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Sci Rep
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Scientific Reports
2045-2322
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10.1038/s41598-024-71681-z
Article
Formal estimation of wireless network services for signal strength and electromagnetic wave association in an International Green University
Fan Yang-Hsin yhfan@nttu.edu.tw

grid.412088.7 0000 0004 1797 1946 Department of Computer Science and Information Engineering, National Taitung University, 369 Sec. 2, University Rd., Taitung, 95092 Taiwan
19 9 2024
19 9 2024
2024
14 2187612 2 2024
29 8 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
The United Nations focuses on 17 urgent problems to call for action in all countries. Goal 7 of the 17 urgent problems is based on affordable and clean energy. Since 2017, National Taitung University (NTTU) has dedicated more time and effort to attain the wisdom, health, sustainability and aesthetics as an international green university. To accomplish this, we adhere and construct a safe radiofrequency and electromagnetic wave environment to achieve healthy and sustainable campus objectives. According to the UI GreenMetric World University Rankings, NTTU was ranked 74th in 2021, 67th in 2022 and 58th in 2023. In this study, we propose a formal estimation of wireless network services for classrooms or smart spaces to achieve the goal of safe radiofrequency and electromagnetic waves. Inside classrooms or smart spaces, better wireless signal strength and safer electromagnetic waves are achieved. Moreover, the proposed method can be used to determine the quantity of wireless access points for a given classroom or smart space to avoid unsafe electromagnetic waves and inappropriate energy consumption. The experimental results show that all benchmarks meet the wireless exposure limits of the WHO and physician safe technologies in the NTTU.

Keywords

Electromagnetic wave
Formal estimation
UN sustainable development goals
Wireless network
Wireless signal
Subject terms

Engineering
Mathematics and computing
issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

Recently, National Taitung University (NTTU) has continually dedicated more time and effort to attain wisdom, health, sustainability and aesthetics in an international green university. We also expect that the United Nations (UN) sustainable development goals (SDGs) can be achieved. Among the SDG issues, the UN focuses on 17 urgent problems to call action for all countries. Goal 7 of the 17 urgent problems is based on affordable and clean energy. We respond to this on our white paper and construct a safe radiofrequency and electromagnetic wave environment to attain healthy and sustainable campuses1. We first review the power consumption from 2015 to 20232, and the data are listed in Table 1. This table shows a downward trend from 2020.Table 1 Power consumption and the number of access points in the NTTU.

Power consumption		Wireless access point	
Year	kw/h		Year	Quantity	
2015	9,543,600		2015	228	
2016	9,841,229	2016	372	
2019	9,955,600		2019	428	
2020	9,852,400	2000	461	
2021	9,484,000	2021	461	
2022	9,531,600	2022	461	
2023	9,471,600	2023	461	

The COVID-19 pandemic has changed teaching activities from the classroom to distance learning. The learning styles of NTTU was modified three times during the months of May and June 2021. The teaching activities were changed from the classroom to the internet. To address the impact of teaching activity changes, wireless network services became important issues. Table 1 shows the number of wireless access points (APs) in NTTU; the APs have gradually increased from 2015 to 2023. One reason for this growth was the greater demand for the internet searches for learning. Another is the COVID-19 pandemic, which changed the classroom teaching to distance teaching. Table 1 illustrates the upward trend year from 2015 by year. As shown in Table 1, the increased APs did not consume more power from 2019 and above. However, an increasing number of APs produce electromagnetic waves; thus, faculty members were concerned on the health effect of these waves.

