Radha Krishna Ganti

A Tractable Approach to Coverage and Rate in Cellular Networks

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.

Modeling and Analysis of K-Tier Downlink Heterogeneous Cellular Networks

Cellular networks are in a major transition from a carefully planned set of large tower-mounted base-stations (BSs) to an irregular deployment of heterogeneous infrastructure elements that often additionally includes micro, pico, and femtocells, as well as distributed antennas. In this paper, we develop a tractable, flexible, and accurate model for a downlink heterogeneous cellular network (HCN) consisting of K tiers of randomly located BSs, where each tier may differ in terms of average transmit power, supported data rate and BS density. Assuming a mobile user connects to the strongest candidate BS, the resulting Signal-to-Interference-plus-Noise-Ratio (SINR) is greater than 1 when in coverage, Rayleigh fading, we derive an expression for the probability of coverage (equivalently outage) over the entire network under both open and closed access, which assumes a strikingly simple closed-form in the high SINR regime and is accurate down to -4 dB even under weaker assumptions. For external validation, we compare against an actual LTE network (for tier 1) with the other K-1 tiers being modeled as independent Poisson Point Processes. In this case as well, our model is accurate to within 1-2 dB. We also derive the average rate achieved by a randomly located mobile and the average load on each tier of BSs. One interesting observation for interference-limited open access networks is that at a given \sinr, adding more tiers and/or BSs neither increases nor decreases the probability of coverage or outage when all the tiers have the same target-SINR.

Interference in Large Wireless Networks

Since interference is the main performance-limiting factor in most wireless networks, it is crucial to characterize the interference statistics. The two main determinants of the interference are the network geometry (spatial distribution of concurrently transmitting nodes) and the path loss law (signal attenuation with distance). For certain classes of node distributions, most notably Poisson point processes, and attenuation laws, closed-form results are available, for both the interference itself as well as the signal-to-interference ratios, which determine the network performance. This monograph presents an overview of these results and gives an introduction to the analytical techniques used in their derivation. The node distribution models range from lattices to homogeneous and clustered Poisson models to general motion-invariant ones. The analysis of the more general models requires the use of Palm theory, in particular conditional probability generating functionals, which are briefly introduced in the appendix.

A primer on spatial modeling and analysis in wireless networks

The performance of wireless networks depends critically on their spatial configuration, because received signal power and interference depend critically on the distances between numerous transmitters and receivers. This is particularly true in emerging network paradigms that may include femtocells, hotspots, relays, white space harvesters, and meshing approaches, which are often overlaid with traditional cellular networks. These heterogeneous approaches to providing high-capacity network access are characterized by randomly located nodes, irregularly deployed infrastructure, and uncertain spatial configurations due to factors like mobility and unplanned user-installed access points. This major shift is just beginning, and it requires new design approaches that are robust to spatial randomness, just as wireless links have long been designed to be robust to fading. The objective of this article is to illustrate the power of spatial models and analytical techniques in the design of wireless networks, and to provide an entry-level tutorial.

Analytical Evaluation of Fractional Frequency Reuse for OFDMA Cellular Networks

Fractional frequency reuse (FFR) is an interference management technique well-suited to OFDMA-based cellular networks wherein the bandwidth of the cells is partitioned into 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. Finally, a SINR-proportional resource allocation strategy is proposed based on the analytical expressions and 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.

Interference and Outage in Clustered Wireless Ad Hoc Networks

In the analysis of large random wireless networks, the underlying node distribution is almost ubiquitously assumed to be the homogeneous Poisson point process. In this paper, the node locations are assumed to form a Poisson cluster process on the plane. We derive the distributional properties of the interference and provide upper and lower bounds for its distribution. We consider the probability of successful transmission in an interference-limited channel when fading is modeled as Rayleigh. We provide a numerically integrable expression for the outage probability and closed-form upper and lower bounds. We show that when the transmitter-receiver distance is large, the success probability is greater than that of a Poisson arrangement. These results characterize the performance of the system under geographical or MAC-induced clustering. We obtain the maximum intensity of transmitting nodes for a given outage constraint, i.e., the transmission capacity (of this spatial arrangement) and show that it is equal to that of a Poisson arrangement of nodes. For the analysis, techniques from stochastic geometry are used, in particular the probability generating functional of Poisson cluster processes, the Palm characterization of Poisson cluster processes, and the Campbell-Mecke theorem.

Comparison of Fractional Frequency Reuse Approaches in the OFDMA Cellular Downlink

Fractional frequency reuse (FFR) is an interference coordination technique well-suited to OFDMA based wireless networks wherein cells are partitioned into spatial regions with different frequency reuse factors. This work focuses on evaluating the two main types of FFR deployments: Strict FFR and Soft Frequency Reuse (SFR). Relevant metrics are discussed, including outage probability, network throughput, spectral efficiency, and average cell- edge user SINR. In addition to analytical expressions for outage probability, system simulations are used to compare Strict FFR and SFR with universal frequency reuse based on a typical OFDMA deployment and uniformly distributed users. Based on the analysis and numerical results, system design guidelines and a detailed picture of the tradeoffs associated with the FFR systems are presented, showing that Strict FFR provides the greatest overall network throughput and highest cell-edge user SINR, while SFR balances the requirements of interference reduction and resource efficiency.

Spatial and temporal correlation of the interference in ALOHA ad hoc networks

Interference is a main limiting factor of the performance of a wireless ad hoc network. The temporal and the spatial correlation of the interference makes the outages correlated temporally (important for retransmissions) and spatially correlated (important for routing). In this letter we quantify the temporal and spatial correlation of the interference in a wireless ad hoc network whose nodes are distributed as a Poisson point process on the plane when ALOHA is used as the multiple-access scheme.

On the Throughput Cost of Physical Layer Security in Decentralized Wireless Networks

This paper studies the throughput of large-scale decentralized wireless networks with physical layer security constraints. In particular, we are interested in the question of how much throughput needs to be sacrificed for achieving a certain level of security. We consider random networks where the legitimate nodes and the eavesdroppers are distributed according to independent two-dimensional Poisson point processes. The transmission capacity framework is used to characterize the area spectral efficiency of secure transmissions with constraints on both the quality of service (QoS) and the level of security. This framework illustrates the dependence of the network throughput on key system parameters, such as the densities of legitimate nodes and eavesdroppers, as well as the QoS and security constraints. One important finding is that the throughput cost of achieving a moderate level of security is quite low, while throughput must be significantly sacrificed to realize a highly secure network. We also study the use of a secrecy guard zone, which is shown to give a significant improvement on the throughput of networks with high security requirements.

Load-Aware Modeling and Analysis of Heterogeneous Cellular Networks

Random spatial models are attractive for modeling heterogeneous cellular networks (HCNs) due to their realism, tractability, and scalability. A major limitation of such models to date in the context of HCNs is the neglect of network traffic and load: all base stations (BSs) have typically been assumed to always be transmitting. Small cells in particular will have a lighter load than macrocells, and so their contribution to the network interference may be significantly overstated in a fully loaded model. This paper incorporates a flexible notion of BS load by introducing a new idea of conditionally thinning the interference field. For a K-tier HCN where BSs across tiers differ in terms of transmit power, supported data rate, deployment density, and now load, we derive the coverage probability for a typical mobile, which connects to the strongest BS signal. Conditioned on this connection, the interfering BSs of the i^{th} tier are assumed to transmit independently with probability p_i, which models the load. Assuming — reasonably — that smaller cells are more lightly loaded than macrocells, the analysis shows that adding such access points to the network always increases the coverage probability. We also observe that fully loaded models are quite pessimistic in terms of coverage.