Investigating small sized metal blockage effects at 60 and 100 GHz using measurements and modeling approaches

Abstract

Millimeter wave (mmWave) technologies at 60 GHz and 100 GHz bands are currently gaining significant attention for its potential to meet the demanding needs of next-generation networks. These include ultra-high data rate, ultra-low latency, high spectral efficiency, and high end-to-end reliability. However, mmWave signals’ blockage remains a critical issue that affects the reliability of mmWave at 60 GHz and at 100 GHz bands due to the significant attenuations induced by the blockers (BLs). Not only blockers that have the size of a human body or even larger can affect the signal, but also smaller objects with much narrower dimensions, as narrow as 4 cm, can severely affect the signal strength and introduce an attenuation that reaches up to 12 dB at 100 GHz. In this paper we have conducted new measurements and presented results for three small copper sheets at each frequency band, aiming to investigate the blockage effect of small-sized metal objects on signal strength at these two frequency bands. Also, we have examined the performance of the knife-edge diffraction (KED) blockage model of the third-generation partnership project (3GPP) standards body and its evolved version named the mmMAGIC blockage model in such scenarios. Furthermore, we investigated the applicability of the two blockage models in capturing the attenuation characteristics of other materials-such as wood and glass. Experimental results supported by numerical models have shown that the induced peak attenuations are 5(12) dB, 10(23) dB, 23(23) dB for 4 $\times$ 4 cm, 8 $\times$ 8 cm, 16 $\times$ 16 cm copper blockers, respectively, at 60(100) GHz mmWave bands. Also, we have shown that both the 3GPP and mmMAGIC simulation models fail to accurately capture the attenuation characteristics of materials other than copper. The findings of this work highlight the importance of considering the dimensions and types of blockages when deploying reliable mmWave and sub-THz communications.

Introduction

The marvelous features of the unlicensed millimeter-wave (mmWave) spectrum at the 60 GHz band, such as wide bandwidth, high-speed communication, and low latency, make it suitable for short-range communications either for indoor or outdoor environments¹. These features become even more beneficial at higher frequencies band. In particular, the at 100 GHz has some fascinating applications beyond 5G^2,3. The anticipation of the coming cellular generation, i.e., the 6th, is to benefit from the advantages of the sub-THz frequency band starting beyond 100 GHz⁴. However, sensitivity to blockage effects is a common challenge that faces communications using both mmWave and THz radio frequency bands^5,6. Blockage phenomena at very high frequency is a critical issue that has attracted the researcher’s attention as they seek to understand its effects on signal strength and network configurations. The impact of blockage attenuation on robust communication links is not only limited to terrestrial communications but also extends to UAV communications within the 60 GHz mmWave band⁷. The results in⁸ show that it is essential to consider and understand the blockage effect behavior while planning the locations of mmWave access points for indoor and outdoor environments.

Investigating the blockage effect extends beyond mere lab measurements but by introducing some mathematical models that simulate the blockage effects on signal strength. For the 60 GHz, the authors of⁹ alongside their work on channel modeling for 60 GHz IEEE 802.11ad have used a multiple knife edge (KED) concept to model measured human blockage effects. A similar model was applied in¹⁰ as well. Besides the KED model, the authors of¹¹ have introduced some cylinder and hexagon models that represent the human blockage effect. The performance analyses for an outdoor mesh network in¹² show that the presence of blockers has a notable impact on mmWave communications at 60 GHz. The authors of¹³ analyzed the effect of blockages on indoor environments such as shopping malls and offices. Human blockage effects have been considered at the frequency band of 60 GHz and have been investigated in several studies such as^14–17. Also, some empirical results for human blockages at 60 GHz were presented in¹⁸. The authors of¹⁹ investigated the effect of selfblocking caued by human in the mmWave bands.

As a part of the network topology evolution, the researchers in²⁰ examined the impact of human blockage in the frequency band above 100 GHz. Other studies have explored material characteristics related to blockage effects in sub-THz bands; references^21–23 have provided measured penetration loss values for materials like glass and drywall.

Furthermore, introducing models for the blockage effect was aimed by several standard bodies. Channel models for frequencies below 100 GHz have been proposed by standard bodies and organizations, including third-generation partnership projects (3GPP)²⁴ and Millimeter-Wave Mobile Radio Access Networks for Fifth Generation Integrated Communications (mmMAGIC)²⁵. Alongside channel models, each standard body has introduced a simple blockage model for the measured attenuations. These models are based on the knife-edge diffractions concept. The performance of each model will be investigated in this paper.

