Analysis of coverage-oriented small base station deployment in heterogeneous cellular networks

Physical Communication 38 (2020) 100908

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Analysis of coverage-oriented small base station deployment in heterogeneous cellular networks ∗

Muhammad Sajid Haroon a , ,1 , Ziaul Haq Abbas b , Fazal Muhammad c ,2 , Ghulam Abbas d ,3 a

Telecommunications and Networking (TeleCoN) Research Lab, GIK Institute of Engineering Sciences and Technology, Topi, 23640, Pakistan Faculty of Electrical Engineering, GIK Institute of Engineering Sciences and Technology, Topi, 23640, Pakistan c Department of Electrical Engineering, City University of Science and Information Technology, Peshawar, 25000, Pakistan d Faculty of Computer Science and Engineering, GIK Institute of Engineering Sciences and Technology, Topi, 23640, Pakistan b

article

info

Article history: Received 8 April 2019 Received in revised form 24 September 2019 Accepted 25 October 2019 Available online 31 October 2019 Keywords: Heterogeneous cellular networks Poisson point process Poisson hole process Stienen’s model Coverage probability Reverse frequency allocation

a b s t r a c t In heterogeneous cellular networks (HetNets), dense small base station deployment (SBSD ) offers a scalable and low-cost mechanism to meet the fifth generation (5G) needs of ubiquitous coverage and high throughput. However, due to high transmit power of macro base station (MBS), small base station (SBS) users experience severe MBS interference (MBS-I), and additionally, SBS coverage is significantly reduced when it is located near MBS. Furthermore, MBS edge users (MBS-EUs) experience signalto-interference ratio (SIR) degradation due to their distant locations. To overcome such limitations, we propose Stienen’s cell based coverage-oriented SBS deployment (CO-SBSD ) model. According to Stienen’s model, SBSD is avoided near MBS due to strong SIR reception from MBS and limited SBS coverage. However, in MBS edge area, SBSD enhances MBS-EUs coverage. Due to locations and density dependencies, performance characterization under Stienen’s model remains a challenging task as compared with the traditional Poisson point process (PPP) based models. Nevertheless, we demonstrate that the performance can be approximated in a tractable manner. Furthermore, we use spectrally efficient and effective interference abating scheme known as reverse frequency allocation (RFA) in conjunction with CO- SBSD , to mitigate MBS-I. Based on stochastic geometry framework, expressions for coverage probabilities are derived. The proposed CO- SBSD results in enhanced coverage performance as opposed to uniform-SBSD model. Moreover, RFA compliment the network performance gain by abating interference. Analytical and simulation results show that the proposed CO-SBSD , using Stienen’s model along with RFA employment, outperforms all other methods. © 2019 Elsevier B.V. All rights reserved.

1. Introduction 1.1. Motivation Demand for ubiquitous coverage with high data rate is increasing exponentially, which forces the cellular network operators to increase the capacity as well as improve the efficiency of the network. Mobile data usage has increased by 200 percent in recent years [1]. The network operators, thus, seek more advanced and flexible network topologies, different from the traditional planned macro base station (MBS) networks, to achieve the high ∗ Corresponding author. E-mail addresses: [email protected] (M.S. Haroon), [email protected] (Z.H. Abbas), [email protected] (F. Muhammad), [email protected] (G. Abbas). 1 Student Member, IEEE.

2 Member, IEEE. 3 Senior Member, IEEE. https://doi.org/10.1016/j.phycom.2019.100908 1874-4907/© 2019 Elsevier B.V. All rights reserved.

end-user demands [2]. Heterogeneous cellular networks (HetNets), which comprise of energy efficient and low cost densely deployed small base stations (SBSs) in the MBS coverage area, are considered a promising solution for the fifth generation (5G) cellular networks to meet end users high traffic demand. [3– 5]. Traditionally, locations of MBSs, SBSs, and users are uniformly deployed via independent homogeneous Poisson point processes (PPPs) in HetNets [6,7]. However, such a random and user-centric SBS deployment (SBSD ) introduces new network design challenges and, thus, limits the performance gain [7]. In the state-of-the-art, SBS is pre-configured to transmit with low power [8,9], which results in reduced coverage near MBS [10, 11]. More interestingly, increasing the SBS density in uniformSBSD model does not improve the network coverage due to high interference [10]. Therefore, users experience high interference due to dense uniform-SBSD inside the coverage region of MBS and, hence, reduced network performance [12]. Moreover, MBS edge users (MBS-EUs) experience low signal-to-interference ratio (SIR) due to their distant locations [10]. Furthermore, offloaded

2

M.S. Haroon, Z.H. Abbas, F. Muhammad et al. / Physical Communication 38 (2020) 100908

users receive severe MBS interference (MBS-I) due to its high transmit power [13]. To address the aforementioned challenges, we propose Stienen’s cell based coverage-oriented SBSs deployment (CO-SBSD ), where SBSs are assumed to be deployed in the low coverage area to reduce interference and improve SIR in 5G HetNets. MBS-I is one of the performance-limiting factors in HetNets due to high MBS transmit power [2,10]. Hence, a proactive interference mitigation technique is required to reduce MBS-I and enhance network performance. Several useful interference mitigation techniques are studied in the state-of-the-art, such as fractional frequency reuse (FFR) [14], soft fractional frequency reuse (SFFR) [15], and reverse frequency allocation (RFA) [16]. In FFR, the total available bandwidth is split into small sub-bands to reduce interference and, thus, improve coverage. However, this is spectrally inefficient due to limited resource utilization. On the contrary, SFFR is spectrally more efficient than FFR because both SBS and MBS users simultaneously use the same band in different coverage regions. Similarly, RFA is another effective and spectrally efficient method to abate interference, in which SBS and MBS users use sub-carriers in reverse fashion for uplink (UL ) and downlink (DL ) in a multi-region environment. In this work, we use RFA together with CO-SBSD to enhance the network performance gain. 1.2. Related work In [17], MBSs, SBSs, and users are considered to be uniformly distributed using PPPs. The authors perform both converge and rate analyses of k-tier HetNets and compare it with a conventional MBS-tier network. Furthermore, they conclude that adding more tiers and/or cells neither increases nor decreases the coverage probability. The results show enhanced coverage by employing their proposed model. In [18], energy-efficient user association and power allocation in millimeter wave-based HetNets are proposed while focusing on load balancing, energy harvesting, quality of service, and interference. Moreover, the complexity of their proposed model is analyzed and compared with existing systems via simulations. The results show considerable improvement in coverage by employing their proposed model. In [19], nonuniform HetNet (Nu-HetNet)4 model is proposed, where SBSs near MBS are assumed to be muted. However, SBSs remain active in MBS edge area (MBS-EA). The results of their proposed model show better coverage and rate performances as compared with uniform-SBSD . In [20], the authors propose CO-SBSD in MBS coverage region where SBSs can be switched ON/OFF based on their distances from MBS. Their proposed network topology with fewer SBSD enhances performance gain as compared with the uniform-SBSD . In [21], the authors extend the work studied in [20] and analyze the coverage and rate for their proposed network topology. The analysis shows significant improvement in both coverage and user throughput. Similarly, Stienen’s model is studied for the analysis of nonuniform-SBSD [22]. Tractable expressions for coverage probability and rate are derived based on reasonable approximations for their proposed model. The results indicate significant improvement in MBS coverage, while SBS coverage and energy efficiency remain the same. In this paper, we propose the use of Stienen’s cell based CO-SBSD model to improve MBS-EUs coverage. Furthermore, we probabilistically compare both the proposed model and uniform-SBSD model. The proposed model yields better coverage with fewer SBSD due to interference mitigation. 4 The terms CO-SBS , Nu-SBS and Nu-HetNet are used interchangeably in D D this paper.