Internet classroom activities and social media tools have rapidly increased. Additionally, an increasing number of teachers and students search the internet via mobile devices. The use of wireless networks inside classrooms, libraries and dormitory rooms is inevitable. To provide better wireless network services, many researchers have examined the indoor positioning system (IPS) issue. Subedi, Hwang and Pyun.3 used an IPS with energy savings, low cost and architecture simplicity and presented a weighted k-nearest neighbor (Wk-NN) approach by measuring the received signal strength (RSS) data of Wi-Fi and Bluetooth low energy (BLE) beacons. Their experimental results showed that BLE achieved better distance estimation and fingerprinting positioning accuracy than Wi-Fi with the two factors of identical access point (AP) deployment and signal attenuation conditions. For location fingerprinting for indoor positioning research, a significant phase involves collecting data from various indoor locations via a received signal strength indicator (RSSI) between the Wi-Fi router and the user device, and the data are then stored in a database. However, RSSI values with irregular fluctuations from various environments produce accurate, stable, fast, and precise issues. Javed et al.4 presented 1-D convolutional neural networks (CNNs) to solve dataset scalability and RSSI fluctuations and to track user problems as hurdles and non-walkable. Experimental results reported the accuracy was 70.50% and 81.23%, respectively, in 3.47 m mean localization error. However, CNN technology may not be able to solve the location-based service (LBS) application issue on floor identification for multiple buildings and has adverse effects on device diversity. Chen et al.5 combined the cosine similarity method and CNN model to achieve multi-floor classification. They reported that the state-of-the-art floor classification accuracy based on experimental results was 98.37% for the training accuracy and 99.51% for the test accuracy by training the dataset 5 times.

For indoor location, Arif et al.6 presented a Voronoi-based interpolation method to improve accuracy and precision in comparison with the k-nearest neighbor (k-NN) and inverse distance weighting (IDW) methods. Another research study involved the design of indoor wireless radio networks. Kausar et al.7 improved the ray tracing-based propagation prediction algorithm to a three-dimensional (3D) ray tracing algorithm. The results obtained from all scenarios of the five considered environments show that the maximum accuracy and computation time are increase to 87.27% and decrease to 33.60%, respectively, in comparison with those from the existing algorithms. To locate people or objects at a room, D'hoe et al.8 proposed a signpost algorithm with MAC addresses and RSS data for indoor location estimation on a ZigBee-based wireless sensor network. Various RSS localization algorithms have been proposed in9–12.

Wang et al.13 aimed at performing regression tasks to design a denoising supervised autoencoder named Wi-Fi DSAR. Its concept was based on two vectors. One was strong resistance to noise for the received Wi-Fi signal, and the other was robustness to prevent overfitting of the fingerprint database. The experimental results were compared with three open datasets named DSI, IPIN2016 and IPIN2020, which reduced the average positioning error by 20–50%. Zhang and Xu14 applied not only stacked denoising autoencoders but also multilayer perceptrons with a self-attention mechanism. The experimental results from a public dataset such as UJIIndoorLoc achieved great robustness and improved the positioning accuracy and stability. Cui et al.15 proposed a sparse autoencoder and deep belief network algorithm for positioning an object in an indoor localization environment. The simulation results revealed greater accuracy and stability and average positioning accuracy at 1.13 m. For the unrecorded reference points causing incomplete fingerprint datasets, Park et al.16 proposed a dropout autoencoder fingerprint augmentation approach to reconstruct clean signal features for localization accuracy via deep neural network (DNN)-based regression.

Pointr17 reported the main disadvantages of location fingerprinting for indoor positioning as follows: (1) The fingerprinting technique was not suitable for venues whose layout was updated. (2) The fingerprinting technique worked only online. (3) The installation and maintenance were not easy. (4) The accuracy and stability were insufficient. (5) This method had a higher cost. (6) The method was not easily scaled. They adopted machine learning algorithms to indoor positioning to collect the related signals among the beacons, sensors, Wi-Fi access points, and smart lighting to obtain the correct path and orientation for user pathfinding.

In location-based service research, Shaflut18 continuously collected sensor data for the time of all class members, distance and variable circumstances to provide location-based services at Albaha University. The current location and time of both instructors and students were calculated to find suitable lecture-conducing solutions.

Hindia et al.19 proposed an enhanced handover algorithm for the instability handover problem. The proposed approach could not only reduce the vertical and horizontal handover redundancy but also enabled users to select the most appropriate target network. The simulation results revealed that a reduction in horizontal and vertical redundant handover was achieved and that the signal strength, delay and connection were improved.

