An Indoor Path Loss Prediction Model Using Wall Correction Factors for Wireless Local Area Network and 5G Indoor Networks

A modi ﬁ ed indoor path loss prediction model is presented, namely, effective wall loss model. The modi ﬁ ed model is compared to other indoor path loss prediction models using simulation data and real-time measurements. Different operating frequencies and antenna polarizations are considered to verify the observations. In the simulation part, effective wall loss model shows the best performance among other models as it outperforms 2 times the dual-slope model, which is the second best performance. Similar observations were recorded from the experimental results. Linear attenuation and one-slope models have similar behavior, the two models parameters show dependency on operating frequency and antenna polarization.


Introduction
The ability to locate a target object in an indoor environment has many potential applications: for example, in security, emergency services, and health care and commercial fields (Pierleoni et al., 2016;Suits et al., 2014;R. Zhang et al., 2013). However, it is difficult to provide accurate location by radio means because of the complex multipath propagation within buildings (Obeidat et al., 2016).
Multipath propagation of wireless signals within buildings has been extensively studied in the context of the deployment of cordless phones (Keenan & Motley, 1990) and wireless local area networks (WLANs) (Borrelli et al., 2004;Crow et al., 1997;Kong et al., 2004). Propagation from outdoors to indoors has been studied in the context of cellular networks (Damosso & Correia, 1999). More recently, there has been significant interest in developing indoor location technologies, in many cases relying on the opportunistic exploitation of available WLAN signals (Zekavat & Buehrer, 2011) and deploying WLAN in the millimeter-wave band (Moraitis & Constantinou, 2004).
Propagation models have been developed and can be broadly categorized as predicting either median signal strength (path loss and shadowing) like Motley-Keenan model (MKM; Keenan & Motley, 1990) or channel behavior (fading across time or frequency) like Saleh-Valenzuela model (Saleh & Valenzuela, 1987). Path loss models predict the signal level (averaged over several wavelengths or a wide bandwidth) at a given distance from the transmitter (Keenan & Motley, 1990), while channel models describe the stochastic or deterministic variation of the signal level (narrow band) and the time dispersion (wideband) at that location (Saleh & Valenzuela, 1987). With the advent of multiple input, multiple output systems, spatial channel models have been introduced. The 3-D indoor environment comprises walls and floors, windows and doors, corridors, stairwells and lift shafts, and fixtures and furniture, which can be regarded (using radar parlance) as clutter (Remcom, 2017a).
The delay on each raypath is related to the path length, while the amplitude, phase, and polarization depend on the combination of spreading losses and losses due to transmission through, reflection from or diffraction around obstacles, which in turn depends on their structure and material electrical properties (Saunders & Aragón-Zavala, 2007). At frequencies above the ultrahigh-frequency band, penetration and diffraction losses tend to increase (Wells, 1977). In the millimeter-wave band surface roughness becomes more significant, leading to an increase in diffuse reflected components. However, the essential ray optical geometry remains the same, so that multipath components have the same delay, even if they are more attenuated (Haneda et al., 2016;Pascual-García et al., 2016).
This highly complex channel behavior is captured by ray tracing software. However, there are practical limits on the accuracy with which the detail of building structures or clutter can be characterized or the extent to which the material electrical properties can be accurately known (Obeidat et al., 2016). There are also compromises made in the number of raypaths that can be found by the software within the constraints of a reasonable run time and memory requirement (Remcom, 2017b).
The ray optical view of the propagation mechanisms leads naturally to a description of the channel in terms of its impulse response as given by Hashemi (1993). In the indoor channel, rays have been observed to arrive in clusters, as modeled by Saleh and Valenzuela (1987). The clusters can be associated with angles of arrival and departure in developing spatial channel models (Spencer et al., 2000). The impulse response will vary with position, and if the terminal (or clutter) is moving, this translates into time variation.
Despite the obvious underlying complexity of the indoor channel, Keenan and Motley (1990) looked to provide a straightforward engineering model for path loss. Their approach was to consider the various walls and floors obstructing the straight-line path between transmitter and receiver and to factor in a best fit loss per wall or floor of each identifiable type, for example, stud partition (drywall) or concrete block walls and suspended concrete floor beams or wooden floors. When these losses were factored in, they found a residual free space variation with distance (i.e., power law index of 2). A deficiency of their model was its tendency to overpredict loss where there are many floors or walls (presumably because there is an alternative, lower-loss path around those obstacles).
Other models have been proposed from simple power laws, two-slope or multislope models (Andrade & Hoefel, 2010;Lott & Forkel, 2001;Pahlavan & Levesque, 2005) to those that use the Keenan and Motley concept with some added sophistication to reduce the loss per floor as the number of floors increase (Serôdio et al., 2012). Waveguiding, for example, along corridors can lead to path loss indices approaching one, while the presence of clutter within the first Fresnel zone of a ray can lead to indices of 4-6 beyond a breakpoint as for ground wave propagation (Rappaort, 2002).
In this paper, several indoor path loss models and their associated parameters are examined and tested. A modified method named effective wall loss model (EWLM) to estimate the path loss is proposed. The performance of the proposed method was compared to other related methods in terms of various frequency spectrums covering WLAN and millimeter-wave frequencies; the effect of antenna polarization was also studied. Simulated and measured test results were presented in which it shows the proposed method outperformed the other tested models. The organization of this paper is as follow: section 2 investigates different indoor path loss prediction models, and section 3 describes the experimental setup of the simulations and measurements and the procedure followed to estimate model parameters. Section 4 presents simulation and experimental results and a comparison between indoor path loss models and the modified model, and finally, conclusion is drawn.

