase and a three-phase scheme, respectively. In the two-phase scheme both relays are only allowed to transmit with half the power in order to ensure fair comparison between the different schemes. Moreover, for the one-relay case and the two-phase scheme, each terminal must serve double the target rate, whereas in the three-phase scheme, each terminal has to serve three times the target rate to ensure that the amount of transmitted information remains constant. We show the following correspondences when decode-and-forward relaying and selection combining is applied in Rayleigh fading environments: For the one-relay case gamma prop 1/radic(pout) and for both two-relay schemes gamma prop 1/³radic(pout)ldr We further show that an increase in data rate of 1 bit/s/Hz results in a required increase of signal-to-noise ratio of 6 dB for the one-relay case and the two-phase two-relay scheme, and an increase of 9 dB for the three-phase two-relay scheme.