Both academic institutions and college campus researchers are also concerned with Wi-Fi APs working for network coverage issues. Chanpinit et al.20 reported that installing one Wi-Fi-AP per three rooms (1:3) was the most acceptable solution with the lowest financial budget among the 12 installation patterns in the campus dormitory. Naik and Bapat21 aimed to vary the rectangular receiver node geometry to present an indoor wireless local area network (WLAN) propagation model. Their experimental results provided better signal coverage based on the measured data from the campus college of Belagavi, India. Naik and Bapat22 focused on improving the localization performance of LOS and OLOS. Their simulation results showed that the localization accuracy was improved for the path loss exponent by increasing the number of wireless nodes.

Problem description

The NTTU white paper declared a safe radiofrequency and electromagnetic wave environment was constructed to achieve healthy and sustainable campuses. The World Health Organization (WHO)23 and physician safe technologies24 have reported wireless exposure limits of 4.5 × 106 μW/m2 and 10 × 106 μW/m2, respectively. As online teaching activity demands continually increase, more Wi-Fi APs are sequentially set up and deployed. Thus, faculty members are concerned on the effect of electromagnetic waves on human health. In addition, more Wi-Fi APs consume more energy, and the signal fluctuates. Therefore, using a Poynting vector to measure the value as the directional energy flux spreads per unit area and per unit for more Wi-Fi APs eliminates this fear of becoming an important issue.

Stronger electromagnetic waves can provide better RSSs for wireless network services. Most of the aforementioned studies focus on measuring and analyzing the statistics of the RSSI values in corresponding to different algorithms, methods and approaches. The RSSI is a relative index of signal strength. It is used to measure the relative quality of a received signal between the Wi-Fi AP and the device. The IEEE 802.11 standard defines its values from 0 to 255. However, each chipset manufacturer can define their own RSSI value scale as either 0–60 or 0–100. Different scales of points easily cause differences in the next strategy. To avoid unforeseen mistakes, we use a more standardized absolute measure of signal strength. The decibel-milliwatts or dBm is an electrical power unit in decibels (dB) with 1 milliwatt. The power in decibel-milliwatts (PdBm) is defined as follows:1 PdBm=10×log10(PmW/1mW)

where P represents power consumption. The consumption of 10 mW add 10 dBm. Therefore, 0 dBm = 1 mW, 10 dBm = 10 mW, and 30 dBm = 1000 mW. Basically, a value closer to 0 dBm has the better signal strength.

The quantity of Wi-Fi APs and the signal strength of Poynting vector of electromagnetic waves constitute a trade-off issue. Typically, more Wi-Fi APs radiate more electromagnetic waves. Given that both factors are synchronous operations, the challenge associated with sufficient wireless network services is how to deploy the appropriate number of Wi-Fi APs with reasonable interference intensity and energy consumption. To achieve the international green university objective, we propose a formal estimation approach for the RSS and electromagnetic wave to construct healthy and sustainable campuses. We select a smart space, as shown in Fig. 1, which is located on the second floor in NTTU Library and Information Center. The space consists of a business area, room 1, room 2, room 3, and room 4 that are widely used by students, faculty members, and visitors.Fig. 1 Case study building at the National Taitung University Library and Information Center.

