Deterministic 5G mmWave Large-Scale 3D Path Loss Model for Lagos Island, Nigeria

5G millimeter wave (mmWave) application in mobile connectivity to realize high-speed, reliable communication is attributed with high path loss. This paper presents a detailed 3D ray-tracing technique at 28 GHz for Lagos Island to investigate five unique path loss scenarios: path loss, free space path loss with antenna pattern, free space path loss without antenna pattern, excess path loss with antenna pattern, and the excess path loss without antenna pattern for an urban environment. The Close-In (CI) model, Floating Intercept (FI) path loss model, and a root mean square error (RMSE) are used to model and evaluate the best path loss model for Lagos Island. The average achieved FI ( $\alpha,\beta, \sigma $ ) parameters were 189.92352, 0.1654, and 0.66948, While the average CI ( $\eta,X\sigma $ ) parameters were 2.309355 and 56.236425. From all the scenarios evaluated, the lowest path loss exponent achieved was 0.45, while the highest path loss exponent was 3.8. We have established that the FI path loss model accurately characterizes path loss for the Lagos Island environment with the lowest RMSE of 0.0359 dB and the highest RSME of 0.0997 dB. In contrast, the CI model over-predict the path loss at 28 GHz with the lowest RMSE of 0.0495 dB and the highest RMSE of 2.2547 dB. This work opens up a new area of research on mm-Wave at 28 GHz in Lagos Island, and the results obtained from this work can be used to benchmark future studies on mmWave in a similar environment.


I. INTRODUCTION
The exponential growth in data demand, communication infrastructure, mobile subscription, and high mobile and IoT devices penetration has significantly stretched the cellular bandwidth requirements. Future communication technology needs to improve spectral efficiency, increase the bandwidth and improve the spectrum reuse technology to overcome the current technology limitations. 5G mm-Wave communication promises diverse user applications like smart cities, IoT, industrial automation, and vehicular communication, this is due to its ultra-low latency and massive network capacity associated with higher performance and improved efficiency. Despite the high expectation of 5G, mm-Wave suffers two major drawbacks; high path loss and high penetration The associate editor coordinating the review of this manuscript and approving it for publication was Wei Feng .
losses. The mm-Wave has been shown to operate in extreme power-limited regimes with limited freedom to utilize spatial antenna layout and enhanced bandwidth freedom [1]. Research on adopting artificial neural network (ANN) and deep learning network algorithms like convolutional neural network (CNN) to establish the relationship between the propagation channel features is gaining traction to achieve the expected performance. One possible solution to compensate for the high path loss and penetration losses is to use many antenna elements in a small cell setup. To overcome this challenge, Bao, et al. [2] proposed a novel deep CNN model for precoding channel parameters to optimize a combiner neural network architecture aimed at maximizing the spectral efficiency per small cell. The 5G vision is to achieve a flexible radio access scheme supporting massive machine-type communications. 5G mm-Wave communication has been associated with high path loss, high absorption rate, and critical loss through the foliage. Chen [3] proposed developing a 28 GHz 5G small cell mm-Wave platform to overcome the 5G shortcomings. For optimal location and coverage of transmitter antenna in the mm-Wave network, path loss modeling is crucial. Many approaches have been developed to model path loss using empirical, deterministic, and artificial neural network (ANN) based models. Path loss prediction techniques are valuable tools that can help network optimization engineers deploy base stations, determine base station setup location, transmitting/receiver antenna selection, operating frequency, and interference feasibility studies. Radio propagation models are grouped into empirical and deterministic models. Deterministic models are theoretically based on diffraction principles [4], integral equation [5], ray tracing [6], and parabolic equations [7]. Empirical models are based on drive test measurement of the target areas, examples include; Okumura-Hata [8], standard propagation model [9], and COST 231-Hata model [10]. These models are computationally easy to implement in time and cost-effective. However, they are not as accurate as alternative models as they cannot be adopted for a new environment without adjustment. Cheerla, et al. [11] developed an optimized COST 231-Walfisch-Ikegami (CWI) model using Newton's method at frequencies 800 and 1800 MHz. This method proved efficient to accurately predict path loss than the empirical CWI model while validated using actual field measurements. Therefore, it is imperative to study the environment and carry out detailed simulations before conducting a pilot study and implementing the capital-intensive mm-Wave infrastructure. Hence, this research aims to perform a detailed 3D raytracing simulation of Lagos Island, Nigeria, at 28 GHz. Erunkulu, et al. [12] grouped simulated path loss models into three categories depending on the carrier frequencies, for 28 GHz, the Close-In, Alpha-Beta-Gamma (ABG), and Floating Intercept models are used to characterize path loss at the transmitter to receiver height of 30 m to 2 m respectively. In this work, we present a thorough path loss analysis using CI and FI path loss model at 28 GHz for a transmitter-to-receiver (TR/RX) height of 20/2 m. Other researchers and service providers can adapt the results obtained from this work before implementing 5G network infrastructure to benchmark their study for a similar environment.  representing Lagos Island. (v) To determine the optimum TX-RX distance to guide the actual implementation of 5G mm-Wave infrastructure.
