Tightened upper bounds for distributed Alamouti´s code with a non-regenerative relay

In this paper, we consider a cooperative system with distributed Alamouti´s code that includes a source, a non-regenerative relay and a destination. The relay uses the amplify-and-forward protocol and all links experience independent Rayleigh fading. First, we present a novel approximation method in the series expansion for the error function. Then, we derive, based on the conditional expectation method, an upper bound of the BER performance in a summation of number of easily calculated components. This bound exhibits the even approximation errors for all SNR range and approaches to the exact system performance when the number of components increases. The upper bound is validated with simulation results and it is more accurate and flexible compared with other approximation methods.