1 Introduction
To date, the world’s mobile industry has reached the 5 billion subscriber milestone, and in 2025, it is forecasted to reach 5.8 billion subscribers [gsma2018mobileeconomy]. ITUR envisions that these mobile subscribers will be served by the Enhanced Mobile Broadband (eMBB) as part of the fifth generation (5G) of mobile networks [shafi2017tutorial]. Some of whom will access the network through indoor hotspots in environments such as transportation hubs, sports arenas, and convention centres. The eMBB will provide mobile services over multigigabit/s rate links, enabled by the highdensity deployment of networks that utilise the spectrum available in mmWave (mmWave) frequencies. However, the application of mmWave frequencies to cellular networks requires a new set of assumptions to be taken into account in the system design.
The propagating mmWave signals suffer from high path attenuation and low penetration through materials such as building walls. It means that mmWave signals transmitted from outdoor base stations will be confined to streets and other outdoor areas [PiKhan_2011]. This creates a situation where an independent tier of mmWave AP should be deployed to ensure coverage to UE in indoor areas, as we illustrate in Fig. 1.
Yet, coverage can still be deteriorated by human bodies, as they introduce as much as 40 dB of attenuation [collonge2004influence, lu2012modeling, bai2014analysisSelfBlockage], which may be enough to lose the connection between AP and UE.
In order to combat the detrimental effects of blockages, one would be tempted to increase the AP density to maintain connectivity [bai2014analysisSelfBlockage]. However, here comes another challenge — intercell interference. Although the increase in network density (densification) may improve the network capacity by allowing for an increase in spatial reuse [hwang2013holistic], if not implemented carefully, it may lead to excessive interference causing an increase in interference and a deterioration of the system’s performance. In stateoftheart literature, the interference mitigation can be achieved by intercell interference coordination (ICIC) techniques, which demand high signalling overhead [yoon2018distancebased]. One simpler way to reduce the interference is to restrict the signal propagation through the use of directional antennas mounted on the ceiling. Thus, the mainlobe of the directional antenna beam is pointed downwards to confine the signal’s power to a limited space.
Ceiling installations of mmWave access points have been considered in the literature, e.g., [yiu2009empirical, dong2012link, leong2004robust], yet proposed analysis was restricted to single link performance. While, in stateoftheart literature, we can find coverage and throughput analysis of such deployments operating in microwave frequencies, e.g., [Ho2016downward], the same analysis for deployments operating in mmWaves becomes more complicated due to the susceptibility to blockages. To address this, in this work we consider a large indoor scenario where APs operating in mmWave frequencies (mmWave AP) are mounted on the ceiling to form a gridlike pattern, and fixed directional transmissions are set to illuminate selected spots on the ground. We consider a confined venue, where we assume that there is no outdoortoindoor interference.
We consider a channel model where human bodies are the main source of signal blockage. The shadowing effects, as well as multipath propagation, are modelled as fading, whose parameters depend on the body blockage, as well as the path loss parameters. We align the parameters of our channel model with those coming from the empirical measurements by Yoo et al. in [yoo2017measurements].
Our objective is to study the effects of different blockage scenarios on the optimal system design parameters (such as AP density and antenna mainlobe beamwidth) and on the network performance. For this purpose:

We develop a model of body blockage that matches the geometry of the ceilingmounted AP deployment, and we derive an analytical expression for the probability of blockage.

We analyse the impact of both AP density and body blockage on the performance through our simulation framework. The simulation source code we developed is available online (see Appendix A).
Based on an extensive simulation campaign:

We find that coverage and ASE (ASE) achieve peak performance when there is a joint optimal beamwidth configuration of the ceilingmounted AP antennas facing downwards and the directional UE antennas facing the AP, for a given AP density.

We find that there exists a tradeoff in beamwidthdensity configuration, in which the same configuration optimises either coverage or ASE, but not both.

We find that the optimal beamwidthdensity configuration for coverage depends on the body blockage probability, as the configuration needs to compensate for increased interference, shadowing or path loss.
In what follows, we provide an overview of the related literature, description of our system model, and indepth analysis of the numerical results obtained, and explaining the lessons learnt on the design of dense indoor mmWave networks.
