Comparing Capacity Gains of Static and UAV-based Millimeter-Wave Relays in Clustered Deployments
Margarita Gapeyenko†, Vitaly Petrov†, Dmitri Moltchanov†, Shu-ping Yeh?, Nageen Himayat?, and Sergey Andreev†
†Tampere University, Tampere, Finland
?Intel Corporation, Santa Clara, CA, USA
Abstract—The prospective millimeter-wave (mmWave) net- works are envisioned to heavily utilize relay nodes to improve their performance in certain scenarios. In addition to the sta- tionary mmWave relays already considered by 3GPP as one of the main focuses, the community recently started to explore the use of unmanned aerial vehicle (UAV)-based mmWave relays.
These aerial nodes provide greater flexibility in terms of the relay placement in different environments as well as the ability to optimize the deployment height thus maximizing the cell performance. At the same time, the use of UAV-based relays leads to additional deployment complexity and expenditures for the network operators. In this paper, we offer a mathematical framework and a numerical study that allow for comparing the capacity gains brought by the static and the UAV-based mmWave relays in different scenarios. For each of the relay types, we investigate both uniform and clustered deployments of human users in the cell by also taking into account mmWave-specific propagation, blockage, and resource allocation considerations.
Our study reveals that the highest capacity gains when utilizing the UAV-based relays instead of the static ones are observed in clustered deployments (up to 31%), while the performance difference between the UAV-based and the static mmWave relays under a uniform distribution of users is around3%.
Index Terms—5G, New Radio, mmWave, UAV, relay I. INTRODUCTION
The use of the millimeter-wave (mmWave, 30–300GHz) spectrum is one of the major innovations introduced in fifth- generation (5G) wireless networks. The New Radio (NR) access technology designed by 3GPP specifically for 5G opens a large space for novel advanced applications that require high data rates and low latencies [1]. At the same time, the coverage range of a typical mmWave cell is expected to be around100–
200m [2] leading to a dense network deployment to cover wide urban areas. Therefore, the community is now actively exploring different approaches to provide substantial coverage under decreased deployment costs of mmWave infrastructure.
One of the promising solutions in this field is the de- ployment of NR relays, as described by 3GPP in their TR 22.866 [3]. The relay nodes provide a cheaper alternative to fully-functional NR base stations (BSs) to densify the network where appropriate [4]. Currently, the investigations continue towards the integrated access and backhaul solutions (IAB, [5], [6]), so that the backhaul traffic from/to NR relays can be supported by wireless links.
As a further step, the academia and industry are currently investigating the potential use of mobile NR relays to comple- ment static relaying in certain scenarios [7]–[10]. These mobile
relays deployed on cars or unmanned aerial vehicles (UAVs) can be used to support mmWave networks in the situations where the use of static mmWave relays is not feasible or not appropriate. The flying UAV-based mmWave relay nodes should provide additional flexibility for the network operator as: (i) UAV-based relays can be placed at the desired location and height, thus maximizing the target performance indica- tors [11], [12]; and (ii) UAV-based relays can be efficiently (re)deployed following the dynamic fluctuations in the data rate demand (moving crowds, spontaneous events, etc.) [13].
At the same time, the use of UAV-based mmWave relays brings additional design, technological, and regulatory chal- lenges [14]–[16]. First, the weight of the UAV-based mmWave equipment has to be maintained under a certain limit [17].
Then, automated or semi-automated control of flying UAVs must be implemented. Among others, the noise restrictions, safety, and battery lifetime/charging concerns have to be addressed. All of these bring potentially higher capital and operating expenses brought by UAV-based mmWave relays vs. static mmWave relays and thus question the benefits of using UAV-based mmWave relays for the operator.Therefore, a comprehensive study specifically tailored to comparing the performance of a mmWave network when enhanced by either static or UAV-based relays is of a high importance.
