Average Rate of Downlink Heterogeneous Cellular Networks over Generalized Fading Channels: A Stochastic Geometry Approach

Abstract

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 MGFbased 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.Index Terms-Heterogeneous cellular networks, aggregate interference modeling, stochastic geometry, average rate.

Coverage and rate analysis in the uplink of millimeter wave cellular networks with fractional power control

“…(17) where g in (d) is a normalized gamma variable with parameter N L , a k and b k are defined in earlier in Section 2, (d) follows from the probability generating functional of the PPP [12], and the independence of the interference link directivity gain G z with probability distribution G z = a k with probability b k . Furthermore, λ is thinned by A L to capture R z that are LOS to their serving BS.…”

“…Recently, the use of stochastic geometry-based analysis was proposed to assess the capacity of conventional UHF cellular systems in [12][13][14][15][16][17]. Focusing on the downlink channel of the conventional UHF cellular networks, the authors in [12] modeled the BS location as a Poisson point process (PPP) on the plane and derived the signal-tointerference-and-noise-ratio (SINR) coverage probability and the average rate of a typical user.…”

“…The authors in [13] also included a per-user fractional power control (FPC) in their model. The results in [12] have also been extended to the multitier UHF cellular networks in [14][15][16][17] and for systems performance analysis in [18][19][20]. However, as a result of blockage and the different propagation model, the result obtained for the UHF networks are not applicable to the mmWave networks.…”

Dense Small Cell Networks: From Noise-Limited to Dense Interference-Limited

“…The closest system model to the one in this paper are in [13]- [15], [18]- [23]. In [18], the transitional behaviors of interference in millimeter wave networks was analyzed, but it focused on the medium access control.…”

“…In [22], a tractable performance evaluation method, i.e., the intensity matching, was proposed to model and optimize the networks. Renzo et al [23] also introduced an analytical framework based on the strongest average received signal power associations scheme which is applicable to general fading distributions, including composite fading channels, to analyze the average rate of heterogeneous networks using a single-slope path loss model.…”