In this paper, our contributions include; (a) developing a unique deterministic path loss model using the ray-tracing simulation technique at 28 GHz for Lagos Island, Nigeria. The proposed path loss model has been tuned to fit the target environment by calculating the path loss exponent, shadow factor, the random Gaussian standard deviation parameters. (b) Further to this, close-in (CI) and floating intercept (FI) path loss models have been computed for various scenarios to decide the best model to represent large-scale path loss at a 28 GHz environment. (c) Lastly, this work opens up a new area of research on mm-Wave at 28 GHz in Lagos Island and the surrounding environment by using the results obtained in this work to benchmark future works in research, 5G pilot study, and infrastructure implementation. The rest of this paper is organized as follows: Section II discusses the background and related works and depicts a tabular review of key parameters considered in this work. Section III presents the methodology. Section IV presents the results and discusses the results obtained in different scenarios. Section V concludes the article.

II. BACKGROUND AND RELATED WORKS
5G mmWave are associated with high path losses and absorption losses. However, reflection and scattering allow wireless links to be established between the transmitter and receiver in LoS and NLoS. Due to mmWave small wavelength, air and water's molecular size greatly determines the free space achievable across the mmWave spectrum. Temperature and humidity impact the excess attenuation resulting from VOLUME 9, 2021 absorption. Higher mmWave band suffers from very high excess attenuation over distance. Rappaport, et al. [13] attribute the absorption losses to excess path loss caused by oxygen absorption and environmental factors. The excess path loss causes an additional effect on the propagation channel by adding attenuation in the link. The excess path loss for a 60 GHz channel results in an additional 28 dB to the free space path loss. One recommended way to overcome the mmWave path loss is by increasing the antenna size at either the receiver or transmitter. Antenna gain is limited to the effective surface area of the antenna, which directly relates to the permissible path losses. In an LoS mmWave channel, the most effective communication with a directional antenna occurs in the boresight alignment; therefore, the antenna position, location, and pattern affect the communication channel by either increasing the path loss or lowering the path losses. For antennas with a fixed beam pattern, the transmitter should be physically pointed toward the receiver to minimize path losses. In NLoS communication channels, effective communication is best when the antenna pointing is toward one or more dominant reflections within a single beam. The NLoS channel is best when there is a complicated beam pattern that can place energy on multiple propagation paths. The antenna used for NLoS requires some adaptivity to achieve a desirable NLoS channel. Future mmWave antenna should be adaptive with high antenna gain, beamwidth, and beam pointing mechanism to offset and adjust to specific interference levels. Throughout this work, we refer to NLoS environment as path loss scenario, LoS environment as FSPL, which evaluate the effect of antenna pattern on path loss. Hence we consider the case of LoS as FSPL with antenna pattern and FSPL without antenna pattern. The absorption loss is referred to as excess path loss with antenna pattern and excess path loss without antenna pattern. An LoS environment is characterized by a direct non-obstructed path between the transmitter and receiver; an NLoS environment is when the channel has no direct unobstructed path between receiver and transmitter.
Path loss prediction is the ability to forecast the attenuation effect on radio signal propagation with a good level of precision [14]. It is crucial for network planning in wireless communication systems [15]. Extensive field campaigns measuring RSS from the transmitter station to the receiver station helps to generate data needed for propagation path loss determination of a desired wireless network [12], [16]- [18] in a densified cellular network infrastructure [19]. Al-Samman, et al. [20] proposed a path loss prediction model for 5G mm-Wave and future 6 GHz wireless communication. The authors developed a new path loss model to account for the path loss associated with 5G networks by introducing a frequency-dependent attenuation factor. Grøtli and Johansen [21] proposed using UAVs for data collection to find the fastest path to solve multi-task missions for direct and multi-hop communication applications. This work concluded that it is possible to improve the propagation signal strength by adopting multiple UAVs for path planning before network infrastructure deployment. Path loss distribution depends on the general characteristics of the area under study [22].
