Before presenting the propagation mechanisms in indoor environments and applying the propagation and prediction models, it is necessary to consider the free-space path loss (FSPL). Free space is considered to be a completely unobstructed region, meaning that there are no obstacles or surfaces interacting with the electromagnetic wave propagating between the transmit and receive antennas. Figure 1 illustrates two antennas perfectly aligned and separated by a distance r in free space. Assuming that the transmit and receive antenna have gains G _T and G _R, respectively, compared to an isotropic antenna and that the transmit power is denoted by P _T, the receive power is given by (Johnson, 1961): P R = G R G T λ 4 π r 2 P T , (1) where r is the separation distance between the transmit and receive antennas in m, λ = c/f is the wavelength with c being the phase speed of the wave and f being the operating frequency in Hz. The FSPL is given by the ratio between the transmit power and receive power and it is usually presented in dB as (Johnson, 1961): L FS = 92.44 + 20 ⁡ log f + 20 ⁡ log r , (2) where f is the frequency in GHz and r is the distance between the transmitter and receiver in km.

Equation 1 and Equation 2 show that, for a fixed separation distance and a fixed antenna gain at the transmitter and receiver, the FSPL is proportional to the square of the carrier frequency. This implies in high FSPL at the mm-wave frequency band, when compared to the sub-6 GHz band (Rappaport et al., 2015). Figure 2 presents a comparison between the FSPL obtained at 2.4 and 5 GHz bands, which are mostly used for indoor Wi-Fi networks and the 60 GHz band. Assuming equal transmitter power levels, omnidirectional antennas and no system losses, FSPL at 60 GHz is, respectively, 28 and 22 dB higher than the 2.4 and 5 GHz frequencies. It is important to highlight that the FSPL is a result of the fact that the receive antenna cannot interact with the entire radiation pattern of wavefront (Johnson, 1961). In this context, this loss can be compensated by directional antennas and antenna arrays, which have a substantial gain when compared with omnidirectional antennas. At 60 GHz, the free-space wavelength is 5 mm, which enables arrays with a large number of antennas, as more antennas can fit into a small circuit board or chip. Furthermore, FSPL can be reduced using multiple-input multiple-output (MIMO) and beamforming techniques, as the signals can be directed to a specific point in space (Rappaport et al., 2015).

Although the high FSPL can limit the range of links operating in mm-wave, the severe attenuation at the 60 GHz band can be beneficial in indoor environments, since frequencies can be reused between neighboring rooms. This approach allows for simultaneous transmissions in a given building (Park and Gopalakrishnan, 2009). This means that several hotspots can be placed in an indoor environment without interfering with each other, increasing the network capacity/m² at 60 GHz. Directional antennas and beam forming can also be advantageous for frequency reuse, as the narrow beams help mitigate interference (Park and Gopalakrishnan, 2009). Figure 3 illustrates a typical dense office environment of 4 cubicles adjacent to each other. The cubicles are separated by a partition wall whose penetration loss must be taken into account. Note that the links can operate at 60 GHz simultaneously without interfering with each other in this scenario. However, there are also a number of scenarios where the interference is non-negligible and the links cannot co-exist unless there is a mechanism to mitigate interference. Therefore, evaluating the propagation and channel characteristics in an indoor environment is critical in determining the overall performance of 60 GHz systems (Park and Gopalakrishnan, 2009).

Indoor propagation models at 60 GHz must consider several characteristics, such as reflection properties of different surfaces, diffraction, blockage, and scattering. These characteristics substantially impact communications on mm-waves (Deng et al., 2016). Due to the short wavelengths, ranging from 1 to 10 mm, the mm-wave signals propagation mechanisms are drastically different from those of sub-6 GHz and, therefore, must be analyzed and studied in order to properly model and evaluate wireless communications systems operating in these frequencies.

