International Journal of Antennas and Propagation

Volume 2017, Article ID 8243490, 15 pages

https://doi.org/10.1155/2017/8243490

## Modeling and Characterization of the Uplink and Downlink Exposure in Wireless Networks

^{1}Telecom ParisTech, Paris, France^{2}Whist Lab Common Laboratory of Orange Labs and Institut Telecom, Paris, France^{3}Ghent University, Ghent, Belgium

Correspondence should be addressed to Anis Krayni; moc.liamg@inyark.sina

Received 4 January 2017; Revised 14 April 2017; Accepted 3 May 2017; Published 11 June 2017

Academic Editor: Antonio Iodice

Copyright © 2017 Anis Krayni et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper deals with a new methodology to assess the exposure induced by both uplink and downlink of a cellular network using 3D electromagnetic simulations. It aims to analyze together the exposure induced by a personal device (uplink exposure) and that induced by a base station (downlink exposure). The study involved the major parameters contributing to variability and uncertainty in exposure assessment, such as the user’s posture, the type of wireless device, and the propagation environment. Our approach is relying basically on the modeling of the power radiated by the personal device and the ambient electric field, while taking into account the effects of human body shadowing and the propagation channel fluctuations. The exposure assessment as well as the human-wave interactions has been simulated using the finite difference in time domain method (FDTD). In uplink scenarios, four FDTD simulations were performed with a child model, used in two postures (sitting and standing) and in two usage scenarios (voice and data), which aimed to examine the exposure induced by a mobile phone and a tablet emitting, respectively, at 900 MHz and 1940 MHz. In the downlink scenario, a series of FDTD simulations of an exposure to a single plane wave and multiplane waves have been conducted, and an efficient metamodeling of the exposure using the Polynomial Chaos approach has been developed.

#### 1. Introduction

The rapid developments in wireless network technology have strengthened the presence of electromagnetic waves in our everyday lives. Hence, the exposure to near and far electromagnetic fields is becoming increasingly a matter of public concern. The exposure is determined by the SAR* (Specific Absorption Rate)* (W/Kg), which quantifies the power absorbed by human tissues from electromagnetic radiations. Several studies have been conducted to characterize, on one hand, the exposure induced by the base stations (downlink exposure) [1] and, on the other hand, that induced by wireless devices (uplink exposure) [2]. In most of these studies, both types of exposure were studied separately. However, in the context of wireless networks that are now so widely present in everyone’s environment, a reliable characterization of exposure requires taking into account both uplink and downlink radio waves. Basically, for a given duplex communication, these waves are not independent and involve a power management protocol [3]. The downlink radiation is mainly impacted by the propagation environment, particularly through the attenuation suffered by the signal wave before arriving at the receiver [4]. In the other side, other than the propagation environment, the uplink radiation is dependent on the user’s activity, on the network (e.g., the rate and the QoS), and fundamentally on the performance of the device’s antenna [5]. Actually, the wireless devices are often placed in the proximity of the user’s body, which is a conducting system. Accordingly, a strong coupling effect takes place between the human tissues and the antenna [6]. These interactions can affect severely the antenna radiation properties, which are strongly involved in adjusting the uplink power [7]. The purpose of this paper is to discuss a numerical approach to characterize the variability associated with both links radiations as well as the resulting exposure, using electromagnetic simulations and statistical analysis.

Compared to previous research [8, 9], this work involves the use of an anatomic child model under various postures, including standing and sitting position. Furthermore, it aims at introducing a methodology for characterizing the uplink power fluctuations as a function of shadowing effects caused by the human body and the multipath fading. In the downlink, this study deals with a metamodeling approach allowing prediction analytically of the exposure induced by a complex propagation environment.

In fact, a FDTD simulation incorporating a human body with a resolution of 1-2 mm is very expensive in time calculation and resources, which often impedes the study of a large number of exposure configurations. Our proposed method consists of extracting an input-output transfer function, linking the exposure induced by multiple plane waves to the parameters contributing in the variability of their total electric field, using a regression metamodel approach in the postprocessing of a finite subset of FDTD simulations.

This study is a part of an European project called LEXNET [10], supported by the European Commission under the FP7, was established to minimize the exposure induced by wireless systems. The rest of this paper is organized as follows. The second section presents the methodology used in the modeling of the uplink power and the electric field received from a fixed base station. The third section illustrates the materials used to prepare the simulations. Section 4 is reserved to discuss the results as well as the statistical analysis of the uplink exposure variability. Section 5 focuses on the investigation of the exposure to single and multiple plane waves. In this section, we discuss the use of Polynomial Chaos (PC) [11] approach in the metamodeling of the multipath exposure. In the last section, we apply the proposed results to realistic traffic measurements. A global conclusion is drawn in the end of the paper.