2 Related Work
Ceilingmounted AP with fixedbeam antennas is an option for quick and lowcost deployments as recommended by ITUR [itur_m.23760], facilitating AP densification. Dense deployments have been initially investigated in [Ho2016downward] for microwave frequencies. In that work, Ho et al. have shown that the ceilingmounted deployment with directional antennas was able to provide gains in throughput four times higher than the deployment with omnidirectional antennas. Herein, we investigate the performance of such deployment considering the use of mmWave communication. Hence, the blockage effects on the mmWave signal should be taken into account in the investigation, as the works in [yiu2009empirical, dong2012link, leong2004robust] have shown that the link performance from a single ceilingmounted mmWave transmitter can be degraded by human body blockage.
Dense mmWave networks have been widely studied for outdoor scenarios [andrews2017modeling, bai2014analysisBlockageUrban, bai2015coverage, bai2014analysisSelfBlockage] and much of the blockage modelling and their results are used for studying indoor scenarios as well. In [bai2015coverage], Bai and Heath have shown that there is a finite optimal AP density for coverage, with fixed AP and UE beamwidth configurations, which is given by the transition from a noiselimited regime to an interferencelimited regime when increasing AP density. In [bai2014analysisSelfBlockage], Bai and Heath have proposed a cone blocking model to characterise the blockage by the user’s body, and they have shown that selfbody blocking effects can reduce the average throughput of dense outdoor mmWave networks by about 10%. Furthermore, coverage performance in dense indoor mmWave networks has been studied in [venugopal2016device, niknam2018interference]. They have analysed the blockage probability of multiple bodies besides the user body, modelling human body blockages as circles randomly placed in a finitearea. In [venugopal2016device], Venugopal et al. have shown that, in devicetodevice communication, interference in dense networks is significantly affected by blockage. This has also been shown by Niknam et al. in [niknam2018interference], where their results for a point process AP deployment have shown that increasing blockage density improves coverage as the number of blocked interferers increases. However, the analyses above have not considered the height difference between the AP and UE in the blockage modelling.
When considering the AP height, the geometry of the blocking objects becomes significant for the blockage analysis. As demonstrated by Gapeyenko et al. in [gapeyenko2016analysis], the received signal strength can be maximised when an optimal AP antenna height is deployed. This antenna height depends on the height and diameter distribution of the blockers. Also, considering both blocker and AP antenna height, there is an area around the AP where the blocker does not obstruct the link as the LOS goes over the obstruction, as observed in [dong2012link, jain2019impact]. These works use their analytical framework to study the optimal AP height or AP density that minimise the blockage probability. In our analysis, considering AP and UE directivity and taking the threedimensional geometry of AP deployment and blockages into account, we study the optimal density and antenna configurations for the ceilingmounted setup that maximises coverage and spectral efficiency.
In our previous work [firyaguna2017coverage], we analysed only the selfbody blockage effects without any other blockage source, and no fading nor receiver directionality were assumed. In this paper, we build on our previous work by extending our model. Precisely, we assume the receiver UE has a directional antenna which aligns to the transmitter AP, and we assume the presence of large and smallscale fading. Also, we consider multiple bodies that can potentially block the signal from an AP to the UE, and we provide an analytical model for the blockage probability. Then, we show the effect of the ceilingmounted deployment on network densification by investigating the impact of both AP and UE mainlobe beamwidths configuration on the intercell interference under body blockage conditions.
3 System Model
In this section, we introduce our model of a mmWave indoor network. The considered environment is an indoor confined area where there is no interference from outdoor signals. The AP are deployed on a hexagonal grid, and they are installed on the ceiling at some height above the UE level, with fixed directional antennas illuminating the floor below. We consider a UE randomly located in the squareshaped indoor venue. The AP that provides the desired signal to the UE is referred to as the serving AP, while the other APs are referred to as interfering APs. In our notation, we use the subscript to denote the parameters related to the AP, the subscript to denote the parameters related to the UE, and the subscript to denote the body parameters. We assume human bodies are the main source of blockages for the mmWave signals and change the link state between LOS (LOS) and NLOS (NLOS). Thus, we assume that both path loss and channel gain have different characteristics in each state. These characteristics are modelled according to empirical channel measurements described in [yoo2017measurements].