One-Slope Model
A fast and simple model is also termed as simplified path loss model where the received power at a point is given by (Lott & Forkel, 2001) where P 0 is the received power at a 1 m away from the transmitter, which can be estimated using free space formula or experimentally (Goldsmith, 2005), n is the path loss exponent, which is calculated using interpolation (Zvanovec et al., 2003), and d is the distance from transmitter. Path loss is dependent on range (distance) and path loss exponent (Goldsmith, 2005). In Alexander and Pugliese (1983) various values of decay index n are presented, the values ranging from 1.2 due to waveguiding effects in corridors to 6.1 for dense office environment (Rappaort, 2002). In outdoor to indoor propagation at 1.7 GHz, decay index n found to be 1.495 for corridor single floor; 1.524 through corridors in that building and 3.25 for rooms single floor and 3.31 in rooms through building (Davies et al., 1990). Devasirvathan (1991) proposed another approach, the experiments were carried out on range of frequencies (0.85, 1.9, 4, and 5.8 GHz), and it was concluded that total loss L is the sum of free space loss L FS and loss factor a in the range of (0.3 to 0.6 dB/m) depending on frequency and building (Devasirvathan, 1991).

Linear Attenuation Model
where d represents distance in meter.

Dual-Slope Model
Propagation within indoor environment was categorized depending on the first Fresnel zone clearance, the "near transmitter propagation," where no obstruction in the first Fresnel zone and the path loss exponent is less than 2 due to waveguiding, and "breakpoint propagation" when the furniture falls in the first Fresnel zone where path loss exponent becomes larger than 2, the model is shown in equation (3) where n 1 , n 2 are the path loss exponents and d bp is the breakpoint distance. Calculation of the breakpoint distance is done either theoretically as in Andrade and Hoefel (2010) or experimentally as in Nuangwongsa et al. (2009).

Partitioned Model
In this model, path loss is estimated based on predetermined values of n and distance between transmitter and receiver (Pahlavan & Levesque, 2005):

ITU-R P.1238 Indoor Model
An empirical model accounts the losses due to penetration through floors within the same building (ITU, 2012): where L f (N(F)) is the floor penetration loss, which varies with frequency, type of floor, and number of floors between the transmitter and receiver (N(F)). Based on enormous measurements, the model gives typical values for n and L f (N(F)) for different indoor environments, which are available in ITU (2012), in the case both the transmitter and receiver are in the same floor then L f = 0.

Motley-Keenan Model
The wide range of n makes the use of OSM insufficient (Keenan & Motley, 1990); MKM considers the effect of walls and floors, including their types and numbers (Keenan & Motley, 1990;Lima & Menezes, 2005).
where L FS , L C , N w , N f , L w , L f , i, and j are the free space loss, constant term (loss at d 0 = 1 m), number of walls, number of floors, wall loss factor, floor loss factor, type of wall, and type of floor, respectively.

