I Introduction
The FifthGeneration New Radio (5GNR) wireless standardization efforts are an important component in the successful commercialization of millimeter wave (mmW) technology [2, 3, 4, 5] for enhanced mobile broadband applications. In this direction, a number of (multiinstitutional) efforts have focussed on the scope and scale of unfavorableness in wireless propagation at mmW carrier frequencies relative to sub GHz systems [6, 7, 8, 9, 10]. These studies show that while propagation losses at mmW frequencies are typically higher than with sub GHz systems in both indoor and outdoor settings, these losses are not^{1}^{1}1In particular, for nonlineofsight (NLOS) links, [10] shows a nominal path loss degradation at GHz relative to GHz of dB, dB and dB at a coverage distance of m in an indoor office setting, m in an Urban Micro setting, and m in a shopping mall setting, respectively. This degradation is computed as dB at a coverage distance of m where and denote the path loss exponent at the two carrier frequencies in the scenario of interest. significantly worse at the mmW regime. These additional propagation losses can be overcome by array gains reaped from the use of larger antenna arrays (at both ends) [11, 12, 13, 14, 15, 16, 17, 18], increased effective isotropic radiated power (EIRP) levels [19], and system design that aids in opportunistic signaling by leveraging time, frequency and space diversity [20, 21, 22, 23].
Nevertheless, as the 5GNR design process marches towards the accelerated schedule of early commercial deployments, important aspects that determine the viability of mmW technology in practice, such as outdoortoindoor penetration and blockage, have to be addressed carefully. Outdoortoindoor penetration through different types of residential/office materials has been studied extensively; see e.g., [9, Appendix E], [10]. These works report that the reflection response and penetration loss are a function of the material property, frequency, polarization and incident angle, and significantly deep signal reception notches spread over several GHz of the spectrum are observed. Such an observation motivates the need for system designs that support both frequency and spatial diversity.
In the context of spatial diversity, given the use of large antenna arrays and the diminishing beamwidths of the directional beams with antenna dimensions [15, 16, 17, 18], mmW systems are susceptible to signal blockage much more than sub GHz systems are. In particular, mmW systems are susceptible to selfblockage, which is shadowing from the user itself in the form of hand blocking and blockage from other body parts. This can cause a complete blockage of the user equipment (UE) antennas depending on the antenna position relative to the hand. In addition, there are blockages from the environment around the UE in the form of buildings, foliage, or other obstructions (static blockage) and humans, vehicles, or moving obstructions (dynamic blockage).
Prior Work: In prior work, a human blockage model has been included in the (ad) GHz wireless standardization efforts [8, Sections 3.3.8, 3.5.7, 5.3.9, 8]
. This model captures the probability of a cluster blockage event and the distribution function of power attenuation for these events, both via raytracing studies. Wideband
GHz human blockage measurements over a GHz bandwidth has been performed in [24] and the authors study the comparative model fits between the double knife edge diffraction (DKED) and the uniform theory of diffraction (UTD) modeling frameworks showing that the DKED framework underestimates blockage loss and the UTD framework overestimates it.The Mobile and wireless communications Enablers for the Twentytwenty Information Society (METIS) project has proposed a human blockage model based on the DKED framework in [9, pp. 3941, 160162]. A blockage model is proposed by the 3GPP Rel. 14 channel modeling document [6, pp. 5357] for mmW system modeling under two variants: a stochastic variant (Option A) and a mapbased variant (Option B). Both these variants assume a dB flat loss for selfblockage. A modified version of the METIS model based on GHz human blockage measurements using horn antennas has been proposed to account for directional transmissions in [25, 26, 7] and these studies show that human blockage could cause signal attenuation on the order of  dB depending on the distance between the human and the transmitter/receiver. Another work that studies UE antenna modeling in formfactor UE designs at GHz from a blockage consideration is [27]. This study illustrates performance losses with the hand phantom model and recommends the use of subarray diversity to overcome these losses. The readers are pointed to [28, 29] for recent studies on design tradeoffs of 5G antenna arrays with formfactor considerations.
Contributions: With this backdrop, we first note that most of the prior works focus specifically on human blockers in a lowmobility indoor setting with short transmitreceive distances using horn antennas for measurements. On the other hand, the use of a phased array ( antennas) at the UE end implies that the beamwidth^{2}^{2}2For example, a beam with progressive phase shifts (or a constant phase offset) over a element linear array is expected to lead to a dBbeamwidth of , whereas a horn antenna typically has a dBbeamwidth on the order of  at mmW frequencies. at the UE side is expected to be much larger than that seen with a horn antenna. Such differences can lead to a significant variation between the blockage modeling experiments with a formfactor UE design and horn antenna measurements. In general, while formfactor UE designbased blockage modeling studies provide the gold standard in terms of understanding the implications of blockage at the UE end, such studies are currently difficult to obtain due to the still ongoing design, manufacture, development and testing of mmW technology supporting UEs/chipset solutions.
