Exact Error Analysis for the Piecewise Linear Combiner for Decode and Forward Cooperation with Two Relays

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Exact expressions are obtained for the Bit Error Rate (BER) for coherent and non-coherent Decode and Forward (DF) cooperative systems with two relays. The Piecewise Linear (PL) combiner, a close approximation to the Maximum Likelihood (ML) detector, is employed at the receiver. BER analysis is done using a contour integral approach for evaluating the Gil-Pelaez integral involving the Characteristic Function (CF) of the decision variable. Previous attempts relied on a direct approach, that imposed restrictions on the location of the relays. In this paper, this restriction has now been removed.