Closed-form BEP of Demodulate-and-Forward using two-relay over Rayleigh fading environments

In this paper, we derive exact closed form expressions for Binary Error Probability (BEP) when using as modulation constellations Quadrature Phase Shift Keying (QPSK) in two-hop two-relay network. We consider Adaptive Demodulate-and-Forward (ADmF) for asynchronous regenerative relays. Each relay cooperates, if its received Signal-to-Noise-Ratio (SNR) corresponding to source-relay link exceeds a required threshold. When at least one relay cooperates, the destination combines the received signals using Maximum-Ratio-Combining (MRC). Otherwise, the destination receives only the source signal. A selection of numerical results is used to verify the exactness of the proposed analytical expressions.