Main contributions

As discussed above, for both frequency bands, i.e., 60 GHz and 100 GHz, models for human blockage effects have been proposed in several research studies such as^14–17. Also, the penetration losses caused by some materials were studied in^21–23. However, there is a lack of literature exploring the impact of narrow-dimensions metal obstacles on the attenuation behavior for the 60 GHz and 100 GHz. In our earlier investigations^26,27, we examined certain small metal sheet objects, albeit within the 28 GHz frequency band. However, the findings cannot be extrapolated directly to much higher frequency bands, such as 60 GHz and 100 GHz. Moreover, the metal objects examined in this paper are even smaller and narrower compared to those studied in previous research. To the best of our knowledge, no other existing papers investigate the blockage effects of narrow objects and study the applicability of the 3GPP blockage model at these two bands: 60 and 100 GHz. Thus, results of this paper will pave the way for other researchers to understand the behavior of blockage effects resulting from narrow objects at very high frequency bands. The main contributions of this study are summarized as follows:

1. Conducting two measurement experiments, one at 60 GHz mmWave band, in an anechoic chamber, and one at 100 GHz, to investigate the blockage effects on the signal strength of three various small metal sheets, which have narrow-dimensions relative to human bodies.

2. Evaluating and analyzing the performance of both 3GPP and mmMAGIC knife-diffraction methods in modeling the blockage measurements of the small metal sheets at 60 GHz and 100 GHz. Additionally, it investigates the applicability of these blockage models in capturing the attenuation characteristics of other materials, specifically wood and glass.

3. Investigating several parameters that affect the depth and severeness condition of the blockage attenuations, such as the width of the main propagation beam, the TX-RX distance, and the carrier frequency.

The rest of the paper is organized as follows: first, the system model is introduced in system model section, where the simulation blockage models are presented. That is followed by the measurement settings section that shows the setup for two experiments: one for 60 GHz and the other for 100 GHz. Then, the results and discussion are presented in a separated section.

System model

LOS propagation

In the absence of any obstructions, specifically a clear line-of-sight (LOS) path, the Friis equation²⁸ can be employed to determine the received power at each point of the User Equipment (UE), as follows:

$$\begin{array}{c}\hfill P_R=P_T+D_t+D_r-L_{\mathit{FS}}-L_{\mathit{Blocker}}\text{(dB)}\end{array}$$ 1

The variables $D_t$ and $D_r$ represent the directivity of the antennas, while $L_{\mathit{FS}}={(4\pi d/\lambda )}^2$ denotes the path-loss in free space. It is worth mentioning that the wavelength, $\lambda$, is much smaller than the direct LOS path, d, which implies the consideration of a far-field assumption. For such high frequency, besides the significant increase in the path loss, the electromagnetic wave suffers additionally from atmospheric absorption²⁹. The atmospheric loss is not always linearly related to the frequency bands; there are few exceptions, where some frequency bands have lower atmospheric loss than others, such as around 100 GHz, in comparison with the band around 60 GHz. Furthermore, in scenarios where blockers lies in the LOS path between the transmitter and receiver, a novel parameter, denoted as observed blockage loss $L_{\mathit{Blocker}}$ is introduced in Eq. (1). This study is dedicated to examining the effects of this blockage parameter in various scenarios. The focus of this paper is exclusively on the LOS path, with the exclusion of other weaker reflected paths³⁰.

Blockage simulation models

The 3GPP blockage model

The 3GPP standard body²⁴ has introduced a blockage model that represents the obstacle by a screen, as shown in Fig. 1. According to the knife-edge diffraction (KED) theory, the diffracted rays around the four edges of the screen can be used to compute the blockage attenuation. Furthermore, instead of taking into account all four edges with an assumption of infinite screen height³¹, the observed blockage loss is exclusively presented as follows:

$$\begin{array}{c}\hfill L_{\mathit{Blocker}}=-20{log}_{10}\left(1,-,\left(F_{w1},+,F_{w2}\right)\right)\text{(dB)}\end{array}$$ 2

where $F_{w1}$, and $F_{w2}$ are the shadowing values associated with the two edges. Each of these values is equal to:

$$\begin{array}{c}\hfill F=\frac{\text{atan}\left(\pm ,\frac{\pi }{2},\sqrt{\frac{\pi }{\lambda }\left(D_1,+,D_2,-,d\right)}\right)}{\pi }\end{array}$$ 3

where $\lambda$ is the wavelength, the TX-RX distance is represented by d, and the screen-TX/RX nodes ditances are denoted by $D_1$ and $D_2$ respectively, as shown in Fig. 1.

Figure 1.

