The Limitations of Campus Wireless Networks: A Case Study of University of Nigeria, Nsukka[Lionet]

This work studied the effects of physical environment (trees and buildings) obstructions on the Lionet in Nsukka campus of the University of Nigeria. The effects of these obstructions were measured by the variation in path loss and received signal strength as functions of distance using computer simulation and field measurement. The simulation results were compared with the field measurement results, conducted under free space condition and where the Lionet signal was obstructed by trees and buildings. The results show that trees and buildings have significant effects on the path loss and the received signal strength of the Lionet. The study therefore recommends that the power level of the Lionet should be improved for efficient performance, more access points should be deployed at locations where obstructions are prevalent, and Lionet should possibly migrate from wireless to fibre optic network.

Studies on the effects of vegetation and buildings on the transmitted radio signal have been done. Propagation measurements through vegetation over a range of frequencies have been carried out in rain fo rests of India between 50 -800 MHz [9], through a single tree between 1 and 4 GHz, in a forested urban park between 0.9 and 1.8 GHz, in various foliage and weather condition between 2 and 60 GHz [10]. The effects of vegetation on GSM signal propagation in rural areas has been studied [11]. A lso, a good number of research works on data acquisition were reviewed. These dealt with measurements to study the effects of a single tree, a line o r mu lt iple lines of tress along the streets or buildings, a small forest, and a large forest covering a region on the propagated radio signal [10] [12][13] [14]15]. Investigation of foliage effects on a propagated radio signal via data logging for point-to-point link at 5.8 GHz was reviewed. The result showed that point-to-point link which was obstructed by a single t ree and a ro w of t rees recorded an average of 12.2615 dB and 4.6306 dB excess path losses respectively [10]. In [16], study on the influence of trees on radio channel at frequencies of 3 and 5 GHz shows that the excess path loss was between 1 and 16 dB. For the measurements carried out in the residential areas and homes for the transmission frequency in the 5.85 GHz band, building penetration attenuation was reported at an average of 14 d B [10].
The present study is motivated by the undesirable poor signal reception, loss of data packets, and delay in uploading and downloading of data, frequently experience fro m the radio wave signal transmitted by the Lionet within the University environ ment. The study investigates the extent of signal attenuation due to the trees and buildings, by using spectrum analyzer (SPECTRA N HF 6080) to monitor the mean path loss and received signal strength from one of the Lionet's signal access point in the University. The modeling equations describing the signal attenuation due to tree and building obstructions are developed for detail analysis and in-depth understanding of the scenario. A computer simu lation programs based on MATLAB is used to study the variations in the path loss and received signal strength as functions of the separation distance between transmitting and receiving antennas to validate the results from the spectrum analyzer.

Suggested Tree Path Loss Propagation Model
Path loss prediction of Lionet signal passing through a tree includes; free space loss plus tree loss factor (L tree ). The tree loss factor is included in the model to account for the increase in attenuation of the received signal strength when the receiver is placed behind a tree. Mathematically, this becomes [10].
PL tree = L FS + L t (1) PL tree = Path loss in the presence of a tree L FS = Free space loss L t = Tree loss factor The geometry of the propagation model is shown in figure  1. As illustrated in the figure, the access point radiates a spherical wave that can reach a client behind a tree, r is the separation distance between the transmitt ing and the receiving antenna, P i corresponds to the power emitted (incident power) fro m the transmitting antenna, P r is the received signal strength (received power level) by the receiving antenna, P s and P a correspond to the power scattered and power absorbed by the elements of the tree canopy.

