Introduction
The demand for more performant wireless networks is continuously increasing. Applications such as autonomous vehicles, Internet of Things (IoT) and Industry 4.0 require extremely reliable, ultra-low latency and very high throughput wireless connectivity [1]. The fifth generation (5G) of cellular networks has addressed these needs with a number of solutions [2], [3]. One such technology is Massive Multiple-Input-Multiple-Output (MaMIMO) [4]: a large number of antennas in the transmitter (Tx) enables precoding (or beamforming [5]) to exploit the environment’s spatial diversity, thereby increasing the network capacity [6]. Commercial MaMIMO deployment is ongoing [7, Sec. 5], [8]. This has prompted the research literature to focus on the question “What is next?”, proposing Distributed MaMIMO proposed as a prospective sixth generation (6G) technology [9]. A MaMIMO base station (BS) is distributed (DMaMIMO) when its antenna elements are located in different geographic positions [10], i.e., the separation is much larger than the wavelength. When the separation is electrically small, channel capacity is hindered by unfavorable propagation conditions (reduced “mutual orthogonality among the vector-valued channels to the terminals” [11]) and pilot contamination [12]. When the separation is electrically large, the channel orthogonality increases with antenna density [13]. Also, the broader paradigm envisions a cell-free MaMIMO network of Access Points (AP), effectively removing pilot contamination [13], [14]. Another way 5G delivers on its ultra-low latency and exceptional data throughput is by increasing the operating frequency. The first frequency band (FR1) around 3.5 GHz is employed by the majority of commercially sold 5G BSs in Europe. The second frequency band (FR2) around 28 GHz is also known as the mm-Wave 5G band. In ideal conditions, the larger bandwidths enables record-breaking data rates [15], [16]. However, the higher free-space path loss limits the use of mm-Waves to short UE-to-BS distance, such as near an AP. Therefore, DMaMIMO and high mm-Waves frequencies are two 6G directions that work constructively.
The assessment of human exposure to electromagnetic fields (EMFs) is of great importance for public health [17]. The International Commission on Non-Ionizing Radiation Protection (ICNIRP) provides internationally accepted safety guidelines that limit certain exposure metrics [18]. While worst-case exposure has been the subject of much research guaranteeing safety [19], [20], less is known about realistic exposure. To achieve this, the propagation and exposure steps need to be rigorously integrated into one method, for example by hybridizing ray tracing (RT) with the finite-difference time-domain (FDTD) method [21] or a spherical near-field transformation with FDTD [23]. Recently, the influence of DMaMIMO on the behavior of hotspots and their resulting exposure has been examined at 3.5 GHz [24]. The latest update of the ICNIRP guidelines in 2020 [18] introduces the absorbed power density
comparison between distributed and collocated MaMIMO BS exposure;
quantification of the new basic quantity
for new MaMIMO technologies.$S_{\mathrm {ab}}$
Methods
A. Configurations
Figures 1a and 1b each show a realization of the two industrial environments studied. In both, a closed concrete (
Two indoor industrial environments studied. Shown here are examples of realizations with randomly selected scatterers. The Rxs in red merely indicate their position and do not scatter any rays. Some walls and the ceiling are shown transparent for clarity in this figure.
1) Collocated (COL) and Distributed MaMIMO (DIS) Channels
The room’s footprint is square and has dimensions 50
Three UEs receive a signal. The number of Rxs is chosen low to reduce computational costs. The number of channel realizations is chosen high (100) to enable a statistical analysis of the exposure distributions. The first UE is placed at a horizontal separation from the BS (henceforth UE separation) of 2.5 m. The second and third have a UE separation of 7.5 and 12.5 m.
2) Line-Of-Sight (LOS) and Non-Line-of-Sight (NLOS) Channels
The room’s footprint is rectangular with dimensions 40
3) Parameters
The n77 and n261 frequency bands are used throughout the numerical pipeline. In the following, we refer to these as the 3.5 and 28 GHz bands, respectively. Their spectrum parameters are listed in Table 1. Two realistic BSs are modeled for 5G coverage at these frequencies. Their physical parameters are listed in Table 3.
The parameters used for the RT simulations are shown in Table 2. These parameters are sufficient to accurately predict the channel in the modeled indoor environment [22]. The MaMIMO BS is an array consisting of equally spaced dual-polarized antenna elements. Their parameters are also listed in Table 3. The inter-element spacing in the collocated MaMIMO BS is
B. RT-FDTD
The hybrid RT-FDTD tool developed in [21] is extended to mm-Wave frequencies. The fundamental method is the same: the scattered EMFs by plane waves (PWs) are first stored and then combined based on the full channel matrix. The schematic specifies how this fundamental method is looped over all parameters of interest, for one configuration. The RT and FDTD initialization followed by their hybridization are detailed schematically in Fig. 2.
