Analysis of Multi-tier Uplink Cellular Networks with Energy Harvesting and Flexible Cell Association Ahmed Hamdi Sakr and Ekram Hossain Abstract—We model and analyze a K-tier uplink cellular network with flexible cell association where all transmissions are powered by energy harvesting from ambient interference. Each cellular user transmits data to the corresponding base station (BS) only when the amount of energy harvested is sufficient to perform channel inversion towards the serving BS. Furthermore, the data transmitted can be successfully decoded only when the signal-to-interference-plus-noise ratio (SINR) at the receiver is above a predefined threshold. With flexible cell association, users are not necessarily associated with their nearest BS where a different bias factor is added to each network tier. We use tools from stochastic geometry to evaluate the performance of the proposed system model in terms of the coverage probability of a generic user associated with the k-th tier. We show that energy harvesting can be a reliable source to power cellular users with short-range communication, e.g., small cell users. In addition, we show that energy harvesting can achieve high coverage performance by optimizing different network parameters such as the BS receiver sensitivity as well as the bias factors. Keywords: Energy harvesting, K-tier cellular networks, up- link transmission, flexible association, power control, coverage probability, stochastic geometry. I. I NTRODUCTION Radio frequency (RF) energy harvesting in cellular networks has recently attracted significant attention to power wireless devices motivated by the issue of global greenhouse gas emis- sions increase [1]. On the other hand, overlaying macrocells by different classes of smaller and lower-power base stations (BSs) such as femtocells and picocells is considered as one solution to improve the spectral efficiency of cellular networks, hence, it is called a multi-tier network. In the context of ambient RF energy harvesting in wireless networks, the authors in [2] use power beacons to power uplink transmissions where no power control is assumed under an outage constraint. In the cognitive radio network in [3], the authors use the RF energy transmitted by primary users to power underlaying secondary users where all users transmit with the same power. The authors in [4] consider a device- to-device network that is powered by harvesting energy from the concurrent transmissions of a downlink cellular network where all D2D transmitters have a fixed power level. On the other hand, in the context of modeling uplink cellular A. H. Sakr and E. Hossain are with the Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Canada (emails: Ahmed.Sakr@umanitoba.ca, Ekram.Hossain@umanitoba.ca). This work was supported by a Strategic Project Grant (STPGP 430285) from the Natural Sciences and Engineering Research Council of Canada (NSERC). networks, the authors in [5] provide a framework to model a single-tier network in which all users perform fractional power control where users are assumed to constitute a Poisson Point Process (PPP) and each user has one BS in her vicinity. In [6], the authors present a general framework for modeling uplink transmission in multi-tier networks where users use truncated channel inversion power control to satisfy a certain received power threshold. In this work, we consider uplink transmission when all users are powered only by the harvested RF energy from the ambient interference that results from the concurrent downlink transmissions by all network tiers. Channel inversion power control is used by all users to ensure that the power received at the corresponding BS is higher than the receiver’s sensitivity. We also consider the case when users do not necessarily associate with the nearest BS for any reason such as the load per BS. That is, each network tier has a specific bias factor that is added to the decision criterion of the association. Note that the idea of flexible cell association has been used for downlink networks, e.g., in [7]. After harvesting energy and associating with a certain BS, each user transmits only when power harvested is enough to perform channel inversion. Note that a user may suffer outage due to either insufficient harvested energy or low SINR received at the serving BS. We use statistical modeling based on stochastic geometry to capture the randomness of the network topology, e.g., BSs’ and users’ locations [8], [9]. In particular, for analytical tractability, we use independent PPPs to model the locations of BSs and users. We evaluate the performance of our system model in terms of SINR coverage probability, transmission probability, and overall coverage probability. We show the effect of varying the different parameters of the network on (such as receiver sensitivity and bias factors) on the performance metrics. The contributions of the paper can be summarized as follows: • Using stochastic geometry, we provide a tractable analyt- ical framework to model and analyze the performance of energy harvesting in multi-tier uplink cellular networks with flexible cell association. Furthermore, we consider a practical system model in which users perform power control in order to mitigate the near-far problem. • We show that energy harvesting can provide an accept- able performance for uplink transmissions in cellular networks especially for users with short-range communi- cation links. Furthermore, we show that adjusting network