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

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