The path loss value depends on the propagation environment; urban, suburban, and rural areas are estimated to have different path loss exponents. An urban environment is estimated to experience a path loss of 30-50 dB generated due to high-rise and other city buildings. The ground terrain is estimated to generate a path loss of 90 dB for every 1 km covered [23]. The effect of path loss on sea and ocean surfaces has been reported by [24], Also, Hrovat, et al. [25] research shows that path loss is experienced in tunnels used for metro stations and trains caused by obstacles and traffic in the road and railway tunnel which results to additional signal attenuation, increasing the propagation signal's delay spread. Also, moving objects in the tunnel causes additional path loss accounting for poor communication quality in the tunnel environment. In practice, cellular coverage prediction can be achieved through geometric mathematical models using computer simulations for ray tracing. Using a high computational computer to run cellular coverage prediction saves on time and cost of the incurred drive test. Several vendors have developed 3D modeling software that has been adopted in various works. There are two main models adopted to model path loss prediction: a) drive test measurement campaign, b) propagation simulation modeling using ray tracing and ray launching. In drive test campaigns, sophisticated software and measuring tools are used to measure the propagation characteristics. Presently, ray tracing techniques have been extended to model ANN and CNN-based path loss prediction models by combining 3D models with 2D satellite imagery to develop generic path loss prediction methods [26]- [29] and [30]. While considering 3D digital maps, a given map's accuracy depends on how the terrain, foliage, and city buildings are portrayed; also captured detailed features like building footprints, building edges, facades, street features, vertical and horizontal, and the transmitting and receiving antennas position. Lastly, the path loss prediction by the 3D ray-tracing simulation method offers flexibility and controllability in changing model parameters that are impossible to tune and calibrate in field first-hand practice and serve as a testbed for emulation studies. The main disadvantage of running the 3D ray-tracing simulations is the high computational complexity and time associated with simulations. Ahmadien, et al. [26] proposed using 2D satellite image models based on convolutional neural networks to overcome this challenge. Their works showed that path loss distribution could be predicted for wireless networks' various frequencies under varying transmitter and antenna heights. To save on the computational complexity of 3D tracing, Ates, et al. [31] proposed a deep learning model using convolutional neural networks (CNNs) with 88% accuracy on path loss exponent and 76% accuracy on large-scale shadowing factor. The author used 3D ray tracing to train and test the model after extracting the relevant features in the 2D satellite images. The deep neural network takes a 2D satellite image as the input and returns a channel parameter prediction. For successful deep learning modeling, a large dataset is needed for the training and testing set. In 3D modeling, ray tracing is effective in obtaining path loss value and bit error rate (BER). An efficient deep learning model requires massive data to train, test, and validate the model. This data can be generated via a 3D ray-tracing simulation of the target area using propagation modeling software.
Other researchers have applied 3D ray-tracing to model path loss propagation [32]. Charitos, et al. [33] adopted a 3D ray-tracing channel to predict the spatial and temporal multipath ray components of radio propagation between an LTE base station and a vehicle. These simulation results are then compared to the actual drive test measurement conducted in the exact area covered by the simulation. This virtual drive test results in higher reliability and repeatability with an accuracy higher than of measured value. The simulation of path loss using a 3D ray-tracing model offers a powerful and cost-effective alternative to on-street drive test campaigns as several parameters can be modeled. Thrane, et al. [34] compared the effectiveness of using deep learning techniques utilizing drive test measurement data and satellite images for ray tracing to model path loss models. The developed deep learning model improved path loss prediction with over 1 dB for the cellular network at 811 MHz and 4.7 dB at 2630 MHz. A comprehensive review of the existing path loss model based on the ray-tracing model was done [34]. This review focused on the path loss accuracy achieved by adopting 3D tracing techniques on outdoor propagation scenarios. The authors concluded that digital maps introduce a certain level of uncertainty in the ray tracing models. Still, they offer the best possible and reliable path loss predictions despite the high computational requirements. Han, et al. [35] proposed a novel double regression model utilizing an NS-2 simulator that allowed the sender and receiver to move without abrupt changes in the correlated space path loss. The author aimed to overcome the difficulties introduced by sender and receiver in motion by producing spatially correlated path loss in mobile-to-mobile simulation. The model accuracy was validated using drive test campaigns that maintained a spatial correlation of path loss to the empirically observed indoor and outdoor scenarios.
