Impact of Correlation between Interferers on Coverage Probability and rate in Cellular Systems

When the user channel experiences Nakagami-m fading, the coverage probability expressions are theoretically compared for the following cases: (i). The N interferers are independent $\eta$-$\mu$ random variables (RVs). (ii). The N interferers are correlated $\eta$-$\mu$ RVs. It is analytically shown that the coverage probability in the presence of correlated interferers is greater than or equal to the coverage probability in the presence of independent interferers when the shape parameter of the channel between the user and its base station (BS) is not greater than one. Further, rate is compared for the following cases: (i). The user channel experiences $\eta$-$\mu$ RV and the $N$ interferers are independent $\eta$-$\mu$ RVs. (ii). The N interferers are correlated $\eta$-$\mu$ RVs. It is analytically shown that the rate in the presence of correlated interferers is greater than or equal to the rate in the presence of independent interferers. Simulation results are provided and these match with the obtained theoretical results. The utility of our results are also discussed.