The installation locations of Wi-Fi APs include classrooms, smart spaces and meeting rooms. These areas are classified as medium-density indoor environments. Moreover, considering the Wi-Fi AP cost and the existing compatible network systems, we adopt the FortiAP-221C device. Two FortiAP-221C devices of the service set identifier (SSID) are set as MROL1-AP05 and MROL2-AP06, which work on a Wi-Fi 5 system with a 2.4/5 GHz frequency, omnidirectional antenna and 2 × 2 MIMO. Figure 2a displays a number of measured Wi-Fi AP signals by the Wi-Fi Analyzer application25, named MROL1-AP05, MROL2-AP06, and Love in the air in Fig. 1. The top three RSSI values are approximately -46, -58 and -80 dbm. In essence, a lower value of dbm results in better signal strength for wireless communication. The experimental results show that the range of signal strength for surfing the internet is from 0 to − 80 dbm. Therefore, wireless access points other than MROL1-AP05, MROL2-AP06 and Love in the air result in worse signal strength. On the other hand, the antenna radiation patterns of the FortiAP-221C data sheet26 are shown in Fig. 2b–d. On the H-plane in Fig. 2c, either 2.4 or 5 GHz has a nearly circular shape. For the other E-plane pattern in Fig. 2d, the 2.4/5 GHz frequency radiation fluctuate more than those in the H-plane. Two planes also illustrate the associations of the FortiAP-221C center and degree factors. However, the better signal strength consumes more energy than the worse signal27. Specifically, a high RSS is closely associated with the electromagnetic wave power density. We aim to address in detail to gain better wireless network services, electromagnetic strength and energy consumption; this is an international green university goal for constructing a safe radiofrequency and electromagnetic wave environment.Fig. 2 Antenna radiation patterns of Fortinet 221C Wi-Fi AP and measured signal strength of Wi-Fi APs in 2F, information network services section, library and information center at NTTU.

Formal estimation

As the demands of wireless network services of learners greatly increase, better wireless network services are needed. Traditionally, increasing the number of Wi-Fi APs can efficiently improve wireless network service; however, the following factors points need to be considered: the number of newly added Wi-Fi APs; the location of deployment; and the radiation of each Wi-Fi AP from the electromagnetic wave. To identify those effects in the NTTU campus, we present a formal estimation approach to balance these factors to gain better wireless network service, electromagnetic wave strength and less energy consumption.

Single wireless access point service scope

Given the measured wireless access point signal strength, such as MROL1-AP05 in Fig. 2a, the service scope is located inside the ellipse, as shown in Fig. 3a. Five devices marked with white circles on the ellipse can surf the internet with different signal strengths. We observe that the service scope is an ellipse that was measured by a mobile application25. Considering that the signal strength may be of arbitrary size rather than specific to an ellipse, we derive the spread of the wireless network services by using the integration theory of mathematics for various ellipses as follows. For an ellipse with the x radius equal to a and the y radius equal to b in Fig. 3b, the parameterization of the ellipse can be expressed in (2).2 x=acosθy=bsinθ

Fig. 3 MROL1-AP05 wireless access point signal strength.

The area of Fig. 3b is equally divided into two symmetrical regions. One region with a dotted line can be calculated via (3).3 f11(x)=12A=∫0aydx=∫0π2bsinθdx

Replacing x with acosθ in (4) yields the following:4 =∫0π2bsinθ·d(acosθ)=∫0π2bsinθ(-asinθ)dθ=∫0π2-absin2θdθ

The double-angle formula and power-reduction formula are shown in (5):5 cos2θ=1-2sin2θsin2θ=1-cos2θ2

sin2θ in (4) is replaced with (5) to produce the following equation:6 =∫0π2-ab1-cos2θ2dθ=ab2∫0π2-(1-cos2θ)dθ=ab2∫π201-cos2θdθ=ab2(θ+sin2θπ20)

The above mathematical induction of the service scope for half of a single wireless access point (Fig. 3b), can be extended to one ellipse (Fig. 3c). Thus, Lemma 1 and Theorem 1 are derived naturally.

Lemma 1:

An Wi-Fi AP has the characteristics of signal strength and electromagnetic waves if all the equivalent signal strengths and electromagnetic waves completely belong to the scope, as shown in Fig. 3a.

Theorem 1:

An Wi-Fi AP measures the signal strength and electromagnetic wave if all the equivalent signal strengths and electromagnetic waves completely belong to the scope, as shown in Fig. 3a.