Path loss and atmospheric absorption are significant sources of propagation loss in mm-Wave wireless communication [13]. Maccartney, et al. [36], conducted an extensive ultra-wideband mm-Wave propagation measurement campaign at 28 and 73 GHz in New York. This work showed that novel large-scale path loss models are more straightforward and more physically based than previous 3GPP and ITU indoor propagation models. Other similar work by Sun, et al. [37] to investigate the prediction accuracy of 5G wireless communication concluded that the alpha-betagamma (ABG) model of large-scale path loss model in the microwave and mm-Wave under-predicts path loss, while relatively close to the transmitting antenna and over-predict path loss while far from the transmitter. Further, the results indicated that the physically based two-parameter CI model and three-parameter CIF model offer computational simplicity. In the sequel to this work, Rappaport, et al. [38] conducted extensive measurement campaigns for typical base station-tomobile access scenarios in dense urban environments. This work showed that path loss exponent was immense in a highly populated urban environment like New York City than in Austin. With extensive propagation measurement, it is possible to introduce new path loss models that predict signal strength as a function of distance from the transmitter and the transmission frequency for both indoor and outdoor scenarios. Bhuvaneshwari, et al. [39] suggested a hybrid model that combined the Walfisch-Ikegami model and ray-tracing techniques to simulate path loss prediction. This hybrid model reduced the path loss prediction error by 69.9% and relative error by 7.31%. These results was validated by conducting a field campaign in Hyderabad, India, on a GSM 900 MHz network. Table 2 summarises various research conducted at mm-Wave bands.
The simulation model's performance can be validated with actual field measurement for an urban area, using models like COST-231 Walfish-Ikegami (COST-WI). COST-WI considers the hard to find finite details of the environment like road width, heights of buildings, streets orientations, and foliage, limiting the use of such models in other areas. Other models include COST-231 [10]. Batalha, et al. [48] conducted an extensive measurement campaign for an indoor scenario at mm-Wave frequencies. Field measurement data was used to develop a path loss adjusting model through the minimum mean square error (MMSE) method for a close-in path loss model in LoS and NLoS conditions. The author proposed modeling the path loss using 28 GHz frequency for indoor environment, and using the 3D ray-tracing model can achieve this. Degli-Esposti, et al. [49] evaluated indoor propagation at mm-Wave by adopting a 3-D ray-tracing model in a small office setup. Using a customized 3D tracing software with three reflections and one transmission, enabled internal office object diffraction and single-bounce diffuse scattering. Later, using the effective roughness model to factor the propagation environment, they considered the best compromise between the accuracy of the results and the central processing unit (CPU) computational requirements. Table 3 represents a taxonomy of related empirical and deterministic path loss models at mm-Wave band.

III. METHODOLOGY
3D ray tracing is a state-of-art deterministic path loss modeling technique. It provides detailed site-specific information necessary to simulate an accurate path loss model [61], [62]. Ray tracing engines offer the flexibility of changing the carrier frequency, transmit, and receiver antennas. In principle, deterministic methods offer higher accuracy than empirical models as they are based on geometric optics. Still, the high computational requirement and time required to model path loss is a factor to consider. Ray tracing methods depend on a precise 3D map model of an area of interest encompassing terrain databases, buildings, and foliage databases.
They use an optimization algorithm that calculates the minimum mean square error with the least standard deviation to form the best fit. Ref [57]- [59], [63] proposed a ray tracing simulation technique to model path loss at 28 GHz. Kamboh, et al. [64] carried out a 3D ray-tracing at 60 GHz mm-Wave using a simulation model developed in MATLAB. The author used the 5G 3GPP propagation model to compute the received signal strength and path loss. We present a large-scale path loss model at 28 GHz using a 3D map of Lagos Island as a study area, covering coordinates of 6.271735 N to the north, 6.27437 N to the south, 3.235466 E to the southeast, and 3.234122 E to the west. The 28 GHz carrier frequency was preferred for it gives a good tradeoff between unfavorable channel characteristics like path loss, rain fading, propagation loss, transmission through foliage loss, and atmospheric absorption effect. This frequency band has been piloted and implemented in Korea, the US, China, and Japan for the outdoor environment [65]. To achieve high data throughput in a small cell operating on short distances, 28 GHz offers the best carrier frequency [66]. One of the shortcomings of this frequency is susceptibility to high path loss and atmospheric absorption. To overcome the high path loss effect, Karthikeya, et al. [67] proposed