3.1 Directivity Gain
We assume the APs utilise fixed directional transmission due to its advantage of simplicity. It does not require phase shifters, which usually require complex processing for precise adjustments [itur_m.23760]. We assume the UEs can steer the directional reception, which is perfectly aligned to the direction of the serving AP, since there are efficient beam search techniques for static devices within short distances in mmWave systems [ku2016efficient]. We assume the antenna pattern follows the conebulb model, which allocates the most significant part of the signal’s energy to the mainlobe, as illustrated in Fig. 1(a), while conserving the total energy of the propagating signal [ramanathan2001performance]. The cone represents the mainlobe attached to a single bulb representing the sidelobe. The mainlobe directivity gain is given by , is the sidelobe gain, is the beamwidth of the mainlobe, is the area of the spherical cap, and is the surface area of the sphere of radius .
The directivity gain is then a function of the beamwidth, normalised over a given spherical surface as in:
(1) 
where , and . Thus, fixing the sidelobe gain , we can calculate the mainlobe gain as a function of the beamwidth, as illustrated in Fig. 1(b):
(2) 
3.1.1 AP Directivity Gain
The UE has the maximum transmit directivity gain when the UE is positioned under the area illuminated by the AP’s mainlobe, i.e., the UE is inside the projected circle of radius:
(3) 
as illustrated in Fig. 3. Otherwise, the transmit directivity gain is the sidelobe gain . Therefore, we can express the transmit directivity gain as:
(4) 
where is the projection of the distance from the AP to the UE onto the horizontal plane.
3.1.2 UE Directivity Gain
The signal has maximum receive gain when the UE’s mainlobe illuminates the transmit AP. We consider the UE’s mainlobe is pointed towards the serving AP. Thus, an AP is illuminated by the UE’s mainlobe cone when the AP is located in the conic^{1}^{1}1 In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane. shape projected around the serving AP on the ceiling surface, as illustrated in Fig. 4.
As the UE gets further apart from the serving AP, the UE’s mainlobe elevation lowers, and eventually, the lateral surface of the cone becomes parallel to the UE level, making the illuminated area in the ceiling to transit from bounded to unbounded. This event happens at a distance of :
(5) 
Hence, we assume that, if the UE is close to the serving AP, i.e., , the illuminated area is bounded and the conic shape is a circle of radius :
(6) 
If the UE is far enough from the serving AP, i.e., , the conic projected in the ceiling becomes unbounded, thus we assume that the illuminated area is a circular sector^{2}^{2}2 A circular sector is the portion of a disk enclosed by two radii and an arc. The length of the radii is limited by the deployment area. with central angle equal to the UE beamwidth, as illustrated in Fig. 3(b). Thus, since the UE’s directionality is aligned with the serving AP orientation, an AP is illuminated by the UE’s mainlobe when the AP orientation falls within the illuminated area around the serving AP. Therefore, we can express the receive directivity gain as:
(7) 
where is the orientation of the given AP and is the serving AP orientation.
3.2 Body Blockage
In this model, the main factor that describes how likely it is for a human body to shadow signals to/from the UE is the UE’s position with respect to the body. We assume that a body facing^{3}^{3}3Without loss of generality, we assume that all bodies, not only the user’s body, are facing the UE. The effect of having a body not perpendicular to the UE, i.e. smaller , is to have a smaller blocking angle, which is equivalent to the body being at a longer distance . the UE shadows an area given by a rectangle of height and width . The UE is in front of the body at a distance from the body centre as shown in Fig. 5.
In the horizontal plane, the obstructed space can be quantified by its angle (shadowing angle) . The parameter determines the space obstructed by the body in the vertical plane.