A wide range of studies is available in the literature for spectrum allocation techniques including FFR and SFFR. In [23], SFR is analyzed with both uniform and nonuniform-SBSD (Nu-SBSD ). Expressions for coverage probability of their proposed model are derived. The result shows Nu-SBSD with SFR result in better coverage due to reduced interference. In [24], analytical models for FFR and SFR, based on PPP, are proposed. Furthermore, tractable expressions for the considered performance metrics in their proposed models are derived. The results show that SFR is spectrally more efficient, whereas FFR provides the highest gains in the lowest average SIR scenario. In [25], variants of RFA are proposed with improved network performance gain as compared with other schemes. Based on the RFA ability to effectively mitigate intra-tier interference, we use CO-SBSD in conjunction with RFA employment. 1.3. Approach and contributions In the state-of-the-art, locations of MBSs, SBSs, and users are modeled as randomly deployed points in a 2-dimensional plane by using stochastic geometry framework [21,26]. When compared with realistic networks, modeling of MBSs, SBSs and users locations using PPPs is as accurate as traditional grid model [26]. Moreover, stochastic geometry provides more tractable and accurate analytical results for coverage and throughput analysis [27]. In this work, we show the impact of CO-SBSD using Stienen’s model in contrast with uniform-SBSD model, assuming two-tier HetNets. In addition, we employ RFA to mitigate MBS-I and further improve network efficiency. Furthermore, coverage probability expressions for the considered models are derived. According to Stienen’s model, the available MBS coverage region, AM , is divided into two non-contiguous ⋃regions,g center region, AcM , and outer region, AoM , s.t., AM = g ∈(c ,o) AM . SBSs are assumed to be deployed only in AoM using Poisson hole process (PHP), while locations of MBSs and users are modeled using PPP, as shown in Fig. 1. Here, a circular disk around the MBS represents Stienen’s cell. MBS-AUs and SBS-AUs in the figure denote the MBS associated users and SBS associated users, respectively. Due to location and density dependencies, performance characterization under Stienen’s model remains a challenging task as compared with the traditional PPP-based analysis [28]. The performance of the proposed model is, however, approximated in a tractable manner. Furthermore, to model a more realistic network, AcM around MBS is taken with a random radius. Additionally, in this paper, we use the RFA in conjunction with CO-SBSD to abate inter-cell-interference. According to RFA, SBS-AUs and MBS-AUs, use sub-carriers in reverse fashion for uplink (UL ) and downlink (DL ) in a multi-region environment. Therefore, CO-SBSD along with RFA employment reduces network interference due to efficient spectrum utilization and avoidance of SBS distribution near MBS. The main contributions of this paper are given as follows: (1) Ultra-densification in uniform-SBSD gives rise to insensible coverage improvement. Therefore, more SBSD results in reduced coverage due to increased interference. We propose CO-SBSD , where SBSs are deployed in the MBS-EA while SBSD near MBSs is avoided. The proposed set-up leads to improved MBS-EUs coverage due to reduced interference with fewer SBS requirement. (2) Due to location and density dependencies, performance characterization under Stienen’s model remains a challenging task as compared with the traditional Poisson point process (PPP) based models. Nevertheless, we demonstrate that the performance can be approximated in a tractable manner with the proposed system model consideration.

M.S. Haroon, Z.H. Abbas, F. Muhammad et al. / Physical Communication 38 (2020) 100908 Table 1 Notation summary.

Table 2 Different point processes.

Notation

Description

φM and φS

PPPs of MBSs and SBSs, respectively

φS , φν,M φ˜ S

PPPs of MBS-AUs and SBS-AUs, respectively

βi

SIR threshold of iBS, ∀ i ∈ {M, S}

R◦

Radius of Stienen’s cell

PM , PS

Transmit power of MBS and SBS, respectively

λM , λS , λν,M , λν,S λ˜ S , λ˜ ν,S

MBSs, SBS, MBS-AUs and SBS-AUs, respectively

Pr , i

Received power from iBS, ∀ i ∈ {M, S}

α

3

PHP of SBSs

Point process with repulsion

Point process with zero interaction

Matern hard-core process

Poisson cluster process

Strauss process

SBS and SBS-AUs PHP based densities, respectively

Point process with attraction

PPP

Neyman–Scott process

Perturbed lattice

Matern cluster process

Poisson hole process

Thomas cluster process

Path loss exponent, α > 2

g

g

AM , AS

MBS and SBS coverage regions, s.t., g ∈ {c , o} AcM −1

d1 , d2

Coverage limits for

θ

Angle between R◦ ∆

|h|

Rayleigh fading gain

DL , UL

Downlink and uplink

and

AoM ,

respectively

and rM

rj , rk

User distances from jth- and kth-tiers

SIRi

SIR received from iBS, ∀ i ∈ {M, S}

UAc

Typical user located in AcM

UAo

Typical user located in AoM

rM

Distance between the U and MBS rM Ratio of rM to R◦ , i.e., ψ = R◦

M M

ψ

2. System model

ϱ

Denote the Stienen’s cell based CO-SBSD

ζ

Denote the uniform-SBSD

∗

Denote the RFA employment

(3) In HetNets, a fraction of MBS-AUs are offloaded to SBSs in order to balance the load across the network and increase throughput. However, offloaded SBS-AUs experience low SIR due to strong MBS-I. Therefore, RFA along with CO-SBSD is considered in order to reduce interference and to efficiently utilize the available radio resources. Furthermore, we characterize coverage probability against SIR threshold, densities of MBSs, SBSs, MBS-AUs, and SBSAUs. Our results demonstrate that the proposed model improves MBS-EU performance by interference mitigation and optimal SBSD . (4) Expressions for coverage probabilities are derived while assuming the following network scenarios: (i) uniform-SBSD with RFA, (ii) uniform-SBSD without RFA, (iii) CO-SBSD model with RFA, and (iv) CO-SBSD model without RFA. Moreover, analysis is performed on typical user5 the U located, (i) inside Stienen’s cell and, (ii) outside Stienen’s cell. Furthermore, based on the expressions of coverage probabilities, analytical and simulation results are drawn and are validated through simulation. 1.4. Organization of the paper and notations The rest of the paper is organized as follows. In Section 2, we present the system model. In Section 3, coverage probabilities of the proposed model are derived. Numerical and simulation results with discussion are presented in Section 4. In Section 5, the paper is concluded. The notations used in the paper are listed in Table 1. 5 According to the Slivnyak Theorem, a typical user at origin simplifies and retains the statistical properties of a PPP [2].