the design of a co-polarized stacked antenna with a pattern diversity for indoor base stations. Similarly, [68] proposed the use of large-scale antenna arrays to extend the 5G mm-Wave band coverage to lower the effect of path loss. Figure 1 shows the 3D map and the google earth map of the study area. Figure 1(a) depicts the exact position of our study area marked by the green grid bound at coordinates 6.272192/3.234164, 6.271736/3.235836, 6.270134/30235321, and 6.270655/3.233879. The study area covers a distance of 560m with an average elevation of 2.4 m, elevation gain of 11.4m, a maximum slope of 5.7%-8.7%, and an average slope of 1.3%-0.9%. Figure 2 presents a step-by-step simulation block diagram. First, we imported a 3D map into the software, then the terrain, building, and foliage databases were loaded. For terrain, the material used was dielectric half-space of type ITU dry earth for 28 GHz. The building material considered was a one-layered dielectric of ITU concreate 28 GHz type. The signal waveform applied was a sinusoid, with a carrier frequency of 28 GHz and effective bandwidth of 3000MHz. Four transmitting 30 dBm halfwave dipole antenna with the 28 GHz sinusoid waveform base stations were set up with the coordinates grid edges at the origin longitude of 3.39219575502601 and origin latitude of 6.4562764716583. Receivers were positioned in the XY grid at the height of 2 meters with a spacing of 5 meters. Figure 3 represents the study grid with the base station and receiver layout and a google map showing the study map. Wireless Insite software runs on several propagation models; amongst them, An X3D study simulation was set to utilize the APG acceleration technique with two diffractions and six reflections on an intel-based Graphic Processing Unit (GPU) workstation running Nvidia GeForce 1050 architecture. The study setup was configured to extract five scenarios of path loss data: path loss, free space path loss with antenna pattern, free space antenna without antenna pattern, excess path loss with antenna pattern, and excess path loss without antenna pattern. Also, other extracted data were received power files, interference and noise data associated with each TX antenna.

A. SIMULATION SETUP: POINT-TO-MULTIPOINT
In this scenario, the aim was to study the effect of different path loss scenarios in a 5G mm-Wave communication considering the effect of the antenna pattern in the channel throughput and capacity. For this setup, four half-wave dipole transmitter antennas were fixed, as shown in Figure 4. In this scenario, the study focussed on path loss, excess path loss without antenna pattern, excess path loss with antenna pattern, free space path loss without antenna pattern, and free space power without antenna pattern. The TX antennas were labeled TX1, TX2, TX3, TX4, as presented in Figure 4 (b).
Following the steps highlighted in figure 2, the simulation was implemented using a Windows 10 OS, Intel Core i7-8750 H CPU 2.2 GHz, 2208 MHz, 6 Cores, 12 logical processors, Intel Optane+932 GB HDD, and Nvidia GeForce GTX 1050 Graphic Processor with 4 GB dedicated memory. The simulated path loss data were extracted in a text file format and later converted to a CSV file. Table 4 shows the statistical analysis of the simulated path loss data extracted at various transmitter points.

B. 28GHz LARGE SCALE PATH LOSS MODEL FOR URBAN SMALL CELLS ANALYSIS
Path loss is defined as the power loss attenuation between the transmitter and the receiver station [14].i.e., PL (dB) = Transmitted power (Pt) dB -Received power (Pr) dB PL (dB) = 10log 10 Pt Pr (1) where Pt is the power transmitted while Pr is the power received at the close-in reference point. Free space path loss is a non-negative number defined as the power loss attenuation between the transmitter and the receiver station while path gain is a negative path loss.
PL (dB) = 10log 10 Pt Pr = −10 log 10 G t G r λ 4πR 2 (2) where, Pr is the power at the receiving antenna, Pt is the output power of the transmitting antenna, G t , G r is the gain of the transmitting and receiving antenna respectively, λ is the signal wavelength and R is the distance between the transmitter and receiver.
Free space path loss with antenna pattern scenario is achieved when the antenna pattern is included in the communication system design, the free space loss is calculated from the equation (2) by assuming that the transmitter and receiver antenna polarization match perfectly, the space loss in free space reduces to: Free space path loss without antenna patterns occurs when the antenna pattern is ignored and an isotropic pattern is assumed, the free space reduces to: L FSPL without AP (dB) = −10 log 10 G t G r λ 4πR  where L F SPL (dB) is the free space path loss with the antenna patterns. similarly, the excess path loss with antenna pattern scenario is defined as a measure of the loss above that due to free space losses, Its derived as: The excess path loss without antenna pattern (dB) is the measure of the loss above that due to the free space without antenna pattern losses. derived as: L Excess Pl without AP = L path (dB) − L FSPL without AP (6) Also, equation (2) can be extended to factor in the effect of shadowing factor to describe the path loss model at a reference distance d 0 .