Reflected, diffracted and scattered waves from nearby objects result in the multipath fading effect, which influences on the performance of indoor wireless communication systems. Reflection is the dominating factor in the channel delay profile at 60 GHz. Considering a perfectly smooth surface, the reflection would lead to a single wavefront. However according to experimental investigations presented in Maltsev et al. (2010c), each reflected path actually consists of a number of wavefronts propagating in different directions. Because of the fine structures of the reflected surfaces, these wavefronts are closely spaced to each other in time and angular displacements. Hence, the clustering approach is suitable for 60 GHz signal propagation modeling, where each cluster consists of corresponding line-of-sight (LOS) or non-line-of-sight (NLOS) reflected paths (Gustafson et al., 2013). Diffraction occurs when the bending of waves takes place in the same medium. Considering that the dimensions of typical obstacles are large compared to the 60-GHz signal wavelength, diffraction becomes insignificant, as sharp shadow zones are formed (Gustafson et al., 2013). In addition, the 60-GHz propagation channel has a quasi-optical nature, meaning that waves tend to propagate in a straight line. Since the angle of diffraction and size of wavelength are directly proportional, propagation due to diffraction is not viable at the 60 GHz frequency range. Consequently, most of the transmission power is propagated between the transmitter and receiver through LOS and low-order reflected paths (Maltsev et al., 2010b; Sharmin and Boby, 2020).

Transmissions at 60 GHz in indoor environments are highly vulnerable to human blockage due to the small wavelength and the use of narrow beams. Thus, a person crossing the link causes its temporary blockage, which can last as long as the person stands between the transmit and receive antennas. Therefore, it is necessary to characterize and categorize the human blockage at 60 GHz links based on human activity and evaluate its effect on the systems QoS. Moreover, when analyzing the characteristic of the blockage, a 60 GHz device is able to identify its type and determine which action can be taken to minimize the effects of the blockage. In Figure 4, the interaction of propagation mechanisms in internal environments with the human body is illustrated. Characteristics, such as antenna type, link height and the person’s position, have great relevance on the link quality, considering that human-body attenuation of up to 30 dB have already been reported in the literature (Collonge et al., 2004; Semkin et al., 2018). Retransmission and fast session transfer (FST) are some of the mechanisms to deal with the blockage problem for long periods of time. The IEEE 802.11ad standard model considers the above mentioned phenomena in order to predict the attenuation introduced by the wireless channel (Hersyandika, 2016).

The physical characteristics of the materials present in an indoor environment, e.g., building materials, furniture, partitions, and openings (windows, doors, etc.), also play an important role in indoor signal propagation at 60 GHz mainly because these characteristics impact the signal penetration loss (Zhao et al., 2013). In Anderson and Rappaport (2004), penetration loss measurements were conducted at 2.5 and 60 GHz in a typical office environment. The obstacles present between the transmitter and receiver were separated in five categories: drywall, whiteboard, clear glass, mesh glass, and clutter, i.e., office furniture such as chairs, desks, bookcases, and filing cabinets. Table 1 presents a summary of all attenuation factors found in this experiment. Comparing the measured penetration losses, the attenuation introduced by the drywall remained almost constant. On the other hand, the attenuation of whiteboard and mesh glass increases when the frequency varies from 2.5 to 60 GHz. Moreover, the attenuation introduced by clutter decreases when the frequency varies from 2.5 to 60 GHz, since the first Fresnel zone at 60 GHz is considerably smaller, and, therefore, fewer objects are capable of perturbing the signal. The authors in Anderson and Rappaport (2004) also found that the attenuation of the clear glass at 60 GHz is smaller than the attenuation observed at 2.5 GHz. However, the justification for such phenomenon has not been reported in literature and it requires further investigation.

Although high levels of material penetration loss degrade link quality and limit the coverage area, it can mitigate interference from neighboring rooms and improve spatial reuse gain. Therefore, 60 GHz signals can be confined to a single room and several hotspots can be placed in an indoor environment, enabling high capacity wireless networks (Park and Gopalakrishnan, 2009).

The CI path loss model uses a CI reference distance based on the FSPL and accounts for the frequency dependency of the path loss. In this model, the path loss in dB is given by (Sun et al., 2016b) L CI f , d = L FS f , d 0 + 10 n ⁡ log 10 d d 0 + χ σ CI , (3) where d ≥ d ₀ is the 3-D Tx-Rx separation distance in meters, f is the carrier frequency in GHz; d ₀ is the close-in free space reference distance, chosen large enough to be in the antenna far-field region; n denotes the PLE; and χ σ CI is a zero-mean Gaussian random variable with a standard deviation of σ dB, which represents the large-scale signal fading (i.e. shadowing). In (Eq. 3), L _FS(f, d ₀) denotes the FSPL evaluated using Eq. 2.