This section focuses on the proposed network layout which considers both uniform-SBSD (see Fig. 1(a)) and Stienen’s cell based CO-SBSD (see Fig. 1(b)) models, with and without RFA employment. In uniform-SBSD model, MBSs, SBSs, and users are deployed using PPPs. However, in CO-SBSD using Stienen’s model, MBSs and users are assumed to be uniformly deployed through independent PPPs while SBSs are only distributed outside the Stienen’s cell with radius R◦ (denoted as d1 in case of uniformSBSD model) via PHP. Furthermore, mathematical preliminaries are developed in this section, which will be used for the evaluation of coverage performance in Section 3. 2.1. Network layout with assumptions This paper considers a two-tier HetNet, comprises of MBSand SBS-tiers with densities λM and λS , respectively. According to the uniform SBSD model, MBSs, SBSs, and users are deployed using PPPs φM , φS and φν respectively. However, in CO-SBSD using Stienen’s model, MBSs and users are uniformly deployed through independent PPPs φM and φν , respectively, while SBSs are deployed using PHPs φ˜ S . The U is considered to be located at the origin in accordance with Slivnyak Theorem. Probability density function (PDF) of the U located at (distance )rM from 2 , where serving MBS is given by frM (rM ) = 2πλM rM exp −πλM rM rM > 0 [5]. According to Stienen’s cell based CO-SBSD , SBSs are assumed to be deployed using Poisson hole process (PHP) (see Definition 1 below). Classification of different point processes are indicated in Table 2 [2]. The network is considered to be interference limited and therefore the effect of noise is ignored. We consider a fully loaded network, where all the cells have at least one user associated with them. αM and αS are the path loss exponents for MBS and SBS, respectively, s.t., αM = αS = α due to outdoor model consideration. Although different path loss exponents for MBS and SBS can be adopted to match real deployments scenarios [29,30], however, in this paper, identical path loss exponents are assumed for the sake of tractability of the numerical analysis [22,31]. We also assume a fully loaded HetNet,6 where the BSs are in always-transmitting state and, thus, suitable for always-full-buffer scenarios [13,35]. |h| is the power gain of Rayleigh fading assumption, i.e., |h| ∼ exp (1). User association follows maximum long term average received power7 [3]. R◦ is the radius of Stienen’s cell around MBS and is equal to half of the distance from closest interfering MBS as shown in Fig. 1(b). R◦ ∆−1 denotes the distance between the two 6 Load-aware network modeling, such as those discussed in [32–34], can also be considered, however, it will increase the analytical complexity. 7 Maximum received power averaged for a longer duration of time.

4

M.S. Haroon, Z.H. Abbas, F. Muhammad et al. / Physical Communication 38 (2020) 100908

Fig. 1. Two-tier HetNet model, where φM , φS , φν,M and φν,S are the PPPs of MBSs, SBSs, MBS-AUs and SBS-AUs, (represented by dots, triangles, pentagrams and asterisks in Fig. 1a) respectively. Similarly, φ˜ S is a PHP of SBSs (represented by triangles in Fig. 1b). The analysis are performed on the U while considering it inside and outside the Stienen’s cell.

nearest MBSs where ∆ = 1/2. Hence, PDF of R◦ with respect to its closest neighbor can be obtained as fR◦ (R◦ ) = 2π λM R◦ ∆−2 exp −πλM (R◦ /∆)2 .

(

)

(1)

Lemma 1. Under Stienen’s cell based CO-SBSD model assumption in two-tier HetNet, the effective density of SBSs is denoted as λS p, where p = 1 + ∆2

(

)−1

.

(2)

Proof. According to PHP, the proposed model considers exclusion area with radius R◦ around MBS. Moreover, for each point j ∈ ψM , ⋂ all the points of ψS A (j, R◦ ) are removed, where A is the area around jth MBS with radius R◦ . In the proposed model, effective 2 intensity of SBS-tier is given as, λS p, where p = e−λM π R◦ [36]. Now as R◦ is a random variable in line model, the [ with2Stienen’s ] value of p is transformed to p = ER◦ e−λM π R◦ . Finally, (2) can be obtained by taking expected value of the PDF found in (1).

■

Definition 1 (Poisson Hole Process). Let φ1 , φ2 denote the independent uniform PPPs with intensities λ1 and λ2 , respectively. Further, let

Ξ≜

⋃ {x ∈ φ1 : b(x, r)}

(3)

be the union of all disks of radius r centered at a point of φ1 . The Poisson hole process is defined as

φ ≜ φ 2 \Ξ .

(4)

In the Poisson hole process, each point in φ1 carves out a hole of radius r from φ2 .

Fig. 2. RFA model in two-tier HetNet.

circular disks around MBSs can be constructed with a radius equal to half of the distance between the center of MBS and its closest neighbor. For this particular set-up, analysis is performed on the U, which is assumed to be located inside or outside the disk around MBS. Moreover, in Fig. 1(b), D is the distance between the U and its closest neighbor interfering MBS, R◦ ∆−1 is the distance between two closest interfering MBSs, while rM = φ R◦ denotes the distance between the U and the associated MBS. Moreover, we use RFA as an interference mitigation technique together with CO-SBSD to further improve the network performance.

2.2. Stienen’s cell based coverage-oriented SBS deployment Stienen’s cell based CO-SBSD is one of the favorable choices to reduce network interference and, thus, enhance coverage. Hence, the proposed set-up is intended to improve MBS-EU performance with smaller SBSD in the available region. In this paper, we use Stienen’s cell based CO-SBSD strategy, where SBSs are assumed to be deployed outside the circular disk of radius R◦ around MBS using PHP as shown in Fig. 1(b). It can be noted that radii of circular disks around MBSs are assumed to be random. Moreover, these

2.3. Reverse frequency allocation

Traditional cellular networks are based on frequency division duplex to mitigate interference in the network [2]. However, HetNets use co-channel deployment to obtain high throughput. This, however, results in increased interference between different tiers of base stations (BS), if both tiers operate at the same time.

M.S. Haroon, Z.H. Abbas, F. Muhammad et al. / Physical Communication 38 (2020) 100908

Improved spectral efficiency8 is obtained by using separate subbands for both UL and DL . Therefore, in our proposed model, we use RFA to mitigate interference and increase spectral efficiency. In RFA, different sub-bands between SBSs and MBS are used in g AM ∀ g ∈ (c , o) in a complementary fashion as shown in Fig. 2. In Fig. 2, according to RFA, the total allocated frequency, F , is divided into two sub-bands, i.e., F1 and F2 , such that F = ⋃ z ∈(1,2) Fz . Here, F1 and F2 denote the sub-bands of MBS to be used in AcM and in AoM , respectively. Sub-bands F1 and F2 are further divided into UL and DL sub-carriers and are modeled as F1 = F1,UL + F1,DL and F2 = F2,UL + F2,DL , respectively. The sub-bands, F1 and F2 , of the MBS are used as the frequency sub-bands, F1′ and F2′ , for the SBSs but in reverse directions with corresponding alternate regions, AoS and AcS , respectively. The bands, F1′ and F2′ , for SBSs are further divided into UL and DL sub-carriers and are given as F2′ = F2′ ,U + F2′ ,D and F1′ = F1′ ,U + F1′ ,D , respectively. L L L L RFA based resource partitioning not only enhances the coverage but also reduces interference as there is no dedicated spectrum distribution allocated for SBS transmission. Thus, by employing RFA, the whole MBS frequency spectrum is made available to SBS but in reverse fashion and in alternate regions.