where PL(d) represents path loss (dB) at transmitter distance (d), while PL(d 0 ) is the path loss associated with the reference distance d 0 . X σ is a random Gaussian variable with zero mean and standard deviation representing shadowing factor in the environment. η is the path loss exponent [69]. In urban areas, shadowing describes the random variable about the distantdependent large-scale path loss model. This effect is caused by obstruction from buildings, foliage, and other structures, causing random propagation effects. Shadow fading is an essential statistical parameter to model large-scale fading for simulation purposes. It describes the possible path loss value expected while using a distant dependent path loss model without prior knowledge of the site-specific details of an environment. Shadow fading is accurately represented as a log-normal distribution about a distant-dependent mean path loss [69]. Also, path loss can be expressed as: where PL (dB) present the mean path loss over the distances in dB, while α is the floating intercept (FI) in dB. β is the path loss exponent expressed as the linear slope and can be extracted using a best fit linear regression to equation (8), and d represents the TX-TR separation distance. From equations (7) and (8), we can derive shadow factor as: Similarly, path loss values are calculated from the measured power delay profile (PDPs) by integrating the area under the PDP to obtain the received power at each location and antenna pointing angle. These calculated values are normalized to obtain a channel graph at each antenna pointing combination [41]. The linear slope value β of the path loss exponent η is derived as: where d i is the separation distance between the antenna and the receiver, d is the average distance of all d i Values in dB, PLi is the iterated path loss value of all the measured data set as a distance-dependent variable. The floating intercept α (dB) represents the tilt in the path loss model of equation (11). It is calculated by substituting equation (8) into (7) and making α (dB) the subject as in equation (11).
The standard deviation σ (dB) (random Gaussian variable) of the path loss models can be calculated as: where N is the total number of receiver points in the XY grid, adopting the formulated equations expressed in equation (1) to equation (12). MATLAB was used to model the regression fit for the various path loss scenarios as discussed in Figure 5,  To evaluate the accuracy of the CI and FI model developed, statistical error for each scenario was calculated using the mean absolute error (MAE), mean square error (MSE), and the root mean square error (RMSE), as shown in the following equations: where Pl S i denote the simulated path loss measurement, Pl i present the predicted path loss data using the CI and FI path loss models, and Pl S−Mean i represents the mean of simulated path loss data.

IV. RESULTS AND DISCUSSION
Large-scale path loss experienced between the transmitter and receiver stations is represented as a function of distance using a path loss exponent value. The acceptable path loss is between 2.7 to 3.5 for urban areas, 3 to 5 for shadowed areas, 2 for in buildings LoS, for obstructed in-building is between 4 to 6, and 2 to 3 for an obstructed environment with factories [69]. For LoS mmWave at 28 GHz, the acceptable path loss is between 1.8 and 2.2 but changes to 4 and 5 in NLoS conditions or LoS when the transmitter and receiver are not in boresight alignment [13]. In this work, the achieved path loss varies between 0.45 dB to 3.8 dB. Lagos Island can be categorized as an urban environment with high-rise buildings causing shadowing and propagation signal obstruction; also, there are a number of large warehouses and factories within Lagos Island, thus fitting the acceptable environment to calculate the path loss exponent from all the scenarios presented in this work, the derived path loss exponent is within the range of acceptable path loss exponent. Figure 5 presents a path loss model at 28 GHz as a function of the distance between the transmitter at TX1 to the receiver grid. For this scenario, the TX-RX is 10.13 m to 488.292 m. The simulation measures the various path losses associated with the 7300 receivers in the grid. Figure 5(a) represents the path loss scenario data point. In contrast, Figure 5(b) shows the resultant modified path loss model with floating intercept and shadow factor computed to develop a matching path loss model at 28 GHz for Lagos Island. The calculated path loss exponent for path loss, FSPL with antenna pattern, FSPL without antenna pattern, Excess path loss with antenna pattern, Excess path loss without antenna pattern for TX1 were 1.46, 2.1974, 2.2019, 3.0098, and 3.0143, while the corresponding shadow factors were 34.7234, 52.2174, 52.3254, 71.5225 and 71.5225, respectively. The difference in path loss across the 5-scenarios is as discussed in Table 5. The transmitter TX2 was positioned in a highly developed area with multiple high-rise buildings, and some receivers were obstructed from the TX2 line of sight. In this scenario, the magenta color represents the high path loss effect attributed to the high-rise buildings. Figure 6(a) illustrates the VOLUME 9, 2021  path loss models for TX2. However, the impact of path loss was reduced after modifying equation (4) to introduce the shadow factor, as shown in Figure 6(b).
