The exact average bit error probability (BEP) performance of decode-and-forward (DF) cooperative systems with multiple relays for binary phase-shift keying (BPSK) signals in Rayleigh fading channels is derived. Two types of receivers, i.e., a λ-maximal ratio combining (λ-MRC) receiver and a piecewise linear (PL) receiver, are examined.
The characteristic functions (CFs) of the decision statistics are derived and used for the derivation of the BEPs. Closed-form integral-free solutions for the BEPs are obtained.