In indoor environments, d ₀ is often equal to 1 m (Fryziel et al., 2002). This choice has proven to be accurate and stable over a vast range of microwave and mm-wave frequencies and also creates a standardized modeling approach (Sun et al., 2016b).

The CIF model is derived from the CI model and is also suitable for multi-frequency modeling. The path loss for the CI model is given in dB by (Eq. 4) when d ₀ = 1 m (Sun et al., 2016b). L CIF f , d = L FS f , d 0 + 10 n 1 + b f − f 0 f 0 log 10 d + χ σ CIF , (4) where d ≥ 1 m is the 3D Tx-Rx separation distance in meters, f is the carrier frequency in GHz; n represents the severity of the attenuation with the distance (similar to the PLE in the CI model); χ σ CIF is a zero-mean Gaussian random variable with a standard deviation of σ dB, which represents the signal shadowing; and b is a parameter that describes the dependence of path loss with the weighted average of all frequencies considered in the model. In other words, this parameter represents the linear dependence of the attenuation on the frequency. The average frequency f ₀ is given by (Sun et al., 2016b) f 0 = ∑ k = 1 K f k N k ∑ k = 1 K N k , (5) where K is the number of unique frequencies and N _k is the number of path loss data points corresponding to the kth frequency f _k . Note that the CIF model simplifies to the CI model when f ₀ = f or b = 0, i.e. when there is no frequency dependence on path loss.

In the CIF model, the breakpoint distance is defined as the distance where the PLE transitions from free space (n = 2) to the asymptotic two-ray ground bounce model of n = 4 (MacCartney and Rappaport, 2017), which is comprised of a direct ray and a ground reflected ray (Perera et al., 1999). In other words, the breakpoint distance is used as a threshold for an increased path loss coefficient and, therefore, is used as a large scale fading parameter (Zöchmann et al., 2017). Generalizations of the CIF model consider different slopes of path loss before and after a breakpoint distance, known as dual-slope (DS) CIF model. The path loss predicted by the DS CIF model is given by Eq. 6, where d _BP is the breakpoint distance in meters. Note that the DS CIF model requires five parameters to predict path loss, whereas the single-slope (SS) model requires only two parameters (Rappaport et al., 2017). L CIF dual f , d = L FS f , d 0 + 10 n 1 1 + b 1 f − f 0 f 0 log 10 d , 1 < d ≤ d BP L FS f , d 0 + 10 n 1 1 + b 1 f − f 0 f 0 log 10 d BP + 10 n 2 1 + b 2 f − f 0 f 0 log 10 d d BP , d > d BP (6)

Assuming distance d in meters and frequency f in GHz, the path loss for the ABG model is given by (Sun et al., 2016b): L ABG f , d = 10 α ⁡ log 10 d + β + 10 γ ⁡ log 10 f + χ σ ABG , (7) where d ≥ 1 m, α and γ are parameters that show the path loss dependence on distance and frequency, respectively, β is an optimized offset value for path loss in dB, and χ σ ABG is a zero-mean Gaussian random variable with a standard deviation of σ dB, which represents the signal shadowing.

Similarly to the CIF model, the ABG model is also generalized for DS path loss before and after the breakpoint distance. Equation 8 presents the ABG DS prediction model, where d _BP is the breakpoint distance in meters (Sun et al., 2016b). The DS ABG model requires five parameters to predict path loss, whereas the SS require only three. These coefficients are defined aiming to minimize the error between the predicted path loss and the measured data (Rappaport et al., 2017). L ABG dual f , d = 10 α 1 ⁡ log 10 d + β 1 + 10 γ ⁡ log 10 f c , 1 < d ≤ d BP , 10 α 1 ⁡ log 10 d + β 1 + 10 γ ⁡ log 10 f c + 10 α 2 ⁡ log 10 d d BP , d > d BP . (8)

The channel models defined in 3GPP TR 38.901 (3GPP, 2019) are generally applicable over the frequency range between 0.5–100 GHz and include several scenarios of interest. The InH office scenarios are valid for distances up to 150 m and are typically comprised of open cubicle areas, walled offices, open areas, and corridors. In addition, the base stations (BSs) are mounted at a height of 2–3 m, either on the ceilings or walls. The path loss models are presented for both LOS and NLOS conditions and employ 3-D Tx-Rx separation distance d _3D that accounts for the BS height (h _BS) and user equipment (UE) height (h _UE), as illustrated in Figure 5.

