In this paper we develop a tractable framework for SINR analysis in downlink heterogeneous cellular networks (HCNs) with flexible cell association policies. The HCN is modeled as a multi-tier cellular network where each tier's base stations (BSs) are randomly located and have a particular transmit power, path loss exponent, spatial density, and bias towards admitting mobile users. For example, as compared to macrocells, picocells would usually have lower transmit power, higher path loss exponent (lower antennas), higher spatial density (many picocells per macrocell), and a positive bias so that macrocell users are actively encouraged to use the more lightly loaded picocells. In the present paper we implicitly assume all base stations have full queues; future work should relax this. For this model, we derive the outage probability of a typical user in the whole network or a certain tier, which is equivalently the downlink SINR cumulative distribution function.The results are accurate for all SINRs, and their expressions admit quite simple closed-forms in some plausible special cases. We also derive the average ergodic rate of the typical user, and the minimum average user throughput -the smallest value among the average user throughputs supported by one cell in each tier. We observe that neither the number of BSs or tiers changes the outage probability or average ergodic rate in an interference-limited full-loaded HCN with unbiased cell association (no biasing), and observe how biasing alters the various metrics. perhaps relay BSs [5]. Heterogeneity is expected to be a key feature of 4G cellular networks, and an essential means for providing higher end-user throughput [6], [7] as well as expanded indoor and cell-edge coverage. The tiers of BSs are ordered by transmit power with tier 1 having the highest power. Due to differences in deployment, they also in general will have differing path loss exponents and spatial density (e.g. the number of BSs per square kilometer). Finally, in order to provide relief to the macrocell network -which is and will continue to be the main bottleneck -lower tier base stations are expected to be designed to have a bias towards admitting users [6], since their smaller coverage area usually results in a lighter load. For example, as shown in Fig. 1, a picocell may claim a user even though the macrocell signal is stronger to the user. The goal of this paper is to propose and develop a model and analytical framework that successfully characterizes the signal-to-noise-plus-interference ratio (SINR) -and its derivative metrics like outage/coverage and data rate -in such a HCN with arbitrary per-tier association biases. A. Motivation and Related WorkThe SINR statistics over a network are, unsurprisingly, largely determined by the locations of the base stations (BSs). These locations are usually unknown during the design of standards or even a specific system, and even if they are known they vary significantly from one city to the next. Since the main aspects of the system must work across a...

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.

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Although various linear log-distance path loss models have been developed for wireless sensor networks, advanced models are required to more accurately and flexibly represent the path loss for complex environments. This paper proposes a machine learning framework for modeling path loss using a combination of three key techniques: artificial neural network (ANN)-based multi-dimensional regression, Gaussian process-based variance analysis, and principle component analysis (PCA)-aided feature selection. In general, the measured path loss dataset comprises multiple features such as distance, antenna height, etc. First, PCA is adopted to reduce the number of features of the dataset and simplify the learning model accordingly. ANN then learns the path loss structure from the dataset with reduced dimension, and Gaussian process learns the shadowing effect. Path loss data measured in a suburban area in Korea are employed. We observe that the proposed combined path loss and shadowing model is more accurate and flexible compared to the conventional linear path loss plus log-normal shadowing model.

This paper proposes a self-optimized coverage coordination scheme for two-tier femtocell networks, in which a femtocell base station adjusts the transmit power based on the statistics of the signal and the interference power that is measured at a femtocell downlink. Furthermore, an analytic expression is derived for the coverage leakage probability that a femtocell coverage area leaks into an outdoor macrocell. The coverage analysis is verified by simulation, which shows that the proposed scheme provides sufficient indoor femtocell coverage and that the femtocell coverage does not leak into an outdoor macrocell.