The recent studies provide a numerical evaluation of the scenarios where UAV is acting as a BS or a relay. In [18], the authors conducted a mathematical analysis and demonstrated a significant gain in the sum-rate with UAV-BS as compared to the ground BS in the scenario with uniformly distributed user equipments (UEs). Further, in [19], a simulation study revealed the gain in the fifth percentile of spectral efficiency up to 38%
with UAV-BSs acting as relays as compared to the ground BSs without relay support. The work in [20] proposed an optimized UAV trajectory algorithm to maximize the throughput of users uniformly distributed in a cell. The authors in [17] conducted a simulation study and demonstrated throughput gains in the scenario with UAV-based relay vs. a scenario with a number of small cells.
However, to the best of our knowledge, a comprehensive analytical study comparing the projected performance gains of static vs. UAV-based mmWave relays and taking into account the 3GPP propagation and signal blockage models, as well as potentially non-uniform deployment of mmWave human users has not been completed to date.
The contributions of our work are summarized as follows:
• A mathematical framework capable of analyzing the performance gains of static mmWave relays and UAV- based mmWave relays is proposed using the tools of stochastic geometry and probability theory. The frame- work captures both uniform and clustered deployments of human users, 3GPP-ratified mmWave propagation and blockage models, as well as the mmWave radio resource sharing between direct and relay connections.
• The developed framework is then applied to quantify capacity and blockage probability for the considered deployments. It is particularly suited to contrast the performance gains of UAV-based vs. static mmWave relays in different conditions. The presented numerical study allows to identify the situations where the use of UAV-based mmWave relays brings the maximum relative benefits over static relays utilization (e.g., up to 31%
higher capacity).
II. SYSTEM MODEL
1) Deployment: We assume a circular area of interest with radiusRA, see Fig. 1 and Fig. 2. The NR-BS is located at the center of the area at a height ofhA. The human-body blockers form a Poisson Point Process (PPP). The blockers are modeled by cylinders with the density ofλB, the height ofhB and the base radius of rB.
We consider two types of mmWave relays: (i) UAV-based relay and (ii) static relay. The UAV-based relay is located at the heighthD with the possibility to vary both its height and 2D location in the cell. The height of the static relay is hS
with no option to change it or its 2D location.
2) UE Distribution and Relay Locations: We consider two different distributions of the UEs: (i) uniform UEs and (ii) clustered (non-uniform) UEs. The number of UEs in a cell is a Poisson random variable N with the parameterλUπR2A. In clustered UE deployment, a fraction of UEs,(1−K), are grouped around pointClocatedrCdistance away from the cell edge. The circle of radiusrC contains a(1−K)N uniformly distributed UEs. The rest ofKNUEs are uniformly distributed across the cell. Note that when K → 1 the clustered model reduces to a uniformly distributed UE deployment. The height of the UEs is fixed and equals to hU.
In both deployments, the relays are assumed to deliver capacity boosts to the UEs. It has been shown in [21] that for the uniform distribution of UEs, it is especially beneficial to place the relays at the cell edge. In that case, the relays can support the UEs having a low SNR on the link from the NR- BS to the UE. Therefore, we follow [21] and assume that both static and UAV-based relays are located at the cell edge for a uniform deployment of the UEs. Moreover, the projections of both static and UAV-based relays are assumed to be uniformly distributed over the cell edge.
In clustered UE deployment, clusters may appear unex- pectedly making impossible to predict the placement of static relays and deploy it closer to the cluster. Therefore, we assume that the static relay is deployed at the cell edge. In contrast,
UE
Backhaul link NR-BS coverage
UAV-based relay coverage
Access li nk
RA hA
hU
UE NR-BS coverage
Static relay coverage RA
hA
hU
Access li nk
Backhaul link
Fig. 1. Uniform UE deployment.
UE
Backhaul link NR-BS coverage
UAV-based relay coverage
Access link
RA hA
hU
UE NR-BS coverage
Static relay coverage RA
hA
hU
Backhaul link
Access link
rC
C rC
C
β
Fig. 2. Clustered UE deployment.
the UAV-based relay is expected to benefit from its flexible location and should be placed in the center of the cluster.