We assume that the signal from an AP can be obstructed by the UB (UB) (the body holding the UE) or by other RB. We define these events as selfbody blockage and randombody blockage, respectively. We assume that all bodies (UB and RB) have the same size ( and are constant). The UB is fixed at distance from the UE, while the RB are uniformly placed, thus the distance from the UE to an RB is random. We define the orientation with respect to the body as the angle between the line joining the UE to the body’s right shoulder of the body and the line joining the UE to the AP. Then, we assume that the UB and RB orientations, and
angles respectively, are uniformly distributed in
.Given the body blockage and our ceilingmounted deployments, we can construct a model of user device shadowing as depicted in Fig. 5. From the geometry of the model, and assuming all APs at the same height , we define as the radius of the blockage free zone for a given UEbody pair (illustrated in Fig. 4(a)):
(8) 
where an AP inside this zone will always be in LOS with the UE, regardless of the body orientation. The AP outside this zone will have the LOS obstructed whenever the body is in between the UE and the AP (considering their projections onto the twodimensional plane). For a given distance between UE and AP, and a given distance between UE and body blockage, and denoting the indicator function, we define the following events: The event ’AP outside’ = [the AP is outside the blockage free zone], as illustrated in Fig. 4(a), occurs when the distance from the AP to the UE is greater than the blockage free zone radius , i.e.:
(9) 
The event ’body between’ = [the body is in between the AP and the UE], as illustrated in Fig. 4(c), occurs when the body orientation angle is smaller than the body shadowing angle , i.e.:
(10) 
Note that the UB shadowing angle is constant since the UB is at a fixed distance from the UE. The RB shadowing angle is a random variable since the distance from the UE is random, and its distribution is derived in Appendix
B. The event ’AP blocked’ = [the AP is blocked by the body] is the intersection of the events [the AP is outside the blockage free zone] and [the body is in between the AP and the UE], i.e.:(11) 
Then, averaging over all the random locations of the body blockages, including the user body, and the distance between the UE and an AP, we define the following for a given pair UEAP: Assuming that one body is enough to cause signal blockage, the event [AP being blocked by a body (UB or RB)] can be expressed as [at least one RB is blocking] or [UB is blocking]. We define the probability of this event as:
(12) 
We define the blockage state as which can take values from the set , where the is given by the event [AP being blocked by a body (UB or RB)], with the being the complementary event. Thus, we express as:
(13) 
3.3 SignaltoInterferenceplusNoise Ratio
In this work, we make the following assumptions to compute the SINR: We assume that the blockage event for each AP is independent, i.e., there is no correlation in the blockage process of AP near each other, even though in reality they could be blocked by the same body [venugopal2016device]. Therefore, we can determine the probability of blockage as a function of the AP distance. In Section 4, we test this assumption and check whether the correlation in body blockage has any impact on the network performance.
We model the mmWave signal propagation considering the experimentallyvalidated channel model proposed in [yoo2017measurements]. The model is composed of the path loss, largescale fading (shadowing) and smallscale fading, whose parameters assume one of two values according to the blockage state . We assume the path loss conditioned on is:
(14) 
where is the path loss at 1 metre distance under free space propagation, is the attenuation exponent, is the Euclidean distance from the AP to the UE, and is the projection of the distance from the cell centre to the UE onto the horizontal plane (we refer to this as 2Ddistance, as shown in Fig. 3
). We assume the shadowing is modelled as Gamma distribution and the smallscale fading as Nakagamim.
We express the received power at the UE from an AP with blockage state as:
(15) 
where is the transmit power, is the AP directivity gain given in (4), is the UE directivity gain given in (7), is the path loss given in (14), is the shadowing gain, and is the smallscale fading gain.
Based on the assumptions made above, we can express the SINR at a UE as follows :
(16) 
where is the serving AP, with denoting the set of APs, and is the thermal noise power. Note that, because is a random event, , , are random variables whose distributions are functions of the system parameters (, , , , , ). A summary of all the system deterministic parameters and random variables is provided in Table I and in Table II, respectively.
