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.Comment: IEEE Journal on Selected Areas in Communications, vol. 30, no. 3, pp. 550 - 560, Apr. 201

Analytical Evaluation of Coverage-Oriented Femtocell Network Deployment

This paper proposes a coverage-oriented femtocell network deployment scheme, in which the femtocell base stations (BSs) can decide whether to be active or inactive depending on their distances from the macrocell BSs. Specifically, as the areas close to the macrocell BSs already have satisfactory cellular coverage, the femtocell BSs located inside such areas are kept to be inactive. Thus, all the active femtocells are located in the poor macrocell coverage areas. Based on a stochastic geometric framework, the coverage probability can be analyzed with tractable results. Surprisingly, the results show that the proposed scheme, although with a lower defacto femtocell density, can achieve better coverage performance than that keeping all femtocells in the entire network to be active. The analytical results further identify the achievable optimal performance of the new scheme, which provides mobile operators a guideline for femtocell deployment and operation.Comment: 6 pages, 7 figures, published in IEEE International Conference on Communications (ICC'13

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.Comment: to appear, IEEE Transactions on Wireless Communication

Optimal Non-uniform Deployments in Ultra-Dense Finite-Area Cellular Networks

Network densification and heterogenisation through the deployment of small cellular access points (picocells and femtocells) are seen as key mechanisms in handling the exponential increase in cellular data traffic. Modelling such networks by leveraging tools from Stochastic Geometry has proven particularly useful in understanding the fundamental limits imposed on network coverage and capacity by co-channel interference. Most of these works however assume infinite sized and uniformly distributed networks on the Euclidean plane. In contrast, we study finite sized non-uniformly distributed networks, and find the optimal non-uniform distribution of access points which maximises network coverage for a given non-uniform distribution of mobile users, and vice versa.Comment: 4 Pages, 6 Figures, Letter for IEEE Wireless Communication