3) Propagation and Blockage Models: We assume that the system operates in a crowded environment, with humans that may block the propagation path between the NR-BS and the UE or between the relay and the UE. The probability that a link is occluded by a human body follows [22] and is given in Section III.
Following [23], we assume that the received signal power is degraded by 20 dB when any of the human blockers occlude the mmWave link. To model the path loss between the NR-BS and the UE we use 3GPP UMi Street-Canyon model [24] with the blockage enhancements defined as
L(x) =
(32.4 + 21.0 log10d+ 20 log10fc, LoS nB, 52.4 + 21.0 log10d+ 20 log10fc, LoS B, (1) whered=p
x2+ (hA−hU)2 is the 3D distance in meters, fc is the carrier frequency in GHz, and LoS nB/LoS B refers to the non-blocked/blocked LoS, respectively. For the consistency between both static and UAV-based relays the pathloss equation is defined similarly to (1).
4) UE Association: We assume that every UE is asso- ciated with the NR-BS or the relay having the best time- averaged signal-to-noise ratio (SNR). Since the propagation is a monotonously decreasing function of distance, this asso- ciation type is similar to connecting with the nearest node.
Therefore, a UE is associated to the NR-BS if the distance to the NR-BS is smaller than that to the relay.
We thus can identify the zones where the UE is associated with the NR-BS or the relay. For that, we connect the location points of the NR-BS and the relay on a 2D plane and then draw a perpendicular line going through the center of the line, see Fig. 1 and Fig. 2. With that, the initial circle is divided into two zones. All the UEs located in the zone with the NR- BS will be associated with that NR-BS as per the Voronoi tessellation theory [25]. Other UEs left in the zone with the relay will be associated with that relay.
5) Resource Allocation and Backhaul: We assume that there is a total bandwidth of B for all access in the system.
Following [5], the relay to the NR-BS wireless backhaul link is considered to operate in the out-of-band mode. The access resources are divided equally between all the UEs in the cell, that is, irrespective of its association point a UE receivesB/N share of bandwidth. Therefore, as in real-world, the relay will receive resources proportional to the number of its served UEs.
III. ANALYTICAL FRAMEWORK
In this section, we develop a mathematical framework for assessing the mean per UE capacity for static and UAV-based relays. We start with the uniform distribution of UEs within the NR-BS coverage (see Fig. 1) and then extend our approach to the case of the clustered UE deployment (see Fig. 2).
A. Uniform UE Deployment
The UE capacity in the presence of a relay link can be written as
CU = 1−pR
pnB,ACA,nB+ (1−pnB,A)CA,B + +pR pnB,RCR,nB+ (1−pnB,R)CR,B
, (2) where pR is the probability that the UE is connected to the relay, pnB,A and pnB,R are the non-blockage probabilities for the links BS-UE and relay-UE, CA,nB and CA,B are the capacities that a UE receives in non-blocked and blocked states when connected to the NR-BS, CR,nB and CR,B are the capacity that a UE receives in non-blocked and blocked states when connected to the relay.
Note that for the uniform UE deployment, the UAV-based relay is different from the static relay in the ability to vary its height. In what follows, we first consider the capacity derivation for a scenario with the UAV-based relay assistance.
In case of static relays, we follow the same derivation but keep the height of the relay constant.
Taking the expectations of both sides of (2), the mean per UE capacity,E[CU], assumes the following general form E[CU] =(1−pR)(pnB,AE[CA,nB] + (1−pnB,A)E[CA,B])+
pR(pnB,RE[CR,nB] + (1−pnB,R)E[CR,B]). (3)
In what follows, we obtain the unknown terms in (3).
1) Mean Capacity at NR-BS to UE Link: Referring to the Shannon capacity, we may write
CA,nB = B N log2
1 +PR,A,nB(x) N0
, (4)
where PR,A,nB(x) is the NR-BS to UE received power in non-blocked conditions andN0 is the thermal noise.
We determinePR,A,nB(x)as PR,A,nB= 10PU
−LA,nB(√
x2 +(hA−hU)2 )+GA+GU−30
10 , (5)
where LA,nB(p
x2+ (hA−hU)2) is the path loss between the NR-BS and the UE in non-blocked state and PU is UE transmit power.