Body Parameters  Deployment Parameters  

Body width  AP height  
Body height  AP beamwidth  
Distance from UE to UB  Intersite distance  
UE beamwidth  
Signal Power Parameters  Directivity Gain Parameters  
Noise power  Mainlobe gain  
Transmit power  Sidelobe gain  
Illumination radius 
Body Blockage Variables  Signal Power Variables  
Body shadowing angle  Directivity gain  
Body orientation angle  Path gain  
Distance from UE to RB  Shadowing gain  
Blockage free zone radius  Smallscale fading gain  
Received power  
Deployment Variables  
Distance from UE to AP  2D projection of 
4 Analytical Results
In this Section, we provide an analytical expression for the probability of an AP being blocked. We use this expression to reduce the complexity of systemlevel simulation.^{4}^{4}4The simulator would need to compute the inequalities in Definitions 8 and 3.2 for each APbody pair, i.e., times (number of APs and number of RBs, respectively). With the analytical expression, the simulator only needs to calculate the function in (12) for each AP, i.e., times. In addition, we validate the AP blockage event independence assumption by showing that the proposed analytical expressions yield results closely trailing numerically evaluated blockage probabilities obtained from our simulation environment.
To compute the blockage of a signal from an AP at a given distance from the UE, we need to find the expression that gives the probability as a function of the distance. This function depends on two events — the selfbody blockage and the randombody blockage — and on the number of random bodies in the venue. Assuming that the RBs are randomly placed in a squareshaped venue, and the blockage orientation is distributed uniformly, we state the following propositions:
The probability of selfbody blockage is given by
(17) 
Proof:
See the proof in Appendix C.
The probability of blockage by a random body is given by
(18) 
where is the angle of obstruction by the body as a function of a distance , and is the square side length.
Proof:
See the proof in Appendix D.
Considering the probabilities in (18) and (17), and a finite number of RB in the venue, we express the probability of an AP at a distance from the UE being blocked by a body (UB or a RB) as
(19) 
Proof:
Applying the Definition 5, we can express the probability as:
(20) 
To validate the AP blockage event independence assumption, we compare (19) to the outcome of MonteCarlo simulations for the same setup, where the AP blockage events can be correlated (see Fig. 6). We show the results by varying the distance between UE and UB and the number of RBs. We consider a squareshaped venue area of 400400 m and intersite distance of 20 m. For the MonteCarlo simulation, we fix the UE at the origin^{5}^{5}5 When simulating the UE in other positions (e.g., in a corner and in an edge of the squareshaped venue), we found no significant deviation from the results reported for the centre position. and we vary the AP position (distance and orientation with respect to the UE). The UB is at a fixed distance from the UE, and its orientation is uniformly distributed. The RBs coordinates are distributed uniformly in both xaxis and yaxis.
We observe that the expression in (19) is a good approximation compared to the relative frequency of blockages computed by simulation. One should note that when the AP is close enough to the UE ( 5 m) and 30 cm, the probability of blockage is virtually zero, since the AP is inside the selfblockage free zone.
5 Numerical Results
5.1 Simulation Setup
We model our scenario by placing the AP in the centres of a hexagonal cell pattern laid over a 400 400 m area, as exemplified in Fig. 7.
This specific choice of the area size allows us to explore the system behaviour for large intersite distances (up to 200 m). The sidelobe gain is fixed at dB, and the mainlobe gain varies with the beamwidth according to (2). We evaluate the system for a fixed AP height = 10 m. Note that, changing has essentially the same impact on the performance as changing the AP beamwidth, since both and determine the mainlobe illumination area; as a matter of fact, when testing our system for other height values of interest (e.g., heights from 1 to 10 m), we observed no significant deviations from the conclusions we present here. We set the transmit power as 20 dBm, bandwidth as 2 GHz, carrier frequency as 60 GHz, as recommended by ITUR [itur_f.14972]
. We assume perfect equalisation in the frequency domain as the impact of frequency selectivity can be significantly reduced using effective modulation and equalisation techniques for 60 GHz frequencies
[daniels2010upclose]. We set noise figure as 9 dB, and the body parameters as 40 cm and as 40 cm. We consider the UE is associated with an AP corresponding to the strongest longterm received signal power, i.e., without considering smallscale fading gain. We define two selfbody blockage scenarios according to the parameter : = 30 cm represents a scenario of a user operating the UE with the hand, e.g. operating an app, and = 0 cm represents a scenario where the UE is held in a pocket or as a wearable device. These scenarios are in line with the empirical measurements made in [yoo2017measurements]. In addition, we define two random blockage scenarios according to the RB density: 0 RB/m represents a scenario where there is no other blockage besides the user body (empty scenario), and 3 RB/m represents a crowded scenario (such as in a busy transportation hub or a protest march [measuring2019reuters]). The combination of these blockage scenarios give us four different scenarios: emptyhand, emptypocket, crowdedhand, and crowdedpocket. We set the channel parameters as measured for a car park environment according to Table III (based on [yoo2017measurements, Table I]).Environment  UE Position  Path Loss  Shadowing  SmallScale Fading  
LOS  NLOS  LOS  NLOS  LOS  NLOS  
(dB)  (dB)  
Car Park  Hand  1.72  63.4  1.94  65.3  4.48  0.27  1.18  1.52  3.02  4.68 
1.70  59.1  0.61  88.5  1.96  0.75  2.80  0.47  4.21  2.46 
To evaluate the network performance, we consider the following metrics: SINR coverage and ASE. We define the SINR coverage as the probability that the SINR at the UE is larger than the threshold = dB, i.e., , as to ensure high data rate reception with low bit error rate using advanced modulation and coding schemes. The ASE is the average spectral efficiency, , divided by the cell area.