Receiver
Access Point P i P s P r r P a

Figure 1. Geometry of tree Canopy
A tree canopy contains randomly distributed and oriented branches and leaves that fill most of the canopy space. In this study, branches are modeled as circular cylinders while leaves are modeled as thin disks as described in [17]. The branches in the t ree canopy are classified into five size categories denoted as N b . The nu mber of leaves and branches are represented by n l and n b respectively, where the subscript b is an element of �b 1 , … b N b � and b N is used to denote branches of the nth size category.
Attenuation of radio wave propagating through a tree is primarily due to scattering and absorption caused by both leaves and branches.
Some assumptions made while try ing to reduce the complexity of the model include: • Loss due to the trunk as a result of diffract ion is considered negligib le [18].
• The tree is so tall that there is no diffraction.
• The leaves are assumed to be identical and homogenous.
• The tapered nature of the individual branches is neglected.
Fro m figure 1, the power balance in the volu me is; P i = P r + P s + P a (2) For a sphere of rad ius r with center at the ray intersection, the beam subtends an area A on the sphere surface. The solid angle is given by [19]; The infinitesimal element of solid angle can also be written in terms of elementary area dA on any surface. The element of solid angle is; Study of University of Nigeria, Nsukka[Lionet] dΩ = dA r 2 (4) The incident power ( P i ) is readily related to power density S(r) , the magnitude of the time-average pointing vector as [11]; P i = S av ( r ) A (5) P i = S av ( r ) r 2 dΩ (6) The received power level can be written as [18]; P r = S ( r + dr ) r 2 dΩ (7) As the incident power travels downwards in the tree canopy, it undergoes both absorption and scattering by the leaves and branches of the canopy [11]. The power loss (P l ) contributed by the scattering and absorption of incident power by the leaves, represented by their number n l and branches classified into N b different size categories represented by their number n b is: Therefore equation (8) beco mes; P l = P i (〈 σ τ 〉) r 2 drdΩ (9) Superscript b and l refer to leaves and branches of the canopy Substituting equation (6), (7) and (8) into equation (2) we have; S ( r ) r 2 dΩ = S ( r + dr ) r 2 dΩ + S ( r ) 〈 σ τ 〉 r 2 drdΩ (10) This simp lifies as; S ( r ) = exp (− 〈 σ τ 〉 r + c) (11) S ( r ) = De −〈σ τ 〉r (12) where D = S iso ( r ) is the emitted power density in a spherical wave generated by an isotropic antenna with a time-average transmitted power P t , [1].
S iso ( r ) = P t 4πr 2 Substituting equation (13) into equation (12) we have; S ( r ) = P t 4πr 2 e −〈σ τ 〉r , r ≠ 0 For a more realistic antenna, the radio wave is not only transmitted in the desirable direction but also in other less desirable direct ion. A co mmonly used parameter to measure the overall ability of an antenna to direct radiated power in a given direction is their directive gain [18].
A desirable property during transmission between two antennas is that the ratio between the transmitted and received power should be as high as possible. Thus; P r P t = λ 2 D t D r ( 4πr )2 e −〈σ τ 〉r (15) Where; D t = the directivity gain of the transmitting antenna. D r = the directiv ity gain of the receiving antenna. λ = the wavelength. The equation (15) can only be employed when the leaves and branches occupied all spaces between the transmitting and receiving antenna. To get a more realistic expression for the attenuation of the emitted rad io wave, we considered a case whereby the radio signal traversed estimated number of leaves and branches before getting to a receiver. The improved formu la of equation (15) beco mes; P r P t = λ 2 D t D r ( 4πr )2 e −〈σ τ 〉 (16) Transforming equation (16) into decibels and exp ressing it in the path loss form yields; Since n l �〈σ s l 〉 + 〈σ a l 〉� (17)

Expectation Value of the Total Cross Section
The total cross section ( 〈 σ t 〉 ) is the su m of the cross section due to absorption and scattering of incident power density by a single leaf and a single branch. It is written as: The value of total cross section depends on canopy attributes such as size, shape, dielectric properties of leaves and branches, and orientation of leaves and branches in relation to the direct ion of the propagation of radio wave [17][19] [20]. Here, we assumed that the total cross section is a function of o rientation angles, the nu mber of leaves and branches, the size of the leaves and branches, and the shape of the leaves and branches. Figure 2 shows the interaction of incident power with a single leaf or a single branch. The orientation of leaves and branches determine how radio wave is being intercepted and absorbed as it traverses the tree canopy.
For the orientation angle of the leaves and branches with respect to the reference frame, we used two variab les (θ, ϕ) to describe it.
where; θ = Elevation orientation angle of leaves and branches of the tree canopy. ϕ = A zimuthal orientation angle of leaves and branches of the tree canopy.
The normal of the disc is denoted by n and the symmetry axis of the cylinder by m. Fro m figure 2, the normal vector which also is valid for the symmetry axis of the cylinder can be written as; n = X cos θ cos ∅ − Y cos θ sin ∅ + Z sinθ (20)