The path loss exponent for the various models is 0.4503, 0.7544, 0.7571, 0.9891, 0.9865 for path loss, FSPL with antenna pattern, FSPL without antenna pattern, Excess path loss with antenna pattern, Excess path loss without antenna pattern, respectively, while the show factor is 11.1472, 18.6742, 18.7394, 24.4187, 24.4839, respectively. Table 6 presents the parameters for this setup.
Popoola, et al. [70], while determining the optimal parameter for an ANN-based path loss prediction model, concluded that the TX-RX distance is a significant parameter. From this work, it can be shown that a receiver in the LoS distance resulted in lower path loss presented in the yellow color of Figure 7 than the NLoS scenario presented in magenta color.
The path loss model represented in Figure 7(a) indicates the simulated value, while Figure 7(b) illustrates the modified path loss model for the various case considered in TX3 as shown in Figure 7. The calculated shadow factor for this scenario were 34.7234, 52.2174, 52.3254, 71.6305, and 71.5225 for path loss, FSPL with antenna pattern, FSPL without antenna pattern, Excess path loss with antenna pattern, Excess path loss without antenna pattern, respectively.
The corresponding critical parameters for these scenarios are represented in Table 7.
For transmitter point TX4, the path loss exponent calculated using equation (7) for the various scenarios is 1.7734, 2.0781, 2.7180, 3.8098, and 3.8000, while the shadow factor was 43.5272, 66.4687, 66.7102, 93.5086, and 93.2670 for path loss, FSPL with antenna pattern, FSPL without antenna pattern, Excess path loss with antenna pattern, Excess path loss without antenna pattern. Figure 8(b) shows that the modified path loss model had improved exponent and shadow factor hence the lower path effect. Table 8 represent the TX4 key parameter adopted to develop Figure 8.

1) FI PATH LOSS MODEL AND CI PATH LOSS MODEL ANALYSIS
The FI model is obtained by performing a least square regression of the simulated path loss in the various scenarios. The key parameters for the FI model are (η, β, σ ). The CI model is obtained from simulated data by calculating the path loss exponent (η) and shadow factor X σ . Figure 9(a) represents the path loss model, the close-in (CI), and the floating intercept (FI) path loss model for TX1. The FI (α, β, σ ) parameters are 211.9816, 0.1387, and 0.4061, respectively, while the CI (η, X σ ) parameters   Figure 9(b) represents TX2, the FI (α, β, σ ) parameters are 236.0442, 0.1135, and 0.1304, the CI (η, X σ ) parameters are 0.4503 and 11.1472. Figure 9 (c) shows the TX3 FI (α, β, σ ) parameters with 211.8493, −0.1946, and 0.8398 respectively. The CI model for this scenario has an exponent (η) value of 1.744 and a shadow factor of 42.8493. For transmitter point TX4, the CI model and FI model is represented by Figure 9(d), the path loss exponent for this scenario is 1.7734 with a shadow factor of 43.5272, the FI model gives a floating intercept of 197.4515, a standard deviation of 0.5091 and a random gaussian variable of 0.3676. comparing FI and CI models, we conclude that the FI model gives a better approximation of the path loss effect while the CI model increases the path loss. Table 9 presents a statistical summary of the CI model and FI model key parameters as represented in Figure 5 to Figure 8, showing the simulated path loss model, close-in model, and the floating intercept model for TX1, TX2, TX3, and TX4.

2) MODIFIED AVERAGE FI AND CI PATH LOSS MODELS
According to [14] the average path loss at a distance (d) also called local mean attenuation (LMA) decreases with distance due to the free space path loss and signal obstruction. Path loss model has been represented using CI model and FI model as discussed by [36]- [46], and [47] using equation (1) to equation (7) as discussed in the previous section. From this premise, we develop generic path loss models by taking the average values of each scenario simulated and VOLUME 9, 2021  representing TX1, TX2, TX3, and TX4 as a single value, as shown in Table 10.
For a CI model, we use the average value for η and X σ to calculate a regression fitting model to develop   (16) where PL(d) dB is the average path loss at each transmission station, η is the average path loss exponent, d is the average distance between the transmitter and the receiver point, and X σ is the average shadow factor for the transmitter points.
