Exact analysis of the piecewise linear combiner for decode and forward cooperation with three relays

Exact expressions are obtained for the bit error rate (BER) for coherent and noncoherent decode and forward (DF) cooperative systems with upto three relays between the source and destination. The piecewise linear (PL) combiner 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. This removes restrictions on relay location, imposed by the direct approach. Simulation results are provided to support the analysis and the relay diversity gain is demonstrated through BER plots