The Expectation Value of the Total Cross Section
The general expression for the expectation value of total cross section of a single leaf and a single branch of the tree canopy is; where dΩ = cosθ dθ dϕ is the solid angle, Ω l ,b ( θ, ϕ ) equals the probability density function for the azimuthal and elevation orientation angle of the leaves and branches of the tree canopy.
Based on the fact that leaves and branches in the canopy are randomly placed, we employed a statistical based approach to characterize the leaves and branches of the canopy. This relat ion takes the fo rm of probability density function. The probability density for the leaves and branches in the azimuthal coordinate ϕ is assumed to be uniformly distributed over the tree canopy volume fro m 0 ≤ ϕ < 2π. Also, the probability density for the leaves and branches in elevation coordinate θ is considered to be uniformly distributed and of the form; Elevati on and azi muthal orientati on angle of leaves in the tree canopy: None of the leaves in the tree canopy were found to exhibit a preferred azimuthal o rientation angle; also the leaves have no preferred elevation orientation angle. Thus, the cross sections of the leaves are averaged over ϕ and θ with 0 ≤ ϕ < 2π , ϕ The mean cross section of a single leaf o f a tree canopy is Elevati on and azi muthal orientation angle of the branches in the tree canopy: None of the branches of the tree were found to exhibit a preferred azimuthal orientation angle; also the branches have no preferred elevation orientation angle. Thus, the cross-sections of the branches are averaged over ϕ and θ with 0 ≤ ϕ < 2π, ϕ b ( ϕ ) = 1, The mean cross section of a single branch of a tree canopy is By co mbining equation (23) and (24) for the case of mean cross section of a single leaf and a single branch of a tree canopy; we obtain an expression for the equivalent cross section of the leaves and branches of the tree canopy as; As previously stated, the cross section of a single leaf and a single branch are σ tl and σ tb ; the number of leaves and branches of a tree canopy are n l and n b ; and b = b 1 , b 2 , … . . b n is the number of branches of different size categories. In order to get an estimated value of the nu mber of leaves and branches per unit volume of the tree canopy, we counted the number of branches grouped into five categories and the number of leaves that are attached to the respective branch. The estimated number of leaves and branches with their corresponding radius and length/thickness per unit volume of the tree canopy is listed in the table 1.

Suggested Building Path Loss Propagation Model
Path loss prediction of the Lionet signal passing through a building includes; free space loss plus building loss factor. The building loss factor is included in the model to account for the increase in attenuation of the received signal strength when the receiver is placed behind a building. The expression for the path loss from the trans mitting antenna to the receiving antenna in the presence of a build ing is; PL building = L FS + L buiding (26) where; PL building = Path loss in the presence of building. L FS = Free space loss. L building = Bu ild ing loss factor. The geometry of the propagation model is shown in figure  3.
Modeling Lionet signal transmitted through a building involves three steps; the first step relating the output of the Lionet signal fro m the transmitter to the building, the second step is called an indoor event, and the third step relating the propagation of the signal down to the receiver antenna.
As illustrated in the figure 3, a transmitting antenna radiates rays that can reach a receiving antenna.
H t = the transmitting antenna height Study of University of Nigeria, Nsukka [Lionet] H r = the receiving antenna height w b = the width of the build ing d 1 = the distance from the transmitting antenna to the building d 2 = the distance from the building to the receiv ing antenna t = the window and wall thickness. d t = the path length fro m the transmitting antenna to the building in the direction of signal propagation. d in = the path length inside the build ing in the direct ion of signal propagation. d r = the path length fro m the build ing to the receiv ing antenna in the direction of signal propagation. θ = the incidence angle on the window and wall of the building. Some assumptions made while try ing to reduce the complexity of the model include: • The access point is assumed to be in a transmitting mode, while the receiver is assumed to be in the receiv ing mode.
• The length of the building is assumed to be infinitely large, so no diffract ion effects could happen due to the corners of the building.
• The building window and wall are made of certain kind of material, wh ich had relative permitt ivity ε r and conductivity σ.
• The height of the building is so high compared to the transmit antenna height, so no propagation over the roof exists.
• The Lionet signal co mes fro m outside the building, penetrates into it through a window and wall. Likewise the signal going fro m inside the building to outside.
• The d irection o f signal propagation does not change for the signal moving inside the building.
• The internal layout of the build ing was not specified.

