Effect of Outdated CSI on Handover Decisions in Dense Networks

Abstract

We consider an ultra-dense network (UDN) where each mobile is attached to the access point (AP) which provides the best reference signal received power (RSRP) according to both path-loss and small scale fading. In order to evaluate the effect of outdated channel state information (CSI) brought by feedback delay on handover decisions, we first derive the estimated and accurate handover probability according to outdated and perfect CSI respectively. Further, two metrics are proposed to measure the handover failure, i.e., false handover probability (FHP) and miss handover probability (MHP). Simulations show that in sparse or ultra-dense networks, the imperfection of outdated CSI is acceptable for handover decisions. But in between, i.e., dense networks (medium-size networks), handover decisions are very sensitive to the user velocity and CSI imperfection.

Full text

1089-7798 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LCOMM.2017.2720162, IEEE
Communications Letters
1
Effect of Outdated CSI on Handover Decisions in
Dense Networks
Yinglei Teng, Mengting Liu, and Mei Song
Abstract—We consider an ultra-dense network (UDN) where
each mobile is attached to the access point (AP) which provides
the best reference signal received power (RSRP) according to
both path-loss and small scale fading. In order to evaluate the
effect of outdated channel state information (CSI) brought by
feedback delay on handover decisions, we first derive the esti-
mated and accurate handover probability according to outdated
and perfect CSI respectively. Further, two metrics are proposed
to measure the handover failure, i.e., false handover probability
(FHP) and miss handover probability (MHP). Simulations show
that in sparse or ultra-dense networks, the imperfection of out-
dated CSI is acceptable for handover decisions. But in between,
i.e., dense networks (medium-size networks), handover decisions
are very sensitive to the user velocity and CSI imperfection.
Index Terms—outdated CSI, handover failure, ultra-dense
network, stochastic geometry.
I. INT ROD UC TI ON
TO meet the 1000-fold data traffic demand growth foreseen
in the 5th Generation (5G) networks, increasing the num-
ber of access points (APs) is deemed as a promising solution,
thus resulting in ultra-dense networks (UDNs). Meanwhile, the
cell coverage shrinks with the densification of APs, which also
means that the mobile users would experience more frequent
handoffs [1]. Thereby, mobility management becomes vital for
dense network wherein the handover decision plays a key role
on the guarantee of quality of service (QoS) for mobile users.
Over the last years, considerable efforts have been devoted
to the study of handover performance in UDNs utilizing
stochastic geometry methods. Most of these works which as-
sume that the mobile user connects to the nearest AP evaluate
handover probability (HP) by only considering the path-loss
effect [2]–[4]. Besides, only few works take the effect of small
scale fading into consideration. In [5], with a more general
model including both slow fading (log-normal shadowing) and
fast fading (Rayleigh fading), the mobile in the network is
assumed to be served by the AP providing the instantaneous
strongest mean signal power. However, one defect of [5] is that
the effect of channel imperfection is ignored. Due to the users’
mobility, outdated channel state information (CSI) caused by
feedback delay has become a non-negligible impact on the
accuracy of handover decisions. By now, the previous work
is limited to mobility performance, and there are potential
Y. L. Teng, M. T. Liu, and M. Song are with the Beijing Key Labora-
tory of Space-ground Interconnection and Convergence, Beijing University
of Posts and Telecommunications (BUPT), Beijing, China, 100876 (email:
lilytengtt@gmail.com, liumengting@bupt.edu.cn, songm@bupt.edu.cn). This
work was supported in part by the National Natural Science Foundation of
China under Grant No. 61427801 and No. 61302081, and the 863 Project
under Grant No. 2014AA01A701.
gaps for the study of the effect of channel imperfection
on handover decisions. Is the handover decision using just
large scale fading or perfect/outdated CSI trustable under
different mobility cases or diverse density network? Motivated
by these questions, we investigate the effect of outdated CSI on
handover decisions in UDN using stochastic geometry theory.
However, several technological challenges are to be addressed:
(i) Typical HP analysis is achieved using stochastic geometry
and Euclidean geometry theory. However, the introduction of
small scale fading would change the tractable Poisson-Voronoi
topology and make the theoretical analysis far from easy to
handle; (ii) The impact of outdated CSI on HP and handover
failure probability needs to be characterized; (iii) New metrics
should be defined to effectively measure the effect of channel
imperfection on handover decisions.
In this letter, UDNs are modeled as a homogeneous Poisson
point process (HPPP). By applying the displacement theorem,
the aggregated small scale and large scale fading can be
described by a modified HPPP. Meanwhile, Jakes’ scattering
model is utilized to address the outdated CSI. Finally, to mea-
sure the handover failure probability brought by the channel
imperfection, we propose two metrics including false handover
probability (FHP) and miss handover probability (MHP).
II. SY ST EM MO DE L
A. Network Model
In this letter, a single-tier UDN is considered where the
M-antenna APs and single-antenna users are modeled by
two independent HPPPs (Φoand Φu) with density λoand
λurespectively. In this letter, we adopt the transmit antenna
selection (TAS) scheme, i.e., the mobile user always selects
the best antenna with the highest channel gain. And we assume
that each AP transmits at a constant power P. For each mobile
user zi∈Φu, i = 0,1,2,· · · , it connects to the AP which
provided the best reference signal received power (RSRP).
B. Propagation Model
Both large scale and small scale fading are considered in
the propagation model. The large scale effect is denoted by
L(zi) = di(t)−α, where di(t)denotes the distance between
the mobile ziand its serving AP APiat time tand αis the
path-loss exponent. The small scale fading is considered to be
constant during a specific time slot but changes in different
time slots. In this letter, the small scale fading φi,m (t)from
antenna mof APito the mobile user at time tis assumed
as a zero-mean Gaussian random variable with variance µ,
i.e., φi,m (t)∼ CN (0, µ). Thus, the channel gain hi,m (t) =

