Average Rate of Downlink Heterogeneous Cellular Networks over Generalized Fading Channels - A Stochastic Geometry Approach (1303.0529v2)

Abstract: In this paper, we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks. The framework leverages recent application of stochastic geometry to other-cell interference modeling and analysis. The heterogeneous cellular network is modeled as the superposition of many tiers of Base Stations (BSs) having different transmit power, density, path-loss exponent, fading parameters and distribution, and unequal biasing for flexible tier association. A long-term averaged maximum biased-received-power tier association is considered. The positions of the BSs in each tier are modeled as points of an independent Poisson Point Process (PPP). Under these assumptions, we introduce a new analytical methodology to evaluate the average rate, which avoids the computation of the Coverage Probability (Pcov) and needs only the Moment Generating Function (MGF) of the aggregate interference at the probe mobile terminal. The distinguishable characteristic of our analytical methodology consists in providing a tractable and numerically efficient framework that is applicable to general fading distributions, including composite fading channels with small- and mid-scale fluctuations. In addition, our method can efficiently handle correlated Log-Normal shadowing with little increase of the computational complexity. The proposed MGF-based approach needs the computation of either a single or a two-fold numerical integral, thus reducing the complexity of Pcov-based frameworks, which require, for general fading distributions, the computation of a four-fold integral.

• The paper introduces a stochastic geometry framework utilizing the moment generating function (MGF) to accurately compute the average downlink rate in heterogeneous cellular networks.
• This novel MGF-based methodology significantly reduces computational complexity, requiring only one or two numerical integrals compared to traditional methods.
• The study identifies a saturation point where increasing base station density provides diminishing returns on average rate improvements, highlighting the need for advanced interference management.

Analytical Framework for Downlink Rates in Heterogeneous Cellular Networks

The paper titled "Average Rate of Downlink Heterogeneous Cellular Networks over Generalized Fading Channels -- A Stochastic Geometry Approach" presents a systemic framework to compute the average downlink data rate in heterogeneous cellular networks using stochastic geometry for interference modeling. This paper is authored by Marco Di Renzo, Alessandro Guidotti, and Giovanni E. Corazza, and it addresses the challenges of modeling cellular networks due to the randomness in base station (BS) positioning and channel characteristics.

Methodology

The paper models a heterogeneous cellular network as a superimposition of multiple tiers of base stations (BSs), characterized by distinct parameters such as transmit power, density, path-loss exponents, and fading distributions. Each tier represents a class of BSs, mirroring actual network deployments like macrocells, microcells, and femtocells. A long-term averaged maximum biased-received-power tier association scheme is employed in which a mobile terminal associates with the BS offering the highest expected received power, taking into account biasing to optimize offloading across tiers.

The key analytical novelty of this framework lies in the use of the moment generating function (MGF) to handle aggregate interference instead of relying on coverage probability (Pcov) computations traditionally used. This approach only requires computing either a one-fold or a two-fold numerical integral for general fading distributions, which is a significant reduction in complexity compared to the four-fold integral of existing approaches.

Results and Discussion

The framework is validated through extensive simulations, demonstrating its applicability across various fading conditions and network parameters. It shows that the MGF-based methodology is not only simpler and computationally efficient but also robust across a range of scenarios, including for interference-limited networks typical of dense urban deployments.

Notably, the paper quantifies the relationship between the density of BSs and the average rate, asserting an upper limit beyond which increasing BS density does not significantly improve rates. This suggests a saturation point in network densification strategies without parallel advancements in interference management techniques.

Future Directions

The implications of this research are profound, particularly as networks evolve towards dense heterogeneous architectures in 5G and beyond. The insights provided could inform the design of policies around BS deployment, power control, and tier association strategies. As cellular networks continue to converge with other wireless technologies via cognitive and opportunistic spectrum use, the stochastic geometry approach might incorporate more complex interactions further, such as user mobility and network load dynamics.

Future investigations may build on these foundations to explore complex receiver techniques, such as MIMO, and their interaction with diverse cellular architectures. Additionally, the effective integration of this model with network optimization methods could be key in managing trade-offs between energy efficiency, spectral efficiency, and QoS in future wireless networks.