Free S pace Loss Model
The equation for free-space propagation between two antennas is given by the Friis transmission equation [21]; where; P t = the transmitted power P r = the received power level D t = trans mit antenna directiv ity gain D r = receive antenna directivity gain r = the transmit and receive antenna distance of separation c = the velocity of light f = the transmission frequency

Buildi ng Loss Factor
When the Lionet signal passed from the building to the receiving antenna, an expression for the build ing loss factor is written as: L building = L pen + L in + L pen + L dd (28) where; L pen = Penetration losses L in = Indoor losses L dd = Distance dependent losses Here, we considered only the signal that passed through the window and wall. For the two scenarios, their signal strengths are summed up. The angle that the Lionet signal made with the window and wall is obtained fro m Fro m equation (29), expression for the elevation angle is Once the elevation angle is known, the expressions that relate the distances d t , d in , and d r with θ are d t =

Penetration Losses
Losses as a result of Lionet signal coming fro m outside to the inside of a building are group into two; window penetration loss and wall penetration loss. These losses were modeled using Fresnel Transmission Coefficient (FTC). This parameter characterizes the level of signal strength coming fro m outside into the building. The exp ression for the Fresnel Transmission Coefficient was given as [22]; By normalization, the dependence of penetration losses with the Fresnel Transmission Coefficient is; The penetration losses are the same both when the signal is coming fro m outside the building, and when is co ming fro m inside to outside of the building due to reciprocity law [22].
We assumed that the Lionet signal traversed two windows and two walls before getting to a receiving antenna. We present below a method of obtaining the window penetration loss and wall penetration loss.

Window Penetrati on Loss
The Lionet signal penetrates two windows made of glass before getting to the receiving antenna positioned at a distance away from the transmitting antenna. The window penetration is illustrated in Figure 4.   Table 2 shows the parameters and formu las employed for predicting the window penetration loss. (dimensionless) T S1 = 2 cos θ cosθ + �ε r1 − sin 2 θ Fro m the in formation g iven in the table 2, loss as a result of the penetration of the Lionet signal through a glass window is given by; where; L 1 = the window penetration loss ε r1 = the relat ive permittivity of the window made of g lass T s1 = the Fresnel Transmission Coefficient of the window Wall Penetration Loss The Lionet signal penetrates two walls made of concrete before getting to the receiving antenna positioned at a distance away from the transmitting antenna. The wall penetration is illustrated in Figure 5.  Table 3 shows the parameters and formu las employed for predicting the wall penetration loss.

Table 3. Wall Penetration Loss Parameters and Formulas
Parameters Formulas Fro m the in formation g iven in the table 3, loss as a result of the penetration of the Lionet signal through a wall made of concrete is; Where; L 2 = the wall penetration loss ε r2 = the relative permittiv ity of the wall made of concrete T S2 = the Fresnel Transmission Coefficient of the wall In order to evaluate the Fresnel Transmission Coefficient, which measures the quantity of the building penetration loss, the relativ ity permitt ivity of the materials of interest is considered. Suitable values were gotten from literature. For glass, its relative permittivity has been found to be 4 [23]. Therefore, the relative permittiv ity of the window made of glass (ε r1 ) is assumed as 4. For the wall made of concrete, the relative permittiv ity at 1.7 GHz and 18 GHz are 4.62 and 4.11 respectively [23]. Fro m these results, it is obvious that the relative permittivity o f the concrete wall does not vary significantly due to frequency changes, therefore the relative permittiv ity of the concrete wall (ε r2 ) is assumed as 4.62. Study of University of Nigeria, Nsukka[Lionet]