1089-7798 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LCOMM.2017.2720162, IEEE
Communications Letters
2
|φi,m (t)|2is an exponential random variable with mean µ, i.e.,
hi,m (t)∼exp 1
µ. Suppose the random variables φi,m (t)for
all the APs, antennas and time slots are independent identically
distributed (i.i.d). Then the RSRP (accurate) from antenna m
of APito the mobile ziat time tis
yi,m(t) = hi,m (t)L(zi)P=(hi,m(t))−1
αdi(t)−αP. (1)
Different from the previous works on HP analysis in [2]–[4],
we assume a practical scenario where the feedback CSI from
the APs is delayed and the mobile user makes the handover
decision using outdated CSI. Due to the adoption of TAS
scheme, the mobile user ziselects the best antenna with the
highest channel gain at time texpressed as
Hi(t) = max
m=1,2...M hj,m (t), j = 1,2. . . (2)
Accordingly, the mobile is connected to the AP providing
the best antenna. Then the serving AP transmits useful signals
to the mobile and the RSRP from APiwhich is outdated by
feedback delay and can be denoted as
˜yi(t) = ˜
Hi(t)−1
αdi(t)−α
P. (3)
In (3), due to the short time delay (ms level), the change of
di(t)would be rather small which can be ignored. And ˜
Hi(t)
is τdtime-delayed channel coefficient version of Hi(t). The
correlation between ˜
Hi(t)and Hi(t)can be modeled by the
Jakes’ scattering model which is based on a sum of sinusoids
approach to simulate Rayleigh fading channel [6]. Then we
can obtain the probability distribution function (PDF) of ˜
Hi
(variable tis removed due to the i.i.d. character) as
g˜
H=g˜
H(x)=M
M−1