[ = Er , I D L

exp −

UL

i φ ,Ac ,Iφ o ν,τ ,Ai i i

[

= Er , I D L

(

UL i φ ,Ac ,Iφ o ν,τ ,Ai i i

riα βi ( D Pr ,Li

5

D

U

Iφ L,Ac + Iφ L i

)] ) o

ν,τ ,Ai

i

( ( ))] ⏐⏐ DL UL ⏐ α exp −s Iφ ,Ac + Iφ ,Ao ⏐ r i βi ν,τ i i i s=

D

Pr ,Li

[

( ( )) ( ( )) D U E DL exp −s Iφ L,Ac ×E UL exp −s Iφ L ,Ao ν,τ I I

= Er i

i

φi ,Aci

φν,τ ,Aoi

i

[

]

i

] (s) × LI UL

= Er i L I D L

φi ,Aci

φν,τ ,Aoi

(s) .

(8)

(1) Coverage probability of uniform-SBSD for MBS associated U in AcM with RFA: Coverage probability of uniform-SBSD for MBS ∗ associated U in AcM with RFA employment, PAcoc v,ζ (βM ), is given as M

[ ∗ PAcoc v,ζ M

]

(βM )=ErM LI DL (s) |s=rMα βM×LI UL (s) |s=rMα βM η . φM ,AcM

(9)

φν,S ,AoM

The Laplace transform of the interference from MBS-tier in DL , L DL (s), is obtained as I φM ,AcM

3. Analysis of coverage probability

λM πβM d1(2−α) rMα 2 F1 I α/2 − 1 φM ,AcM ( ( )α ) 2 2 rM × 1, 1 − , 2 − , −βM − α α d1 ( ( )α )) ′ λM πβM y (2−α) rMα 2 2 rM . , 2 − , −βM 2 F1 1, 1 − α/2 − 1 α α y′

(

In this section, tractable expressions for coverage probabilities are derived while assuming the following network scenarios; (i) uniform-SBSD with RFA, (see Section 3.1), (ii) uniform-SBSD without RFA (see Section 3.2), (iii) CO-SBSD model with RFA (see Section 3.3), and (iv) CO-SBSD model without RFA (see Section 3.4). Moreover, analysis is performed on the U located (i) inside Stienen’s cell and (ii) outside Stienen’s cell as shown in Fig. 1(b). 3.1. Coverage probability of uniform-SBSD with RFA In uniform-SBSD scenario, we deploy SBS uniformly throughout the analysis region along with RFA employment to mitigate interference. Uniform-SBSD is shown in Fig. 1(a). Coverage proba∗ bility, PAcoc v,ζ (βi ), for the uniform-SBSD with RFA while considering i

the U in Aci can be written as

(

D

I φν,S ,AoM

( L UL

I φν,S ,AoM

(s) = exp

−

λν,S πη1 βM d(12−α) rMα 2 F1 α/2 − 1

1, 1 − 2/α, 2 − 2/α, −βM η1

×

(5)

(

rM

i

D

Here, βi is the SIR threshold while SIRi L denotes the DL received D SIR from iBS. SIRi L can be expanded as D

SIRi L =

D Pr ,Li D Iφ L,Ac i i

2

|hi | ri

(6)

UL

+ Iφν,τ ,Ao

t ,DL

j∈φi

Pj

∑

t ,UL

k∈φν,τ

Pk

. −α

i

U

o ν,τ ,Ai

M

frM |UAc (rM ) =

|hk |rk

i

, therefore

∗ PAcoc v,ζ i

(βi ) = P ⎝

D Pr ,Li D Iφ L,Ac i i

2

|hi | ri

⎞

−α

U

L + Iφν,τ , Ao

1 − exp −λM π d21

(

)

) .

> βi ⎠

i

frM |UAo (rM ) =

) ( exp −λM π d21

M

(14)

) .

(15)

Coverage probability expression of uniform-SBSD for MBS asso∗ ciated U in AcM for uniform-SBSD with RFA, PAcoc v,ζ (βM ), can be M

written as [10,16] PAcoc v,ζ (βM ) = M

∫

d1 y′

L DL

I φM ,AcM

L UL

I φν,S ,AoM

frM |UAc (rM ) drM .

(16)

M

By substituting (10), (13), and (14) into (16), we obtain PAcoc v,ζ (βM ) ∗

as (11). 8 Information rate that can be transmitted over a given bandwidth in a communication system.

2 2πλM rM exp −λM π rM

(

∗

⎛

2 2πλM rM exp −λM π rM

M

(7)

Here, i ∈ (M, S)BS and τ ∈ (M, S)BS ∀ i ̸ = τ . Due to RFA employment, DL received interference is the sum of DL interference D from MBS-tier in Aci , Iφ L,Ac and UL interference from SBS-tier in Aoi , Iφ L

. (13)

M

Pr ,Li |hi |2 ri −α

|hj |rj−α +

d1

Similaly, UAo associated with MBS located at rM has PDF given by

i

D

= ∑

)α ) )

See Appendix B for the proof of (13). UAc associated with MBS located at rM has PDF given by [16]

(

−α

(10)

See Appendix A for the proof of (10). See Box I for Eqs. (11) and (12). Similarly, the Laplace transform of the interference from SBSAUs in UL , L UL (s), is obtained as

(

)

PAcoc v,ζ (βi ) = P SIRi L > βi . ∗

(s) = exp

L DL

M

(2) Coverage probability of uniform-SBSD for MBS associated U in AoM with RFA: Coverage probability expression of uniform-SBSD

6

M.S. Haroon, Z.H. Abbas, F. Muhammad et al. / Physical Communication 38 (2020) 100908

( ( )α ) ′ λM πβM y (2−α) rMα λM πβM d(12−α) rMα rM J α, −βM − × α/2 − 1 d1 α/2 − 1 1 − exp −λM π d1 y′ )) ( ( )α ) ( ( )α λν,S πη1 βM d(12−α) rMα rM rM 2 rM drM . J α, −βM − J α, −βM η1 − λ M π rM y′ α/2 − 1 d1 ( ( ( )α ) ∫ ∞ λM πβM d(12−α) rMα λν,S πη1 βM d1(2−α) rMα 2π λM rM cov ∗ ( ) PAo ,ζ (βM ) = exp − J α, −β − × M M α/2 − 1 d1 α/2 − 1 exp −λM π d21 d1 ) ( ( )α ) rM 2 − λM π rM rM drM . J α, −βM η1 ∗ PAcoc v,ζ M

2πλM

(βM ) =

∫

(

(

d1

exp

) 2

(11)

(12)

d1

Box I.

for MBS associated U in AoM with RFA, PAcoo v,ζ (βM ), can be obtained M as

[

∗

PAcoo v,ζ (βM ) = ∗

L DL

M

I φM ,AcM

d1

L UL

I φν,S ,AoM

frM |UAo (rM ) drM . ∗ PAcoo v,ζ M

(βM ) can be

M

M

(18) and (19) in Box II, respectively.