The KED screen represents a blocker positioned midway between the transmitter and the receiver ends. Based on the four diffracted paths around the KED screen, the 3GPP and mmMAGIC standard bodies used this KED model to compute the blockage attenuation from Eqs. (2) and (4) respectively. The figure is from²⁷.

However, the simulation blockage model adopted by the 3GPP standards body, which we applied in this study, does not prioritize the detailed shape of the blocker. Instead, it considers the main body of the blocker (BL) and represents any object with different shapes, using an absorbing KED screen that has the primary width and height of the object, as illustrated in Fig. 1. Moreover, the material type and roughness are not considered in the blockage model. Although this approach seems simplistic, it effectively captures the blockage effect. The simplicity of this model is one of its main advantages.

The mmMAGIC blockage model

As we have shown in²⁷, the simplicity of the 3GPP blockage model leads to some limitations. The observed blockage attenuation could be underestimated since the 3GPP blockage model does not account for phase variations occurring between the four diffracted paths. Therefore, the researchers of²⁵ have improved the model to address this limitation, where they defined some parameters that solve the phase variations issue. These are: $p{h}_{\mathit{ij}}$, Ph, and $cos{\phi }_{\mathit{ij}}$. For the improved mmMAGIC blockage model, the observed loss is computed as follows:

$$\begin{array}{c}\hfill L_{\mathit{Blocker}}=-20{log}_{10}\left(1,-,\prod _{i=1}^2,\sum _{j=1}^2,s_{\mathit{ij}},\left[\frac{1}{2},-,\frac{p{h}_{\mathit{ij}}}{\mathit{Ph}},F_{\mathit{ij}}\right]\right)\text{(dB)}\end{array}$$ 4

The signed term, denoted as $s_{\mathit{ij}}$, takes the value of 1 if it is NLOS (non-line-of-sight). In the case of LOS, $s_{\mathit{ij}}$ is determined by the function $\text{sgn}$ $\left(D,1_{\mathit{ij}},+,D,2_{\mathit{ij}},-,D,1_{\mathit{ik}},-,D,2_{\mathit{ik}}\right)$, where $\text{sgn}(.)$ is a function that determines the sign of the argument. The scalar k = mod$(j,2)+1$. The rest of the variables are defined as follows:

$$\begin{array}{cc}\hfill F_{\mathit{ij}}& =cos{\phi }_{\mathit{ij}}\left[\frac{1}{2},-,\frac{1}{\pi },{tan}^{-1},\left(\frac{V_{\mathit{ij}}\pi }{2}\right)\right]\hfill \end{array}$$ 5

$$\begin{array}{cc}\hfill p{h}_{\mathit{ij}}& =exp\left[\frac{-\text{j}2\pi }{\lambda },\left(D,1_{\mathit{ij}},+,D,2_{\mathit{ij}}\right)\right]\hfill \end{array}$$ 6

$$\begin{array}{cc}\hfill \mathit{Ph}& =exp\left[\frac{-\text{j}2\pi d}{\lambda }\right]\hfill \end{array}$$ 7

$$\begin{array}{cc}\hfill V_{\mathit{ij}}& =\sqrt{\frac{\pi }{\lambda }\left({D{1}_{\mathit{ij}}}^{\text{proj}},+,{D{2}_{\mathit{ij}}}^{\text{proj}},-,{d_i}^{\text{proj}}\right)}\hfill \end{array}$$ 8

Equation (5) incorporates the variable $cos{\phi }_{\mathit{ij}}$, which takes into consideration the increase in diffraction loss within the shadow zone behind the blockage screen, as shown in Fig. 1. This could be simplified to the 3GPP blockage loss equation, represented by Eq. (2), by setting the values of the new parameters: $p{h}_{\mathit{ij}}$, Ph, and $cos{\phi }_{\mathit{ij}}$ to one.

Measurement setting

The main aim of this paper is to investigate the blockage effect of narrow-dimensions metal sheets at two different frequency bands: 60 GHz and 100 GHz. Thus, we have carried out measurement campaigns at an anechoic chamber where copper sheets block the LOS signal between two horn antennas. The copper sheet blocker perpendicularly crosses the line of sight at the midpoint between the transmitter and receiver ends, as shown in Fig. 2. To investigate the blockage effect alone, we have performed cable calibration and eliminated the effect of path loss before plotting the blockage attenuation. In other words, the plots would only represent the blockage attenuation. It is important to note that the blocker is crossing the line of sight at a distance within the far-field region, which starts from $\ge (2D^2/\lambda )$.

Figure 2.

The block diagram of the setup for the $1^{\mathit{st}}$ experiment: the 60 GHz carrier frequency.