To produce the mean UE capacity, we need to obtain the capacities of the UE connected to the NR-BS/relay in blocked/non-blocked states. As shown in (4), this capacity is a function of two random variables (RVs), N is the number of UEs, andDA(DR) is the 2D distance from NR-BS to UE (relay-UE).
We first consider the fraction of two RVs, where the first RV is the numeratorC1=Blog2(1 +PR,A,nBN (x)
0 )and the second RV is the number of UEs within the coverage,N. Following [26], we consider the Taylor series expansion around ~µ = (E[C1], E[N])for the fraction of two RVs as
E[CA,nB] = E[C1]
E[N] −Cov(C1, N)
E2[N] +V ar(N)E[C1] E3[N] . (6) Since the considered RVs are independent,Cov(C1, N) = 0. Recalling the properties of PPP, we know thatE[N] =λUS, V ar(N) = λUS, where S = πR2A is the NR-BS coverage area, the capacity in (7) can now be expressed as
E[CA,nB] = E[C1](λUS+ 1)
(λUS)2 . (7)
Hence, to determine E[C1], we need to obtain the prob- ability density function (pdf) of distance between randomly chosen UEs within the coverage of NR-BS, DA. Using the geometrical arguments in Fig. 1,fDA(x)can be written as
2πx
πR2A−R22A(2π/3−sin(2π/3))
, 0< x < RA/2,
2πx−2xarccos(RA2x) πR2A−R
2 A
2 (2π/3−sin(2π/3))
, RA/2< x < RA. (8) Finally, the mean capacities of the UE connected to the NR- BS in non-blocked,E[CA,nB], and blocked,E[CA,B], states are provided below
SλI + 1 Sλ2I
Z RA
0
BfDA(x) log2
1 + PR,A,nB(x) N0
dx, SλI + 1
Sλ2I Z RA
0
BfDA(x) log2
1 + PR,A,B(x) N0
dx. (9) 2) Mean Capacity at Relay-UE Link: The mean capacity at the relay-UE link is derived similarly. We thus sketch these derivations briefly. Particularly, the Shannon capacity at the
E[CU] =Kh
(1−pR)(pnB,AE[CA,nB] + (1−pnB,A)E[CA,B]) +pR(pnB,RE[CR,nB] + (1−pnB,R)E[CR,B])i + (1−K)h
(1−pR,c)(pnB,A,cE[CA,c,nB]+(1−pnB,A,c)E[CA,c,B])+pR,c(pnB,R,cE[CR,c,nB]+(1−pnB,R,c)E[CR,c,B])i . (10)
relay-UE link is CR,nB = B
N log2
1 +PR,R,nB(y) N0
, (11)
while the received power is PR,R,nB = 10PU
−LR,nB(√
y2 +(hD−hU)2 )+GR+GU−30
10 , (12)
where LR,nB(p
y2+ (hD−hU)2) is the path loss between the relay and the UE in non-blocked state.
The pdf of distance from the relay to a randomly chosen UE within the relay coverage, fDR(y)is
2yarccos(2RAy )
R2 A
2 (2π/3−sin(2π/3))
, 0< y < RA/2,
2yarccos(2RAy )−2yarccos(RA2y)
R2 A
2 (2π/3−sin(2π/3))
, RA/2< y < RA. Then, the mean capacities of the relay-UE link in non- blocked and blocked states, E[CR,nB] and E[CR,B], are provided similarly to (9).
An additional unknown that one needs to determine is the probability to be connected to a relay. Recalling the association rule, it is provided by the fraction of the area belonging to the relay assistance and the total area, see Fig. 1, which is
pR= 2π/3−sin(2π/3)
2π . (13)
3) Blockage probability: The remaining unknowns are the blockage probabilities at NR-BS to UE and relay-UE links.