We propose to address these shortfalls by an intelligent mix of measurements with a formfactor UE prototype (as reported in [23]
) and electromagnetic simulation studies for formfactor designs where such studies can supplant measurementbased insights. In particular, simulation studies are useful to understand the loss in spatial coverage with blockage. On the other hand, mmW measurements provide the best estimate for loss in signal strength as well as timescales at which blockage disruptions happen. In this work, we provide a complementary mix of simulation studies and measurement studies for both self and dynamic blockage.
In this direction, we first study selfblockage by considering electromagnetic simulations of antennas at and GHz in the proximity of the hand and identifying the spatial regions corresponding to signal blockage with different user grips. These simulation studies illustrate the blockage of a large spatial region in the UE’s local coordinate system depending on whether the UE is held in a Portrait or Landscape mode. We then study the loss incurred by the hand with different grip experiments using the GHz prototype reported in [23]. In contrast to prior work that shows high selfblockage losses ( to dB), our studies show that a median loss of dB is incurred by the hand even in the most pessimistic scenario of a hard hand grip. The beamwidth differences between horn antennas and a phased array design is likely to account for such wide discrepancies.
To model dynamic blockage, we conduct simulation studies to capture the impact of objects at the UE end in the form of angular regions blocked and losses incurred with a DKED model. We study the efficacy of the simulated loss data with measurement studies sing the GHz prototype. Our studies show that though there are some discrepancies between simulated loss and true measurements, simulated data can offer a reasonable firstorder estimate of blockage losses and can thus be useful for scenarios like vehicular applications, where loss estimation with measurements is considerably more complicated and difficult. These studies lead to the proposal of a statistical blockage model that has many attractive properties: i) parsimonious (captured by a small number of model parameters), ii) efficacious (captures the real impact of blockages), and iii) computationally efficient (easily useable in a system simulator framework) in studying the performance of mmW systems.
We then consider the question of timescales at which mmW signals are disrupted due to blockage. Such timescale estimation is important to understand the scope of mmW beamforming solutions, their robustness/stability and the nature of mitigation mechanisms to handle blockage without serious link degradation. With some prototype studies, we show that these timescales can be attributed to physical movements of the source of blockage (hand in the case of selfblockage, humans/vehicles in the case of dynamic blockage, etc.). Thus, the dynamics of these blockers capture the timescales at which mmW signals get disrupted and measurement studies show that they are on the order of a few ms (or more). Given the subms (or a few ms) effective latencies targeted by 5GNR for beam/subarray switching, it appears that the deleterious impact of blockages can be addressed by a robust beam management procedure at the PHY layer level. In terms of PHY layer solutions, network densification, design of multiple subarrays and capability to switch beams/subarrays at the UE end, and alternate fall back mechanisms could address these challenges.
Organization: This paper is organized as follows. Sections II and III consider self and dynamic blockage from both electromagnetic simulation studies and measurement perspectives, and simple statistical models are proposed to capture the effect of these blockages. Section IV considers the question of timescales at which blockage events happen. Section V proposes multiple approaches to combat the effect of blockages and Section VI concludes the paper.
Ii SelfBlockage
The focus of this section is on understanding the impact of selfblockage in terms of the spatial/angular coverage lost as well as the loss incurred over the blocked angles.
Iia Loss in Spatial/Angular Coverage
Objects that are electrically small at microwave frequencies become electrically large at mmW frequencies, and small objects (which have the size of a few mm’s) located in the proximity of the antennas affect the antenna performance and deteriorate both their efficiencies and radiation patterns. For example, antennas placed on the display side can be affected by the liquid crystal display (LCD) shielding, LCD glass, component shields, as well as other objects such as camera(s), speaker, microphone, sensors, etc.
To investigate the effect of the antennas’ surroundings on its performance (especially its radiation pattern), the antenna module is placed over a simplified model of a UE (corresponding to a typical size of mm) and studied in an electromagnetic simulation framework. The model of the UE simulated consists of several layers of materials: Glass with a thickness of mm, LCD shielding which lies beneath the glass and extends mm from the edge of the glass, and the FR4 board^{3}^{3}3Note that “FR4 (or FR4) is a grade designation assigned to glassreinforced epoxy laminate sheets, tubes, rods and printed circuit boards. FR4 is a composite material composed of woven fiberglass cloth with an epoxy resin binder that is flame resistant.” See https://en.wikipedia.org/wiki/FR4 for more details. with a thickness of mm that is separated by an mm air gap from the LCD shielding. Also, a battery and few shielding boxes of random sizes are placed over the printed circuit board. All the metallic objects are connected to the ground plane of the board which covers its bottom plane.
