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New, exact closed-form expressions are derived for the Probability Density Function (PDF) and the Cumulative Distribution Function (CDF) of the instantaneous end-to-end Signal-to-Noise Ratio (SNR) of Amplify-and-Forward (AF) relaying systems with "Full" selection diversity. The direct path, from the source to the destination, as well as multiple dual-hop paths, through intermediate relays, are considered in the selection set. The selection process follows a maximum SNR policy, such that the path of the maximum end-to-end SNR is used as the communication link, whether this path is the direct path or one of the dual-hop paths.
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