Schematic detailing the full numerical pipeline for a configuration. The initialization consists of independent RT and FDTD parts. Using the colored data, the hybridization step yields exposure quantities. A labeled box indicates its contents are looped over the dimension denoted by the for all symbol
For the FDTD initialization and exposure evaluation, a number of adaptations are made. These are shown visually in Fig. 3. A Multimodal Imaging-Based Detailed Anatomical Model of the Human Head and Neck (MIDA) [25] is used as a phantom. The phantom is highly detailed and features a spatial isotropic resolution of
FDTD-domain. A hotspot is shown in yellow around the focus point in blue. Increased surface absorbed power density
C. Computational Considerations
The MaMIMO BS requires the knowledge of the wireless channel to perform the precoding. We calculate the channel matrix coefficient as the sum of the signals with different directions of arrival (DoAs) [27]. A signal is the electric field’s
The higher frequency results in prohibitively large computational costs (due to, e.g., the Courant limit [28]). Therefore, the execution time of each FDTD simulation at 28 GHz is reduced by a combination of techniques. First, the workflow of Fig. 2, including pre- and post-processing, is parallelized on a high-performance computing cluster with 40 CPUs and a performant GPU. Second, the ray approximation is more justified at higher frequencies, reducing the number of required rays in the RT simulations. As a result, the number of reflections and diffractions is decreased, as shown in Table 2. Finally, at 27.9 GHz the millimeter-sized voxels overresolve the model’s head features. This gives us the freedom to reduce the voxel size to
In configuration 1, the number of channel realizations is chosen large (100). Therefore, we study the exposure distributions in this configuration. In configuration 2, the number of receivers is chosen large (9). Thus, we study the influence of position in this configuration.
D. Exposure Assessment
The reference levels defined by the ICNIRP for human exposure at both 3.5 and 28 GHz is the power flux density \begin{equation*} \eta _{\gamma } = \frac {\gamma }{\gamma _{\mathrm {limit}}} \cdot 100 \% \,.\tag{1}\end{equation*}
The values of \begin{equation*} \alpha = \frac {\eta _{\mathrm {b}}}{\eta _{\mathrm {r}}} \cdot 100\% \,\tag{2}\end{equation*}
Results
A. General Results
In Figures 4 through 7, results from the first configuration (COL/DIS) are presented in a matrix of plots, comparing across frequency (the 3.5 and 28 GHz frequency bands) and BS type (the collocated and distributed MaMIMO BSs). The main interest is how the exposure values are distributed for each of these cases. The vertical axes reads the Cumulative Distribution Functions (CDFs) of the exposure quantity from the 100 channel realizations. The bottom horizontal axes of the plots are the normalized exposure quantities. The top horizontal axes is scaled such that it displays the corresponding
Reference quantities normalized for a 1 W radiating BS in configuration 1. Clarification of this figure is provided in Section III-A. In the distributed MaMIMO case, two exposure clusters can be seen, delimited around
Basic quantities normalized for a 1 W radiating BS in configuration 1. Clarification of this figure is provided in Section III-A. In the distributed MaMIMO case, exposure clusters can be seen, shown in cyan on the horizontal axis. For 28 GHz, three are seen, delimited around 0.05mW/m2 and 0.15mW/m2.
Reference quantities normalized for a 1 W radiating BS and for 1 W total incident power on the Rx in configuration 1. Clarification of this figure is provided in Section III-A. No clusters are observed.
Basic quantities normalized for a 1 W radiating BS and for 1 W total incident power on the Rx in configuration 1. Clarification of this figure is provided in Section III-A. Clusters, shown in cyan on the horizontal axis, are only observed in the distributed MaMIMO 28 GHz case, delimited around
In Fig. 8 and 9, results from the second configuration compare the 3.5 and 28 GHz bands side by side. The main interest is how the exposure values depend on position to the BS and presence of a blocker. The left and right vertical axis indicates the relevant exposure quantity and its corresponding
Reference quantities normalized for a 1 W radiating BS in configuration 2. Clarification of this figure is provided in Section III-A. The exposure is closer to the limit for 3.5 GHz than for 28 GHz.
Basic quantities normalized for a 1 W radiating BS in configuration 2. Clarification of this figure is provided in Section III-A. The exposure is closer to the limit for 3.5 GHz than for 28 GHz.
B. Configuration 1: COL vs DIS
In general, the Rxs closest to the BS have the highest exposure, in particular for the first Rx. However, the focus of this configuration’s analysis is not on position, but on the distributions of exposure quantities. One hundred channel realizations were necessary to sufficiently resolve the exposure distributions.
