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

Prasanna Herath,Witold A Krzymień,Chintha Tellambura

doi:10.1186/s13638-018-1120-7

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.

Highlights

Both uplink and downlink transmit power control (TPC) is an integral part of modern cellular system standards (e.g., Long-Term Evolution (LTE), LTE-advanced) to control the transmit power of mobile stations (MSs) and base stations (BSs), respectively, in order to mitigate inter-cell and intra-cell interference, while achieving energy savings, improving connectivity, and maintaining a required signal-to-interference-plus-noise ratio (SINR) [1]
The simplest uplink TPC is to ensure that all user transmissions reach the same SINR at the base station (BS), which requires that those encountering high
Comparing the performance of three power control schemes, we show that at low SINRs, compensating for both path loss and shadowing improves the coverage probability

Summary

Introduction

Both uplink and downlink transmit power control (TPC) is an integral part of modern cellular system standards (e.g., Long-Term Evolution (LTE), LTE-advanced) to control the transmit power of mobile stations (MSs) and base stations (BSs), respectively, in order to mitigate inter-cell and intra-cell interference, while achieving energy savings, improving connectivity, and maintaining a required signal-to-interference-plus-noise ratio (SINR) [1]. [27, 28] have investigated the uplink coverage probability of arbitrary, but fixed, realization (meta distribution of SIR) of Poisson cellular networks Both these references consider fractional PLI power control. Our work [4] investigates coverage probability of a single-tier cellular network in composite Rayleigh-lognormal fading channels, where we consider fractional inversion of path loss and complete compensation of shadowing. The results of this research are not fully applicable for modern OFDM or discrete Fourier transform spread OFDMA (DFT-s-OFDM)-based cellular uplink With this motivation, in our previous work [4], we investigated fractional compensation of path loss and complete inversion of shadowing (number 3 in the list below) in an OFDMA/DFT-s-OFDM-based cellular network considering more practical composite Rayleigh-lognormal fading channels.

Scheme 1

Scheme 2

Scheme 3

Proofs of lemmas and theorems

Conclusions

Proof of Theorem 3