Interference modeling in clustered device-to-device networks with uniform transmitter selection

This paper investigates the interference statistics in a clustered device-to-device network, where the cluster centers form a Poisson point process and each active receiver device selects the transmitter randomly following the uniform distribution. The statistics of the number of intra/inter-cluster interferers is first analyzed for both finite and infinite number of receivers per cluster. In addition, for the special cases where the numbers of transmitters and receivers differ significantly, simplified expressions are given. Then, using these derived probability distributions of the number of interferers, the Laplace transforms of intra/inter-cluster interference are established and simple approximations for the special cases are obtained as well. Our results show the following: 1) with the concurrent uniform transmitter selection, the distribution of the number of intra/inter-cluster interfering devices differs greatly from the truncated Poisson distribution assumed in the literature; 2) the model assumed in the literature underestimates the coverage probability specially for a small number of transmitters/receivers; and 3) unlike the model assumed in the literature, the ASE of the proposed model increases with the number of transmitters/ receivers when the average number of active receivers is relatively small, while it does not monotonically vary with the number of transmitters/receivers when the average number of active receivers is large.