(a)  (b) 
(a)  (d) 
(b)  (e) 
(c)  (f) 
For the antenna design, multiple subarray units (corresponding to placement of antennas on the Long and Top edges of the UE) in the Portrait and in Landscape modes, as illustrated in Figs. 1(a)(b), are considered. These antenna modules are designed on a relatively low loss dielectric substrate (Rogers 4003) and are placed on the FR4 substrate. The antenna elements are either dipole elements or dualpolarized patch elements. Antennas are designed for the respective carrier frequency and are simulated with and without hand at every azimuth and elevation angle ( and ) in the spherical coordinate system.
To understand the impact of hand, the human hand is modelled as a homogeneous dielectric with the dielectric properties of skin tissue. In general, the skin permittivity decreases with an increase in frequency while its conductivity increases [30, 31, 32]. In particular, a relative dielectric constant and conductivity S/m are used at GHz with CST Microwave Studio (a commercial electromagnetics simulation software suite). The hand dielectric properties determine the penetration depth into the hand and the reflection of electromagnetic waves from the hand. At the range of frequencies considered ( and GHz), the penetration depth into the hand is very small (corresponding to a high degree of reflection) ensuring a high degree of blockage by the hand.
The maximum gain of all the antennas without hand, with hand in the Portrait mode and with hand in the Landscape mode are plotted as twodimensional contour plots (across ) in Figs. 2(a)(c) for GHz. From Fig. 2(a), in the absence of hand, almost the entire sphere is covered around the UE illustrating both the necessity and the goodness of the multisubarray UE design. On the other hand, the presence of hand in either the Portrait or Landscape modes adversely affects the radiation coverage as seen from the blue areas^{4}^{4}4Note that the heat map adjacent to the gain plots illustrate the strength of signal coverage. (defined as signal strengths below dBi) in Figs. 2(b)(c). The region in blue stretches from behind the palm to the thumb (associated based on the corresponding  angles). Furthermore, it is seen that the long edge module does not play an important role in signal reception in the Portrait mode as it is blocked with the fingers resulting in significantly deteriorated antenna efficiencies. On the other hand, the short edge is not affected much with the presence of the hand ensuring that diversity from subarrays is critical for seamless communications. For the Landscape mode, the antennas along the long edge are unobstructed leading to better coverage than the short edge antennas.
While the electrical properties of the hand are different between and GHz, the hand still acts as a lossy reflector and can severely deteriorate antenna performance. In general, the skin permittivity and conductivity decreases and increases with frequency, respectively. Based on [30, 31, 32], a relative dielectric constant of and conductivity of S/m are used at GHz and simulations (as above) are redone. Figs. 2(d)(f) plot the coverages without hand, with hand in the Portrait and Landscape modes, respectively, for GHz. Compared to GHz, at GHz, the electrical size of the UE and hand are almost doubled while the antenna size is approximately reduced to half. This prevents the radiation of the antennas located on the top and left sides to leak to the right or bottom sides of the UE. Thus, even in the absence of hand, complete radiation coverage around the UE is quite challenging (as seen from the streaks of blue without the hand in Fig. 2(d)).
In the Portrait mode in Fig. 2(e), the left edge of the phone is obstructed by the fingers which causes blockage on the left side as well as back side of the hand. This forms a dead zone between to from the Zaxis, which is perpendicular to the hand. The high gain radiation coverage occurs in front of the phone due to radiation from the patch antennas located at the top edge. In comparison, the back of the phone which is illuminated by the top edge dipoles shows slightly lower gain. In the Landscape mode in Fig. 2(f), while neither subarray at the UE is blocked severely, the hand still prevents the top edge dipoles to radiate towards the back of the hand and most of the radiation is reflected or absorbed.
IiB Loss in Signal Strength
The blockage loss incurred by the hand in the studies of Sec. IIA are plotted in Fig. 3
(a) [see curves grouped as “Simulations”]. In particular, the cumulative distribution function (CDF) of the maximal gain from all the antennas in both polarizations is compared between the
Freespace mode (without the hand) and Portrait/Landscape modes (with hand) and plotted here. These studies show that the loss appears to be in the range of to dB (with negative values corresponding to signal energy boosting due to hand reflection at certain angles). In particular, Fig. 3(a) shows that blockage loss is possible for up to and of the angles in Portrait and Landscape modes, respectively. However, these estimates are sensitive to the hand phantom model used in the simulation studies (see Fig. 1). In particular, the tightness of the hand grip around the UE determines what fraction of electromagnetic energy is captured by the antennas with a tighter/harder grip leading to significant losses (and vice versa). The nature of the air gap between the fingers also determines what fraction of energy is captured as multiple reflections from the skin surface, which can assist signal reception in certain angles. Thus, while the above simulation studies could be used for studying loss in angular coverage, using them directly for loss in signal strength could be questionable.In this context, some measurement studies from [25, 26, 7] suggest a loss of even up to to dB with hand and body blockage. However, all these measurements are based on the use of horn antennas and cannot be extended easily to formfactor UE designs. To understand the loss possible with the hand, measurement studies are performed with a GHz experimental prototype capturing the attributes of a 5G basestation as well as a formfactor UE design and operating in a timedivision duplexing framework. With this prototype, the baseband analog inphase and quadrature (IQ) signals are routed to/from the modem to an IQ modulator/demodulator at GHz center frequency. The GHz intermediate frequency signal is translated to GHz using a GHz tunable local oscillator (with a MHz step size). The basestation end of this system is a planar array (made of a waveguide design) that allows analog beamforming using tunable four bit phase shifters and gain controllers. The UE end is a formfactor design made of four selectable subarrays, each a four element phased array of either dipoles or patches with locations on the UE as illustrated in Fig. 1(a). More details on the design parameters of the prototype are provided in [23].