Table 1 presents a summary of the measurement settings. For this research, we have conducted two slightly different measurement setups for two carrier frequencies: 60 GHz and 100 GHz. For each scenario, three copper sheets of various sizes were investigated. The three blocker sheets are chosen to be relatively small, taking into account two distinct aspects. Firstly, their sizes are small compared to the dimensions of a human body. Note that numerous studies in the literature have explored such human-body size blockers at lower carrier frequencies. Additionally, the blockers under consideration are small in relation to the beamwidth of the main beam, an aspect further examined later in this paper. The following subsections provide a summary of the settings for each blocker.

Table 1.

Lab measurement settings.

The setup for the 1st experiment: for the 60 GHz carrier frequency
Transmit power	− 12.1 (dBm)
TX-RX distance	1.97 (m)
TX-blocker distance	1.06 (m)
Antenna type	22.5 dBi, QWH-VPRR00 50–75 GHz from QuinStar
Antenna dimensions	3.8 $\times$ 2.9 (cm)—diagonal (D)= 4.78 (cm)
Spectrum analyzer	Keysight N5227A
Height of TX, RX and $\text{Blocker}_{}^{\ast }$	1.32 (m)
Carrier frequency	60 (GHz)
Offset distance (sample space)	0.5 (cm) $\approx \lambda$
TX/RX Azimuth and Elev. (HPBW)	${10}^{\circ }$
The setup for the 2nd experiment: for the 100 GHz carrier frequency
Transmit power	− 20 (dBm)
TX-RX distance	1.64 (m)
TX-blocker distance	0.8 (m)
Antenna type	23 dBi, MN: QGH-WPRR00 from QuinStar
Antenna dimensions	1.95 $\times$ 2.55 (cm)—diagonal (D)= 3 (cm)
Spectrum analyzer	Keysight N5227A
Height of TX, RX and $\text{Blocker}_{}^{\ast }$	14.5 (cm) above the table level
Carrier frequency	100 (GHz)
Offset distance (sample space)	0.5 (cm)
TX/RX Azimuth and Elev. (HPBW)	${10}^{\circ }$
The copper blockers’ dimensions (width $\times$ height)
1. 1st Blocker	4 $\times$ 4 (cm)
2. 2nd Blocker	8 $\times$ 8 (cm)
3. 3rd Blocker	16 $\times$ 16 (cm)
Other blockers’ dimensions (width $\times$ height $\times$ thickness)
4. 4th blocker (wood)	16 $\times$ 16 $\times$ 0.8 (cm)
5. 5th blocker (glass)	16 $\times$ 16 $\times$ 0.6 (cm)

*The TX and RX are aligned to the center of the blocker.

Measurement setting for the 60 GHz experiment

The measurement experiments were conducted in the anechoic chamber at King Saud University. First, as shown in Figs. 2 and 3, the 60 GHz signal was optically generated by heterodyning two coherent optical carriers using a photonics setup which comprises an electro-optic frequency comb source (FCS), a wavelength selective switch (WSS), and a high bandwidth photo-mixer. The FCS was built using a low phase-noise and Hertz-rang linewidth optical source (NKT-Photonics Koheras ADJUSTIK), a 40 GHz optical phase modulator (EOspace PM-5V5-40-PFA-PFA-UV), and a 30 GHz analog signal generator (Keysight E8257D). This generates a coherent comb signal with a subcarrier spacing of 30 GHz. Thereafter, the WSS (Finisar 4000S) was used to select two optical subcarriers with 60 GHz spacing. Then, a 70 GHz photodiode (PD, Finisar XPDV3120R) was used as a photo-mixer to generate the 60 GHz MMW signal. The MMW signal was then amplified using a low-noise amplifier (LNA, QuinStar QLW-50754530) to obtain an RF transmitted power of − 12.1 dBm. The MMW signal is wirelessly transmitted using a pair of horn antennas (HA, QuinStar QWH-VPRR00 50–75 GHz, 22.5 dBi gain) over a free space distance of 1.97 m inside the anechoic chamber. Finally, the received 60 GHz is analyzed using a 67 GHz microwave network analyzer (Keysight, PNA N5227A) to measure the received RF power. The signal blocker was placed in the middle distance between the directional transmitter and receiver horn antennas (i.e., $\approx$ 1 m from the transmitter). It is worth noting that the signal blocker was fixed on a translation stage which allows the blocker to move left and right, with respect to the LOS path, with a 0.5 cm horizontal displacement. The height of all setup components (i.e., two horns and blocker) was 1.32 meters.

Figure 3.

A blocker crossing the LOS in an anechoic chamber for the first experiment at 60 GHz. The inset shows different materials (copper–glass–wood) under test.