COST231 Indoor Model
A more sophisticated model is given by COST231, which adopts the concept of Keenan and Motley model (Pedersen, 1999). The model assumes a linear increase of loss as the number of walls increase, and nonlinear increase of loss with respect to the number of floors as the average floor losses tend to decrease when the number of floors increase; the model is given in equation (7) (Pedersen, 1999;Serôdio et al., 2012): where L C is the resultant wall losses obtained by applying multiple linear regression to the measurements, n f is the number of encountered floors, b is an empirical constant, L wi is wall losses of type i, and L f is the floor loss. An extension has been made so that individual wall losses decrease as the number of walls increases which gives better performance (Serôdio et al., 2012).

Dominant Path Model
DPM is similar to Motley and Keenan method; however, instead of considering the direct ray, the dominant rays are considered instead (Wölfle et al., 1997). It considers the main rays that contribute most of the energy; using this model will reduce the dependency of having a fine detailed simulated environment, and it also reduces the computational time as it considers less rays (Wolfle & Landstorfer, 1998). Minimum losses for DPM are computed as in equation (8) (Plets et al., 2012): where L FS is the free space loss, WL is cumulated wall losses, and w I is interaction loss, which depends on type of wall, operating frequency, and the angle of bend made by the propagation.

Average Wall Model
Average wall model (AWM) was proposed by Lloret et al. (2004) as a fast design model for indoor radio coverage where few measurements are required as they are collected 1 m away from the transmitter and each wall in the facility. This model is similar to MKM; however, the way losses are calculated is different, losses from the same type of walls are averaged, and the total loss after each wall is the result of multiplication of the average losses with total number of encountered walls. The first wall loss is estimated at 1 m away from the wall by finding the difference between the path loss estimated from measurements and the losses due to free space propagation as shown in equation (9) (Lloret et al., 2004): where P r1 is the received signal strength (RSS) 1 m from the first wall and d 1 is the distance between the transmitter and the point, which is located 1 m from the first wall. Losses of following walls are estimated similarly after excluding previous wall losses (Lloret et al., 2004). In order to exclude the multipath effect, the mean value for the losses of the same type of walls is given by the following: 10.1002/2018RS006536

Radio Science
where v is the total number of encountered walls. The path loss at distance d can be expressed as shown in equation (11), where L is the number of encountered walls.

Effective Wall Loss Model
The AWM captures the changes in the propagation environment; therefore, wall losses may be positive or negative. In fact, these losses can be considered as correction factors rather than losses. Using the "average" will superimpose the effect of all walls and then assume that all walls will contribute equally, which is not necessarily true. The main problem with this model is the assumption that the main source of signal fading are the walls; therefore, similar walls will affect the signal similarly. Although this is partially true especially for millimeter waves as will be shown later, there are many other sources that affect the signal strength (SS) level mainly multipath.
The AWM superimposes the multipath effect; however, the effects of multipath fading give a fingerprint about how waves in specific region behave. Also, the concept of averaging does not reflect a scientific impact as it is unlikely that the last wall loss will affect the measurements at locations much before that wall. Another limitation to the AWM is that it does not consider the effect of line-of-sight (LOS) propagation where path loss exponent will be less than the free space path loss exponent due to waveguiding effect.
Due to these limitations, we adopt the AWM with two modifications: first, the path loss estimated at a point depends on the losses due to the encountered wall only rather than using the concept of averaging. The second modification includes the effect of path loss exponent in the region between the transmitter and the first wall, which may be affected by waveguiding effect. For non-line-of-sight (NLOS) propagation areas the effect of path loss exponents is already embedded with the wall correction factors. In order to distinguish it from the AWM, we refer to the last modification as EWLM. The path loss at distance d can be expressed as follows: where n is 2 for NLOS propagation, while for LOS propagation it is estimated by best fitting, L is the number of encountered walls. It is worth mentioning that W avg in equation (11) depends on total wall losses of the same type; therefore, applying equation (11) will consider the effect of walls before and after the point of interest. Walls after the point of interest are unlikely to contribute significantly to the RSS compared to those before the point; therefore, EWLM considers the effect of walls, which are only before the point of interest. Even if the walls are of the same type, both models will work differently as shown in the incoming sections; however, they will have similar results after the last encoun-

Methodology and Experimental Setup
In the first part of our analysis, different indoor path prediction models were examined and compared to the EWLM using data obtained from ray tracing software called Wireless Insite®, which has been extensively