In our hand loss studies, the formfactor UE is grabbed by the hand at normal speed and the hand completely covers/envelops the active antenna arrays as illustrated in Fig. 3(b). All the subarrays at the UE side except the enveloped subarray are disabled in terms of beam switching thus allowing us to capture the blockage loss in terms of received signal strength differentials. We define an RF event relevant for these studies as one where the received signal strength indicator (RSSI) drops from the steadystate value by at least dB. From our experiments, such RF events are recorded and for each RF event, ten RSSI minimas^{5}^{5}5Due to constraints on the postprocessing of data, RSSI minimas can be recorded to only within a dB precision. spanning the entire event are separately recorded. The link degradation is computed as the RSSI difference between the steadystate RSSI value and the ten minimas. The empirical CDF of hand blockage loss corresponding to these data points is also plotted in Fig. 3(a) [grouped under “Measurements”]. From this plot, we note that observations of  dB hand blockage loss from [25, 26, 7] may be too pessimistic to capture real measurements based on formfactor UE designs. More reasonable estimates for hand blockage loss are on the order of  dB with a median loss of dB.
(a)  (b) 
We now consider a number of model fits for the hand blockage loss data. The efficacy of each model (for the loss data) is captured by the KolmogorovSmirnov (KS) distance [33], defined as,
where and denote the CDFs with the empirical data and the corresponding model, respectively. Since the KS distance only captures the worstcase deviation between the two CDFs, we also consider a dataweighted KS (WKS) distance, defined as,
A better model fit for the data is captured by smaller KS and WKS distances (and vice versa).
Hand blockage  Body blockage  
Model  Parameters  Parameters  
Gaussian:  ,  ,  
Weibull:  ,  ,  
Gaussian mixture:  , ,  , ,  
, ,  , ,  
,  ,  
Gaussian Weibull mixture:  , ,  , ,  
, ,  , ,  
,  , 
The empirical mean and empirical standard deviation of the hand blockage loss data are
dB and dB, respectively. The functional forms as well KS and WKS distances of the different models considered here are presented in Table I. In terms of the models, we first consider a Gaussian density^{6}^{6}6Theoretically, a Gaussian approximation to the loss can result in a value that is negative due to the Gaussian tail. Independent of whether negative loss values make sense, for all practical purposes, such realizations are not seen in numerical studies due to the extremely low probability of such occurrences. Thus, we will not bother with these technical difficulties in this paper. with mean and standard deviation being the empirical mean and empirical standard deviation values (as above). This model fit is plotted in Fig. 3(a). From this plot, we observe that the Gaussian density overestimates both the lower and upper tail values of loss and underestimates the bulk. That is, the measured data has a heavier lower tail than the Gaussian density can fit. This mismatch is also reflected in the high KS and WKS distances with this model (see Table I). To overcome this problem, we consider a Weibull density^{7}^{7}7Note that the Weibull density , where and are the scale and shape parameters, is commonly used to model “timetofailure” of a certain process with capturing the failure rate of the process. In particular, , and capture decreasing, constant, and increasing failure rates of the process with time. that is typically used to model heavy tailed data. While the Weibull density improves the KS and WKS distances, from Fig. 3(a) as well as Table I, we see that there is no dramatic improvement in fit with this model. Note that both these models are described by two parameters.For a better fit, we therefore consider models with more parameters. While different model families can be considered, we start with a Gaussian mixture with the hope that these Gaussians can individually capture the upper and lower tails better. The parameters for the Gaussian mixture are learned using the Expectation Maximization algorithm as described in Appendix
A. In contrast to the expectation, our results show that the best Gaussian mixture model fails to capture the data accurately as the tails of one Gaussian component lead to a poor fit for the other Gaussian component (and
vice versa). In fact, the Gaussian mixture leads to a good fit only at the bulk. To remedy this misfit, we consider a GaussianWeibull mixture model as an alternate candidate. Since an analogous Expectation Maximization solution (as in Appendix A) appears to be difficult due to the complicated structure of the Weibull density, we use a local search over the parameter space neighborhood initialized with the individual Gaussian model and Weibull model parameters, respectively. The objective of this optimization is to minimize the WKS distance of the consequent model fit. As observed from both Fig. 3(a) and Table I, the optimized GaussianWeibull mixture fits the empirical data better suggesting its utility as a generative model for hand blockage loss.IiC Proposed Statistical Model
Based on the studies in Sec. IIA and IIB, we propose a simple square region approximation for spatial/angular blockage with the hand. This approximation is captured by the center of the blocker (, ), and the angular spread of the blocker (, ) in azimuth and elevation with the blocking angles captured as and in azimuth and elevation, respectively. For the blockage loss, we propose a lowcomplexity variant captured by the Gaussian fit and a relatively highercomplexity variant captured by the GaussianWeibull mixture fit from Table I. These proposals lead to the statistical model in Table II (in the local coordinate system around the UE) for selfblockage.