Taking the average CI parameters and substituting them in equation (16) For the FI model, we compute the average values as represented in Table 10 to develop equation (21) as: (PL) FI dB = α + β FI .10.log 10 (d) + σ FI (21) where PL (dB) is the developed path loss model, α gives the average floating intercept value of the transmission points, β FI represent the average slope of the TX scenario points and σ FI represent the average random Gaussian parameter expressed as a standard deviation of the Gaussian random variable of the simulated data. For each transmitter point, this is calculated as shown in equation (22) to (25): TX 2 F I = 227.16132 + 0.1693log 10 TX 4 F I = 163.53226 + 0.61380log 10 Figure 10 shows the corresponding plots of the developed CI and FI path loss model. The newly defined CI model and FI models show the optimal path loss for each transmitter point.

3) PERFORMANCE EVALUATION OF THE LARGE SCALE mmWAVE PATH LOSS MODEL
The prediction accuracy of the path loss model is evaluated using the RMSE. The best performance is exhibited when the RMSE values are close to 0 dB. However, the acceptable RMSE values for urban areas are 6-7 dB, while suburban areas range between 10-15 dB [69]. Table 11, Table 12,  Table 13, and Table 14 represent the statistical error evaluation value for the simulated data against the CI and FI path loss model developed for TX1, TX2, TX3, and TX4. The RMSE value for the TX1 path loss was 0.4061 dB, while the   Table 13.   TX1, TX2, TX3, and TX4,  respectively. Table 11, Table 12, Table 13, and Table 14 show that the FI model had the smallest RMSE value (dB) than the CI model for all the scenarios across all TXs. This signifies that the FI model gives the best path loss prediction across all the scenarios considered in this work. The CI model had a considerably higher RMSE value(s) (dB) in all cases.
Therefore it overpredicted the corresponding path losses in all the considered scenarios. Hence, we report that for Lagos Island, the FI path loss model accurately predicts path loss at 28 GHz for a transmitter height of 20 m and receiver height of 2 m.
Comparing the path loss models presented by [36], [37], [40], [41], [44], and [47] with our path loss model, our model shows an optimistic advantage over all reviewed pieces of literature. Our research conducted a large-scale path loss modeling. The simulation model was configured to consider the path loss at any receiver point in the XY grid from the four-transmitter station, the path loss exponent for all the scenarios presented here is with an exponent of 0.45 at TX2, the highest path loss exponent factor was 3.8 at TX4 under the excess path loss with antenna pattern scenario. Ref. [40] model of 28 GHz resulted to a path loss of 0.6 which is higher than our lowest path loss exponent. Ref. [41] reported a path loss exponent of 4.51 at a transmitter height of 17 meters and a receiver height of 1.5 meters. Our model's highest path loss exponent is 3.9888 at Excess path loss with antenna pattern in TX3 at a transmitter height of 20 meters and 2 meters for the receiver grid. The average path loss exponent from all our simulation scenarios is 2.309355, which is less than reported by [36], [41] and [52]. Maccartney, et al. [36] achieved a shadow factor of 10.8 at 28 GHz for the close-in path loss model; this work achieved a shadow factor of 11.1472 with a corresponding linear slope of 0.1135, which is less than achieved by [43] and [45] at mmWave frequency. From the figures presented in this research, the FI model accurately fits the simulated environment, while the CI model gives a pessimistic representation of the study area. The results obtained from this work align with the standard path loss model developed by [36], [40], and [41]. Comparing this work with research done at different mm-Wave band presented in Table 2 shows that this work can be adopted by researcher considering to study path loss in Lagos Island in the 2-73 GHz band.

V. CONCLUSION
Large-scale path loss modeling in the mm-Wave band requires calibration and tuning for the case of the field campaign. This work adopted a 3D ray-tracing deterministic method to model a 5G communication testbed for Lagos Island, Nigeria, using Remcom ray tracing suite, Wireless Insite engine. To the best of our knowledge, no similar work has been carried out in the study area at 28 GHz, making this research relevant to 5G communication service providers intending to carry pilot study or actual implementation and other researchers in this domain. From the CI/FI model analysis, we have established that the FI model has the lowest RMSE value (dB) than the CI model for the scenarios considered and exhibits the best prediction model to perfectly characterize the Lagos Island environment. Lagos Island is an urban area comprising high-rise buildings and highly populated areas; it is necessary to investigate how shadow fading affects the path loss models in such an environment. The shadow factor presented in our model depicts an advantaged model compared to other existing research work done at 28 GHz. This model can guide other researchers working in the mm-Wave band for Lagos Island and can be adapted to other areas. For future work, an actual field campaign at 28 GHz in both LoS and NLoS scenarios with and without antenna patterns will be carried out. Also, a similar study will be conducted to cover the four geographical regions in Nigeria.