Measurement setting for the 100 GHz experiment

The measurement experiments of the 100 GHz blockage analysis were conducted in the photonics laboratory at King Saud university. As shown in Figs. 4 and 5, the 100 GHz signal was optically generated by heterodyning two coherent optical carriers using a photonics setup which comprises an electro-optic frequency comb source (FCS), a wavelength selective switch (WSS), and a 110 GHz bandwidth photo-mixer. The FCS was built using a low phase-noise and Hertz-rang linewidth optical source (NKT-Photonics Koheras ADJUSTIK), a 40 GHz optical phase modulator (EOspace PM-5V5-40-PFA-PFA-UV), and a 25 GHz anlage signal generator (Keysight E8257D). This generates a coherent comb signal with subcarrier spacing of 25 GHz. The WSS (Finisar 4000S) was used to select two optical subcarriers with 100 GHz spacing. Then, the 110 GHz photodiode (PD, Finisar PDV4121R) was used as a photo-mixer to generate the 100 GHz signal. This signal was then amplified using a low-noise amplifier (LNA, QuinStar QLW-75B04030-I2) to obtain an RF transmitted power of − 20 dBm. The 100 GHz signal is wirelessly transmitted using a pair of horn antennas (HA, QuinStar GH-WPRR00, 23 dBi gain) over a free space distance of 1.64 m. Finally, the received 100-GHz is down converted to an intermediate frequency (IF) of 5.6 GHz using an electronic sub-harmonic mixer (SHM-Virginia Diodes WR10SHM). Then, the IF signal is analyzed using a microwave network analyzer (Keysight, PNA N5227A) to measure the received RF power. The signal blocker was placed in the middle distance between the directional transmitter and receiver horn antennas (i.e., $\approx$ 0.8 m from the transmitter). It is worthy to note that the signal blocker was fixed on a translation stage which allows the blocker to move left and right, with respect to the LOS path, with a 0.5 cm horizontal displacement. The height of all setup components (i.e., two horns and blocker) was 14.5 cm above the table level.

Figure 4.

The block diagram of the setup for the 2nd experiment: the 100 GHz carrier frequency.

Figure 5.

A copper blocker crossing the LOS for the second experiment at 100 GHz.

Results and discussion

This section is organized into four main parts. The first part examines the blockage effects at a 60 GHz carrier frequency, while the second part focuses on the blockage effects at a 100 GHz carrier frequency for the same blockers. The third part investigates the blockage effects of different materials, specifically copper, wood, and glass, and assesses the applicability of simulation models in capturing these blockage attenuations. The fourth part analyzes the impact of varying carrier frequency and main beamwidth on the severity of the blockage effect. For the first two parts, we have investigated the blockage effects of three different copper sheet sizes. We show the measured blockage attenuation and compare it with the two blockage simulation models, i.e., the 3GPP and the mmMAGIC blockage models. For each blocker size, Table 2 shows a comparison between the performance of the blockage simulation models, i.e., 3GPP and mmMAGIC, based on the mean squared error (MSE) of the amplitude values, where the whole attenuation curves compared with the benchmark, which is the measured blockage attenuation curve. This will be discussed in detail in the following subsections.

Table 2.

Comparison among the blockage simulation models based on the mean squared error.

Mean squared error
Blocker type and size	Simulation blockage model	$f_c$ = 60 GHz	$f_c$ = 100 GHz
1st blocker: 4 $\times$ 4 (cm)	3GPP	0.0037	0.0142
	mmMAGIC	0.0185	0.013
2nd blocker: 8 $\times$ 8 (cm)	3GPP	0.0345	0.0376
	mmMAGIC	0.0694	0.0585
3rd blocker: 16 $\times$ 16 (cm)	3GPP	0.1647	0.1818
	mmMAGIC	0.2054	0.216

Results for the 60 GHz carrier frequency

Figure 6 presents the measured blockage attenuation caused by the small blocker, which is 4 $\times$ 4 cm. Although the blocker is relatively small, it causes an attenuation that reaches 5 dB when the copper sheet is precisely in the middle between the transmitter and the receiver, with the same distance from both. The size of the attenuation main beam is almost double the width of the blocker sheet, i.e., 8 cm. The 3GPP blockage simulation model well matches the measurement between the two offset cases of values − 4 cm and 4 cm. The mmMAGIC model did not accurately capture the measurement; however, it predicts the fluctuations on the sides well. The computed MSE values of each attenuation curve show a notably low value for the 3GPP model, which is only 0.0037, while it is 0.0185 for the mmMAGIC model.

Figure 6.