Scenario  Blockage loss (in dB)  

Portrait mode  Lowcomplexity :  
Landscape mode  Highcomplexity : GaussianWeibull mixture with  
, , , , , and 
Iii Dynamic Blockage
Iiia Methodology for Modeling Dynamic Blockage
We assume that the dominant signal path(s) between the transmitter (basestation) and the receiver (UE) are in the plane connecting them. In outdoor usecases where the transmitter is on the top of a building or a lamp post, as well as indoor usecases where the transmitter is on/near the ceiling or at the same level as the receiver, such an assumption is reasonable^{8}^{8}8Nevertheless, this assumption significantly simplifies the study done in this work and should be treated as a first attempt at a comprehensive statistical model for blockage. Future studies will consider further extensions of the setup considered in this work. with at least moderate cell sizes. We now propose a simple methodology to capture the impact of dynamic blockers (e.g., humans, vehicles, etc.) that are strewn randomly in the transmitreceive plane.
Relative to a global coordinate system, the azimuth angle of the blockers are assumed to be uniform in and the elevation angle is assumed to be a fixed . Without loss in generality, we assume that (that is, the transmitreceive plane is the horizontal plane). If the blockers are too close to either the transmitter or the receiver, the observed blockage loss can be significant. At the receiver end, such a scenario is already captured by the selfblockage component and at the transmitter end, it is less likely provided the transmitter has a reasonable unobstructed coverage (the precise scenarios considered in this work).
To capture these aspects explicitly, as illustrated in the topview of the transmitreceive plane in Fig. 4(a), the blockers are assumed to lie in a circular region (with radial locations constrained as ) around the receiver. A triangular density function of the form
is assumed for . This density captures the fact that the blocker density grows with since there is more area covered by the circular region with closer to than at . The heights and widths of the blockers are modeled as and where
stands for a uniform random variable over the interval
, and denote the mean height and width of the blocker, and and denote the onesided deviations for the height and width of the blocker, respectively.We propose to model the number of blockers in the region of interest as a Poisson random variable with parameter . That is,
Let the average density of blockers be defined as the number of blockers per unit area. With the model from Fig. 4(a), the average density of blockers is given as . For simplicity, the blocker and the receiver are assumed to be parallel in orientation and the angle subtended at the receiver/UE by the blocker is computed^{9}^{9}9Since the distances tend to be small for both indoor and outdoor usecases, approximations such as and can be inaccurate. as and in azimuth and elevation, respectively.
(a)  (b) 
Human ( m)  Vehicular ( m)  

m  m  
m  m  
m  m 
To study the loss in spatial/angular coverage, we use the parameters from [7]: m and m for human blockers, and m and m for vehicular blockers. For modeling human and vehicular variations, we also use m and m for humans, and m and m for vehicles. In a typical indoor office setting such as the third floor of the Qualcomm building, Bridgewater, NJ with dimensions of sq m and occupied by to humans, the average density of human blockers ranges from to per sq m. Similarly, in a typical outdoor setting of sq m with to vehicles, the average density of vehicular blockers could range from to per sq m. For three choices of and , Table III presents the average density of human and vehicular blockers in the indoor and outdoor cases, respectively. For a human blocker, we assume m and three cases for : , , or m (denoted as Cases ). For a vehicular blocker, we consider m and three cases for : , , or m (also denoted as Cases ). While different choices of can be considered in general, from Table III, we focus on as representative samples to reflect average density of blockers in typical indoor and outdoor deployments.
IiiB Loss in Spatial/Angular Coverage and Number of Blockers
Table IV presents the median, and percentile values of the mean angular blockage in azimuth and elevation for and . From these studies, we note that the mean spatial/angular blockage for both human and vehicular blockers decreases as increases or increases. This is because the blockers are farther away from the receiver as increases and are more likely to be farther away from the receiver as increases. In either case, a smaller angle is casted at the receiver leading to a reduction in the mean angular blockage. Further, this angle has only a weak dependence on . We conclude that a typical mean angular blockage of in azimuth and in elevation are seen with human blockers, and in azimuth and in elevation are seen for vehicular blockers.