3.3. Coverage probability of CO-SBSD with RFA In this section, we derive the coverage probability expression for the MBS associated U, which is assumed to be located inside the Stienen’s cell with RFA employment. Moreover, we consider the employment of RFA in conjunction with CO-SBSD to further mitigate the interference. Under the proposed set-up, expression ∗ for coverage probability, PAcoc v,ϱ (βi ), can be written as

)

> βi ,

M

2 , where rM > 0 [5]. by frM (rM ) = 2πλrM exp −πλrM

Proof.

[ ∗ PAcoc v,ϱ M

(βM ) = ErM ,R◦ LI DL

D Pr ,Li D Iφ L,Ac i i

s=

(24)

D PML

D2 = R2◦ ∆−2 + (ψ R◦ )2 − 2∆−1 ψ R2◦ cos (θ)

∆−2 + ψ 2 − 2∆−1 ψ cos (θ)

(20)

D ≈ R◦

∆−2 + ψ 2 .

(21)

Here, θ is the√ angle between rM and R◦ ∆ as shown in Fig. 1(b). Using D ≈ R◦ ∆−2 + ψ 2 from (25), the Laplace transform of the interfering from closest MBS in DL , LDDL (s), can be evaluated

|hi |ri

,

U

+ Iφ˜ L

o

ν,τ ,Ai

(25)

I

as

D

Pj L |hj |rj

. −α

U

−α ∑

k∈φ˜ ν,τ

(22)

Pk L |hk |rk

By substituting (21) into (20) we get, PAcoc v,ϱ (βi ), as

(

⎛ PAcoc v,ϱ (βi ) = P ⎝ ∗

i

D

D

i

DL

UL

DL

UL

> βi ⎠

U

Iφ L,Ac + I ˜ L

[i

exp −

◦ , I φ ,A c , I ˜ o i i φν,τ ,Ai

[ ◦ , I φ ,A c , I ˜ o i i φν,τ ,A

α

(

ri βi ( D

(

= Eri ,R◦ EI DL

φi ,Aci

D

U

i

i

i

i

L DL

I φM ,AcM

))]

φν,τ ,Aoi

( ( )) D exp −s Iφ L,Ac × EI U L i

′

φν,τ ,Aoi

U

exp −s Iφ L,Ac + I ˜ L

i

[

D

)1/2

.

(26)

φ˜ ν,τ ,Aoi

(

(

UL

exp −s I ˜

φν,τ ,Aoi

( )2−α 2 λM πβM ψ α ∆−1 − ψ R◦ (s) = exp − 2 F1 α/2 − 1 ( ( )α ) ) ψ × 1, 1 − 2/α, 2 − 2/α, −βM . ∆−1 − ψ (

)] )

Iφ L,Ac + I ˜ L i

Pr ,Li

∆−2 + ψ 2

I φM ,AcM

φν,τ ,Aoi

(

)α )−1

ψ

(

φM ,AcM

See Appendix C for the proof of (26). The Laplace transform of the interference from MBS-tier in DL , L′ D L (s), is obtained as

⎞

Pr ,Li |hi |2 ri −α

(

= 1 + βM

∗

i

i

φ˜ ν,S ,AoM

√

−α

Pr ,Li |hi |ri −α

j∈φi

= Er , R

(s) × LI UL

From Fig. 1(b), it is clear that closest interferer is located at distance D from the UAc and at a distance R◦ ∆−1 from the serving M MBS, where R◦ represents the radius of Stienen’s cell. FurtherrM more, we define ψ = as the ratio of rM and R◦ . According to R◦ the Law of Cosines, with minor simplifications, we obtain D as

D

i

φM ,AcM

]⏐ ⏐ (s) ⏐⏐ r α βM . i

−1

SIRi L =

= Er , R

)

(

√

where,

= ∑

(23)

D Pr ,Li

D = R◦

i

D

s=

(1) Coverage probability of CO-SBSD for MBS associated U in AcM with RFA: Coverage probability expression of CO-SBSD for MBS associated U in AcM with RFA can be deduced from (23) as (29).

Based on the mathematical preliminaries and coverage probability expressions derived in Section 3.1, coverage probability expressions for UAc and UAo while considering uniform-SBSD M M without RFA employment, PAcoc v,ζ (βM ) and PAcoo v,ζ (βM ), are given as

D SIRi L

φ˜ ν,τ ,Aoi

(17)

3.2. Coverage probability of uniform-SBSD without RFA

(

(s) × LI UL

The PDF of UAc located at distance rM from serving BS is given

given as (12).

(βi ) = P

φi ,Aci

M

By substituting (10), (13), and (15) into (17),

∗ PAcoc v,ϱ i

= Eri ,R◦ LI DL

∞

∫

]⏐ ⏐ (s) ⏐⏐ r α βi . i

))

]

(27) See Appendix D for the proof of (27).

M.S. Haroon, Z.H. Abbas, F. Muhammad et al. / Physical Communication 38 (2020) 100908

7

PAcoc v,ζ (βM ) = M

( ( )α ) ( ( )α ) ′ λM πβM d(12−α) rMα λM πβM y (2−α) rMα rM rM J α, −β − J α, −β + ′ M M α/2 − 1 d1 α/2 − 1 y′ 1 − exp −λM π d1 y ( ( )α ) ( ( )α ) ′ λν,M πβM η2 y (2−α) rMα λν,M π βM η2 d1(2−α) rMα rM rM − J α, −βM η2 J α, −βM η2 α/2 − 1 d1 α/2 − 1 y′ ( ( )α ) ( ( )α )) (2−α) α (2−α) α λS π η3 βM d1 rM λν,S πη1 βM d1 rM rM rM 2 − J α, −βM η3 − J α, −βM η1 − λ M π rM rM drM . α/2 − 1 d1 α/2 − 1 d1 (

2π λM

∫ d1

(

) 2

exp

(18)

PAcoo v,ζ (βM ) = M

( ( )α ) ( ( )α ) λM πβM d(12−α) rMα λM πβM η2 d(12−α) rMα rM rM J α, −β − J α, −β η M M 2 α/2 − 1 d1 α/2 − 1 d1 exp −λM π d1 d1 ( ( )α ) ( ( )α )) (2−α) α (2−α) α λS π η3 βM d1 rM λν,S πη1 βM d1 rM rM rM − J α, −βM η3 − J α, −βM η1 − λM π rM2 rM drM . α/2 − 1 d1 α/2 − 1 d1 (

2π λM

∫∞

(

) 2

exp −

(19)

Box II. Table 3 Laplace transforms of interference from MBS and SBS. S. No.

