Impact of noise frequency selectivity into the performance of AF relaying systems

In this paper, we present accurate performance analysis of amplify-and-forward (AF) relaying systems by introducing the effect of multipath flat Rayleigh fading channels on the additive white Gaussian noise (AWGN). The second hop channel is seen by the transmitted signal as flat fading when the signal bandwidth is less than the coherence bandwidth. However, the second hop channel is frequency selective fading to the AWGN noise since the AWGN bandwidth is much higher than the coherence bandwidth of the channel. Therefore, taking into account accurate statistical model for the received AWGN noise, a new exact expressions for the moment generating function (MGF) and the complementary error function of the end-to-end signal-to-noise ratio (SNR) are derived, which led to a unified precise expressions for the average bit error rate (BER) analysis of multilevel quadrature amplitude modulation (MQAM) signaling and the ergodic capacity evaluations of AF relaying systems over multipath flat fading channels. Numerical results reveals that the AWGN noise is underestimated since there is a huge degradation in BER analysis when the noise frequency selectivity is taken into account. Further, it is also seen that the noise selectivity has a little effect on the ergodic capacity of AF relaying systems.