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The homogeneous Poisson point process (PPP) is widely used to model spatialdistribution of base stations and mobile terminals. The same process can beused to model underlay device-to-device (D2D) network, however, neglectinghomophilic relation for D2D pairing presents underestimated system insights. Inthis paper, we model both spatial and social distributions of interfering D2Dnodes as proximity based independently marked homogeneous Poisson pointprocess. The proximity considers physical distance between D2D nodes whereassocial relationship is modeled as Zipf based marks. We apply these twoparadigms to analyze the effect of interference on coverage probability ofdistance-proportional power-controlled cellular user. Effectively, we apply twotype of functional mappings (physical distance, social marks) to Laplacefunctional of PPP. The resulting coverage probability has no closed-formexpression, however for a subset of social marks, the mark summation convergesto digamma and polygamma functions. This subset constitutes the upper and lowerbounds on coverage probability. We present numerical evaluation of these boundson coverage probability by varying number of different parameters. The resultsshow that by imparting simple power control on cellular user, ultra-denseunderlay D2D network can be realized without compromising the coverageprobability of cellular user.

Spatial and Social Paradigms for Interference and Coverage Analysis in Underlay D2D Network