Radio Science
validated, especially for the ultrahigh frequency band (Medeđović et al., 2012) and for 802.11 ac frequencies (Dama et al., 2011). The adopted environment for the experiment was the third floor in Chesham building in Bradford University. The model for the building was constructed using the software.
Transmitter and receivers implemented in the environment are both omnidirectional, transmitted power was set to 20 dBm, while receiver sensitivity was set to À120 dBm. Five frequencies were examined, including 2.4, 5.3, 28, 60, and 73.5 GHz, and their corresponding bandwidths are 0.084 GHz (Wu et al., 2004), 0.12 GHz (Koivunen et al., 2007), 0.8 GHz (Maccartney et al., 2015), 2.15 GHz (Technologies, 2017), and 2 GHz (Instruments, 2016), respectively; those frequencies have wide usage for indoor applications. We also investigated two types of polarization: vertical polarization (VP) and circular polarization (CP); settings for Wireless Insite are given in Table 1.
In the second part of the experiments, real-time measurements have been collected from WLAN access points (AP) distributed in the third floor of Chesham building at the University of Bradford; those APs support Wi-Fi coverage on both 2.4-and 5.3-GHz bands. In these experiments, three APs were considered as shown in Figure 1. All APs are similar; this includes the transmitter power, types of antenna used, and bandwidth. For each AP, data are collected over two routes; measurements are taken at 1-m height with 0.5-m spacing between each two measurements. The heights for AP1 is 2.2 m, while for AP2 and AP3 the heights are 2.75 m. A WLAN scanner software called inSSIDer® was used to collect the measurements using a laptop with a calibrated 802.11a/b/g/ac card adapter, these measurements are averaged to remove the effect of fast fading, and the RSS reading is updated every 1 s.  A valid comparison between the different modeling approaches requires that each model is applied to the same data set in order to predict parameters. MATLAB is used to estimate the parameter values, which   Zhang and Hwang (1994).
It is worth mentioning that for the EWLM after each wall the model makes a correction factor either by adding gain or adding loss in order to fit the simulations/measurements. MKM assumes values for wall losses such that it makes the best fit for all simulations (in case of ray tracing) or measurements (in case of actual measurements) from all different routes; these losses are different from correction factors used by AWM and EWLM. OSM, DSM, and LAM look for the best fitting for the simulations/measurements (different values for n and a can be used to describe the propagation channels within corridors and rooms. DPM uses the cumulated wall losses and interaction losses; this is required to identify all possible direct paths and their

Radio Science
corresponding bent angles as mentioned in Plets et al. (2012). After that, cumulated wall losses and interaction losses are calculated using Table 4 and Figure 6 in Plets et al. (2012).
As shown in Figure 1, measurements are taken from AP1 on the yellow routes, while they were taken from AP2 and AP3 on the red and blue routes, respectively. The simulation includes many routes within the floor to cover different scenario and to verify the observations. Figure 2 shows a 3-D view for the simulated environment; the colors are different for different features. Material dependence on operating frequency plays a major role in determining the radio coverage, as shown in equation (13); the attenuation rate A (dB/m) is a function of conductivity σ and relative permittivity ε r (ITU, 2015).
However, both ε r and σ are functions of the operating frequency as shown in equations (14) and (15), respectively (ITU, 2015): where α, β, γ, and δ are given by ITU (2015). As the operating frequency is changing, the interaction between waves and building material will change accordingly. Table 4 shows the values of ε r and σ adopted in our experiment, which are calculated using equations (14) and (15).