Following [22], the blockage probability as a function of the 2D distance xis
pB(x) = 1−e−2rBλB
h xhB−hU
hA−hU+rBi
. (14)
Accounting for random UE locations and different heights of UE and NR-BS, the blockage probability for the NR-BS to UE link is
pB,A= Z RA
0
fDA(x)
1−e−2rBλB
h xhB−hU
hA−hU+rB
i
dx, (15) while the blockage probability for the relay-UE link is
pB,R= Z RA
0
fDR(y)
1−e−2rBλB
h yhB−hU
hD−hU+rB
i
dy. (16) Finally, the blockage probability for a randomly chosen UE irrespective of the link type is delivered by
pB= (1−pR)pB,A+pRpB,R. (17) B. Clustered UE Deployment
Consider now the clustered UE deployment within the NR- BS coverage area. In this case, a similar procedure is applied
as per above. The key difference here is that now there are two sets of UEs, the UEs uniformly distributed within the area and the UEs clustered inside a smaller circle. To obtain the UE capacity, one needs to find the pdf of distances from NR- BS/relay to UEs in these sets. We first outline the derivation for the UAV-based relay assistance scenario. The static relay is assumed to be uniformly distributed on the cell circumference, which results in different distance from the NR-BS/static relay to the UE. The latter is given in Appendix.
Using the geometrical arguments in Fig. 2, the pdf of distance from the NR-BS to the UE uniformly distributed within the NR-BS coverage area, fDA(x), is given by
2πx πR2A−R22A
2 cos−1RA2−rc
RA −sin 2 cos−1RA2−rc
RA
, x∈(0,RA2−rc),
2πx−2xcos−1
RA−rc 2x
πR2A−R22A
2 cos−1RA2−rc
RA −sin 2 cos−1RA2RA−rc
, x∈(RA2−rc, RA).
Similarly, the pdf of distance from the NR-BS to the UEs (connected to the NR-BS) in the cluster,fDA,c(x), is
2xcos−1 (x2 +(RA−rc)2−r2 c) 2x(RA−rc) r2
c 2
2 cos−1RA−rc
2rc −sin 2 cos−1RA−rc
2rc
,x∈(RA−2rc,RA2−rc),
2xcos−1 (x2 +(RA−rc)2−r2 c)
2x(RA−rc) −2xcos−1RA2x−rc
r2 c 2
2 cos−1RA−rc
2rc −sin 2 cos−1RA2rc−rc, x∈(RA2−rc, rc).
The remaining pdf of distances from UAV-based relay to UE uniformly distributed within the UAV-based relay cov- erage, fDR(y), and from UAV-based relay to UE uniformly distributed in the cluster and connected to the UAV-based relay, fDR,c(y), are provided by
2πy
R2 A 2
2 cos−1RA2−rc
RA −sin 2 cos−1RA2RA−rc, y∈(0,RA2−rc),
2πy−2ycos−1RA2y−rc
R2 A 2
2 cos−1RA2−rc
RA −sin 2 cos−1RA2RA−rc
, y∈(RA2−rc, rc),
2y
h
π−cos−1RA2y−rc−π−cos−1y2+(RA−rc)2−R2Ai
R2 A 2
2 cos−1RA2−rc
RA −sin 2 cos−1RA2−rc
RA
,y∈(rc,RA),
2πy πr2c−r2c2
2 cos−1RA−rc
2rc −sin 2 cos−1RA2rc−rc, y∈(0,RA2−rc),
2πy−2ycos−1RA2y−rc πr2c−r2c2
2 cos−1RA−rc
2rc −sin 2 cos−1RA2rc−rc, y∈(RA2−rc, rc).
The mean UE capacities at NR-BS to UE and UAV-based relay-UE links in blocked and non-blocked states are then obtained similarly to (9) by substituting the appropriate pdfs.
Similarly to the uniform deployment of the UEs, we also
obtain the probability for the UE to be associated with a UAV- based relay for the part of UEs uniformly distributed within the NR-BS coverage area
pR= 2 cos−1 R2RA−rc
A
−sin 2 cos−1R2RA−rc
A
2π . (18)
While for the UEs distributed inside the cluster, the probability to be associated with a UAV-based relay is obtained as follows
pR,c= 2 cos−1 RA2r−rc
C
−sin 2 cos−1RA2r−rc
C
2π . (19)
Finally, the mean UE capacity is provided in (10), where (1−K)is the fraction of clustered UEs.
