This paper presents a tutorial on stochastic geometry (SG) based analysis for cellular networks. This tutorial is distinguished by its depth with respect to wireless communication details and its focus on cellular networks. The paper starts by modeling and analyzing the baseband interference in a basic cellular network model. Then, it characterizes signal-tointerference-plus-noise-ratio (SINR) and its related performance metrics. In particular, a unified approach to conduct error probability, outage probability, and rate analysis is presented. Although the main focus of the paper is on cellular networks, the presented unified approach applies for other types of wireless networks that impose interference protection around receivers. The paper then extends the baseline unified approach to capture cellular network characteristics (e.g., frequency reuse, multiple antenna, power control, etc.). It also presents numerical examples associated with demonstrations and discussions. Finally, we point out future research directions. arXiv:1604.03689v1 [cs.IT] 13 Apr 2016 2 paper can be extended to other types of wireless networks that impose interference protection around receivers.A. Using SG for Cellular Networks SG was mostly confined to ad hoc and sensor networks to account for their intrinsic spatial randomness. In contrast, cellular networks were mostly assumed to be spatially deployed according to an idealized hexagonal grid. Motivated by its tractability, attempts to promote SG to model cellular networks can be traced back to the late 90's [34], [35]. However, success was not achieved until a decade later [36]- [38]. The theoretical and statistical studies presented in [36]- [38] revealed that cellular networks deviate from the idealized hexagonal grid structure and follows and irregular topology that randomly changes from one geographical location to another. The authors in [36] show that the signal-to-interferenceplus-noise-ratio (SINR) experienced by users in a simulation with actual base station (BS) locations is upper bounded by the SINR of users in idealistic grid network, and lower bounded by the SINR of users in random network. Interestingly, the random network provides a lower bound that is as tight as the upper bound provided by the idealized grid network. However, the lower bound is preferred due to the tractability provided by SG. The authors in [37] show that the spatial patterns exhibited by actual BS locations in different geographical places can be accurately fitted to random spatial patterns obtained via SG. Furthermore, the results in [37] confirm the tight lower bound provided by the random network to the users' SINR in simulations with actual BS locations. Finally, the authors in [38] show that the SINR in grid network converges to the SINR of random network in a strong shadowing environment.Exploiting the tractability of SG, several notable results are obtained for cellular networks. For instance, the downlink baseline operation of cellular networks is characterized in [36]-[42]. Extensions to mu...

A simple approximation for the secrecy outage probability (SOP) over generalized-K fading channels is developed. This approximation becomes tighter as the average signal-tonoise ratio (SNR) of the wiretap channel decreases. Based on this simple expression, we also analyze the asymptotic SOP in the high SNR region of the main channel. Besides simplifying the SOP expression significantly, this asymptotic SOP expression reveals the secrecy diversity order in a general case. Numerical results demonstrate the high accuracy of our proposed approximation results.Index Terms-Asymptotic analysis, generalized-K fading channels, physical layer security, and secrecy outage probability.

Stochastic geometry (SG) has been widely accepted as a fundamental tool for modeling and analyzing cellular networks. However, the fading models used with SG analysis are mainly confined to the simplistic Rayleigh fading, which is extended to the Nakagami-m fading in some special cases. However, neither the Rayleigh nor the Nakagami-m accounts for dominant specular components (DSCs) which may appear in realistic fading channels. In this paper, we present a tractable model for cellular networks with generalized two-ray (GTR) fading channel. The GTR fading explicitly accounts for two DSCs in addition to the diffuse components and offers high flexibility to capture diverse fading channels that appear in realistic outdoor/indoor wireless communication scenarios. It also encompasses the famous Rayleigh and Rician fading as special cases. To this end, the prominent effect of DSCs is highlighted in terms of average spectral efficiency.

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