We are now interested in understanding the number of blockers to be incorporated in a statistical model for dynamic blockage. Table V presents the explanatory power captured by the fraction of the total azimuthal angular blockage captured^{10}^{10}10While we consider the top blockers in terms of angles blocked, alternate criteria such as top blockers in terms of blockage loss can also be considered. The flavor of the results are not expected to change with such alternate criterion. by the top blockers. The median, and percentile values of the explanatory power are presented for human blockers with m, m, and for vehicular blockers with m, m for different choices of . Table V shows that there is a decreasing explanatory power for a fixed as increases, and diminishing returns and increasing model complexity with an increase in for any . The use of the top human and top vehicular blockers can explain over of the blocked angular region up to and suggests a good tradeoff point/compromise between explanatory power and model complexity.
Mean angular blockage (Human)  Mean angular blockage (Vehicular)  
Azimuth (in degrees)  Elevation (in degrees)  Azimuth (in degrees)  Elevation (in degrees)  
Percentiles  

Case 1  
Case 2  
Case 3  

Case 1  
Case 2  
Case 3  

Case 1  
Case 2  
Case 3 
Percentiles  
Human 
Top2  
Top3  
Top4  
Top5  
Top6  
Vehicular 
Top2  
Top3  
Top4  
Top5  
Top6 
(a)  (b) 
IiiC Loss in Signal Strength
For the human body blockage loss, we use the DKED model from [7, 34, 35] with m, and the transmitreceive distance m. Fig. 5(a) plots the CDF of the body blockage loss (solid curves) with different choices of . Also, plotted are Gaussian approximations to the loss estimated from the DKED model (dashed curves). While blockage losses increase as the blockers get close to either the transmitter or receiver, the Gaussian approximation appears to be a reasonable firstorder fit across different choices of .
Nevertheless, these losses are sensitive to the assumptions in the simulation methodology described in Sec. IIIA. Thus, analogous to the measurements reported in Sec. IIB, link reliability studies are conducted in the third floor of the Qualcomm building, Bridgewater, NJ with the experimental prototype described in Sec. IIB to understand the impact of (human) body blockage. In these experiments, as illustrated in Fig. 4(b), the UE side of the prototype is held stationary near the vending machine(s). The UE antenna height is adjusted to m with possible transmission (over an NLOS link) from one of two transmitters. One of these transmitters is at a distance of m from the UE and the other is at a distance of m. Both transmitters are held stationary and are maintained at a height of m. Except for one active subarray, beam switching across different subarrays is disabled. Uncontrolled tests are performed where people could walk by/past the UE at normal pedestrian speeds and at different distances (people could get as close as m from the UE).
The body blockage loss^{11}^{11}11As in the selfblockage studies, RSSI could be recorded to only within a dB precision. corresponding to RF events with humans blocking the UE are recorded and the CDF of this loss data is also presented in Fig. 5(a). The empirical mean and empirical standard deviation for the loss data are dB and dB, respectively. As with the selfblockage studies, the same set of four models (considered earlier) are fitted to the body blockage loss data. The parameters learned in this process as well as the KS and WKS distances between the empirical data and the fitted models are presented in Table I. From this study, we note the best fit for the data again with a GaussianWeibull mixture.
From Fig. 5(a), we observe that there exists a minimal yet distinct difference between the loss estimated from simulation studies and those with measurements. As mentioned earlier, these differences arise from the failure of the simulation methodology to capture real deployment scenarios and addition of more details could bridge this gap. This would be the subject of future investigations. Nevertheless, given the lack of/difficulty in obtaining measurements in outdoor scenarios, the simulation methodology described in Sec. IIIA is considered for vehicular blockers with m, and m. From this study, Fig. 5(b) presents a comparison between human and vehicular blockers in terms of simulation studies. Typical median losses of to dB and to dB are seen in the human and vehicular cases, respectively. These studies illustrate the far more significant impact vehicular blockers could have in real deployments than human blockers making the understanding of such issues more important.
IiiD Proposed Statistical Model
Table VI summarizes the main conclusions of the studies in Sec. IIIB and IIIC in terms of the number, center and angular spread, and loss due to both human and vehicular blockers. While a measurementsdriven loss model is proposed for human body blockage, only a simulationsbased loss model (developed based on the proposed methodology in Sec. IIIA) is available for vehicular blockage. A similar model is proposed by 3GPP to capture blockage effects [6, pp. 5355]. The 3GPP model differs from the proposal in Table VI in terms of the number of blockers and their blockage regions. Further, while a lowcomplexity statistical version of the DKED model is proposed for vehicular blockage in Table VI, a more explicit version is proposed for both body and vehicular blockage in [6]. This explicit version can lead to a substantial complexity in 5GNR system/link level studies. Further, this explicit version critically relies on the DKED model, whose efficacy in capturing loss in the human body blockage case needs further attention as illustrated by the slight mismatch between simulationbased and measurement studies.