Proof:

For a Wi-Fi AP with a signal strength and electromagnetic wave for the scope, as shown in Fig. 3c, the right half of the signal strength and electromagnetic wave belongs to the type shown in Fig. 3b. Thus, the number of signal strengths and electromagnetic waves in Fig. 3c is twice that of the right half. Since Fig. 3b is half of Fig. 3c, the area of Fig. 3c can be calculated via (7). As the signal of the wireless access point spreads out in every direction, their transit routes, which are labeled as f11(x), f12(x), f13(x),…, f1m(x) and are illustrated in Fig. 4, depart from the Wi-Fi AP. Each transit signal, f11(x), f12(x), f13(x),…, and f1m(x), affects the scope, as depicted in Fig. 5. The area of each transit signal is similar to that in Fig. 3c. All form a set of slices, as illustrated in Fig. 5. Each slice uses (7) to calculate their respective area. Finally, the scope of the Wi-Fi AP can be produced by the sum of f11(x), f12(x), f13(x),…, and f1m(x), as shown in (8).7 f1(x)=2f11(x)=A=∫0πbsinθdx

8 S=f11(x)+f12(x)+f13(x)+...+f1m(x)=∑i=1mf1i(x)

Fig. 4 Spread signals of the wireless access points.

Fig. 5 Slices of the wireless access point zone.

Experimentally, most of the Wi-Fi AP locations in NTTU are shown in Fig. 6a; moreover, only one Wi-Fi AP cannot produce sufficient wireless signal strength. If a classroom or smart space has overlapping effect signals, then the overlap scope can be calculated via a set of formulas for Fig. 6b. Therefore, Lemma 2 and Theorem 2 are obtained; this is addressed in Section B.Fig. 6 Overlap effect signals for the dual wireless access points.

Dual wireless access points service scope

For a space with weak signal of wireless network, the addition of a new access point is commonly method to improve the signal. This results in new issues such as the signal overlap of at the deployed location and electromagnetic wave and spread over the whole space. For the signal overlap issue, an ideal layout is the least overlap signal between two wireless access points. Specifically, we expect to create an ideal layout to gain more spread over space with fewer wireless access points and less signal interference. As the overlap scope of two Wi-Fi APs is constantly changing, such as in Fig. 2a, their radiation pattern can be derived as a set of integration theory formulas as follows.

Lemma 2:

Two Wi-Fi APs have the overlap scope of signal strength and electromagnetic waves if all the equivalent signal strengths and electromagnetic waves completely belong to the scope shown in Fig. 6a.

Theorem 2:

Two Wi-Fi APs measure the signal strength and electromagnetic wave if all the equivalent signal strengths and electromagnetic waves completely belong to the scope shown in Fig. 6a.

Proof:

Given an overlap signal for dual Wi-Fi Aps, as shown in Fig. 2a for MROL2_AP06 and ProB, the equivalent and analytical figures are shown in Fig. 6a,b, respectively. We define the function f1(x) in Eq. (9) for MROL2_AP06. The other function f2(x) in Eq. (10) is defined for ProB. The total scope shown in Fig. 6b consists of parts of MROL2_AP06 and ProB. Therefore, we separately compute the radiation scope of MROL2_AP06 as F1(x) and ProB as F2(x).9 f1(x)=-(x+L2)2+R12

10 f2(x)=-(x-L2)2+R22

The area of f1 is expressed in (11):11 F1(x)=∫-(x+L2)2+R12dx

The center of the oval is set from A -L2,0 to (0,0), and F1(x) is expressed in (12):12 F1(x)=∫R12-x2dx

The following is applied:13 x=R1sinθ1>0,-π2<θ1<π2dxdθ1=R1sinθ1dθ1

14 dx=R1cosθ1dθ1

(12) can be used, x2 is replaced with R1sinθ12 and F1(x) is shown in (15):15 F1(x)=∫R12-(R1sinθ1)2dx=∫R12-R12sin2θ1dx

Based on the formula of trigonometry in (16), the following can be defined:16 sin2θ1+cos2θ1=1