The InH-office LOS scenario is similar to the CI model and presents a standard deviation (σ _SF) of 3 dB. For NLOS, the 3GPP TR 38.901 path loss model uses the ABG model lower-bounded by the LOS path loss with a standard deviation (σ _SF) of 8.29 dB, resulting in P L = max P InH - LOS , P InH - NLOS , (9) where P _InH-LOS is the path loss in the InH-office LOS scenario and P _InH-NLOS is the path loss in the InH-office NLOS scenario. Another option is to use the CI model with 1 m reference distance and σ _SF of 8.29 dB for the InH-office NLOS scenario. These path loss models and parameters are provided in Tables 2, 3.

The studies presented in the 5GCM white paper (5GCM, 2016) are an extension of the existing 3GPP models and support 5G operation across frequency bands up to 100 GHz. The indoor scenarios described in this paper include open and closed offices, corridors within offices, and shopping malls. The typical office environment is comprised of cubicle areas, walled offices, open areas, and corridors, where the partition walls are composed of different materials. For the office environment, the APs are mounted at a height of 2–3 m either on ceilings or walls. The shopping malls are generally 2–5 stories high and often include an open area. In the shopping mall environment, the APs are mounted at a height of approximately 3 m on the walls or ceilings of the corridors and shops.

The 5GCM channel models presented in Tables 2, 3 were developed based on the large-scale path loss models CI, CIF, and ABG and also accounts for the 3-D Tx-Rx separation distance d _3D. The LOS indoor-office and shopping-mall models are similar to the CI model and present σ _SF of 3.02 and 2.01 dB, respectively. Note that the indoor-office LOS channel model and parameters are identical to the 3GPP TR 38.901 LOS model. For the NLOS condition, the SS CIF and ABG models were employed with σ _SF of 8.29 and 8.03 dB for indoor-office scenarios, and 7.40 and 6.97 dB for shopping mall scenarios, respectively. In addition, the DS CIF and ABG models were also considered for 5G performance evaluation considering breakpoint distances of 7.8 and 6.9 m for the InH office scenario and 110 and 147 m for the InH shopping mall scenario. According to 5GCM (2016), the DS models may be best suited for InH-shopping mall or large indoor distances (greater than 50 m).

The main objective of the mmMAGIC project (mmMagic, 2017) is to develop advanced channel models for the frequency range of 6–100 GHz. For that purpose, various channel measurements have been conducted for a variety of InH scenarios at multiple frequencies, including 60 GHz. The InH scenarios comprise traditional enclosed offices, semi-closed offices (cubicle areas), and open offices. In this case, the BSs are mounted at a height of 1–5 m and can be placed at the ceilings or on the walls. In addition, channel models were developed for indoor airport scenarios, specifically the gate and the check-in areas, where the BSs should be installed near the ceiling at 4–9 m high.

The mmMAGIC project adopted the ABG path loss model for indoor scenarios, similar to an earlier version of 5GCM (5GCM, 2016), and also accounts for the 3-D Tx-Rx separation distance d _3D (see Tables 2, 3). The parameters for the InH channel model were obtained from combining the results of measurement and simulation campaigns at offices and airports environments. The LOS InH channel model presents σ _SF of 1.18 dB whereas at the NLOS InH scenario the obtained σ _SF is 8.03 dB.

The channel model investigation in the METIS project comprises the analysis of propagation measurements, extensive literature reviews, and simulations. The purpose of this research is to ensure the availability and applicability of relevant propagation models over the frequency range of 6–86 GHz. In this context, the channel model presented in the METIS white paper (METIS, 2015) is similar in form to the ABG model and was adopted for short-range 60 GHz links in shopping mall scenarios, as below P L = A log 10 d + B , (10) where A and B are the curve-fit parameters, presented in Tables 2, 3.