Distance Dependence Losses
Distance dependence losses are dependent on the distance fro m the build ing to the receiv ing antenna. The path loss dependence with distance fro m the building to the receiver was chosen equal to 2 as in the case of free -space loss because it obeys power decays law [1]. The resultant e xpression is;

Experimental Setup and Measurements
The experimental setup for measuring the path loss and received power level under free space condition and where a single tree or a build ing obstructs the Lionet signal are shown in figures 6, 7, and 8, respectively. At the transmitting section, omni-direct ional antenna (WBS 2400) with transmitting power of 19 d B is mounted at the top of 7m height mast H t . Along the transmission path lays either a tree or a building, which obstructs the Lionet signal as in the case shown in figure 7 and 8. The receiving section consisted of a spectrum analy zer (SPECTRAN HF 6080) that was connected to a Laptop (HP G62) loaded by Aaronia test software for data logging, and Uninterruptible Power Supply (UPS) to provide emergency power whenever there is any occurrence of power disruption, which may eventually result in data loss.
The access point of interest is partly impeded by a tree and a build ing as shown in the figures 7 and 8, while part of the access point is free fro m any kind of obstruction as shown in the figure 6. The received power level was measured with SPECTRAN HF 6080 via an o mni-d irectional antenna (WBS 2400). The SPECTRAN HF 6080 was adjusted to a frequency of 2400 MHz at sampling rate of 5000 ms. The receiving antenna is directional wh ile the transmitting antenna has no restriction. Finally, fro m the measured received power level, we obtained the measured path loss for the three scenarios shown in figures 6, 7, and 8.

Path Loss in dB as a Function of Transmitting and
Receiv ing Antennas Distance for the Models The results from simu lation of the free space path loss, suggested tree path loss, and building path loss models are shown in table 4, with their corresponding plots in figure 9. The simulated results fro m the free space path loss are used as a reference point to study the extent a single tree or a building blockage affected the path loss.
Fro m the plot, it is seen that the graph increases in exponential manner; this means that the path loss exponentially increased with the distance of separation between the transmitting and receiving antennas. By further examining the plot for the free space propagation model, it is observed that its graph is lo wer than the graphs obtained when the Lionet signal is obstructed by a single tree or a building. This may be attributed to the fact that the propagation of Lionet signal through free space is free fro m any form of obstruction as compared to the other two cases with obstruction of a tree and building along its communicat ion path.
Another observation made from the plots of the path loss versus the distance of separation between the transmitting and receiving antennas is the dependency of the received signal strength on the variation of the distance decay rate. This is because, increase in path loss results to the gradual decay of the signal strength [11].  Fro m the result of the free space path loss, suggested tree path loss, and building path loss model shown in table 4, received power level for the three scenarios were obtained using the relationships: P r = P t − L FS (40) P r = P t − PL tree (41) P r = P t − PL building (42) We employed equation (40) under free space condition, equation (41) when the Lionet signal was obstructed by a single tree, and equation (42) when the Lionet signal was obstructed by a building. Figure 10 shows that the received power level under free space condition is greater than that when the signal is obstructed by a single tree or a building. The results showed that the distance between the transmitting and receiving antennas and the received power level are inversely related. Furthermore, the received power level under free space condition decreased from the highest power level of -47.07 dB to the lowest power level o f -61.05 dB. Also, when the Lionet signal was obstructed by a single tree, the received power level decreased fro m the highest power level of -62.77 dB to the lo west power level of -76.75 d B. When the signal was obstructed by a building, the received power level dropped from the highest power level of -66.10 dB until the lowest power level o f -80.28 d B. These showed that the received power level decreases as the distance between the transmitting and receiv ing antennas increases.  Table 6 is the results from field measurements taken under free space condition and non line-of-sight condition (areas where the Lionet signal is obstructed by a single tree or a building). Also, their corresponding plots are figure 11.  Figure 11 shows that the output result under the free space condition is higher due to no obstruction fro m trees or a building on the Lionet signal. Th is was attributed to the fact that under free space, the signal was assumed to be travelling under a clear line-of-sight. But in the presence of a tree or a building, part of the energy of the signal was absorbed by the tree canopy elements such as the leaves, branches, and construction materials used for the building etc. Furthermore, the received power level under the free space condition decreased from the highest power level of -51.28 d B to the lowest power level of -54.20 d B. A lso when the signal was obstructed by a single tree, the received power level decreased fro m the highest power level of -55.70 dB the lowest power level of -60.56 d B. When the signal was obstructed by a building, the received power level decreased fro m the highest level of -59.00 dB to the lowest power level of -66.96 dB. These indicated that the received power level under the considered three scenarios are distance dependent. Under the free space condition and when the signal was obstructed by a single tree, the received power level decreased gradually with the distance between 20 and 40 meters range. But when the signal was obstructed by a building a sharp decrease in the received power level was observed. Also the received power level seemed to decay faster with the distance between 80 and 100 meters range for the three conditions. But this was almost constant for the distance between 40 and 80 meters range for the three conditions.