5.2 Coverage and Ase Profile
In this subsection, we evaluate the effect of the intersite distance (network density) on coverage and ASE of a mmWave indoor network with ceilingmounted AP. For now, we focus on the emptyhand scenario. Our investigation reveals that in the ceilingmounted AP setup, the SINR coverage and ASE
present a nontrivial behaviour which can be classified into four regions of operation, as illustrated in Fig.
8.These appear as we change the intersite distance while keeping the AP and UE beamwidths fixed: (I) High mainlobe interference: at high AP density (short ), the beam is too large and causes substantial overlaps among adjacent cells, which results in high interference and, thus, low coverage. However, since the cell area is very small, the ASE is high. Region I (II) Minimum mainlobe interference: the mainlobe illuminates the entire cell with minimum interference to neighbouring cells, yielding high coverage. However, the coverage can be limited by the UE’s mainlobe beamwidth, as large UE beamwidths will illuminate more neighbouring AP and increase interference power. Thus, strong serving signal and minimised interference lead to increased SINR and to high ASE. Region II (III) Low mainlobe illumination: at intermediate AP densities, the coverage is very low due to the lack of mainlobe illumination by the serving AP and due to the presence of neighbouring sidelobe interference; however, this interference decreases as the deployment gets sparser and less AP are illuminated by the UE mainlobe, leading to increased coverage. At the same time when we move towards a sparser deployment, as the cell size becomes larger, the ASE is reduced. Region III (IV) High path loss: in low AP density (large ), the illuminated area by the AP’s beam is so small, compared to the cell area, that it becomes negligible. Therefore, the only signal that can be picked up by the majority of users comes from the sidelobes. This signal is thus weak enough for the UE receive antenna gain to play a major role in mitigating the high path loss and the AP sidelobe attenuation, and thus increasing coverage. The large cell area contributes to an ASE even lower than for the other regions. Region IV
Based on these results, it is clear that a network operating in Region II reaches peak coverage performances. We explore the coverage behaviour for a range of AP and UE beamwidths to identify the configurations that maximise coverage for each intersite distance . In Fig. 9, we indicate the peak coverage with a solid black line. The AP and UE beamwidth configurations that lead to that coverage, for a given , are indicated by the colours above and below the line, respectively. With such configurations, we observe that the peak coverage is high for any intersite distance.
One can see the colour variation on the bars above and below the black line, where cold colours represent small beamwidths and warm colours large beamwidths. This indicates that, for each AP density, there is a specific optimal AP and UE configuration that maximises coverage (see Fig. 12, thin blue line, for exact numerical results). We observe that, when increasing the cell size, larger AP beamwidths (warmer colours) are needed to achieve the peak coverage, as there is the need to illuminate the entire cell. However, UE beamwidth does not have the same monotonic behaviour: With very small cell sizes ( 2 m), the UE beamwidth is small (cold colours), so it does not illuminate many neighbouring APs, and thus, avoids increased interference. As the cell size increases, the average distance between the UE and the serving AP also increases. Hence, the UE’s mainlobe tends to illuminate an increased area, as the mainlobe elevation lowers with the distance to the serving AP. Thus, in order to avoid enhancing the signal power from many interfering APs, the UE antenna should have low directivity gain (with large beamwidths, warm colours). Then, as the cell size becomes large ( 5 m), the serving AP moves further and further away, and high directivity gain is needed to compensate for the increased path loss, decreasing the UE beamwidth.
