Analytical Modeling of Uplink Cellular Networks

Abstract

Abstract-Cellular uplink analysis has typically been undertaken by either a simple approach that lumps all interference into a single deterministic or random parameter in a Wynertype model, or via complex system level simulations that often do not provide insight into why various trends are observed. This paper proposes a novel middle way using point processes that is both accurate and also results in easy-to-evaluate integral expressions based on the Laplace transform of the interference. We assume mobiles and base stations are randomly placed in the network with each mobile pairing up to its closest base station. Compared to related recent work on downlink analysis, the proposed uplink model differs in two key features. First, dependence is considered between user and base station point processes to make sure each base station serves a single mobile in the given resource block. Second, per-mobile power control is included, which further couples the transmission of mobiles due to location-dependent channel inversion. Nevertheless, we succeed in deriving the coverage (equivalently outage) probability of a typical link in the network. This model can be used to address a wide variety of system design questions in the future. In this paper we focus on the implications for power control and see that partial channel inversion should be used at low signal-to-interference-plus-noise ratio (SINR), while full power transmission is optimal at higher SINR.

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

“…It should be noted that the random variables {R z } z∈Z are identically distributed but not independent in general. This dependence is induced by the restriction of having one user served per-BS-per channel, i.e., the coupling of the BS and served user per channel point processes [13,16,23]. Here, we demonstrate that this dependence is weak which motivates our independence assumption for {R z } z∈Z .…”

“…We consider that LOS probability function p(R) = e −βR , where 1/β = 141.4 m. The antenna gain pattern of a BS is assumed to be characterized with M r = 10 dB, m r = −10 dB, and θ r = 30 • , while that of a user is assumed to be characterized with M t = 10 dB, m t = −10 dB, and θ t = 90 • . For comparison purpose, we have also included the conventional stochastic geometry analysis of the uplink channel in [13] that does not differentiate between LOS and NLOS transmission and assumes smallscale Rayleigh fading between the users and BSs (i.e., N L = N N = 1). Note that only one pathloss exponent is defined in [13] and is denoted here as α = α N .…”

“…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.…”

“…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. An extension of the stochastic model to the uplink channel of the conventional UHF cellular network, which is based on the dependence assumption where user and BS point processes are such that each BS serves a single user in a given resource block, is presented in [13]. The authors in [13] also included a per-user fractional power control (FPC) in their model.…”

“…An extension of the stochastic model to the uplink channel of the conventional UHF cellular network, which is based on the dependence assumption where user and BS point processes are such that each BS serves a single user in a given resource block, is presented in [13]. 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].…”