Performance Analysis of Multiple-Relay Cooperative Systems With Signal Space Diversity

In this paper, the idea of signal space diversity is adopted to achieve a full-rate multiple-relay cooperative communication system. The data symbols are rotated at the source, before transmission, by a certain angle to permit signal detection either by the in-phase component or by the quadratic component. The real and imaginary parts of two consecutive symbols are transmitted by the source and $L$ relays. In the first time slot, the real part of the first symbol and the imaginary part of the second symbol are transmitted from the source to the destination and the relay(s) . In the second time slot, the best relay among all decode-and-forward relays forwards the imaginary part of the first symbol and the real part of the second symbol to the destination. The error probability performance of two relaying modes, referred to as reactive and proactive, is analyzed in this paper. In reactive cooperation, the best relay among all relays that decode the source signals correctly participates in forwarding a message to the destination in a preallocated time slot. On the other hand, in the proactive mode, a specific relay is selected, prior to transmission, to participate in the relaying phase. Additionally, asymptotic error probability expressions are derived for both relaying modes. Moreover, power allocation optimization at the source and the relays is carried out using the asymptotic-error-probability-derived formulas. Finally, the outage probability for both relaying modes is investigated, and approximate closed-form expressions are derived.