k=0 M−1
k(−1)
k
ηk
e
−ηk(1+k)x,(4)
where ηk=1
µ(1+k−kρ),ρ= [J0(2πfdτd)]2with J0(•)
denotes the 0th order Bessel function of first kind [9, Eq.
(8.402)]. And fd=f
cvcos ϖindicates the maximum Doppler
frequency with currently used frequency f, electromagnetic
wave propagation velocity c= 3 ×108m/s, the user velocity
v, and the angle between the mobile’s moving direction and
the incident wave direction ϖ(assume ϖ= 0 in this letter).
C. Mobility Model
A simple random walk mobility (RWM) model is utilized
to describe users’ mobility as depicted in Fig. 1(a). Without
loss of generality, we study a typical mobile user z0which
is initially located at the origin O1and connects to APo(the
serving AP) and then shifts to O2after moving a distance v
in unit time at a random angle θ. So vcan also be viewed
as the mobile user velocity. According to the maximal RSRP
association rule, the serving AP is chosen with respect to the
minimal equivalent distance ˜
H−1
αRwhere Ris the distance
between the mobile user and the previous serving AP after
movement. Note that regarding the small scale fading effect,
APois not necessary the nearest AP to the mobile. Specifically,
in Fig. 1(a), H−1
αRis the scaled distance between the user and
its serving AP considering the perfect CSI which is the radius
v
q
1
O
v
q
q
1
O
O
O
O
O
O
O
O
O
O
O
O
O
1
r
R
2
O
1
H R
a
-
1
1
-
1
H R
a
-
o
AP
A
B
(a)
v
q
1
O
2
O
A
B
1
H R
a
-
r
b
j
j
d
S
d
d
S
d
d
v
v
q
q
q
1
1
O
OOOOOO
1
1
2
O
2
v
1
O
O
O
O
O
O
O
O
O
O
O
O
O
O
1
1
1
1
1
H
1
R
-
r
b
b
b
d
d
d
S
(b)
Fig. 1. (a) A mobile user moves from O1to O2(the black solid circles
represent the actual possible positions of the serving AP before and after
movement), (b) An illustration of the calculation of ˜
Sdand Sd.
of the red dash dotted circles. Similarly, ˜
H−1
αRis the scaled
distance considering the outdated CSI and the corresponding
circles are showed by the blue dotted lines.
With respect to the handover protocol, a handover decision
is made once there’s at least one AP (except the serving AP)
can provide a higher RSRP. Thereby, the mobile users always
enjoy the best service during each time slot.
III. HANDOVER FAIL UR E ANALYSIS
To make handover failure tractable, we first derive the
density of the generalized HPPP considering perfect and
outdated CSI respectively. Then estimated and accurate HP
are given according to the outdated and perfect CSI. Further,
we propose FHP and MHP to evaluate the handover failure.
A. Preliminary Analysis
Consider a new process Ξ = ξi=(χi(t)L(zi))
−1, i =
0,1, . . .,χi(t)=hi(t)or ˜
Hi(t)(subscript mis removed due
to the i.i.d. character), where ξidenotes the generalized path-
loss between APiand z0and is indexed in an increasing order,
i.e., ξ0< ξ1< ξ2. . .. Then we have the following theorem.
Theorem 1. Ξis an HPPP with density λ′=λoEχ2
α.
Proof: The proof of theorem 1 is given in Appendix.
Specifically, some special cases are given as follows.
1) when χi(t) = hi(t), i.e., perfect CSI,
λa=λoEhi
2
α=λo∞
0
l2
α1
µe
−l
µdl =λoµ2
αΓ2
α+1.(5)
2) when χi(t) = ˜
Hi(t), i.e., outdated CSI,
λe=λoE˜
H
2
α
i
=λo∞
0l2
αM
M−1

k=0 M−1
k(−1)
k
ηke−ηk(1+k)ldl
=λoM
M−1

k=0 M−1
k(−1)k
1+k[ηk(1+k)]−2
αΓ2
α+1,
(6)
where Γ (•)is the gamma function.
Remark: According to (5) and (6), we can see that an
independent generalized HPPP generates during each time slot.
In this light, the original HPPP Φotransforms into a new HPPP

