Cellular networks are usually modeled by placing the base stations on a grid, with mobile users either randomly scattered or placed deterministically. These models have been used extensively but suffer from being both highly idealized and not very tractable, so complex system-level simulations are used to evaluate coverage/outage probability and rate. More tractable models have long been desirable. We develop new general models for the multi-cell signal-to-interference-plus-noise ratio (SINR) using stochastic geometry. Under very general assumptions, the resulting expressions for the downlink SINR CCDF (equivalent to the coverage probability) involve quickly computable integrals, and in some practical special cases can be simplified to common integrals (e.g., the Q-function) or even to simple closed-form expressions. We also derive the mean rate, and then the coverage gain (and mean rate loss) from static frequency reuse. We compare our coverage predictions to the grid model and an actual base station deployment, and observe that the proposed model is pessimistic (a lower bound on coverage) whereas the grid model is optimistic, and that both are about equally accurate. In addition to being more tractable, the proposed model may better capture the increasingly opportunistic and dense placement of base stations in future networks.

A Tractable Approach to Coverage and Rate in Cellular Networks

As the spectral efficiency of a point-to-point link in cellular networks approaches its theoretical limits, with the forecasted explosion of data traffic, there is a need for an increase in the node density to further improve network capacity. However, in already dense deployments in today's networks, cell splitting gains can be severely limited by high inter-cell interference. Moreover, high capital expenditure cost associated with high power macro nodes further limits viability of such an approach. This article discusses the need for an alternative strategy, where low power nodes are overlaid within a macro network, creating what is referred to as a heterogeneous network. We survey current state of the art in heterogeneous deployments and focus on 3GPP LTE air interface to describe future trends. A high-level overview of the 3GPP LTE air interface, network nodes, and spectrum allocation options is provided, along with the enabling mechanisms for heterogeneous deployments. Interference management techniques that are critical for LTE heterogeneous deployments are discussed in greater detail. Cell range expansion, enabled through cell biasing and adaptive resource partitioning, is seen as an effective method to balance the load among the nodes in the network and improve overall trunking efficiency. An interference cancellation receiver plays a crucial role in ensuring acquisition of weak cells and reliability of control and data reception in the presence of legacy signals.

A survey on 3GPP heterogeneous networks

Femtocells, despite their name, pose a potentially large disruption to the carefully planned cellular networks that now connect a majority of the planet's citizens to the Internet and with each other. Femtocells - which by the end of 2010 already outnumbered traditional base stations and at the time of publication are being deployed at a rate of about five million a year - both enhance and interfere with this network in ways that are not yet well understood. Will femtocells be crucial for offloading data and video from the creaking traditional network? Or will femtocells prove more trouble than they are worth, undermining decades of careful base station deployment with unpredictable interference while delivering only limited gains? Or possibly neither: are femtocells just a "flash in the pan"; an exciting but short-lived stage of network evolution that will be rendered obsolete by improved WiFi offloading, new backhaul regulations and/or pricing, or other unforeseen technological developments? This tutorial article overviews the history of femtocells, demystifies their key aspects, and provides a preview of the next few years, which the authors believe will see a rapid acceleration towards small cell technology. In the course of the article, we also position and introduce the articles that headline this special issue.

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Femtocells: Past, Present, and Future

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.

Heterogeneous cellular networks: From theory to practice

Time-Division Duplexing (TDD) allows to estimate the downlink channels for an arbitrarily large number of base station antennas from a finite number of orthogonal uplink pilot signals, by exploiting channel reciprocity. Based on this observation, a recently proposed "Massive MIMO" scheme was shown to achieve unprecedented spectral efficiency in realistic conditions of distance-dependent pathloss and channel coherence time and bandwidth. The main focus and contribution of this paper is an improved Network-MIMO TDD architecture achieving spectral efficiencies comparable with "Massive MIMO", with one order of magnitude fewer antennas per active user per cell (roughly, from 500 to 50 antennas). The proposed architecture is based on a family of Network-MIMO schemes defined by small clusters of cooperating base stations, zero-forcing multiuser MIMO precoding with suitable inter-cluster interference mitigation constraints, uplink pilot signals allocation and frequency reuse across cells. The key idea consists of partitioning the users into equivalence classes, optimizing the Network-MIMO scheme for each equivalence class, and letting a scheduler allocate the channel time-frequency dimensions to the different classes in order to maximize a suitable network utility function that captures a desired notion of fairness. This results in a mixed-mode Network-MIMO architecture, where different schemes, each of which is optimized for the served user equivalence class, are multiplexed in time-frequency. In order to carry out the performance analysis and the optimization of the proposed architecture in a systematic and computationally efficient way, we consider the large-system regime where the number of users, the number of antennas, and the channel coherence block length go to infinity with fixed ratios.

Achieving "Massive MIMO" Spectral Efficiency with a Not-so-Large Number of Antennas

This article provides an overview of contemporary and forward looking inter-cell interference coordination techniques for 4G OFDM systems with a specific emphasis on implementations for LTE. Viable approaches include the use of power control, opportunistic spectrum access, intra and inter-base station interference cancellation, adaptive fractional frequency reuse, spatial antenna techniques such as MIMO and SDMA, and adaptive beamforming, as well as recent innovations in decoding algorithms. The applicability, complexity, and performance gains possible with each of these techniques based on simulations and empirical measurements will be highlighted for specific cellular topologies relevant to LTE macro, pico, and femto deployments for both standalone and overlay networks.

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G. Boudreau

Papers

Interference coordination and cancellation for 4G networks