The blockage attenuation of (4 cm by 4 cm) copper sheet. Measurements vs. Simulation models: 3GPP Eq. (2), and mmMAGIC Eq. (4). The carrier frequency is 60 GHz.

The copper sheet that is sized 8 $\times$ 8 cm in Fig. 7 leads to an attenuation that has a peak value of − 10 dB, which is almost double the one caused by the 4 $\times$ 4 cm blocker. The mmMAGIC blockage simulation model has two imprecise attenuation peaks that reach up to − 20 dB. The attenuation curve of the 3GPP blockage model performs better than the mmMAGIC model, which appears clearly from the MSE value of 0.0345, compared to 0.0694 of the mmMAGIC.

Figure 7.

The blockage attenuation of (8 cm by 8 cm) copper sheet. Measurements vs. Simulation models: 3GPP Eq. (2), and mmMAGIC Eq. (4). The carrier frequency is 60 GHz.

The measured blockage attenuation curve resulting from the relatively large blocker, i.e., 16 $\times$ 16 cm, shows some fluctuations at the main beam. These fluctuations give an advantage here and make the mmMAGIC model performs better than the 3GPP blockage model. However, the MSE values do not agree with that; in fact, it tips the scales to the 3GPP over the other. Based on Fig. 8, this can be justified by noticing that the fluctuations present in the results of mmMAGIC and measured attenuation are not always aligned perfectly. It is also worth noting that the blockage attenuation around the middle reaches around -23 dB, which is about two times the attenuation caused by the 8 $\times$ 8 blocker. Unlike the case with the small blocker, i.e., 4 $\times$ 4 cm, the width of the main attenuation body, plotted in red in Fig. 8, is almost 16 cm, the same as the size of the blocker sheet but not the double.

Figure 8.

The blockage attenuation of (16 cm by 16 cm) copper sheet. Measurements vs. Simulation models: 3GPP Eq. (2), and mmMAGIC Eq. (4). The carrier frequency is 60 GHz.

Results for the 100 GHz carrier frequency

Another contribution of the paper is to investigate the blockage effect of relatively small blockers at the carrier frequency of 100 GHz. Since the same three copper sheets are used as blockers here, it is worth analyzing the differences between the resulting blockage attenuations at the two carrier frequencies, i.e., 60 GHz and 100 GHz. Figure 9 shows the blockage effect for the same small copper blocker, i.e., 4$\times$4 cm, used in Fig. 6, but for $f_c$ = 100 GHz. For 100 GHz, the measured blockage effect reaches up to -12 dB, which is almost double the attenuation value that appears in Fig. 6 at $f_c$ = 60 GHz. Another disparity between the two experiments is the occurrence of some fluctuations around the middle, i.e., ± 0 offset in Fig. 9. This makes the mmMAGIC model, with its fluctuations feature, performs better than the 3GPP model with MSE values of 0.013 and 0.0142, respectively.

Figure 9.

The blockage attenuation of (4 cm by 4 cm) copper sheet. Measurements vs. Simulation models: 3GPP Eq. (2), and mmMAGIC Eq. (4). The carrier frequency is 100 GHz.

In contrast to experiment 1 conducted at 60 GHz, the 8 $\times$ 8 cm blocker exhibits a distinctive behavior at 100 GHz, where the measured attenuation reveals two attenuation peaks, both reaching − 23 dB, surpassing the value depicted in Fig. 10 by more than twofold. The 3GPP blockage model underestimates the measured attenuation by a considerable difference, which makes the mmMAGIC model better with a small MSE value of 0.0376.

Figure 10.

The blockage attenuation of (8 cm by 8 cm) copper sheet. Measurements vs. Simulation models: 3GPP Eq. (2), and mmMAGIC Eq. (4). The carrier frequency is 100 GHz.

The third copper sheet blocker, with dimensions of 16$\times$16 cm, is depicted in Fig. 11 to demonstrate the extent of signal attenuation at 100 GHz. This figure highlights the shape and number of fluctuation peaks, where the average measured attenuation around the midpoint closely resembles that observed in Fig. 8 for experiment 1 at 60 GHz. While the mmMAGIC model aligns conceptually with the curve of the measured attenuation, the mismatch between oscillation peaks contributes to a higher MSE value compared to that of the 3GPP model.

Figure 11.

The blockage attenuation of (16 cm by 16 cm) copper sheet. Measurements vs. simulation models: 3GPP Eq. (2), and mmMAGIC Eq. (4). The carrier frequency is 100 GHz.