Radio Science
A comparison between different indoor path loss models at 5.3 GHz using vertical polarized antenna is shown in Figure 3; RMSEs of the examined models are presented in Table 5, row 1. In this scenario, the EWLM outperforms other models as it was able to capture the changes in the environments. After each wall, the model makes a correction factor either adding gain or adding loss to fit the simulation data. In the AWM, the first two  As provided from the RMSE values, both OSM and LAM show low performance; this may be due the difficulty to model the simulation data with a monotonic function. The DSM uses two slopes to describe the changes in the environment. Due to this flexibility, it has better results than OSM. Finally, the PM has different path loss exponents; however, it shows good performance if the test environment has similar path loss exponents to the model.
In Figure 4, the mean SS level decays slowly with distance; the RMSEs of the examined models are presented in Table 5, row 2. EWLM has the best performance, while OSM has the second best performance as the path loss exponent found to be around 2; this may be regarded due to waveguiding effect. The DSM has lower performance than OSM, although this model uses two path loss exponents, which gives more flexibility; the model requires more data in order to provide accurate prediction. In this scenario and using lower frequencies, there will not be much losses due to propagation through drywall. As a result, the correction factors will have less significant effect; however, considering the waveguiding effect gives EWLM advantage over AWM as seen in Figure 4. While at higher frequencies, propagation through these walls will lead to greater losses; therefore, the correction factors will have more impact as shown in Figure 5.
In Figure 5 simulation results are presented for the same route whose results are shown in Figure 4, but at higher frequency. The RMSEs of the examined models are presented in Table 5, row 3. In comparison, models that use free space path loss exponent (n = 2) and add walls losses (i.e., EWLM, AWM, and MKM) or models use fixed values of n like PM are both expected to have better performance; this is due to the fact that wall losses tend to be greater as frequency increases as indicated in the metrics in Table 5. At higher frequencies, walls contribute to loss significantly; as a result, the OSM will have less accurate estimation, while the DSM has advantage from having two slopes and hence shows more stability.
In Figure 6 many models predicts the SS sufficiently in the first 11 m and in the last 7 m; however, SS level follows unpredicted behavior in the 11-14-m window where most of them find difficulty to capture these changes as provided by their corresponding RMSE values, which are presented in Table 5, row 4; in this scenario the MKM has the best performance.
Through the experiment, the average RMSE shows an increase as frequency increases as shown in Table 6. Almost all models have larger RMSE values at 28-and 60-GHz band than those at 73.5-GHz band. This  As mentioned earlier, MKM adopts values for wall losses to give best fit for simulations; Table 7 shows the values given for drywalls and concrete walls for the used frequencies; losses for concrete walls and drywall tend to increase with frequency. They also tend to be larger in the case of VP than CP; this is because when a singly reflected CP signal with angle of incidence is greater than Brewster angle, it will be orthogonal to the LOS component, which leads to reduction in multipath interference (ITU, 2012), moving further away from the transmitter incidence angles become greater than the Brewster angle. Figure 7 presents a RSS comparative behavior with distance between VP and CP at 28 GHz; the higher SS in the CP case as receiver is moving further away from the AP can be explained by the effect of the multipath interference reduction as mentioned above. As shown in the incoming discussion, the examined model parameters are found to have less values in the case of CP.
The average path loss exponent versus operating frequency for OSM is plotted in Figure 8; for VP antenna, n tends to increase as frequency increases. However, in the case of CP antenna average value of n tends to decrease as frequency exceeds 28 GHz. This is may be explained due to radio coverage reduction occurred as frequency increased; hence, a lower value for n is obtained.
The value of n for the corridor shown in Figure 1 tends to have slight dependency on the examined frequencies as it has almost fixed value equivalent to 0.9 in the case of VP and (0.6-0.9) in the case of CP.

Radio Science
Path loss exponent is influenced by changes in frequency and polarization and depending on route location within the floor. For example, using 60 GHz and CP antenna, n in corridor routes due to waveguiding effect is found to have a value of 1, while using VP antenna for the same route, it has a value of 1.7. In the case where path is between rooms, where walls are made from concrete, using VP antenna, n reached a value of 5.
The relationship between average attenuation factor and frequency for LAM is shown in Figure 9. As expected a increases as frequency increases, and VP antenna has higher attenuation factor than CP antenna. The mean value for a for VP and CP is 0.67 dB/m and 0.367 dB/m, respectively. Considering Figures 8 and 9, a similarity between OSM and LAM is observed, as the variation of n and a is very similar for many routes on different frequencies and polarization.
This also is proved in Figure 10; as shown both models have similar performance provided from their corresponding RMSE for almost 40% of tested scenarios. While OSM has better performance for frequencies 2.4, 5.3, and 28 GHz, LAM has better performance for frequencies over 28 GHz. The figure also presents PM