IV. NUMERICAL RESULTS
In this section, a numerical comparison between the UAV- based and the static relay assistance is conducted for two representative scenarios: (i) UEs are uniformly distributed within the cell and (ii) part of the UEs are clustered around the pointCas shown in Fig. 2. The proposed analytical framework outlined in Section III is employed to derive the metrics of interest. The default system parameters are provided in Table I.
An attractive feature of UAV-based relays is their ability to adjust the height, thus mitigating the effect of blockage. Hence, we start by assessing the blockage probability for the two considered relay types, under various deployment and system parameters, as demonstrated in Fig. 3. First, we compare our analysis with those obtained via Monte Carlo simulations and observe a clear match for the blockage probability illustrated in Fig. 3(a). Then, analyzing the effect of the relay height shown in Fig. 3(a) for λB = 1, we observe that for both scenarios an increased height of the UAV-based relays allows to reduce the blockage probability. This implies that the UE spends more time in non-blocked conditions. However, as one may observe, the benefits of UAV-based relays are much more visible in the scenario with clustered UEs, where they reach 21% as compared to static conditions for the UAV height of20m and constant height of 10 m for the static relay; they continue to grow further up to a plateau at approximately 0.27 for the chosen set of system parameters. The corresponding gain for the uniform deployment is only 8% for the UAV height of 30m (maximum mean UE capacity, see Fig. 4(a)) and constant height of 10 m for the static relay.
TABLE I
BASELINE SYSTEM PARAMETERS
Parameter Value
Height of NR-BS,hA 10m
Height of static relay,hS 10m
Height of UE,hU 1.5m
Height of a blocker,hB 1.7m
Radius of a blocker,dm 0.2m
Density of blockers,λB 1per m2
Density of UEs 0.0004per m2
Radius of cluster,rC 25m
Radius of cell,RA 150m
Cluster coefficient,K 0.5
Frequency,fc 28GHz
Bandwidth,B 1GHz
UE transmit power,PU 23dBm
After identifying the positive effects of UAV-based relays in non-uniform deployments, we now proceed with understand- ing the impact of the degree of UE clusterization within the NR-BS coverage as captured by the cluster coefficient, K, on the blockage probability as shown in Fig. 3(b). We keep the density of blockers equal to1, while the UAV-based relay height is 20 m, leading to the maximum mean UE capacity (see Fig. 4(a)). Here, observe that the gains of using UAV-based relays are visible even for the slightly clustered environment, where90% of users remain uniformly distributed within the cell. In these conditions, the blockage probability decreases by approximately0.06(from0.53to0.47). By increasing the number of clustered users, the blockage probability decreases linearly by reaching approximately28%when90%of the UEs are clustered. The latter two effects are explained by the fact that more UEs become associated with the UAV-based relay and the average distance between a serving node (NR-BS or UAV-based relay) and the UE decreases.
Assessing the effect of blocker density as illustrated in Fig. 3(c), we also observe that the clustered scenario is characterized by higher gains in terms of the blockage proba- bility. Particularly, for0.9blockers per square meter the gains are only 9% for the uniform UE deployment and improve up to 22% for the clustered deployment with K = 0.5.
Moreover, the benefits of using the UAV relay grow with increased blocker density for both uniform and non-uniform deployments. This effect is due to improved radio channel quality for the UEs by adjusting the height of the UAV to its optimum,hD = 20 m for the clustered UE andhD = 30 m for the uniform UE deployment, as illustrated in Fig. 4(a).
We continue with a comparison of the mean UE capacity as depicted in Fig. 4 by varying the height of the UAV, the density of blockers, and the cluster coefficient. The analytical mean UE capacity is compared with the one obtained through exten- sive Monte Carlo simulations and demonstrates a clear match with those (see Fig. 4(a)). Then, in Fig. 4(a), one may notice a clear benefit from the UAV assistance in comparison with the static relay setup in the scenario with clustered UEs (18%for the same UAV and static relay height of 10m) for λB = 1.