Path Loss in dB as a Function of Transmitting and
Receiv ing Antennas Distance under Free Space, and Non Line-of-Sight Condition Fro m the measured received power level taken under free space and areas where the Lionet signal is obstructed by a single tree or a building, the measured path loss for the three scenarios shown in table 7 were obtained using the relationships: The equation (43) was employed under free space condition, equation (44) when the Lionet signal was obstructed by a single tree, and equation (45) when the Lionet signal was obstructed by a building.   Figure 12 shows that the path loss is higher when Lionet signal was either obstructed by a building or a tree as compared to when the signal was free fro m any form of obstruction. This was attributed to the fact that the propagation of radio signal through free space was not impeded by obstruction as compared when there were obstructed by trees and buildings along its propagation path [10]. Also the path loss increased gradually with distance between 20 and 40 meters range, under free space condition and when the Lionet signal was obstructed by a single tree. The path loss increased sharply when the Lionet signal was obstructed by a building. The path loss seemed to rise faster with the distance between 80 and 100 meters range for the three conditions. But this was almost constant for the between 40 and 80 meters range for the three conditions.

Comparison of the Simul ated Results with the Fiel d Measurement Results for the Three Scenarios
The simulated path loss results and the measured path loss results due to the obstruction of Lionet signal by a single tree and a building were co mpared using the simu lated and measured free space path loss results as the reference point. Co mparing the simulated free space path loss with that due to the effect of a single tree, the losses at different distances under consideration was 15.7dB. For that due to the effect of a build ing, we found the losses at different distances of consideration between 17.5 and 19.23 dB. Also, comparing the measured free space path loss with that due to the effect of a single tree, the losses at different distances under consideration were between 4.42 and 10.64 d B. For the case due to the effect of a building, the losses at different distances under consideration were between 7.72 and 12.84 dB. The result obtained for the scenario where the Lionet signal was obstructed by a single tree, agreed with the field measurement results obtained by Karlsson et al [24] in which the path loss is between 1 and 16 dB at 3.1 and 5.8 GHz frequencies. Also, the results obtained due to the obstruction of the Lionet signal by a building conformed to result of building penetration loss reported by Durgin et al [25] at an average value of 14 d B. This implies that the effects of trees and buildings on campus wireless networks are quite significant.

Conclusions
This work has studied the effects of the obstruction of trees and buildings on the Lionet wireless network. The study revealed that one of the problems that hinder efficient performance of the Lionet wireless network is the presence of trees and built structures. This resulted in poor signal reception, missing of data packets, delay in uploading and downloading of data, and fluctuation of signals. The mathematical models that described this physical problem were formu lated, and simulated in computer program written in MATLA B. The simu lation results showed reasonable agreement with experimental results for the studied three scenarios. The results showed that attenuation due to the presence of trees and buildings in the Lionet communication path is substantial. The results also showed that the Path loss increased, while the received power level decreased with the distance of separation between the transmitting and the receiving antennas, and vice versa. This study therefore recommends that the power level of the Lionet signal strength should be improved for efficient performance; mo re access points should be deployed at locations where obstructions are prevalent, and Lionet should possibly migrate fro m wireless to fibre optic network.