Second-Order Properties for Wireless Cooperative Systems with Rayleigh Fading

Second-order statistical parameters of wireless channels, such as level crossing rate (LCR) and average fade duration (AFD), determine how frequent and the burst length of the channel in bad conditions, so they play an important role in the performance of wireless communication systems. For user-cooperative wireless systems, due to the interactions of multiple channels, it is non-trivial to determine the LCR and AFD of the received signals, which is an open issue. In this paper, we develop an analytical framework to quantify the LCR and AFD of the amplify-and-forward (AF) cooperative system using selection combining (SC) over Rayleigh fading channels. We first analyze the statistics of the two independent fading paths, the AF relay path with a mobile-to-mobile (M2M) channel and a mobile-to-fixed (M2F) Rayleigh fading channel, and the direct path with a M2F Rayleigh fading channel. Then, we derive the expressions of the second-order statistical parameters of the AF cooperative system with SC. Numerical results verify the correctness of our model. The analytical and simulation results reveal the different effect of the motions of the source and the relay nodes, and they can be used to select better relay nodes and assist the design and optimization of error control mechanisms in different layers in wireless cooperative networks.