Interference

Description

Laplace transforms General form

DL

Iφ

1

c M ,A M

UL

Iφ

2

D

S

AcM

DL interference from SBSs in AoM

M

U

Iφ L

4

I φM ,AcM

UL interference from MBS-AUs in

c

ν,M ,AM

Iφ L,Ao

3

L DL

DL MBS-I in AcM

UL interference from SBS-AUs in AoM

o

ν,S ,AM

() •

( •)

(•)

L UL

I φν,S ,AoM

(•)

I˜ φν,S ,AoM

(

−λ˜ ν,S πη1 βM ψ α (1 − ψ)2−α R2◦ (s) = exp 2 F1 α/2 − 1 ( ( )α ) ) ψ × 1, 1 − 2/α, 2 − 2/α, −βM η1 . 1−ψ (28)

See Appendix E for the proof of (28). See Box III for Eqs. (28) and (29). The expression in (24) requires averaging over rM and R◦ . The expression for marginal PDF of ψ , i.e., fψ (ψ), can now be obtained by taking the average over R◦ and ψ , and by substituting rM = ψ R◦ as fψ (ψ) =

∫

|R◦ |fR◦ ,rM (R◦ , ψ R◦ ) dR◦

Laplace transform of the rest of interfereing MBSs in DL

LDU

( •)

Laplace transform of closest MBS-AU interference in UL

′

( •)

Laplace transform of the rest of interfereing MBS-AUs in UL

I L φν,M ,AcM

L DL

I φS ,AoM

( •)

L UL

I φν,S ,AoM

Laplace transform of the interfereing SBSs in DL

(•)

Laplace transform of the interfereing SBS-AUs in UL

The probability that the MBS associated U, located in AcM , is given as pAc = P (xo ∈ B (0, R◦ )) ≈ P (ψ < 1). Hence, the PDF in M (31) can be used to calculate pAc as M

1

∫

fψ (ψ) dψ = 1 + ∆−2

(

p Ac = M

)−1

,

(32)

0

and pAo = (1 − pAc ) = 1 + ∆2

(

M

)−1

M

.

(33)

Coverage probability of CO-SBSD for MBS associated U in AcM ∗ with RFA, PAcoc v,ϱ (βM ), is given as M

∗ PAcoc v,ϱ M

(βM ) =

1

1

∫

p Ac

0

M

∞

∫

(

) D

′

I φM ,AcM

I

L DL × L DL × L UL

0

φM ,AcM

I˜ φν,S ,AoM

(34)

× fR◦ (R◦ ) fψ (ψ) dR◦ dψ. By substituting (1), (26), (27), (28), (31), and (32) into (34), we ∗ obtain PAcoc v,ϱ (βM ) as (29). (2) Coverage probability of CO-SBSD for MBS associated U in A0M with RFA: Similarly to (29), coverage probability expression of ∗ CO-SBSD for MBS associated U in A0M with RFA, PAcoo v,ϱ (βM ), can be

−∞

R◦ × 2π λM Rs ∆−2 exp −πλM (Rs /∆)2

(

=

(•)

M

∞

∞

∫

′

I L φν,M ,AcM

comes from outside B (xo , R◦ (1 − ψ)). Under this assumption, we have

I˜ φν,S ,AoM

Laplace transform of closest MBS interference in DL

LU

The Laplace transform of interference from SBS-AUs in UL , L UL (s), is obtained by considering that the interference

L UL

(•)

I L c φM ,AM I L c φM ,AM

I φν,M ,AcM

I φS ,AoM

LDD LD

L UL

L DL

Description

Expended to

)

( ) × 2π λM ψ Rs exp −πλM (ψ Rs )2 dR◦ ( )−2 = 2∆−2 ψ ∆−2 + ψ 2 .

M

obtained as

0

PAcoo v,ϱ (βM ) = ∗

(31)

M

1 p Ao

M

∫ 1

∞

∞

∫ 0

(

) LDDL × L′ DL I φM ,AcM

I φM ,AcM

8

M.S. Haroon, Z.H. Abbas, F. Muhammad et al. / Physical Communication 38 (2020) 100908

⎛

∫ ∗ PAcoc v,ϱ M

)⎜ 2∆−2 ψ 1 + ∆−2 ⎜ )2 ⎜ ( ⎜ ∆−2 + ψ 2 ⎝

⎞

(

1

(βM ) =

βM ∆2 ψ α α/2 − 1

1+ 0

(

[ ( )2−α ∆−1 − ψ J

(

α, −βM

1

( 1 + βM

)α )

ψ

(

∆−1 − ψ

⎛ )⎜ 2ψ 1 + ∆−2 ⎜ )2 ⎜ ( ⎜ ∆−2 + ψ 2 ⎝

∞

1

( 1 + βM

[ )2−α βM ∆2 ψ α ( −1 1+ ∆ −ψ J α/2 − 1

M

1

)1/2

(29)

( ( )α )] . η1 λ˜ ν,S (1 − ψ)2−α ψ J α, −η1 βM + λM (1 − ψ)

ψ )1/2 ∆−2 + ψ 2 ( (

⎟ ⎟ )α ⎟ ⎟ dψ ⎠

(30)

(

∗

PAcoov,ϱ (βM ) =

)

∆−2 + ψ 2

⎞

(

∫

ψ

(

⎟ ⎟ )α ⎟ ⎟ dψ ⎠

α, −βM

(

)α )] .

ψ

∆−1 − ψ

)

Box III.

× fR◦ (R◦ ) fψ (ψ) dR◦ dψ.

(35)

By substituting (1), (26), (27), (31), and (33) into (35), we obtain ∗ PAcoo v,ϱ (βM ) as (30). ■

×LI DL

φ˜ τ ,Aoi

(s) × LI UL

φ˜ ν,τ ,Aoi

]⏐ ⏐ (s) ⏐⏐ r α βi . i s=

(39)

D Pr ,Li

M

(1) Coverage probability of CO-SBSD for MBS associated U in AcM without RFA: Coverage probability expression of CO-SBSD for MBS associated U in AcM without RFA, PAcoc v,ϱ (βM ), can be calculated

3.4. Coverage probability of CO-SBSD without RFA In this section, we consider Stienen’s cell based CO-SBSD model without using RFA. Using the fact that |hi | ∼ exp (1), expression for coverage probability, PAcoc v,ϱ (βi ), can be written as i

PAcoc v,ϱ i

D SIRi L

(βi ) = P

Proof. Coverage probability expression for MBS can be expressed from (39) as

[

)

(

M

as (47)

> βi ,

(36)

PAcoc v,ϱ M

φν,M ,AcM

φM ,AcM

D

where SIRi L is given as Eqs. (36) and (37) in Box IV. Here, ri denotes the distance between U and its closest serving iBS. Interference with their Laplace transforms are given in Table 3. By substituting (37) into (36), we get PAcoc v,ϱ (βi ) as i