1089-7798 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LCOMM.2017.2720162, IEEE
Communications Letters
3
Φewith density λe. And ˜
H−1
αdican be regarded as a stretched
(˜
H < 1) or shrunken ( ˜
H > 1) transformation of the distance
di. Similarly, considering perfect CSI, Φowould be displaced
by another new HPPP Φawith density λa.
B. Handover Failure Analysis
1) Estimated/Accurate HP: Before conducting handover
failure analysis, we first give the estimated/accurate HP by
Pe
HO =Pthere is at least one AP in ˜
Sd
=2π
0∞
0∞
01−e
−λo˜
Sdg˜
Hf(r)f(θ)d˜
Hdrdθ, (7)
Pa
HO =P(there is at least one AP in Sd)
=2π
0∞
0∞
01−e
−λoSdf(h)f(r)f(θ)dhdrdθ. (8)
Here, g˜
His given by (4), f(h) = 1
µe−h
µ, h > 0and other
variables in (7) and (8) are explained as follows:
i) the PDF of the moving angle θis f(θ) = 1
2πand the
distance distributions between the mobile and it’s serving AP
is given by f(r) = 2πλere−πλer2. What should be noted is
that λeis the density of the new process Φe.
ii) ˜
Sdin Fig.1 (b) is recognized as a “dangerous area”
because handover happens if there’s any AP in it and the area
of ˜
Sdcan be calculated by
˜
Sd=˜
β+ ˜φ ˜
H−1
αR2−˜
βr2+vr sin ˜
β, (9)
where ˜φ=∠O
1AO
2= sin−1vsin β
˜
H
−1
αRand ˜
β=∠AO
1O
2=
cos−1r2+v2−˜
H−1
αR22vr.
iii) similar to ˜
Sd,Sdwith perfect CSI is given by
Sd=(β+φ)h
−1
αR2−βr2+vr sin β, (10)
where β= cos−1


[r2+v2−(h
−1
αR)2]
2vr 


and φ=sin
−1vsin β
h
−1
αR.
From (7) and (8), we can find that the difficulty of figuring
out the mapping relation between the serving AP and the
corresponding AP in the previous Poisson-Voronoi tessellated
Φodissolves by studying the new process Φe. Handover failure
occurs because of the impact of outdated CSI feedback, which
can be divided into two categories, i.e., false handover and
miss handover. Next, both FHP and MHP are studied.
2) FHP: Concerning FHP, we first give its definition as the
joint probability that no handover occurs using perfect CSI but
handover is to be made based on outdated CSI, which means
that the mobile makes a false handover decision and can be
derived as
p
f=PHO using perfect CSI,HO using outdated CSI
=Pthere′s at least one AP in ˜
Sd−Sd
given that ˜
H<h
=2π
0∞
0∞
0h
01−e
−λo(˜
Sd
−Sd)f˜
H, h
f(r)f(θ)d˜
Hdhdrdθ,
wheref˜
H, h=f˜
H,h (x, y) = 1
(1−ρ)µ2e−x+y
µ(1−ρ)×I02√ρxy
µ(1−ρ)[7, Eq.
(6.2)]. ˜
Sdand Sdare given by (9) and (10).
3) MHP: Likewise, MHP is defined as the joint probability
that handover occurs using perfect CSI but no handover
happens based on outdated CSI. In other words, the mobile
misses the handoff. Therefore, MHP can be derived by
AP Density ( )
10-7 10-6 10-5 10-4 10-3 10-2 10-1
Estimated/Accurate HP
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 , Analytical
, Analytical
, Simulation
, Simulation
Handover Probability of DDHP in [2]
/m2
PHO
a
PHO
e
PHO
a
PHO
e
v = 4, 20, 40, 100m/s
0.23%
1.61%
4.03%
6.70%
5.47%
Fig. 2. Estimated/Accurate HP vs. AP density with different user velocity.
AP Density ( )
10-7 10-6 10-5 10-4 10-3 10-2 10-1
FHP/MHP/Handover Failure Probability
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16 pf , Analytical
pm , Analytical
pe , Analytical
pf , Simulation
pm , Simulation
pe , Simulation
/m2
10-6.32 ~10-3.1/m2
10-6.28 ~10-4.55 /m2
10-6.3~10 -3.69/m2
v=20, 40, 100m/s
(a)
Velocity (m/s)
0 20 40 60 80 100
Handover Failure Probability
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
λo=10-5/m2, Analytical
λo=10-5/m2, Simulation
λo=10-4/m2, Analytical
λo=10-4/m2, Simulation
λo=10-3/m2, Analytical
λo=10-3/m2, Simulation
(b)
Fig. 3. (a) FHP/MHP/Handover failure probability vs. AP density with
different user velocity. (b) Handover failure probability vs. user velocity with
different AP density.
p
m=PHO using perfect CSI,HO using outdated CSI
=Pthere′s at least one AP inSd−˜
Sd
given that ˜
H>h
=2π
0∞
0∞
0˜
H
01−e−λo(Sd
−˜
Sd)f˜
H, h
f(r)f(θ)dhd ˜
Hdrdθ.
Finally, we can calculate the total handover failure proba-
bility pHF by summing FHP and MHP as pHF =pf+pm.
IV. SIM UL ATION RESULTS
In this section, we first verify the accuracy of the derived
theoretical expressions by comparing with simulation results.
Note that simulation results are performed by Monte Carlo
methods. Then we test the effect of mobility on handover
failure probability. For the sake of clarity, the simulation
parameters are listed in TABLE I.
TABLE I
SIM ULATI ON PARAMETERS
Symbol Definition Value
λoThe density of APs 10−7∼10−1/m2
λuThe density of users 5×10
−4/m2
αThe path-loss exponent 4
RThe radius of network coverage 1000m
MThe number of antennas of APs 4
τdThe delay of each channel 8ms
vThe user velocity 0∼100m/s
fCommunication frequency 3×109Hz
µThe variance of Complex Gauss
distribution 0.98
Fig. 2 indicates that the analytical results match the simula-
tions well in depicting the estimated and accurate HP. Besides,
as λoor vincreases, some conclusions can also be observed: 1)
The estimated HP Pe
HO is always a bit higher than the accurate

