On the second order statistics of SIR in wireless Nakagami channels

The second order statistical properties of the Signal to Interference Ratio (SIR), namely the autocovariance function, are relevant for several studies in wireless communication channels. Formally, the autocovariance function of SIR can be obtained from its two-dimensional Probability Density Function (PDF). However, for the traditional types of fading channels, the analytical two dimensional PDF's of SIR are rather scarce, and it is possible to say that they are either unavailable or have too complex forms. Moreover, this approach does not allow to see how the covariances of the desired signal and the interference participate in the covariance of SIR. In this paper, we show how these inconveniences can be bypassed allowing and exact analysis of the autocovariance function of SIR in Nakagami fast fading channels. The paper focuses on the efficiency of the derived analytical expression and a detailed discussion about the relevant cases.