⎛ PAcoc v,ϱ (βi ) = P ⎝ i

D Pr ,Li DL

UL

Iφ , A c + Iφ i

= Er , R i

[

DL

UL

α

× exp − i

[

D ,I L

|hi |2 ri −α

c

ν,i ,Ai

> βi ⎠

U

D

+ Iφ˜ L ,Ao + Iφ˜ L τ

◦ ,I

DL

r i βi (

c ,I

φ i ,A i

(

i

UL

D

L c ,I ˜

φν,i ,Ai

(

D

U

D

U

+ Iφ˜ L ,Ao + Iφ˜ L τ

φi ,Aci

(

( ( U exp −s Iφ L

UL

φM ,AcM

( = 1 + βM

(

φ˜ τ ,Aoi

(

(

)))

D

exp −s I ˜ L

φτ ,Aoi

× EI UL

φ˜ ν,τ ,Aoi

(

(

(

U

exp −s I ˜ L

φν,τ ,Aoi

] )))

M

(s) × LI UL

φν,i ,Aci

(s)

D

PML D

(

(

1 + βM

ψ

(

∆−2

)α )]

ψ

( )1/2 ∆−2 + ψ 2 )α )−1

)1/2 + ψ2 )α )−1

ψ ( )1/2 − 2 ∆ + ψ2

.

(41)

I φν,M ,AcM

(41). Thus

( φi ,Aci

s=

Similarly, the expression for Laplace transform of MBS-AU in AcM , LDUL (s), can be derived by using the same approach used for

[ = Eri ,R◦ LI DL

M

)]⏐ ⏐ α ⏐ r βM M

)] −α

(

(

))) c

D

PML

D

exp −|h|βM

,|h|

= EI DL

i

(40)

exp −sPML |h|D

(

))]

ν,i ,Ai

φν,i ,Aci

× EI DL

= EI DL

φν,τ ,Aoi

DL

s=

exp −Iφ L ,Ac s

(

[ φM ,AcM

UL

,|h|

o

U

i

[

(

[

φM ,AcM

φM ,AcM

ν,τ ,Ai

i

× exp −s Iφ ,Ac + Iφ ,Ac + Iφ˜ ,Ao + Iφ˜ ,Ao i i ν,i i τ i ν,τ i [ ( ( ( ))) D = Eri ,R◦ EI DL exp −s Iφ L,Ac × EI U L

(s) = EI DL

= EI DL

)]

L o ,I ˜

φτ ,Ai

DL

c

ν,i ,Ai

i

)

φ˜ ν,S ,AM

Laplace transform of interference from closest MBS to the UAc in M DL can be evaluated as

UL

Iφ L,Ac + Iφ L

D Pr ,Li

φ˜ S ,AoM

I φM ,AcM

o

ν,τ ,Ai

i

]⏐ ⏐ (s) ⏐⏐ r α βM . i o

×LI DL (s)×LI UL

LDDL

◦ ,Iφ ,Ac ,Iφ ,Ac ˜ o ,I o i i ν,i i φτ ,Ai φ˜ ν,τ ,Ai

(

= Er , R

i

⎞

(s)

(s)×LI UL

(βM ) = ErM ,R◦ LI DL

D

L UL

I φν,M ,AcM

(s) = 1 + η2 βM

(

ψ

( )1/2 ∆−2 + ψ 2

)α )−1 .

(42)

M.S. Haroon, Z.H. Abbas, F. Muhammad et al. / Physical Communication 38 (2020) 100908

9

D

Pr ,Li |hi |ri −α

D

SIRi L =

D

U

Iφ L,Ac + Iφ L i

D

c

ν,i ,Ai

i

,

U

+ Iφ˜ L ,Ao + Iφ˜ L τ

(37)

o

ν,τ ,Ai

i

D

= ∑

j∈φi

Pr ,Li |hi |ri −α D

Pj L |hj |rj−α +

U

∑

j∈φν,i

Pj L |hj |rj−α +

D

∑

k∈φ˜ τ

Pk L |hk |rk−α +

U

∑

k∈φ˜ ν,τ

Pk L |hk |rk−α

.

(38)

Box IV. U

Here η2 =

Pν,LM D PML

U

, where Pν,LM is the power transmitted by user D

associated with MBS in UL while PML is the power transmitted by MBS in DL . The interference received from MBSs other than closest MBS is random with respect to UAc . Therefore, we consider that the M

( )) comes from outside B x , R◦ ∆−1 − ψ , (

u

interference to UAc M where xu denotes the user location. The Laplace transform of the interference from MBS-tier in DL , L′ DL (s) is obtained as I

φM ,AcM

( )2−α 2 R◦ −λM πβM ψ α ∆−1 − ψ (s) = exp 2 F1 α/2 − 1 ( ( )α ) ) ψ × 1, 1 − 2/α, 2 − 2/α, −βM . ∆−1 − ψ

Table 4 Simulation parameters. Parameter

Configuration

Channel bandwidth MBS and user distribution SBS distribution

10 MHz PPP PHP (3, 20, 60, 200 and 500)/(6 km2 ) ≈(0.5λS /λM )/(6 km2 ) 1/2 500/(6 km2 ) each 40 dBm, 20 dBm and 10 dBm, respectively 2 < α ≤ 4

λS /λM λ˜ S /λM ∆ λν,M , λν,S PM , PS , Pν αm = αs = α

(

L′ DL I

φM ,AcM

(43) See Appendix F for the proof of (43). Similarly, by using the same approach used for (43), the expression for Laplace transform of interference from MBS-AUs in AcM , L′ UL (s), can be derived as I φν,M ,AcM

(

I

)2−α

−λν,M π η2 βM ψ ∆−1 − ψ α/2 − 1 ( ( × 1, 1 − 2/α, 2 − 2/α, −η2 βM

(s) = exp

′

L UL

( α

φν,M ,AcM

R2◦

(46) U

Here, η1 =

Pu,LS

U

, where Pu,LS is the transmit power of SBS-AUs in

D PML

UL . See Box V for Eqs. (46) and (47). Coverage probability of CO-SBSD for MBS associated U in AcM without RFA, PAcoc v,ϱ (βM ), can be expressed as M

PAcoc v,ϱ M

(βM ) =

1

∫

1

∞

∫

( D

L DL

pAcM

0

I

φM ,AcM

0

× LDUL I

φν,M ,AcM

× L′ DL I

φM ,AcM

) ×L′ UL

2 F1

ψ ∆−1 − ψ

I

)α ) )

.

φν,M ,AcM

× LI DL

φ˜ S ,AoM

fR◦ (R◦ ) fψ (ψ) dR◦ dψ.

