Coverage probability analysis of three uplink power control schemes: Stochastic geometry approach

Abstract

In cellular networks, each mobile station adjusts its power level under control of its base station, i.e., through uplink transmit power control, which is essential to reach desired signal-to-interference-plus-noise ratio (SINR) at the base station and to limit inter-cell interference. The optimal levels of transmit power in a network depend on path loss, shadowing, and multipath fading, as well as the network configuration. However, since path loss is distance dependent and the cell association distances are correlated due to the cell association policies, the performance analysis of the uplink transmit power control is very complicated. Consequently, the impact of a specific power control algorithm on network performance is hard to quantify. In this paper, we analyze three uplink transmit power control schemes. We assume the standard power-law path loss and composite Rayleigh-lognormal fading. Using stochastic geometry tools, we derive the cumulative distribution function and the probability density function of the uplink transmit power and the resulting network coverage probability. It is shown that the coverage is highly dependent on the severity of shadowing, the power control scheme, and its parameters, but invariant of the density of deployment of base stations when the shadowing is mild and power control is fractional. At low SINRs, compensation of both path loss and shadowing improves the coverage. However, at high SINRs, compensating for path loss only improves coverage. Increase in the severity of shadowing significantly reduces the coverage.

Cellular Coverage Probability Is Independent of Base Station Density under Stochastic Geometric Models

“…Examples of such models for DL are [ElSawy et al, 2017, Liu et al, 2020b, Liu and Zhang, 2020, Kouzayha et al, 2021, Bai and Heath, 2015, Chen and Yuan, 2019, Liu et al, 2020a, Ouamri et al, 2020, Lei et al, 2018, Fadouol, 2020, Gao et al, 2019, Ali et al, 2019, Andrews et al, 2016, Kundu et al, 2020, Sadeghabadi et al, 2020, Wang and Gursoy, 2019. On the other hand, examples of such models for DL are [ElSawy et al, 2017, Liu et al, 2020b, Haroon et al, 2021, Herath et al, 2018, Kouzayha et al, 2018, Mariam et al, 2021, Andrews et al, 2016, Jia et al, 2019, Gao et al, 2019, Ali et al, 2019, Kundu et al, 2020, Sadeghabadi et al, 2020, Wang and Gursoy, 2019. We will shortly prove that under the SG model, the cellular coverage probability is independent of λ , both in DL and UL.…”

“…The authors of [Bai and Heath, 2015], in the context of analyzing DL coverage probability of millimeter-wave cellular networks, noted that "coverage does not scale with BS density." Also, the authors of [Herath et al, 2018], while analyzing UL FPC, noted that coverage is " invariant to the density of deployment of BSs when the shadowing is mild and power control is fractional." To the best of our knowledge, the present article is the first to provide a rigorous proof that the coverage probability is independent of the BS density.…”

Stochastic geometric modelling and simulation of cellular systems for coverage probability characterization

“…The Theorems, one for DL and one for UL, prove that the opposite is true; namely that the coverage probability is independent of BS density. This fact has only been alluded to in some articles previously [13,14]. The authors of [13] in the context of analyzing DL coverage probability of millimeter-wave cellular networks noted that "coverage does not scale with BS density."…”

Cellular coverage probability is independent of base station density under stochastic geometric models

“…Examples of such models for DL are [2], [4], [6], [8], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23]. On the other hand, examples of such models for DL are [2], [4], [7], [24], [25], [26], [20], [27], [18], [19], [21], [22], [23]. We prove in this article two theorems that refute this consideration.…”

“…The authors of [12] in the context of analyzing DL coverage probability of millimeter-wave cellular networks noted that "coverage does not scale with BS density." Also, the authors of [24], while analyzing UL FPC, noted that coverage is " invariant to the density of deployment of BSs when the shadowing is mild and power control is fractional." To the best of our knowledge, the present article is the first to provide a rigorous proof that coverage probability is independent of BS density.…”