Generalized SIR Analysis for Stochastic Heterogeneous Wireless Networks:   Theory and Applications
  This paper provides an analytically tractable framework of investigating the statistical properties of the signal-to-interference power ratio (SIR) with a general distribution in a heterogeneous wireless ad hoc network in which there are K different types of transmitters (TXs) communicating with their unique intended receiver (RX). The TXs of each type form an independent homogeneous Poisson point process. In the first part of this paper, we introduce a novel approach to deriving the Laplace transform of the reciprocal of the SIR and use it to characterize the distribution of the SIR. Our main findings show that the closed-form expression of the distribution of the SIR can be obtained whenever the receive signal power has an Erlang distribution, and an almost closed-form expression can be found if the power-law pathloss model has a pathloss exponent of four. In the second part of this paper, we aim to apply the derived distribution of the SIR in finding the two important performance metrics: the success probability and ergodic link capacity. For each type of the RXs, the success probability with (without) interference cancellation and that with (without) the proposed stochastic power control are found in a compact form. With the aid of the derived Shannon transform identity, the ergodic link capacities of K-type RXs are derived with low complexity, and they can be applied to many transmitting scenarios, such as multi-antenna communication and stochastic power control. Finally, we analyze the spatial throughput capacity of the heterogeneous network defined based on the derived K success probabilities and ergodic link capacities and show the existence of its maximum. 
Chun-Hung Liu, Zhu-Kuan Yang, Di-Chun Liang
cs.IT math.IT