1) Reference Quantities
The results of the reference quantities are shown in Figure 4. Realistic values are at most 4% of their limits in 95% of cases for a BS radiating 320 W. All exposure metrics are 2 to 3 times less with a distributed BS compared to a collocated BS. For the distributed BS, more elements are distant from the receivers, reducing the total incoming power. The exposure distribution with the collocated BS can be well modeled by a Ricean fading channel. This suggests that a LOS component or strong reflection path dominates the channel. The distributed BS does not generate a Ricean fading channel. Instead, two regions are identified of low and high exposure (Fig. 4, right), delimited around 0.19 mW/m2. We call these exposure clusters. In the first cluster, a similar exposure distribution to the collocated BS is seen. The standard deviation of the second cluster is 4.5 times broader than the first. These results can be explained as follows. When a UE is surrounded by scatterers, the probability that exposure belongs to the first cluster is highest. The channel resembles that of the collocated BS, because the interaction happens mainly by one or a few nearby antenna elements. When no nearby scatterers shadow the UE, the probability that exposure belongs to the second cluster is highest. The interaction can now occur with a larger number of antenna elements farther from the UE. Therefore, the number of reflections and diffractions taken by the rays is higher. The variability in exposure is thus higher. As seen in Fig. 1a, the scatterers belong to a regular grid, the antenna elements are directly above this grid, and the receivers are located at the center of each grid cell. This set-up makes it possible for receivers to be completely encircled or not by scatterers. Similar exposure distributions are observed when comparing the 3.5 and 28 GHz bands. With the collocated BS, the 95th percentile is 12% lower at mm-Wave frequencies. With the distributed BS, the reduction is 55%. In this case, the standard deviation of the second exposure cluster is much lower. This is likely due to the increased path loss at these frequencies reducing the number of interactions with distant antenna elements.
2) Basic Quantities
The results of the basic quantities are shown in Fig. 5. Realistic values are at most 0.85% of their limits in 95% of cases. Note that these
3) Normalized Results to Incoming Rx Power
Before the precoding step, the total power is split evenly among the antenna elements. In the distributed MaMIMO BS case, the receiver is surrounded by a small number of antenna elements each having a fraction of the total output power. In the collocated MaMIMO BS case, the receiver is near all antenna elements radiating the total output power. The exposure quantities are therefore substantially lower with distributed BSs compared to collocated ones. Commercial distributed MaMIMO BSs do not exist yet; neither do corresponding regulations. It is therefore unknown what realistic total output powers will be of these systems. The output power is presumably higher, and likely dependent on the number of antenna elements and the area covered. Therefore, the above conclusion may not be realistic due to the equal power assumption. There are a number of ways to normalize the exposure quantities such that a fair comparison becomes possible. One of them is dividing the result by the total incoming power \begin{equation*} E^{\text {tot}} = \sum _{i} w_{i} \hat {E}_{i} \,\end{equation*}
\begin{equation*} P^{\text {Rx}} = \sum _{i} |w_{i}|^{2} \,.\end{equation*}
\begin{equation*} \gamma = P_{\text {BS}} \cdot P^{\text {Rx}} \gamma _{\text {1 W}}^{\text {1 W}} \,.\end{equation*}
C. Configuration 2: LOS vs NLOS
Figures 8a and 8b compare the reference quantities as a function of distance at 3.5 and 28 GHz, respectively. Figure 9 does so for the basic quantities. All distance profiles are highly correlated across frequency and exposure quantity. The maximum
Conclusion
The 5G and 6G advances in mm-Wave frequencies and distributed MaMIMO demand realistic exposure assesment. A state-of-the-art hybrid RT-FDTD tool is extended to 28 GHz by including the new absorbed power density as basic quantity set forth by the ICNIRP 2020 guidelines [18]. A multi-dimensional comparison is enabled by increasing the computational efficiency and budget. In a first configuration, clusters are observed in the distribution of exposure quantities for distributed MaMIMO BSs. We discuss the need to normalize the exposure to the incoming power on the Rx. It is shown that exposure clusters are mainly caused by the propagation step. The highest 95th percentile among the exposure quantities expressed w.r.t. to their maximum allowed by ICNIRP is found for collocated BSs at 3.5 GHz, at 4%. With equal power, distributed BSs contribute 2 to 3 times less to all exposure metric than collocated BSs. Exposure is lower at 28 GHz compared to 3.5 GHz, due to the increased path loss. In a second configuration, the influence of UE separation and presence of a NLOS blocker is analyzed. It is found that LOS exposure follows a power law and NLOS exposure shadows the UE. In both configurations, with respect to their limits, basic quantities are 5 to 10 dB lower than reference quantities, guaranteeing ICNIRP’s assumption. In future work, more comparisons with different important factors could be considered. For example, the influence of using a different precoding technique on realistic exposure with distributed MaMIMO at mm-Waves is unknown. Furthermore, the realism of industrial indoor environments could be improved. LIDAR-based models are seen as a good candidate due to their high accuracy. Lastly, the exposure of other 6G technologies such as ELAAs and holographic MaMIMO could be investigated, ideally at sub-THz frequencies.