An autoregressive model for a single-hop relay channel

In this paper, we developed a mathematical model for a single-hop relay-based communication channel. Assuming the transmitter-to-relay and receiver-to-relay channels are non-line-of-sight flat fading channels, we show that the real and imaginary components of the combined single channel have Laplace probability density functions. We, therefore, develop a complex Laplace autoregressive process (AR) that captures the statistical characteristics of the fading process of the relay channel. Such an AR model makes channel simulations simple, and eases formulation of such problems as data detection in a state-space form for convenient application of well-known algorithms. Furthermore, the autocorrelation of the developed Laplace AR model has Yule-Walker type of properties that enables us to configure its parameters to match to the second-order statistical characteristics of the channel through autocorrelation matching. The derivation of the channel model is illustrated through an example and computer simulations.