1089-7798 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LCOMM.2017.2720162, IEEE
Communications Letters
4
one. This can be explained by (5) and (6), which indicates
that the new HPPP Φeis denser than Φa, i.e., λe> λa.
2) The gap between Pe
HO and Pa
HO diminishes with the
increasing AP density or user velocity. Specifically, in the case
of v= 40m/s, the gap decreases from 5.47% to 1.61% when
λoincreases from 10−4/m2to 10−3/m2. Similarly, in the
case of λo= 10−3/m2, this gap drops from 6.70% to 0.23%
when vgrows from 4m/s to 100m/s. 3) In dense networks
(10−5m2<λo<10−3m2) [10], i.e., medium-size networks,
handover probability is very sensitive to velocity shown by
the steep slopes of these curves in Fig. 2. 4) Compared with
the HP of distance-dependent handover protocol (DDHP) in
[2], both the estimated and accurate HP are higher, but they
gradually approach that in [2] with the increasing AP density.
This is because distance dependent fading plays a more and
more dominant role than small scale fading as the network
becomes denser or the user moves faster.
Fig. 3(a) and Fig. 3(b) illustrate the effect of outdated CSI
on handover failure probability pHF comprising both FHP pf
and MHP pm. Two distinct phenomena can be viewed. First,
as shown in Fig. 3(a), there’s a peak phase for FHP/MFP as
well as the total handover failure probability. Specifically, if
we treat the case of pHF >10% as a relative “vulnerable”
region, in the case of v= 20m/s, the “vulnerable” region
is 10−6.32 ∼10−3.1/m2. The reasons behind are that in the
dense network, handover failure is largely affected by both
small fading effect and Doppler effect, while in the sparse
network where the distance based path loss fading dominates,
the handover decision through accurate CSI and estimated CSI
agrees for a very large possibility. However, for UDNs, since
the inter-AP distance is pretty small, ”handover” is always
decided for both accurate and estimated CSI, handover failure
is lowered again. Second, Fig. 3(b) illustrates that pHF first
grows but then declines with the increasing user velocity for
various AP density. This is because when the mobile users
start moving, it would experience a higher handover failure
due to Doppler effect. But when the velocity reaches the
very fast cases, the distance variance begins to dominate and
users are prone to experience a handoff no matter using the
estimated or accurate CSI-based handover scheme. Moreover,
in the decline stage, handover failure probability drops faster
for denser network due to the higher handover probability for
both estimated and accurate CSI cases.
V. CO NC LU SI ON
The effect of outdated CSI on handover decisions in UDNs
is investigated in this letter. Simulations demonstrate that in
sparse or ultra-dense networks, handover failure probability is
rather small but turns higher in dense networks. In other words,
channel imperfection can be tolerant in sparse or ultra-dense
networks. However, in dense networks, handover decisions
are very sensitive to user velocity and CSI imperfection. To