Multiplying by R12 for (16) produces (17):17 R12sin2θ1+R12cos2θ1=R12R12cos2θ1=R12-R12sin2θ1

Replacing (15) with (17) yields (18):18 F1(x)=∫R12cos2θ1dx=∫R1cosθ1dx

Replacing dx with (14) yields (19):19 F1(x)=∫R1cosθ1R1cosθ1dθ1

20 F1(x)=R12∫cos2θ1dθ1

Based on the half-angle formula in (21), the following can be defined:21 cosθ12=±1+cosθ12cos2θ12=1+cosθ12

θ12 and θ1 are replaced with θ1 and 2θ1 in (21) for (20), respectively, to produced (22):F1(x)=R12∫1+cos2θ12dθ1

=R122∫1+cos2θ1dθ1

22 =R122×(θ1+12sin2θ1)+c

(13) can be used to produce the following equation:23 xR1=sinθ1⇒θ1=sin-1(xR1)

Part of (22) can be rearranged as follows:24 12sin2θ1=12(2sinθ1cosθ1)=sinθ1cosθ1

By separately replacing sinθ1 and cosθ1 with xR1 and R12-x2R1, (24) can be used to produce the following equation:25 sinθ1cosθ1=xR1×R12-x2R1=xR12-x2R12

(22) can be used, and θ1 and 12sin2θ1 is replaced with sin-1(xR1) and xR12-x2R12 in (23) and (25) to produce the following equation:26 R122×sin-1(xR1+xR12-x2R12)+c

Similarly, the following can be defined:27 F2(x)=∫R22-x2dx=R222×sin-1(xR2+xR22-x2R22)+c

Figure 7 shows spread signals with overlap effects for dual Wi-Fi APs. The left hand, named MROL2_AP6, has spread signals called f11(x), f12(x), f13(x),…, f1m(x). On the other hand, the named ProB also has a set of signals named f21(x), f22(x), f23(x),…, f2n(x). The overlap effect signals for dual Wi-Fi APs are labeled as f11(x) and f21(x). Both functions are derived in (26) and (27). Other functions, f12(x), f13(x),…, f1m(x) and f22(x), f23(x),…, f2n(x), are derived in (7). (28) is derived from (7), (26) and (27) for the dual Wi-Fi APs with overlap effect signals.28 S=f11+f12...1m+f21+f22...2n=R1122×sin-1(xR11+xR112-x2R112)+c+∑i=2mf1i(x)±R2122×sin-1(xR21+xR212-x2R212)+c+∑j=2nf2j(x)

Fig. 7 Spread signals with overlap effects for dual wireless access points.

Experimental results

Figure 8 shows the case study at 2F of the information network services section, library and information center in NTTU. This case study consists of one business area and four smart offices labelled as room 1, room 2, room 3 and room 4. The four transmitting devices are Wi-Fi APs and labelled as WA, WB, WC, and WD; these are separately arranged in four locations at a height of 2.2 m, and this height is selected for its better transmission. The WA, WB, WC, and WD are implemented by Fortinet FortiAP-221C. Any two devices for WA, WB, WC, and WD are simultaneously set to meet the requirements of internet searching by the e-reader, Apple iPad, tablet computer or mobile devices. These results rely on practical experience and theories. On the other hand, two transmitting devices obtain better transmitting and receiving signals than one transmitting device. For one transmitting device, the measured results of the electromagnetic wave power density and energy consumption were presented by Fan27. For the effect of two transmitting devices, the experimental scenarios and measured results are discussed below.Fig. 8 Case study in the information network services Section 2F, library and information center, NTTU.