This is due to the UAV ability to change its 2D distance. For the scenario with the uniformly distributed UEs, the associated gain is significantly smaller. When increasing the height of the relay, the capacity is affected by two factors: (i) reduction in blockage probability and (ii) higher, on average, distance to the serving node. The latter negatively affects the achieved capacity and is mainly responsible for negligible gains for the uniform UE deployment. In the clustered scenario, the former factor dominates and thus the capacity increases as compared to the case of static relays. As one may observe, for a given set of system parameters, there is an optimal UAV height that maximizes the UE capacity in both UE deployment types, which can be obtained by using the proposed methodology.
As the height increases further, the propagation losses start to affect the capacity more heavily and the UE capacity drops.
Analyzing Fig. 4(a) further and performing a cross- deployment comparison, we may also conclude that only a
0 20 40 60 80 100 Height of UAV, [m]
0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
Blockage probability
Simulator
Decreased by 21%
Decreased by 8%
UAV-based relay, uniform UEs Static relay, uniform UEs Static relay, clustered UEs UAV-based relay, clustered UEs
(a) As a function of UAV height
0 0.2 0.4 0.6 0.8 1
Fraction of UEs outside the cluster 0.2
0.25 0.3 0.35 0.4 0.45 0.5 0.55
Blockage probability
UAV-based relay, clustered UEs Static relay, clustered UEs Decreased
by 28%
Decreased by 9%
(b) As a function of cluster coefficient
0 0.2 0.4 0.6 0.8 1
Density of blockers, [1/m2] 0
0.1 0.2 0.3 0.4 0.5 0.6
Blockage probability UAV-based relay, clustered UEs
Static relay, clustered UEs UAV-based relay, uniform UEs Static relay, uniform UEs
Decreased by 9%
Decreased by 22%
(c) As a function of blocker density Fig. 3. Blockage probability as a function of main parameters.
0 20 40 60 80 100
Height of UAV, [m]
280 300 320 340 360 380 400
Mean UE capacity, [Mbit/s]
Simulator
UAV-based relay, clustered UEs Static relay, clustered UEs UAV-based relay, uniform UEs Static relay, uniform UEs
3%
18%
23%
30 m 20 m
(a) As a function of UAV height
0 0.2 0.4 0.6 0.8 1
Fraction of UEs outside the cluster 300
350 400 450
Mean UE capacity, [Mbit/s]
UAV-based relay, clustered UEs Static relay, clustered UEs
Gain: 31%
90% of UEs are in cluster
Gain: 8%
10% of UEs are in cluster
(b) As a function of cluster coefficient
0 0.2 0.4 0.6 0.8 1
Density of blockers, [1/m2] 300
350 400 450 500
Mean UE capacity, [Mbit/s]
UAV-based relay, clustered UEs Static relay, clustered UEs UAV-based relay, uniform UEs Static relay, uniform UEs
3%
22%
11%
(c) As a function of blocker density Fig. 4. Mean UE capacity as a function of main parameters.
small fraction of gain is due to the varying height of the UAV- based relay, while most of the benefits come from adapting the position of the UAV-based relays with respect to the cluster location. The ultimate reason is that the latter positively affects both the blockage probability and the distance to the serving node, while the former is associated with a negative effect due to the increased distance to the UAV-based relay.
We now proceed by characterizing the extent of the positive effect of clusterization as captured by the cluster coefficient, K, on the mean UE capacity illustrated in Fig. 4(b). As one may observe, the gains of the UAV-based relay increase linearly as the fraction of clustered UEs grows (λB = 1, hD = 20 m). An improvement in the mean UE capacity reaches450 Mbit/s (31%) for a highly clustered environment with only 10% of the UEs uniformly distributed within the NR-BS coverage. On the other hand, it is merely 8% when only10%of the UEs are clustered, thus making the utilization of UAV-based relaying less attractive.