#### 2. Exposure Assessment

In wireless systems, the total exposure induced by such a radio communication is given as the sum of the uplink exposure and the downlink exposure. Two quantities are often used to characterize such exposure: the local SAR and the global SAR. The first is defined as the power absorbed over a cube of 10 g, whose peak value is denoted by . The second is the whole-body average , well known as the ratio of the absorbed power to the whole-body weight.

During a radio communication, the global induced exposure can be deduced from the following system of equations: SAR:where and are, respectively, the and induced by a fixed uplink power of 1 W, respectively. and are, respectively, the matrix and induced by an ambient electric field of 1 V/m, respectively. It should be mentioned that the matrix is used to regroup all , those calculated over the whole body, in a 3D matrix whose dimensions are equal to the dimensions of the user’s body [12, 13]. (W) and (V/m) represent the input power delivered to the personal device and the ambient electric field, respectively.

In both above relationships, the exposure level is calculated using the proportional relationship between the absorbed power and the electromagnetic radiation, which is considered as an unknown time-varying parameter.

##### 2.1. Power Radiated by a Personal Device

This part is devoted to the modeling of the input power delivered to the personal device during an uplink communication. Obviously, this quantity depends on various parameters, including the antenna losses, the propagation channel (shadowing effects, multipath fluctuations), and the network’s requirements in terms of the signal to-noise-ratio (SNR), especially when using a power management protocol [14]. Several studies have been performed to model the uplink power on a wireless network [15]. The vast majority of these studies were largely based on the use of statistical models for multipath channel to characterize the power fluctuations in different propagation scenarios. Among the famous models, we can mention the WINNER II project [16], which provides the main propagation characteristics of a set of specific environments, such as rural, urban, and semiurban regions. For each environment, it gives a prediction of the number of paths existing between any system “transmitter-receiver” as well as their amplitudes, phases, and arrivals and departures directions. In a typical multipath propagation channel, the power should satisfy the following equation:where is the power radiated by the personal device, which takes into account the user-induced losses and the fluctuations of the radio link. Otherwise, is the antenna input power. This unknown quantity is given as the sum of the power absorbed by the users body and the useful power, which can be used to ensure the radio communication. The consideration of this basic relation is justified by the fact that the antenna is assumed well matched (without losses).

To focus only on the impact of the propagation environment and antenna performances, without taking into account the network requirements, the power is kept constant and equal to 1 mW. is the effective gain, which is the gain of the couple “user-antenna.” This couple is considered invariant. In fact, the position of the device with respect to the user’s body is assumed fixed during this study. denotes the total number of paths, including the direct path Line-of-Sight (LOS) and non-line-of-sight (NLOS) path. Each path is parametrized by two angles: an azimuth angle and an elevation angle . These angles are assumed to follow a discrete uniform distribution between and and a normal distribution with a mean of and a standard deviation of , respectively. The elevation is associated with the horizontal plane.

To model the losses induced by the distance, we have intervened an attenuation coefficient . This parameter is generated using an exponential function that depends on the delay spread .where represents the time delay between transmission and reception of a signal. This time parameter is assumed to be uniformly distributed and increasingly arranged between and . is associated with the first path, which is often the LOS. is the root mean square (rms) delay spread.

Three propagation scenarios have been considered:(i)*Line-of-Sight scenario (LOS)*: a very typical propagation of a low probability of occurrence.(ii)*Non-Line-Of-Sight Scenario (NLOS)*: common scenario, such as indoor scenarios.(iii)*Combined LOS/NLOS*: common scenario (e.g., urban scenarios).

In the first case, we recall that the radio transmission can take place only under the LOS path, while in the second scenario we assume the existence of only indirect paths (NLOS) between the user and the base station. The last scenario assumes the existence of both types of paths together during the communication.

To separate mappings between these different scenarios, we note that the first component in (2), , is associated with the LOS path. In LOS environment, takes by assuming a constant path loss normalized to be one.

In pure NLOS scenario, is chosen equal to , while in mixed LOS/NLOS scenario is subject to the Rice factor (), which is given as follows:

All attenuation coefficients are normalized so that the total sum is equal to one.

The main characteristics of each propagation scenario are illustrated in Table 1. A detailed explanation of the proposed methodology as well as considered assumptions is offered in [17].