We determine the approximate cumulative distribution function (CDF) of the uplink signal to interference ratio (SIR) at the base station (BS) when D2D communications are underlaid in a cellular network with uniformly distributed users, in a shadow fading environment. Initially, we determine the probability density function (PDF) of the received normalized powers at the BS and then compute the PDF of the SIR semi-analytically. Next we approximate the normalized interference as a lognormal random variable by extending Fenton-Wilkinson's moment matching method to arrive at an approximate closed form expression of the SIR's CDF. The results show that the first method approximates the CDF well but at the cost of computational complexity. The second method approximates the CDF in the lower SIR region and is easy to implement.
['Anushree Neogi', 'Abhay Karandikar']
Analysis of uplink SIR for cellular network with underlaid D2D communications