Differential modulation for decode-and-forward multiple relay systems

In this paper, differential modulation and demodulation in a multiple relay system using either the decode-and-forward (DF) protocol or the selection relaying (SR) protocol, are investigated. For the DF protocol, the detectors at the destination take the average bit error probabilities (BEPs) of all the source-relay transmissions into account. For a DF single relay system, the exact BEP and its approximation at high signal-to-noise ratio (SNR) are obtained. The approximation of the BEP at high SNR shows explicitly the diversity order and the different effects of the source-relay link and the relay-destination link on the end-to-end error performance. For a DF multiple relay system, a Chernoff upper bound on the BEP and a high SNR approximation for the BEP are obtained. For the SR protocol, some computational complexity is shifted from the destination to all the relays. Each relay computes the instantaneous BEPs of the source-relay transmissions, and uses the instantaneous BEPs to decide whether to transmit or remain silent. The destination performs simple maximal ratio combining (MRC) reception whose error performance is analyzed at high SNR. It shows from an error probability perspective that the SR protocol offers a space diversity order equal to the number of all the potential cooperating nodes.