Interference limited broadcast: Role of interferer geometry

Current generation wireless systems employ high frequency reuse and shrinking cell sizes. Thus, there has been significant recent attention on the analysis of interference limited systems). We consider single input single output (SISO) broadcast (BC) with intercell interference. We allow the received powers from each source of interference to be different For example, for the two interferer case, a user receives average power c1 > 0 from interferer 1 and c2 > 0 from interferer 2 where c1 and c2 need not be equal. We characterize the cumulative distribution function of the resulting signal to interference ratio (SIR) which is a ratio of weighted exponential random variables. It is thus a generalization of the F-distribution which is a scaled ratio of equally weighted exponential random variables. Surprisingly, there is no simple closed form expression for the resulting cdf in the literature. We present a nontrivial calculation that yields a simple, closed form expression for the cumulative distribution function (cdf) of the SIR. We show that this function is a Schur-concave function of the vector of average received powers from the various interferers. Furthermore, we derive a simple closed form expression for the cdf of the SINR. Again, we find that this function is Schur-concave in the average received powers. As a result we conclude that for any average transmit, receive, and thermal noise powers, the probability of achieving any SINR is highest when all interference power originates from a single interferer and lowest when the power is divided equally among the interferers. Opportunistic scheduling (OS) can be an effective tool to mitigate interference. For high signal and interference transmit power, the SINR is well approximated by the SIR. We analyze the scaling of the SIR using OS as the number of users grows for an arbitrary number of interferers. For J received interference powers {cj}j=1 j, the SIR is asymptotically inversely proportional to the geometric mean, (Pij=1 j cj) 1/j.