The IEEE 802.11ad standard (Maltsev et al., 2010a) describes channel models for 60 GHz WLAN systems based on the results of experimental measurements in indoor environments. The InH office scenario is comprised of a cubicle environment, where the wireless AP is located on the ceiling. In both LOS and NLOS scenarios, the path loss model is similar to the CI model. However, no shadowing term is provided in the LOS condition, as the path loss for different antennas configurations match each other very closely and may be approximated by the same polynomial law. For the NLOS condition, the obtained channel model presents σ _SF equals 1.5 dB. In both conditions, the 2-D distance d _2D is employed. These path loss models and parameters are provided in Tables 2, 3.

The channel models were compared considering the BS and the UE heights to be 2 and 1.5 m, respectively, for both indoor office and shopping mall scenarios, defined according to the information available in (5GCM, 2016; mmMagic, 2017; METIS, 2015; Maltsev et al., 2010a). For the InH office scenario, the 2-D distance (d _2D) ranges from 1 to 100 m and the 3-D (d _3D) distance was calculated, based in Figure 5, as d 3 D = d 2 D 2 + h BS − h UE 2 . (11)

The METIS model, presented in Tables 2, 3, considers 1.5 m ≤ d _2D ≤ 13.4 and 4 m ≤ d _3D ≤ 16.1 m for the LOS and NLOS conditions, respectively. However, in order to evaluate the model stability and present a reliable comparison, the shopping mall scenario 2-D distance (d _2D) was extrapolated to 200 m and the 3-D distance (d _3D) was also evaluated by Eq. 11.

Another key observation is that, in this work, the models comparison is based on the worst-case scenario. In other words, the model considered best suited for a particular scenario is the one that obtained the highest path loss. Consequently, it is possible to obtain a conservative prediction and an increased safety margin for a future project link budget. Figures 6, 7 depict the mean path loss versus Tx-Rx distance obtained with the FSPL, 3GPP, 5GCM, and mmMAGIC channel models, and the IEEE 802.11ad standard in the LOS and NLOS InH office scenario, respectively.

As shown in Figure 6, the mean path loss obtained with the IEEE 802.11ad standard is identical to the theoretical FSPL, since the PLE is equal to two and no shadowing term is provided for the LOS condition. Moreover, the 3GPP and 5GCM channel models have the same parameters, yielding identical path loss values. On the other hand, the mmMAGIC model presents a more optimistic channel estimation compared to the other models. For instance, considering a Tx-Rx separation distance of 80 m, free-space/IEEE 802.11ad and 3GPP/5GCM mean path losses are approximately 10 and 5 dB higher than the mmMAGIC path loss, respectively, since the mmMAGIC PLE (equivalent to α in the ABG model) is smaller than those presented by the other models. However, at shorter distances, the four models present very similar mean path loss values. For example, at a Tx-Rx separation distance of 10 m, the obtained mean path loss values are 85.3, 83.5, and 88 dB for the 3GPP/5GCM and mmMAGIC models, and the IEEE 802.11ad standard, respectively. For the NLOS condition, Figure 7 shows that the IEEE 802.11ad standard presents a very optimistic path loss estimation. The obtained mean path loss is only 8.6 dB higher than the theoretical FSPL at a Tx-Rx distance of 40 m. On the other hand, the other six models predict much higher path loss values, even at short distances, which is consistent to the NLOS environment. The DS 5GCM models present high mean path loss and are similar to the other models, although the breakpoint distances used are not visible in Figure 7, since they are very short, i.e., 7.8 and 6.9 m for the DS CIF model and DS ABG model, respectively. It is not clear from the data available in (5GCM, 2016) that the DS models are consistent for InH office scenarios, since the use of a breakpoint distance has not been reported in mm-wave measurement campaigns (Rappaport et al., 2017). In addition, the breakpoint distance measurements and calculations were not detailed in 5GCM (2016). However, for distances greater than the breakpoint, the CIF PLE parameter increases from 2.51 to 4.25 and the ABG α parameter increases from 1.7 to 4.17, which is consistent to theoretical breakpoint definition (MacCartney and Rappaport, 2017). In this context, the 5GCM SS channel models are well suited for InH office scenarios for both LOS and NLOS conditions, although the IEEE 802.11ad standard predicts higher mean path loss values for distances greater than 20 m in the LOS condition.