Metal materials can completely reflect signal waves, making them ideal blockers. However, materials with different properties exhibit varying behaviors. To investigate the impact of blocker material type on signal attenuation, we conducted a measurement campaign using three materials: glass, wood, and copper. All blockers were of uniform size, measuring 16 $\times$ 16 cm, and the same measurement setup was employed throughout the campaign.

Figure 12 presents the attenuation curves for the three blockers. The curves for wood and glass indicate that these materials do not block signals as effectively as copper, allowing signal penetration through the blockers. Notably, both the 3GPP and mmMAGIC simulation models fail to accurately capture the attenuation characteristics of wood and glass. This discrepancy arises because these models assume complete signal blockage, as observed with copper, and do not account for material properties.

Figure 12.

Blockage attenuation of three 16 cm by 16 cm blockers (copper, wood, and glass) at a carrier frequency of 60 GHz. Comparison of measurements with simulation models: 3GPP (Eq. 2) and mmMAGIC (Eq. 4).

The attenuation caused by glass and wood blockers is neither constant nor negligible, reaching up to 15 dB and then fluctuating back to almost zero with large-scale variations. Therefore, it is crucial to modify and enhance the 3GPP blockage model to accurately reflect the attenuation behavior of different materials. This enhancement necessitates the introduction of new parameters into the attenuation equations, a task that will be addressed in future research.

The effect of varying the carrier frequency and the main beamwidth

In our initial research²⁶ focusing on directional antennas, we introduced a variable known as $W_{\mathit{HPBW}}$. This variable calculated using a straightforward formula determines the extent of the maximum coverage area where the main beam, with a half-power beamwidth (HPBW), intersects when encountering a blocker sheet at a specified distance $d_{1|2}$. Essentially, the width of the intersection area between the main beam and the blocker sheet is defined as follows:

$$\begin{array}{c}\hfill W_{\mathit{HPBW}}=2d_{1|2}\text{tan}\left(\frac{{\theta }_{\mathit{HPBW}}}{2}\right)\text{(m)}\end{array}$$ 9

where ${\theta }_{\mathit{HPBW}}$ is the half-power beamwidth angle in degree. This formula determines how much of the main beam would be blocked by the three blocker sheets used in this paper. The ratio between the two will determine if the main beam is partially or completely blocked. In the first experiment detailed in this paper, where the carrier frequency $f_c$ is set at 60 GHz, the $W_{\mathit{HPBW}}$ measures 18.54 cm, surpassing the dimensions of all utilized sheet blockers. In contrast, during the second experiment at $f_c$ = 100 GHz, the $W_{\mathit{HPBW}}$ is reduced to 13.99 cm. This implies that the larger blocker sheet, having a dimensions of 16 cm, would entirely obstruct the main beam at the specified TX-Blocker distance.

Having discussed the blockage attenuation at 60 GHz and 100 GHz in detail, we have seen several parameters that can affect the depth of the blockage attenuation, such as the carrier frequency and the main beamwidth. However, an interesting question should be asked is: which of these two parameters would play a significant role? In the course of our investigation, it is essential to maintain all parameters fixed while systematically altering one at a time. However, as a preliminary step, certain assumptions are made. Despite the 3GPP blockage simulation model not achieving absolute accuracy in capturing the measured attenuation based on the six presented results, it serves as a reasonable indicator that provides a rough explanation of the attenuation phenomenon. Consequently, this model will be employed to gain insights into the extent to which each parameter influences the observed effects. To investigate the impact of the first parameter, we employed Eq. (2) to calculate the blockage attenuation values depicted in Fig. 13. This computation was conducted with the blocker positioned precisely between the transmitter and the receiver, corresponding to an offset of zero where the LOS path is intersected at the center of the blocker. The process was repeated across the carrier frequency ranges from 20 GHz to 150 GHz. Each curve in the figure corresponds to one of the three blockers utilized in this study, all positioned at a specified TX-RX distance of approximately 2 m.

Figure 13.

The blockage attenuation obtained from Eq. (2) versus the carrier frequency. Each curve corresponds to one of the three blockers utilized in this study. The TX-RX distance is 2 m.

Taking the curve of the 16 $\times$ 16 blocker as an illustration, the resulting attenuation at $f_c$ = 150 GHz is − 18 dB, nearly doubling the value observed at $f_c$ = 20 GHz. Notably, within the frequency range of 130 GHz, the change is only − 8 dB, indicating a relatively insignificant difference. The same observations apply to the other two curves.

