Exact error analysis for the piecewise linear combiner for decode and forward cooperation with two relays

Exact expressions are obtained for the bit error rate (BER) for coherent and noncoherent 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. Through simulation results, we verify the validity of the derived analytical expressions.