In Fig. 10, we draw a solid black line that represents the ASE achieved when using the optimal configuration for coverage. We see that the achieved ASE decreases due to both the increased cell area and increased path loss on the serving AP signal power. Therefore, as peak coverage and achieved ASE have opposite trends with respect to the cell size, there is a tradeoff between these two performance metrics. This tradeoff becomes more significant when other blockage scenarios are evaluated as we shall see in the following subsection.
5.3 Body Blockage Impact
In this subsection, we investigate the impact of body blockage on the ASEcoverage tradeoff. To that end, we compare the four different blockage scenarios of interest: emptyhand, crowdedhand, emptypocket, and crowdedpocket. We depict the tradeoff in Fig. 11, where each point of a curve corresponds to the optimal AP/UE beamwidths and AP density configurations that maximise coverage. The circle marks the achievable ASEcoverage for the lowest AP density (largest ), while the marks the achievable ASEcoverage for the highest AP density (smallest ).
In all scenarios, maximum ASE is achieved with the highest AP density, while maximum coverage can be achieved with a lower AP density. Still, we see that coverage in hand scenarios (thin lines) are satisfactory in highlydense AP deployments, but in pocket scenarios (thick lines), coverage is deeply degraded. For instance, if considering a coverage of 80 %, deploying high AP density for pocket scenario is insufficient. To overcome this threshold, low AP density should be deployed at the expense of two orders of magnitude decrease in ASE.
The optimal AP and UE beamwidths that lead to peak coverage for a given are shown in Fig. 12.
We showed in Section 5.2 that minimum AP’s mainlobe overlap is necessary to achieve peak coverage, but now, considering a more severe body blockage, a large overlap is needed to allow the UE to be handedoff to a neighbouring AP. It means that, for the same cell size, a larger AP beamwidth is necessary to achieve peak coverage in pocket scenario (thick lines), than in hand scenario (thin lines), as we observe in Fig. 11(a). Yet, the larger an AP beam overlap is needed, the more interference is added, which is why the peak coverage in pocket scenarios diminishes. In addition, the UE beamwidth in pocket scenarios are smaller than in hand scenarios as the UE needs to use higher directivity gains to compensate for the increased interference, as depicted in Fig. 11(b).
Introducing other randomly distributed bodies, i.e., in crowded scenarios (red lines), we observe from Fig. 11 that coverage is better than in empty scenarios when deploying high AP densities as the random bodies help to block interference. On the other hand, with low AP densities, the random bodies create additional blockages to the serving AP, decreasing SINR.
Comparing the AP beamwidths, we do not observe significant variation between the crowded and the empty scenarios, as the AP beamwidth is mainly affected by the selfbody blockage. Yet, comparing the UE beamwidths, we see that the UE beamwidth in empty scenarios (blue lines) are smaller than in crowded scenarios (red lines), when high AP density is deployed ( 10 m in pocket scenarios and 20 m in hand scenarios). This is because, differently from the crowded scenario, there is no additional blockage to shield from the interference. Thus, the UE needs to have small beamwidths to limit a number of illuminated interfering APs. Furthermore, we see that the optimal UE beamwidth in any scenario is not smaller than 45 . It means that large beamwidths are, in general, more beneficial than very small beamwidths (i.e., pencilbeams) in indoor ceilingmounted AP deployments. This is because small UE beamwidths may still illuminate many APs and increase the interference power with high directivity gains.