Another parameter that requires investigation is the impact of altering the ratio between the dimensions of the blocker sheet and the width of the main beam $W_{\mathit{HPBW}}$ when it intersects with the blocker sheet. Modifying one of these terms is not practical due to the dependency of $W_{\mathit{HPBW}}$ on the antenna type and design. However, a simple way to achieve this is by adjusting the TX-BL distance. Consequently, the ratio between the blocker dimensions and the width of the main radiated beam will change, as evident from Eq. (9). It is important to note that, for the given pair of directional antennas, the determined HPBW angle is 10 degrees. In Fig. 14, similar to the previous findings, we computed the blockage attenuation value with the blocker positioned precisely in the middle between the transmitter and the receiver, corresponding to an offset of zero where the LOS path intersects at the center of the blocker. In this analysis, a single blocker, a 16 $\times$ 16 cm copper sheet, was utilized, and the TX-BL distance was varied, altering the ratio between the width of the main beam and the dimensions of blocker.

Figure 14.

The blockage attenuation, as derived from Eq. (2), is plotted against the carrier frequency. Each curve represents the attenuation observed with a 16 $\times$ 16 cm copper sheet, with variations in the distance between the transmitter (TX) and blocker (BL) to adjust the ratio between the width of the main beam and the blocker width.

Each of the five curves in Fig. 14 represents a specific TX-BL distance. As the blocker sheet moves farther away from the directional antenna, the main beam covers a broader area, resulting in a greater $W_{\mathit{HPBW}}$ than the blocker dimensions. This, in turn, leads to less attenuation, rendering the blockage attenuation more negligible. For instance, at the carrier frequency of 60 GHz, the blue curve represents a TX-BL distance of 1 m, with blockage attenuation at approximately − 14 dB, whereas it reduces to − 8 dB when the blocker sheet is 5 m away from the transmitter, as indicated by the green curve. Moreover, if we increase or decrease these distances, the lengths of the four diffracted paths around the blocker screen in Fig. 1 will vary accordingly. Thus, from Eqs. (2) and (3) in the manuscript, the resulting attenuation will scale accordingly. This is illustrated in Fig. 14. These results underscore the significance of considering the width ratio between the blocker sheet and the main radiated beam, a crucial point in line with the objectives of this paper.

Revisiting the question of which parameter has a greater effect, both the carrier frequency and the main beamwidth are crucial in influencing the resulting attenuation. However, based on Figs. 12 and 13, it appears that for directional antennas, the ratio between the blocker dimensions and the width of the main radiated beam has a more significant impact on the resulting attenuation. This can be explained as follows: Fig. 2 shows that at a carrier frequency of 20 GHz, doubling the blocker size from 4 $\times$ 4 (blue curve) to 8 $\times$ 8 (red curve) nearly doubles the resulting attenuation, increasing from 3 dB to 6 dB. In contrast, for the same blue curve, doubling the carrier frequency from 20 GHz to 40 GHz results in only a slight increase in attenuation, from 3 dB to 4.2 dB. This finding underscores the importance of considering the ratio between the blocker dimensions and the width of the main radiated beam for directional antennas.

Conclusion

The blockage attenuation results of this paper show that even small objects in the size of 4 $\times$ 4 cm can significantly attenuate the signal strength at 60 and 100 GHz when they come midway between the transmitter and the receiver ends. We have carried out measurement campaigns to investigate the blockage effect of three small-sized metal objects on signal strength at these two frequency bands. Our analysis involved evaluating the performance of both knife-edge diffraction (KED) blockage models-namely, the 3GPP and mmMAGIC models-for each metal object. Overall, both models did well matching the measured blockage attenuations with very small MSE, but for some results, one model overperforms the other. However, some scenarios revealed one model outperforming the other. The 3GPP blockage model presents a smoothed curve for the measured attenuation, while the mmMAGIC model accounts for phase variations behind the blocker, thereby offering a more precise match to the fluctuations observed in the measured attenuation. However, the 3GPP and mmMAGIC simulation models do not accurately represent the attenuation characteristics of wood and glass blockers. Consequently, these models require enhancements and modifications to effectively capture the blockage attenuations of various materials. Furthermore, our investigation highlighted the critical importance of considering the ratio between the dimensions of the blocker and the width of the main radiated beam for establishing reliable mmWave and THz communication links. When the blocker size exceeds the dimensions of the main radiated beam, it leads to higher attenuation values, and conversely, when the blocker is much smaller, attenuation decreases accordingly. It is worth mentioning that the results obtained from this work paves the way to study the blockage attenuation of various blockage shapes, blockage positions and different materials

Author contributions

All authors reviewed and approved the final version of the manuscript. They also conducted the proofreading. The corresponding author is responsible for submitting a competing interest statementcompeting interests statement on behalf of all authors of the paper. This statement must be included in the submitted article file.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.