Blocker index  Blockage loss (in dB)  

(Human)  Lowcomplexity:  
Highcomplexity: GaussianWeibull mixture with ,  
, , , , and  
(Vehicular)  Simulationsbased: dB, dB) 
Iv TimeScales of Blockage Events
Understanding the timescales at which blockage events happen can help us mitigate these disruptions in terms of signal quality degradation and even possible link losses. It is important to note that these timescales are determined by the dynamics of blockage, and in particular, the speed at which humans walk (or other blockers emerge and depart) to block a link or the speed at which the hand grabs the UE and blocks the link. Towards this goal, we define the link degradation time as the time required for the RSSI to drop from the steadystate value to its minima in the case of a goodtomoderate channel condition, or the time required for the RSSI to drop from the steadystate value to a complete link loss in the case of a poor channel condition. With this definition, the link degradation time serves as the worstcase time by which a beam switching/link adaptation procedure must be enabled to ensure that mmW coverage remains robust, reliable and seamless.
To understand the scope of link degradation and timescales of blockage events, six experiments are performed with the experimental prototype described in Sec. IIB. The prototype uses a proprietary transmission frame structure where each subframe is us. Analog beamforming with proprietary directional codebooks (see design principles in [16, 23]) is implemented at both the basestation and UE ends. These codebooks correspond to testing the link over transmit side beams and UE side beams ( beams over four subarrays) for a beam scanning periodicity/latency of ms. Thus, any link degradation/loss can be estimated to within an accuracy of ms. The first four of these six experiments correspond to link degradation due to dynamic blockage (humans walking around near the UE) and the last two experiments correspond to selfblockage (the use of the hand). Each experiment corresponds to different link/channel conditions with multiple independent tests performed in these settings. More details on these experiments including the number of tests are provided in Table VII.
Figs. 6(a)(b) capture the CDF of link degradation time across different channel conditions with human body blockage and selfblockage, respectively. The CDFs from the true data are presented with solid lines and piecewise linear estimated fits (across adjacent sample points) are presented with dashed lines. From these plots, we note that the link degradation time generally decreases as the channel condition deteriorates with no substantial difference between hand and body blockage dynamics. Thus these plots suggest that the timescales at which blockages are observed at the UE end are indicative of physical movements (of either humans or the hand) which can be on the order of a few s of ms (or slower). Thus, from Fig. 6, it is not surprising to see that the median value of link degradation time being on the order of  ms for body blockage and ms for hand blockage. Given the subms latencies for beam switching possible in 5GNR, these estimates suggest that blockage events can be handled with a robust beam management procedure.
Experiment  Blockage type  Channel condition  Number of tests 

Body  Good  
Body  Goodtomedium  
Body  Medium  
Body  Poor  
Hand  Poor  
Hand  Good 
(a)  (b) 
V Solutions to Combat Blockage
Multiple solutions can either be individually/jointly considered to handle the deleterious impact of performance degradation with blockage.

Network densification: Beamforming design for mmW systems is expected to leverage directional solution structures due to their robustness with different beamforming architectures and their implementation ease [36, 16, 17]. Thus, both the basestation and the UE are expected to steer their beams towards the dominant clusters in the channel and blockage in these directions can significantly deteriorate the performance of mmW systems. In this context, densifying the network with overlap in coverage across multiple cells [3] can provide higher fade margins to prevent link losses in mmW deployments. Further, the deployment of multiple basestations could lead to the feasibility of different/distinct dominant paths from these basestations to a certain UE via distinct reflectors, scatterers or clusters thereby reducing the risk of dramatic link degradations/failures due to blockage.

Subarray switching: Subarray diversity is critical at the UE end due to the reduced spatial/angular coverage possible with an antenna at mmW frequencies relative to sub GHz frequencies. For example, the typical angular coverage with a dipole/patch antenna is on the order of to implying the necessity of multiple subarrays as well as a careful selection^{12}^{12}12The constraints associated with the location of camera(s), speaker, microphone, sensors, etc. lead to a careful optimization of the location of antennas in a formfactor UE design (see, e.g., Fig. 1). of the locations of these subarrays for full spherical coverage. Thus, coverage over the sphere is realized in a formfactor UE design with distinct subarrays corresponding to distinct clusters in the channel environment. This fact can be leveraged by allowing/enabling a subarray switching procedure via beam management before an established link degrades significantly.