To sum up this section, the ASEcoverage tradeoff becomes more significant as coverage degrades with more severe blockage scenarios. It is more difficult in a scenario with high blockage probability (pocket scenarios) to achieve a certain level of coverage without significantly degrading the ASE, compared to a scenario with low blockage probability (hand scenarios). For instance, for a requirement of ASE bit/s/Hz/m and coverage %, the system configuration for pocket scenarios is restricted to a range of half intersite distances between 20 and 30 m if the venue is empty^{6}^{6}6 When the venue is crowded, it is impossible to meet these design criteria.. For hand scenarios, the goal can be achieved with any half intersite distance 30 m. Moreover, the optimal system configuration should be set depending on the blockage scenario, as the same configuration for one scenario may not be optimal for the others. For instance, to achieve ASE bit/s/Hz/m, cell size and AP beamwidth should be set small (e.g., 3 m, 30 ) for all scenarios, but the optimal UE beamwidth should be large for hand scenarios (e.g., 180 ) and small for pocket scenarios (e.g., 45 ).
6 Conclusion
Herein, we studied the network design aspects of ceilingmounted mmWave AP deployments with directional antennas over a confined area. We showed that, each densification level will require individual AP and UE mainlobe beamwidths configurations to achieve maximum coverage operation. The AP beamwidth increases with the cell size, small UE beamwidths can boost the signal from far APs in sparse deployments, while in dense deployments large UE beamwidths are more beneficial. We also showed that the optimal AP/UE mainlobe beamwidths configuration takes different values depending on severity of the blockage scenario. In the main, large AP beamwidths create enough overlap to allow for handoffs that will mitigate the blockage effects while keeping interference at an acceptable level. Finally, it is necessary for network designers to carefully consider their intended application as there is a fundamental tradeoff where same AP/UE beamwidth and density configurations that optimise coverage do not optimise ASE.
Appendix A
All simulation scripts used to generate the presented results were written in MATLAB^{®} and can be cloned from the following repository:
Appendix B Distribution of Random Body Shadowing Angle
In order to compute the probability of AP being blocked by a random body in Appendix D, we need to calculate the distribution of the random body shadowing angle. Here, since both UE and the body are uniformly positioned, the distance between them is random, which means that the body shadowing angle is also random. Thus we define the body shadowing angle as a function of the random distance to the body (i.e., the closer the body is to the UE, the larger the shadowing angle) and the fixed parameter — width of the body . Then, the distribution of can be obtained from the distribution of using the following change of variable:
(21) 
(22) 
(23) 
where (a) follows from the change of variable in (22). It should be noted that the inversion of the inequality follows from the fact that is a strictly decreasing function. The cdf in step (b) is the distribution of distance between two random points thrown on a square with side given by Equation (53) in [moltchanov2012distance]. That equation is defined for two intervals: and . Here, we consider only the first interval , as we assume that blockages from very far bodies (with distance ) are negligible. Then, the pdf is the derivative of the cdf in (23):
(24) 
where (a) follows from the change of variable in (22), and (b) follows from the change of variable in (21), with as a short notation of the function .
Appendix C Probability of Selfbody Blockage
The event [the AP is blocked by user body] is a specific case of the event given by Definition 3.2, where we know that the user body is at a fixed distance from the UE and its orientation is a random variable uniformly distributed in . Then, the event [the AP is blocked by user body] is given by:
(25) 
where is selfbody blockage free zone and is the selfbody shadowing angle. Therefore, since the body orientation is independent of the distance , the probability of selfbody blockage is:
(26) 
It means that if the UE is at a distance , the probability of selfbody blockage is zero (UE inside the selfblocking free zone). Otherwise, the probability is . Thus, we can express as:
(27) 
Appendix D Probability of AP Being Blocked by a Random Body
Assuming both UE and an RB (not the user) positions are uniformly distributed, the event [the body is in between the AP and UE] depends on the distance from the RB to the UE, on the body shadowing angle (these random variables are discussed in Appendix B), and on the body orientation , which we also assume to be uniformly distributed in for an RB. Then, applying the Definition 3.2 to a random body, the event [the AP is blocked by a random body] is given by:
(28) 
where is the blockage free zone and is the body shadowing angle. Therefore, the probability of blockage by a random body is:
(29) 
where (a) follows from making a change of variables, (b) follows from the independence of and , and consequently, of and , and (c) follows from substituting the cdf of and the pdf of with (24) given in Appendix B.
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