Cooperative Transmission Distance in Multi-relay Communication Systems

In this paper, we present the cooperative transmission distance with multiple decode-and-forward relays in a communication system. The investigation of the transmission distance is focused on how to achieve its maximum by minimizing the average symbol-error-ratio (SER) at the receiver. Firstly, we provide a closed-form formulation of the average SER in a multi-relay system, in which a signal is modulated and demodulated with M-quadrature amplitude modulation and is broadcast by the source and relays through narrow-band Rayleigh fading channels. Secondly, taking asymptotically tight approximation, we optimize the power allocation between the source and relays to minimize the SER. Thirdly, we provide a general expression of the transmission distance with the SER. Finally, we discuss the cooperative transmission distance with different parameters.