Radio Science
performance that shows the poorest performance among all the models due to its limitation by having fixed path loss exponents over predefined distances; however, the model seems to have better performance for 60 and 73.5 GHz.
A comparison between OSM, DSM, and MKM is demonstrated in Figure 11. DSM outperforms both OSM and MKM as it has less RMSE than OSM for almost 72.5% of tested scenarios and less RMSE than MKM for 60.8% of tested scenarios. For low frequencies range of this experiment DSM outperforms MKM, while for millimeter waves MKM has better performance. This can be regarded to the effect of wall losses in SS fading, which is considered by MKM. OSM and DSM show similar pattern with obvious advantage for the DSM, due to the latter flexibility as it has two values for n. The model can capture propagation changes in the environment more efficiently; the gap between the two models increases as frequency increases. On the other hand, MKM outperforms OSM as it has less RMSE for almost 62.75% of tested scenarios. It can also be observed that for higher frequencies, both DSM and MKM are preferable compared to OSM.
A comparison between EWLM, AWM, and MKM is shown in Figure 12. EWLM shows better performance than MKM and AWM for almost 78.4% and 80.4% of tested scenarios, respectively. The model has such advantage because the use of effective wall correction factors enhances SS prediction significantly. When comparing AWM with MKM, the former has less RMSE for almost 56.9% of tested scenarios. The AWM has also better

10.1002/2018RS006536
Radio Science performance in the 2.4-, 5.3-, and 73.5-GHz regions, while it has comparable performance at the 60 GHz. It may be observed that at 28 GHz the AWM has lower performance. This is due to the effect of averaging with makes SS prediction less accurate at higher frequencies; however, as frequency increases the radio wave coverage becomes smaller. Therefore, the encountered walls become less, in such case the AWM works better. It was also observed that when all the walls encountered are from the same type (i.e., either all are concrete or drywall), the performance of AWM is always lower than EWLM.
Considering models performance at all frequencies, DSM shows the second best performance, a comparison between EWLM and DSM is presented in Figure 13; the metrics show better performance for EWLM as it has less RMSE for almost 66.67% of the tested scenarios. At 2.4 GHz DSM has comparable performance with the EWLM; however, as the operating frequency increases EWLM tends to have better results. This is due to considering effects of wall losses as mentioned earlier.
The average error for most models reaches maximum at 28 GHz. This can be explained as follow: as the frequency increases the radio coverage tends to become shorter, so it will have less error. Although at 28 GHz the coverage was less than 5.3 and 2.4 GHz; however, signal variations tend to be greater; therefore, errors are greater. While at 60 and 73.5 GHz the radio coverage becomes much smaller; thus, errors are less than 28 GHz.

Radio Science
One interesting observation noted that although both 60 and 73.5 GHz share the same radio coverage, errors at 60 GHz are greater; this might be because the 60 GHz has more fluctuations than 73.5 GHz.
Although AWM has the advantage for being fast prediction model, it comes at the expense of accuracy. EWLM combines accuracy and speed. The PM has the lowest performance as it has predetermined values for n; in comparison to EWLM it has less RMSE for less than 7.8% of tested scenarios.
The order of the best models according to their RMSE values is EWLM, DSM, MKM, AWM, OSM, LAM, then PM; their respective average RMSEs for all scenarios at all frequencies are shown in Table 8. EWLM has the best performance, while PM has the worst performance. A comparison between the EWLM with no modification (where n = 2 for all scenarios) and with enhancement (n is estimated by best fitting for LOS propagation and 2 for NLOS propagation) is presented in Figure 14; on average the RMSE for all frequencies had reduced by about 1 dB. Compared to other models "EWLM with no modification" had the least RMSE for 27.45% of all tested scenarios; however, by considering the effect of LOS and waveguiding effect the percentage was enhanced to 51% as mentioned above.
In Figure 15 correction factor for concrete wall was found to increase linearly with increasing the operating frequency in the range of (5.3-60 GHz) for both VP and CP cases. While correction factor for drywall tend

Radio Science
to vary linearly with frequency range (2.4-73.5 GHz) for VP and in the range (5.3-60 GHz) for CP. For both types of wall, mean wall correction factor tends to be larger for VP than for CP especially for large frequencies.

