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.

Femtocells are assuming an increasingly important role in the coverage and capacity of cellular networks. In contrast to existing cellular systems, femtocells are end-user deployed and controlled, randomly located, and rely on third party backhaul (e.g. DSL or cable modem). Femtocells can be configured to be either open access or closed access. Open access allows an arbitrary nearby cellular user to use the femtocell, whereas closed access restricts the use of the femtocell to users explicitly approved by the owner. Seemingly, the network operator would prefer an open access deployment since this provides an inexpensive way to expand their network capabilities, whereas the femtocell owner would prefer closed access, in order to keep the femtocell's capacity and backhaul to himself. We show mathematically and through simulations that the reality is more complicated for both parties, and that the best approach depends heavily on whether the multiple access scheme is orthogonal (TDMA or OFDMA, per subband) or non-orthogonal (CDMA). In a TDMA/OFDMA network, closed-access is typically preferable at high user densities, whereas in CDMA, open access can provide gains of more than 200% for the home user by reducing the near-far problem experienced by the femtocell. The results of this paper suggest that the interests of the femtocell owner and the network operator are more compatible than typically believed, and that CDMA femtocells should be configured for open access whereas OFDMA or TDMA femtocells should adapt to the cellular user density.

Coordinated multi-point (CoMP) communication is attractive for heterogeneous cellular networks (HCNs) for interference reduction. However, previous approaches to CoMP face two major hurdles in HCNs. First, they usually ignore the inter-cell overhead messaging delay, although it results in an irreducible performance bound. Second, they consider the grid or Wyner model for base station locations, which is not appropriate for HCN BS locations which are numerous and haphazard. Even for conventional macrocell networks without overlaid small cells, SINR results are not tractable in the grid model nor accurate in the Wyner model. To overcome these hurdles, we develop a novel analytical framework which includes the impact of overhead delay for CoMP evaluation in HCNs. This framework can be used for a class of CoMP schemes without user data sharing. As an example, we apply it to downlink CoMP zero-forcing beamforming (ZFBF), and see significant divergence from previous work.For example, we show that CoMP ZFBF does not increase throughput when the overhead channel delay is larger than 60% of the channel coherence time. We also find that, in most cases, coordinating with only one other cell is nearly optimum for downlink CoMP ZFBF.

A fundamental choice in femtocell deployments is the set of users which are allowed to access each femtocell. Closed access restricts the set to specifically registered users, while open access allows any mobile subscriber to use any femtocell. Which one is preferable depends strongly on the distance between the macrocell base station (MBS) and femtocell. The main results of the this article are lemmas which provide expressions for the signal-to-interference-plus-to-noise ratio (SINR) distribution for various zones within a cell as a function of this MBS-femto distance. The average sum throughput (or any other SINR-based metric) of home users and cellular users under open and closed access can readily be determined from these expressions. We show that unlike in the uplink, the interests of home and cellular users are in conflict, with home users preferring closed access and cellular users preferring open access. The conflict is most pronounced for femtocells near the cell edge, when there are many cellular users and fewer femtocells. To mitigate this conflict, we propose a middle way which we term shared access in which femtocells allocate an adjustable number of time-slots between home and cellular users such that a specified minimum rate for each can be achieved. The optimal such sharing fraction is derived. Analysis shows that shared access achieves at least the overall throughput of open access while also satisfying rate requirements, while closed access fails for cellular users and open access fails for the home user.