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In a large-scale wireless ad hoc network in which all transmitters form ahomogeneous of Poisson point process, the statistics of thesignal-to-interference ratio (SIR) in prior work is only derived in closed-formfor the case of Rayleigh fading channels. In this letter, the mean SIR is foundin closed-form for general random channel (power) gain, transmission distanceand power control models. According to the derived mean SIR, we first show thatchannel gain randomness actually benefits the mean SIR so that the upper boundon the mean spectrum efficiency increases. Then we show that stochastic powercontrol and opportunistic scheduling that capture the randomness of channelgain and transmission distance can significantly not only enhance the mean SIRbut reduce the outage probability. The mean-SIR-based throughput capacity isproposed and it can be maximized by a unique optimal intensity of transmittersif the derived supporting set of the intensity exists.

The Mean SIR of Large-Scale Wireless Networks: Its Closed-Form Expression and Main Applications