Abstract-Cellular uplink analysis has typically been undertaken by either a simple approach that lumps all interference into a single deterministic or random parameter in a Wynertype model, or via complex system level simulations that often do not provide insight into why various trends are observed. This paper proposes a novel middle way using point processes that is both accurate and also results in easy-to-evaluate integral expressions based on the Laplace transform of the interference. We assume mobiles and base stations are randomly placed in the network with each mobile pairing up to its closest base station. Compared to related recent work on downlink analysis, the proposed uplink model differs in two key features. First, dependence is considered between user and base station point processes to make sure each base station serves a single mobile in the given resource block. Second, per-mobile power control is included, which further couples the transmission of mobiles due to location-dependent channel inversion. Nevertheless, we succeed in deriving the coverage (equivalently outage) probability of a typical link in the network. This model can be used to address a wide variety of system design questions in the future. In this paper we focus on the implications for power control and see that partial channel inversion should be used at low signal-to-interference-plus-noise ratio (SINR), while full power transmission is optimal at higher SINR.

The proliferation of internet-connected mobile devices will continue to drive growth in data traffic in an exponential fashion, forcing network operators to dramatically increase the capacity of their networks. To do this cost-effectively, a paradigm shift in cellular network infrastructure deployment is occurring away from traditional (expensive) high-power tower-mounted base stations and towards heterogeneous elements. Examples of heterogeneous elements include microcells, picocells, femtocells, and distributed antenna systems (remote radio heads), which are distinguished by their transmit powers/coverage areas, physical size, backhaul, and propagation characteristics. This shift presents many opportunities for capacity improvement, and many new challenges to co-existence and network management. This article discusses new theoretical models for understanding the heterogeneous cellular networks of tomorrow, and the practical constraints and challenges that operators must tackle in order for these networks to reach their potential.

Fractional frequency reuse (FFR) is an interference management technique well-suited to OFDMAbased cellular networks wherein the cells are partitioned into spatial regions with different frequency reuse factors. To date, FFR techniques have been typically been evaluated through system-level simulations using a hexagonal grid for the base station locations. This paper instead focuses on analytically evaluating the two main types of FFR deployments -Strict FFR and Soft Frequency Reuse (SFR) -using a Poisson point process to model the base station locations. The results are compared with the standard grid model and an actual urban deployment. Under reasonable special cases for modern cellular networks, our results reduce to simple closed-form expressions, which provide insight into system design guidelines and the relative merits of Strict FFR, SFR, universal reuse, and fixed frequency reuse. We observe that FFR provides an increase in the sum-rate as well as the well-known benefit of improved coverage for cell-edge users. Finally, a SINR-proportional resource allocation strategy is proposed based on the analytical expressions, showing that Strict FFR provides greater overall network throughput at low traffic loads, while SFR better balances the requirements of interference reduction and resource efficiency when the traffic load is high.

We leverage stochastic geometry to characterize key performance metrics for neighboring Wi-Fi and LTE networks in unlicensed spectrum. Our analysis focuses on a single unlicensed frequency band, where the locations for the Wi-Fi access points (APs) and LTE eNodeBs (eNBs) are modeled as two independent homogeneous Poisson point processes. Three LTE coexistence mechanisms are investigated:(1) LTE with continuous transmission and no protocol modifications; (2) LTE with discontinuous transmission; and (3) LTE with listen-before-talk (LBT) and random back-off (BO). For each scenario, we derive the medium access probability (MAP), the signal-to-interference-plus-noise ratio (SINR) coverage probability, the density of successful transmissions (DST), and the rate coverage probability for both Wi-Fi and LTE. Compared to the baseline scenario where one Wi-Fi network coexists with an additional Wi-Fi network, our results show that Wi-Fi performance is severely degraded when LTE transmits continuously. However, LTE is able to improve the DST and rate coverage probability of Wi-Fi while maintaining acceptable data rate performance when it adopts one or more of the following coexistence features: a shorter transmission duty cycle, lower channel access priority, or more sensitive clear channel assessment (CCA) thresholds. Therefore, a mathematical approach would be helpful for more efficient performance evaluation and transparent comparisons of various techniques. A fluid network model is used in [19] to analyze the coexistence performance when LTE has no protocol modifications. However, the fluid network model is limited to the analysis of deterministic networks, which do not capture the multi-path fading effects and random backoff mechanism of Wi-Fi. A centralized optimization framework is proposed in [20] to optimize the aggregate throughput of LTE and Wi-Fi. However, the analysis of [20] is based on Bianchi's model for CSMA/CA [21], which relies on the idealized assumption that the collision probability of the contending APs is "constant and independent".In recent years, stochastic geometry has become a popular and powerful mathematical tool to analyze cellular and Wi-Fi systems. Specifically, key performance metrics can be derived by modeling the locations of base stations (BSs)/access points (APs) as a realization of certain spatial random point processes. In [22], the coverage probability and average Shannon rate were derived for macro cellular networks with BSs distributed according to the complete spatial random Poisson point process (PPP). The analysis has been extended to several other cellular network scenarios, including heterogeneous cellular networks (HetNets) [23]-[25], MIMO [26], [27], and carrier aggregation [28], [29]. More realistic macro BS location models than PPP are investigated in [30]-[32]. Stochastic geometry can also model CSMA/CA-based Wi-Fi networks. A modified Matérn hard-core point process, which gives a snapshot view of the simultaneous transmitting CSMA/CA nodes, has been proposed and validated...