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In this paper, the authors 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, they present a novel approximation method in the series expansion for the error function. Then, they 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.
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