The first benchmark, called benchmark 1, consists of WA and WB, which are located in the business area and room 2, respectively. The locations of WA and WB are the near the center of the business area and four rooms because they are usually considered to have better transmitting coverage. This results from the rule of thumb; thus, we design this case to verify it. Moreover, the effects of overlap for WA and WB on signal strength and degree of decrease from the near center is also measured. The second benchmark, benchmark 2, is composed of WC and WD, which are located nearby rooms 1 and 4. One location is set at the left edge, and the other is set at the right edge. This benchmark is used to investigate the degree of decrease in signal strength from the two edges of the smart space. In addition, the minimum energy consumption for the overlapping electromagnetic waves can be measured. Next, two experiments were separately designed using WA with WD and WB with WC, to measure the overlap effect of electromagnetic waves between the near center of the smart space and the edges of the two sides.

Table 2 shows the results of electromagnetic wave power density and energy consumption for groups G0, G1, …, to G7 of benchmarks 1 and 2 as measured with the Tenmars TM-196 instrument. The locations of G0, G1, …, to G7 are determined with a rule of thumb for users who use smartphones to communicate to WA, WB, WC or WD. For G0 in benchmark 1, the WA and WB serve 34 and 63 dbm signal strength, respectively. These results indicate that the WA supplies better signal strength for users than the WB because of the smaller number of signals. However, the maximum electromagnetic wave power density is 6000 ± 2000 µW/m2 among the locations. For G1, the WA and WB supply 56 and 37 dbm signal strength, respectively. The WB has better signal strength than WA. The electromagnetic wave power density is 2500 ± 500 µW/m2. Both G0 and G1 have higher electromagnetic wave power densities due to their location near WA and WB. G2 receives 71 and 74 dbm from WA and WB, respectively, and the signal strength is weaker than those of G0 and G1. This is caused by the locations, which are on the far side of the WA and WB. On the other hand, the electromagnetic wave power density is 30 ± 3 µW/m2. The next location, G3, receives 75 and 77 dbm from WA and WB, respectively, with an electromagnetic wave power density of 70 ± 5 µW/m2. In a comparison of the signal strengths of G2 and G3, the transmitting quality is similar, but the latter has a higher electromagnetic wave power density than the former. This may be caused by the wall between the transmitter and receiver in G3. For G4, the WA and WB provide 47 and 66 dbm signal strength, respectively, with an electromagnetic wave power density of 55 ± 5 µW/m2. Another evaluation point, G5, is near G4; for G5, the signal strengths of WA and WB provide 57 and 71 dbm, respectively, with an electromagnetic wave power density and 25 ± 2 µW/m2. The signal strength of G4 is better than that of G5. On the other hand, the electromagnetic wave power density of G4 is greater than that of G5. For G6, the signal strengths of WA and WB is 65 and 52 dbm, respectively, with an electromagnetic wave power density of 25 ± 5 µW/m2. These results show that the signal strength of WB is superior to that of the WA. For G7, the signal strengths from WA and WB are 45 and 62 dbm, with an electromagnetic wave power density of 80 ± 20 µW/m2.Table 2 RSSI and power flow of an electromagnetic field for G0, G1,…, to G7 to WA and WB and WC and WD.

Smartphone	Benchmark 1	Benchmark 2	Benchmark 3	Benchmark 4	
-dbm	EM. wave	-dbm	EM wave	-dbm	EM wave	-dbm	EM wave	
WA	WB	μ W/m2	WC	WD	μ W/m2	WA	WD	μ W/m2	WB	WC	μ W/m2	
G0	34	63	6000 ± 2000	69	82	90 ± 5	32	79	6000 ± 2000	57	54	90 ± 5	
G1	56	37	2500 ± 500	72	71	40 ± 10	64	81	120 ± 20	39	73	2500 ± 500	
G2	71	74	30 ± 3	35	-	45 ± 5	69	-	15 ± 10	70	37	100 ± 50	
G3	75	77	70 ± 5	-	48	38 ± 2	76	40	50 ± 3	84	-	25 ± 2	
G4	47	66	55 ± 5	74	77	50 ± 10	53	69	60 ± 5	60	80	53 ± 10	
G5	57	71	25 ± 2	77	71	15 ± 3	68	72	25 ± 2	65	91	30 ± 10	
G6	65	52	25 ± 5	49	89	30 ± 5	66	87	20 ± 1	66	49	20 ± 3	
G7	45	62	80 ± 20	68	77	80 ± 5	39	80	20± 10	54	64	60 ± 10	