The channel models comparison for the LOS and NLOS InH shopping mall scenarios is presented in Figures 8, 9, respectively. It can be obeserved from Figure 8 that the METIS and the free-space model predict very similar path loss values. Moreover, the 5GCM path loss is approximately 3 dB lower than the path loss obtained with the METIS model at a Tx-Rx separation distance of 100 m. For the NLOS condition, depicted in Figure 9, the path loss predicted by the METIS model is practically constant and less than the FSPL for distances greater than 53 m, due to the very small B parameter. By contrast, the 5GCM DS CIF and ABG channel models predict much higher path losses, specially for distances higher than the respective breakpoint distances (i.e., 110 and 147 m), as shown in Figure 9. In this case, the CIF PLE increases from 2.43 to 8.36 and the ABG α increases from 2.9 to 11.47 for distances greater than the breakpoint. Although the 5GCM white paper predicts that the DS models may be best suited for greater distances ( > 50 m), it is not clear that the DS 5GCM and obtained breakpoints are consistent to real measurements in InH shopping scenarios. Since the METIS model is hardly realistic for the NLOS condition, the 5GCM models are well suited for InH shopping mall scenarios, considering that the DS models yield higher path loss values at greater distances for the NLOS condition.

The comparison between the models and the measurement campaign is based on the mean-squared error (MSE), a widely used metric that depends on the average squared difference between the estimated values and the actual value, evaluated as (Yates and Goodman, 2014): e MSE = 1 n ∑ i = 1 n Y i − Y ̂ i 2 , (12) where n is the number of data points, Y _i represents the measured values, and Y ̂ i represents the estimated values. The lower the MSE value, the better the estimator (Yates and Goodman, 2014). Therefore, the MSE can define the quality of the channel models path loss estimation and evaluate which ones present the most realistic predictions compared to the measurements.

The measurement campaign chosen for the comparison was conducted on the fourth floor of Durhan Hall, Virginia Tech campus, where the structure is made of steel-reinforced concrete, with drywall interior walls, cement blocks, ceramic tiles, carpeted floors and suspended panel ceilings. A total of 8 transmitters and 22 receivers were used in this campaign and the locations were chosen to be representative of a wide range of typical femtocellular propagation scenarios in a working environment, where a low transmission power will serve a single room or part of a floor. The measurements were based on the transmitter and receiver locations in office cubicles and corridors and specifically refer to broadband propagation effects that can be verified in a typical office building, in LOS and NLOS conditions. Pyramidal horn antennas, which had a gain of 25 dBi, were used to compensate path loss in the 60 GHz frequency measurements (Anderson and Rappaport, 2004).

Table 4 presents the mean path loss obtained from the theoretical free-space, 3GPP, 5GCM and mmMAGIC channel models, the IEEE 802.11ad standard, and the measurement campaign results, available in Anderson and Rappaport (2004), for indoor office environments. In addition, Tables 5, 6 present the obtained MSE for each channel model, condition, and environment for comparison. As shown in Table 5, the IEEE 802.11ad standard presents the lowest MSE under the LOS condition in the office cubicle environment. Moreover, it was found that the mmMAGIC model presents the most accurate prediction, i.e., lowest MSE value, under the NLOS condition. By contrast, mmMAGIC channel model presents the least realistic prediction under the LOS condition, i.e. highest MSE value, whereas, for the NLOS condition, the 5GCM SS CIF model was considered the least accurate. Note that, under the NLOS condition, the models present the lowest MSE values, compared to the LOS condition, ranging from 43.88 to 70.02, with the best- and worst-case scenarios being the mmMAGIC and 5GCM SS CIF models, respectively. Considering that the office cubicle environment may have more obstacles and partition walls than the corridor, this results are consistent to the scenario.

The obtained MSE values for the office corridor environment, presented in Table 6, show that the IEEE 802.11ad standard presents the best prediction performance under the LOS condition. On the other hand, the mmMAGIC model presented the lowest MSE under the LOS condition, compared to the other models. Note that, under the NLOS condition, the channel models presented very high MSE values, ranging from 160.36 to 345.5, with the best- and worst-case scenarios being the IEEE 802.11ad standard and 5GCM SS CIF models, respectively. Considering that the office corridor environment may have less obstacles and walls, compared to the cubicle environment, the LOS condition is more likely, which is consistent to the MSE results. Nevertheless, the results presented here may not be accurate for the entire range of indoor scenarios, since it was based on specific measurements and environments.