Finally, Fig. 4(c) illustrates the impact of blocker density on the mean UE capacity. We observe that the benefit of using UAV-based relays is minimal across the considered range of blocker densities for the uniform UE distribution. For the clustered UE deployment withK= 0.5, the gain is substantial for all the blocker densities and improves from 11% to 22%
in extremely crowded conditions. This is explained by the significantly enhanced SNR as a result of the reduction in the
blockage probability and smaller, on average, distance between the relay and the UEs.
V. CONCLUSIONS
In this paper, we investigate the capacity improvements in mmWave communication systems brought by static mmWave relays vs. UAV-based mmWave relays. We particularly focus on two representative scenarios: (i) uniform distribution of mmWave UEs within a cell and (ii) clustered deployment of mmWave UEs within a cell. We develop a mathematical framework capable of capturing the features of both static and UAV-based mmWave relaying as well as different UE deployments. The contributed methodology is then applied to estimate the capacity gains brought by the mmWave relay nodes in each of the considered setups.
Our numerical study particularly highlights that: (i) a UAV- based mmWave relay provides an incremental (3%of capacity improvement) gain over a static mmWave relay when serving the cell-edge users in uniform deployments of UEs; (ii) in contrast, the use of a UAV-based mmWave relay results in up to31%higher user capacity vs. static mmWave relaying when serving clustered UEs; (iii) a notable gain in the clustered deployments is mainly caused by more flexible placement of the UAV-based relay (up to18%gain), while its ability to adapt the height brings the additional5%for the particular deploy- ment parameters. We expect that the contributed framework
and the presented numerical results may assist in appropriate design choices (static mmWave relay vs. UAV-based mmWave relay) across different configurations of the prospective 5G NR networks. The delivered methodology can be further extended for the deployments with multiple relay nodes per cell as well as for other metrics of interest, including outage probability.
APPENDIX
Further we provide a pdf of distance from the NR-BS/static relay to the UE located in the cluster. Recall that the static relay is uniformly distributed on the cell circumference in the clustered UE deployment scenario. Therefore, two different cases occur: (i) the static relay serves a cluster of UEs as well as the UEs uniformly distributed in the cell and (ii) the static relay serves only UEs uniformly distributed in the cell. The case (i) corresponds to the angle β∼ U(0,2π)(see Fig. 2) in a range(cos−1(RRA/2−rC
A−rC ),2π−cos−1(RRA/2−rC
A−rC )), while the case (ii) occurs for all other values of β.
First, we derive the pdf of distance from the NR-BS to the UE in the cluster,fDA,c(x)for the case (i), asfDA,c(x) =
2αx
πr2C, whereα= cos−1x2+(RA−rC)2−r2C 2x(RA−rC)
. Note that the case (i) corresponds to the scenario when the cluster of UEs is not in the coverage of the static relay.
Next, the pdf of distance from the NR-BS to the UE in the cluster, fDA,c(x), for the case (ii) is delivered as
2αx
πr2C−SR, RA−2rC< x < RA/2,
x(2πβ+α−cos−1(RA/2x))
πr2C−SR , RA/2< x < t, (20) whereSR=r2Ccos−1(RA2 −RA2 cos(2π−β)+r rC2 cos(2π−β)
C )andt=
r
R2A
4 +(rCsin(cos−1(RA2 −RA2 cos(2π−β)+r rC2 cos(2π−β)
C )))2.
Finally, the pdf of distance from the static relay to the UE in the cluster, fDR,c(y), for the case (ii) is derived as
2
cos−1 y2 +l
2−r2 C 2yl
x
SR , l−rC < y < RA/2,
y
cos−1y2+l2yl2−r2C
+cos−1RA2y
−cos−1R2A+l2−2(RAlRA−rC)2
SR ,
RA/2< y < t,
(21)
wherel=p
R2A+(RA−rC)2−2RA(RA−rC) cos(2π−β).
We can now obtain the mean UE capacity following (9) and (10) with appropriate pdf of distance and integrate it over the angle β∼ U(0,2π).
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