Benchmark 2 changes from WA and WB to WC and WD. The G0 measured data for WC, WD and the EM wave are 69 dbm, 82 dbm and 90 ± 5 µW/m2, respectively. These results show that WC supplies better signal strength than WD. For G1, both WC and WD serve signal strengths of approximately 72 and 71 dbm, respectively, with an electromagnetic wave power density of 40 ± 10 µW/m2. Based on the results of G0 and G1, we estimate the locations of the signal strength edge near G0 or G1. For G2, only one data point is measured as 35 dbm from the WC. The other data point from WD is not able to be measured; this is potentially due to distance and the location. Similarly, G3 is only able to measure WD. For G4 and G5, the quality of the signal strength is similar, but the former has stronger electromagnetic wave power density than the latter. For G6 and G7, Wc provides better signal strength than WD. Moreover, the electromagnetic wave power density of G6 is less than that of G7.

Table 2 shows the results of benchmarks 3 and 4 for evaluating the electromagnetic wave spread from the near center and edge. In benchmark 3, the results from G0 for WA and WD are 32 and 79 dbm, respectively, with electromagnetic wave power density of 6000 ± 2000 µW/m2; these results are similar to those of benchmark 1. The data from G0 show that the location has the strongest electromagnetic wave power density and the best signal strength. For G1, WA provides better signal strength than WD, with an electromagnetic wave power density of 120 ± 20 µW/m2. For the location at G2, WD is not able to be measured; hence, WA has the lowest the electromagnetic wave power density effect results. The G3 in contrast to G2 receives better signal strength from WD. G4, G5, G6 and G7 communicate to the WA to achieve better signal strength. The electromagnetic wave power density gradually decreases from 60 ± 5 to 20 ± 10 µW/m2. Benchmark 4 individually changes the locations of WA and WD to WB and WC. The results from G0 show that WB or WC provides similar signal strength qualities. For G1, the signal strength of WB is better than that of WC. The electromagnetic wave power density of G0 and G1 are 90 ± 5 µW/m2 and 2500 ± 500 µW/m2, respectively. G2 receives the best signal strength from WC and has the electromagnetic wave power density of 100 ± 50 µW/m2. For G3, only the WB can supply service. Compared with G4 and G5, WB or WC provides similar signal strengths, but G5 has a lower electromagnetic wave power density. The last two results show that G6 and G7 separately communicate between the WC and WB to achieve better signal strength, but G6 has a lower electromagnetic wave power density. Based on the results in Table 2, the measured electromagnetic wave data meet the wireless exposure limits from the viewpoint of the World Health Organization (WHO)23 and physicians’ safe technology24.

Conclusions

Wireless network service demand greatly increases at NTTU because an increasing number of students learn through e-learning. To provide better wireless network service with good signal coverage and electromagnetic wave effects, we propose a formal estimation approach to identify the spread scopes for each wireless access point. Network administrators need to evaluate the number of wireless access points for deployment in classrooms or spaces. Moreover, different wireless access points result in the signal overlap effect, which needs to be considered. For the electromagnetic wave issue, we measure the data for the G0, G1,…, G7 locations, which are located inside the signal spread areas. The experimental results indicate that the highest value of the electromagnetic wave is located near the wireless access point. Another results show that the wireless signals of all benchmarks can provide the wireless network demand for all users. Third, benchmark 1 gains a better signal spread scope than the other benchmarks; however, benchmark 2 transmits the lowest amount of electromagnetic waves. Finally, all benchmarks meet the wireless exposure limits of the WHO and physician safe technologies at NTTU with a safe radiofrequency and electromagnetic wave campus.

Author contributions

Y.-H.F. did all works wrote the complete.

Data availability

All data generated or analysed during this study are included in this published article.

Competing interests

The author declares no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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