In this context, mmW measurements reported in [37] for indoor environments (office and shopping mall) suggest that (on average)  distinct clusters corresponding to distinct directions appear to be within a power differential of dB of each other implying a reasonable level of path diversity for indoor mmW deployments. Similarly, in outdoor mobility tests with the prototype reported in [23, Sec. IV], interbasestation beam switching and handover are shown to be both feasible and important with blockages from static geographical/topographical blockages/features, foliage, etc.

Fall back mechanisms: With the above background, there could also be scenarios where the network is not densified sufficiently or the channel environment is sparse ensuring that there are no better clusters to switch to. In these scenarios, the UE is left with little choice but to continue to use the degraded link with some codebook enhancements (possibly proprietary from an implementation standpoint). These enhancements could help improve the array gain seen at the UE side by performing a maximum ratio combining of the effective channel corresponding to the true channel and the nearfield effects of the hand. Alternately, the UE could consider fall back to legacy carriers (such as 4G/LTE) or 5GNR carriers such as those at sub GHz frequencies.
Vi Concluding Remarks
Given the prospects of accelerated deployment of 5GNR systems, there has been an emerging interest on a number of issues that need to be addressed to make these systems technically viable and commercially profitable [28, 29]. The focus of this work is on one such aspect: blockage of mmW signals due to the user itself (hand or body parts) as well as humans or vehicles in the vicinity of the UE. To the best of our knowledge, the impact of blockage as well as their implications in terms of PHY layer mechanisms to ameliorate their impact have not been reported for or GHz systems (two important usecases of 5GNR), especially with formfactor UE designs.
In this context, our studies at and GHz show that large parts of the spatial/angular coverage area can be blocked by the hand. This is because the user’s hand and body serve as primary obstacles in obscuring the radiation coverage of the UE antennas with the size of the hand being large relative to the UE. We also report measurementdriven studies of loss due to selfblockage with a GHz experimental prototype. Our studies show that in contrast to prior reports of to dB blockage losses, even a hard hand grip with formfactor UEs could see significantly lower losses in the range of to dB (with a median loss of dB). These discrepancies arise because of the beamwidth differences between prior studies that are based on horn antenna measurements (much smaller beamwidths) relative to formfactor phased arrays (that could have larger beamwidths). These relative beamwidth differences allow much higher signal energies to be radiated/captured in formfactor UEs. In the more optimistic scenario of looser hand grips with gap between fingers, some antenna elements can radiate/capture signal energy through the air gaps leading to even further reduced blockage losses.
We also propose a simulation methodology for capturing the impact of dynamic (human and vehicular) blockers in the vicinity of the UE. The spatial/angular coverage lost is studied and the DKED model is used to estimate the loss due to the blockers. Comparisons with measurement data of the blockage loss with human blockers in an indoor office setting shows a reasonable firstorder fit with the data from the proposed simulation methodology. Given the difficulties in obtaining measurementbased estimates for loss with vehicular blockers in outdoor deployments, the proposed simulation framework could serve as a reasonable substitute for system level studies. In this context, the proposed simulation methodology as well as the statistical model generated from the data has already had some farreaching impact on channel modeling at 3GPP. In particular, Option A of the blockage model in the 3GPP Rel. 14 channel modeling document [6, pp. 5355] is based on ideas expounded in this paper.
Another contribution of this work is in terms of understanding the timescales at which blockage events and their disruptions can be seen to impact the UE side. Based on experiments with the GHz prototype, we show that these blockage events can be attributed to physical movements and the timescales at which these disruptions happen are on the order of a few ms (or more). These estimates offer insights into the feasibility of mitigation mechanisms to address blockage impairments. Given a rich channel environment, network densification (as seen from the basestation perspective) or the use of multiple subarrays (as seen from the UE perspective) can help given that the 5GNR standard allows subms (or a few ms) effective latencies in beam/subarray switching. In the case of a sparse channel environment (e.g., rural settings, highways, etc.), mitigation mechanisms could be fall back on to legacy carriers or proprietary codebook enhancements (on top of the steadystate beamforming codebooks used at the UE end). The design of PHY layer enhancements to realize these ways forward could be the subject of interesting future work in this area.
a Parameter Learning for a Gaussian Mixture Model
Let and denote the density functions of the two Gaussians in the mixture corresponding to parameters . That is,
with the mixture model corresponding to a mixture probability given as
We use to denote the log likelihood function for the data (denoted as ) and an unobserved latent variable, . The observation comes from Model 1 (captured by ) if , or from Model 2 (captured by ) if . This log likelihood function is given as
where denotes . Since we do not know , we replace it with its conditional expectation:
and perform the Expectation Maximization algorithm for learning the parameters [38, 8.5.1, pp. 272275 and Algorithm 8.1]. To keep this paper selfcontained, we provide the parameter learning algorithm corresponding to stopping at iterations below. The choice of is determined by an a priori choice of based on a stopping criterion.
∎
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