conclude, the observations in this letter provide the theory
evidence suggesting that sophisticated speed-aware handover
protocols need to be studied, especially in dense network
where more accurate CSI is requested for making a handover
decision. However, in sparse or ultra-dense network, the ac-
quisition of CSI becomes loose.
APP EN DE X A: PROO F OF TH EO RE M 1
Let Υ = {zi, χi}∞
i=0 be the marked point process. Since
the marks χi, i = 1,2, . . . are i.i.d, Υis still an HPPP with
intensity λodz ⊗pχ(l)dl. Applying the displacement theorem
[8, theorem 1.3.9], we can get that Ξis an HPPP with intensity
Λ (A) = λoR2⊗Rp((z, l), A)pχ(l)dzdl
=λoR2⊗R1{(lL(z))−1∈A}pχ(l)dzdl, (11)
where p((z, l), A)is the probability kernel for Borel A∈R+.
First, we give the derivation of Λ ((0,T]) when A= (0,T].
Λ ((0,T]) = λoR2⊗R1{(lL(z))−1≤T}pχ(l)dzdl
(a)
=λoR2Fχ(L(z)T)−1dz =λoΦ (T),(12)
where (a) is obtained by assuming Fχ(ε) = P(χ≥ε) =
∞
εpχ(l)dl and we derive
Φ (T)=R2⊗R1{(lL(z))−1≤T}pχ(l)dzdl
(b)
=∞
0pχ(l)2π
0∞
01{r≤(lT )1
α}rdrdθdl
=2π∞
0pχ(l)(lT )1
α
0rdrdl
=πT 2
αEχ2
α,
(13)
where (b) is obtained by plugging L(z)=r−α, z = (r, θ)in (13).
Hence, the intensity of the new process is
λ′=Φ (T)
Φ (T)|χ= 1 λo=Eχ2
αλo.(14)
This concludes the proof.
REF ER EN CE S
[1] H. Kao, et al., “Adaptive Measurement for Energy Efficient Mobility
Management in Ultra-Dense Small Cell Networks,” in Proc. IEEE ICC,
pp. 1–6, July 2016.
[2] S. Sadr and R. Adve, “Handoff rate and coverage analysis in multi-tier
heterogeneous networks,” IEEE Trans. Wireless Commun., vol. 14, no. 5,
pp. 2626–2638, May. 2015.
[3] Y. T. Hong, et al., “Cross-tier handover analyses in small cell networks:
A stochastic geometry approach,” in Proc. IEEE ICC, pp. 3429-3434,
Jun. 2015.
[4] W. Bao and B. Liang, “Stochastic geometric analysis of user mobility in
heterogeneous wireless networks,” IEEE J. Sel. Areas Commun., vol. 33,
no. 10, pp. 2212–2225, Oct. 2015.
[5] T. T. Vu, L. Decreusefond and P. Martins, “An analytical model for eval-
uating outage and handover probability of cellular wireless networks,” in
Proc. Wireless Personal Multimedia Communications (WPMC), pp. 643–
647, Sept. 2012.
[6] N. Ferdinand, D. Benevides da Costa, and M. Latva-aho, “Effects of
outdated csi on the secrecy performance of miso wiretap channels
with transmit antenna selection,” IEEE Commun. Lett., vol. 17, no. 5,
pp. 1822–1834, May. 2013.
[7] M. K. Simon and M. S. Alouini, “Digital communications over fading
channels: A unified approach to performance analysis,” 1st ed., New
York: John Wiley and Sons, 2000.
[8] F. Baccell and B. Blaszczyszyn, “Stochastic Geometry and Wireless
Networks,” Volume I - Theory vol. 3, No 3-4 of Foundations and Trends
in Networking, NoW Publishers, 2009.
[9] I. S. Gradshteyn and I. M. Ryzhik, “Table of integrals,” IEEE Commun.
Mag., 7th ed., New York: Academic, 2007.
[10] M. Ding, et al., “Performance Impact of LoS and NLoS Transmissions
in Dense Cellular Networks,” IEEE Trans. Wireless Commun., vol. 15,
no. 3, pp. 2365–2380, Mar. 2016.