Experimental Results
The experimental study in this paper includes same models investigated in the simulation part in addition to DPM. Figure 1 represents measurements collected in third floor; measurements were taken in different routes to examine more possible scenarios where walls are made from concrete and drywalls. It was observed that radio coverage for 5 GHz band is slightly larger than radio coverage for 2.4-GHz band; this can be explained as the former's effective radiated power is much larger.
A comparison between investigated models is presented in Figure 16 where data are collected from route 2-2 (shown in Figure 1) at 5.3 GHz. It is expected to have a semimonotonic RSS decaying. The RMSEs for the   2892, 5.52, 6.067, 5.4572, 7.62, 5.978, 4.9378, and 14.1928 respectively.
As the first wall is close to the transmitter the correction factor will add more accurate estimation to the results, EWLM has the best performance, and the AWM also shows a good resolution; however, it shows less performance than EWLM; this is due to the effect of last wall loss on averaging, which cause the SS prediction to be pessimistic. Since the RSS follows a semimonotonic decaying, OSM, LAM, MKM, and DSM show a good performance, and the PM use fixed values for n, which underestimate the actual losses in this scenario. DPM uses predefined values for building wall losses; however, the performance was pessimistic; this may be due to that the wall losses recommended are not for universal use as authors claim; also, the model has no difference in performance from other wall loss models if the direct path between the transmitter and the receiver is the path with least losses.
A comparison between all presented models is introduced in Figure 17; the total error for all routes are averaged. For the 2.4 GHz, as shown from the figure and Table 9, the OSM, DSM, and EWLM have the best performance. Similar to observed results from simulation part, EWLM has the most stable performance as the maximum error did not exceed 6.1102 dB and the standard deviation of errors is around 1.156 dB. PM,  Similar to PM, DPM uses predefined wall losses; therefore, the performance was poor as seen by the presented metrics. The advantage of using this model is limited to the scenarios where the transmitter and receiver are separated by one/multiwalls and there is another path, which encounters less number of walls; however, in many cases the best path is the shortest in distance between the transmitter and receiver, which return this model to be similar to multiwall models.
Using higher operating frequency, the EWLM has the best performance provided that it has the lowest values for all metrics as shown in Table 10; the metrics are consistent with the observed results in the simulation part. The AWM has the second best performance and still shows good results in terms of accuracy and stability. The DSM and LAM show comparable performances. The former performance degraded with increasing frequency; however, it still have stable and accurate estimation.
The OSM suffers from poor accuracy; this is because of wall losses at higher frequency, which requires more than one path loss exponent to have accurate estimation. The MKM still suffers from instability; however, it has better performance at 5.3 GHz; this is due to the more effect contribution from the walls at higher frequencies, which have larger values as frequency increases as shown in Table 11. DPM has similar behavior to what was observed at 2.4 GHz; typical values used for wall losses using DPM are presented in Table 11.
Path loss exponent increases as operating frequency increases. Among all tested routes, measurements provided an evidence of path loss exponent dependency on the operating frequency. As observed from the measurements, n varies in the range of (1.93-3.3) at 2.4 GHz and in the range of (3.37-4.35) at 5.3 GHz. The averaged path loss exponent is found to be 2.83 and 3.89 at 2.4 and 5.3 GHz, respectively. Linear attenuation factor also shows an increase as the operating frequency increases. Among the six tested routes, measurements from five routes provided an evidence of linear dependency of the attenuation on the operating frequency; a varies in the range of (0.4-1.6) at 2.4 GHz and (1.2-2.5) at 5.3 GHz. The average attenuation factor for the 2.4 and 5.3 GHz are 0.8166 and 1.6, respectively.   The averaged RMSEs for all scenarios and frequencies are given in Table 12; among all scenarios, EWLM has the lowest RMSE for almost 50% of tested scenarios, while DSM has the lowest RMSE for 16.667% of tested scenarios. EWLM tends to have better performance as the frequency increase that seems to be consistent with the simulation results. Similar to observations in Figure 15, wall correction factor for concrete tends to increase more rapidly as frequency increased, while for drywall the steep was smoother.

Conclusions
A modified indoor path loss prediction model has been presented using ray tracing software and then verified experimentally for 2.4-and 5.3-GHz WLAN frequency bands. In the simulation part, the model was examined and compared to other indoor path loss models at 2.4, 5.3, 28, 60, and 73.5 GHz with different antenna polarization. In the experimental part, the model was compared to same models at 2.4 and 5.3 GHz. In the simulation part EWLM shows the best performance among other models for almost 2 times the second best model. Similar observations were recorded from the experimental results. DSM showed the second best performance provided that it is equipped with sufficient data points. OSM and LAM have similar behavior, and the two models showed dependency on operating frequency and antenna polarization. The PM showed the poorest performance as it has fixed path loss exponents.