× LI UL

φ˜ ν,S ,AoM

(49)

(44)

By substituting the values of (1), (31), (32) (41), (42), (43), (44), (45), and (46) into (49), we obtain PAcoc v,ϱ (βM ) as (47),

The Laplace transform for the SBS-tier in DL is obtained by considering the interference from outside the disk B (xo , R◦ (1 − ψ)), L DL (s), is calculated as

(2) Coverage probability of CO-SBSD for MBS associated U in AoM without RFA: Similarly, coverage probability expression of CO-SBSD for MBS associated U in AoM without RFA, PAcoo v,ϱ (βM ), is

I˜ o φS ,AM

M

M

obtained as

(

L DL

I˜ o φS ,AM

λ˜ S πη3 βM ψ α (1 − ψ)2−α R2◦ (s) = exp − 2 F1 α/2 − 1 ( ( )α ) ) ψ × 1, 1 − 2/α, 2 − 2/α, −βM η3 . 1−ψ (45)

See Appendix G for the proof of (45). By using the same approach used for (45), expression for Laplace transform of the interference received from SBS-AUs in AoM , L UL (s), can be obtained as

PAcoo v,ϱ M

(βM ) =

∫ ∞∫ ∞(

1

(1 − pAc ) M

1

0

LDDL × LDUL × L′ DL I

φM ,AcM

I

φν,M ,AcM

I φM ,AcM

) ×L UL × LI DL × LI UL I

φν,M ,AcM

φ˜ S ,AoM

(50)

fR◦(R◦ ) fψ(ψ) dR◦ dψ.

′

φ˜ ν,S ,AoM

By substituting the values of (1), (31), (33) (41), (42), (43), (44), (45), and (46) into (50), we obtain PAcoo v,ϱ (βM ) as (48). ■ M

4. Results and discussion

I˜ φν,S ,AoM

(

L UL I˜

φν,S ,AoM

−λ˜ ν,S π η1 βM ψ α (1 − ψ)2−α R2◦ (s) = exp α/2 − 1 ( ( × 2 F1 1, 1 − 2/α, 2 − 2/α, −βM η1

ψ 1−ψ

)α ) )

.

In this section, we present numerical and simulation results for the proposed network scenarios. We perform four types of coverage probability analyses of the proposed model including, (i) CO-SBSD without RFA employment, (ii) CO-SBSD with RFA employment, (iii) uniform-SBSD with RFA employment and, (iv) uniform-SBSD without RFA employment. The results are derived

10

M.S. Haroon, Z.H. Abbas, F. Muhammad et al. / Physical Communication 38 (2020) 100908

⎛ 2∆−2 ψ 1 + ∆−2

(

( PAcoc v,ϱ (βM ) = M

∫

∆−2 + ψ 2

)2

) ⎜ ⎜ ⎜ ⎜ ⎝

1

βM ∆ 2 ψ α 1+ α/2 − 1

0

[ (

( ∆−1 − ψ

)2−α

( J

α, −βM

(

ψ ( ) ∆−1 − ψ

)α )

η2 λν,M + J λM

⎞⎛

( 1 + βM

( PAcoo v,ϱ (βM ) = M

∫ 1

∞

βM ∆ 2 ψ α 1+ α/2 − 1

[

∆−2

ψ

⎞ 1

(

ψ

⎟ ⎟ ⎟ dψ )α ⎟ ⎠

1 + η 2 βM ( )1/2 )1/2 ∆−2 + ψ 2 ∆−2 + ψ 2 ( )α )) )α ) ( ( )α ))] . ( ( ( ψ ψ ψ (1 − ψ)2−α ˜ ) + λ˜ ν,S η1 J α, −η1 βM α, −η2 βM ( −1 + λS η3 J α, −η3 βM λM (1 − ψ) (1 − ψ) ∆ −ψ

(

(

⎛

⎞⎛

) ⎜ ⎜ )2 ⎜ ⎜ 2 +ψ ⎝

⎟⎜ ⎟⎜ ⎜ )α ⎟ ⎟⎜ ⎠⎝

2ψ 1 + ∆−2

(

⎟⎜ ⎟⎜ ⎟⎜ )α ⎟ ⎜ ⎠⎝

1

1

(

ψ

(47)

⎞ 1

(

ψ

⎟ ⎟ )α ⎟ ⎟ dψ ⎠

1 + βM ( 1 + η2 βM ( )1/2 )1/2 ∆−2 + ψ 2 ∆−2 + ψ 2 ( )α ) ( )α )) ( ( ( ( ( ( )α ) ( ( )α ))] . ( )2−α ψ η2 λν,M ψ ψ ψ (1 − ψ)2−α ˜ − 1 ) ) + + ∆ −ψ J α, −βM ( −1 J α, −η2 βM ( −1 λS η3 J α, −η3 βM + λ˜ ν,S η1 J α, −η1 βM λM λM (1 − ψ) (1 − ψ) ∆ −ψ ∆ −ψ

(48)

Box V.

Fig. 3. MBS coverage in AoM Vs SIR threshold βM by using (12), (19), (30) and (48).

Fig. 4. MBS coverage in AoM Vs SIR threshold βM by using (29), (30), (47) and (48).

using Matlab (Version 2017a) and simulation parameters are provided in Table 4. Furthermore, different network parameters, such as SIR threshold, densities of SBSs, MBSs, SBS-AUs, and MBS-AUs, are used to analyze their impact on MBS coverage. Analytical and simulation results for coverage probability against different values of βM are shown in Fig. 3. The figure compares coverage probability for uniform-SBSD (UM)9 and Stienen’s cell based CO-SBSD (SM)10 while considering with and without 9 The terms UM and uniform-SBS are used interchangeably in this paper. D 10 The terms SM and Stienen’s cell based CO-SBS are used interchangeably D in this paper.

Fig. 5. MBS coverage in AoM Vs different values of λS /λM and λ˜ S /λM while using (12), (19), (30) and (48).

RFA employment. The figure uses the expressions (12), (19), (30), and (48) for the proposed analysis. It can be observed from the figure that there is a significant improvement in coverage probability by using the Stienen’s cell based CO-SBSD with RFA, as compared with uniform-SBSD scenarios. This is due to the fact that fewer SBSD leads to reduced network interference. Moreover, the figure signifies interference mitigation by employing RFA as compared with No-RFA. For this particular analysis, we consider λS /λM = 60 and βM = −35 dB–10 dB. Furthermore, the figure demonstrates that the higher values of βM lead to the lower coverage due to reduced user association. In Fig. 4, coverage probabilities are compared against different values of βM while assuming that U is located in AcM and AoM . The figure considers SM in conjunction with and without RFA employment by using the expression (29), (30), (47) and (48). The result shows significant improvement of coverage probability in AcM than in AoM due to proximity of the U with MBS. Moreover, SM with RFA in AcM outperforms the rest of the simulation scenarios due to better interference management. Furthermore, this result indicates that the higher values of βM lead to the lower coverage in the considered scenarios because of the reduced user association. Fig. 5 presents coverage probabilities against different values of λS /λM and λ˜ S /λM while considering various network layout scenarios with βM = −20 dB. The results are drawn by using (12), (19), (30), and (48). It can be observed from the figure that increasing SBS density in MBS-EA induces reduced coverage probability in all considered scenarios due to more users association with SBSs. Moreover, the figure depicts that Stienen’s cell based CO-SBSD in conjunction with RFA leads to improved coverage due to better interference mitigation and lower SBSD . Furthermore, it

M.S. Haroon, Z.H. Abbas, F. Muhammad et al. / Physical Communication 38 (2020) 100908

11

Fig. 6. MBS coverage in AcM , and in AoM Vs different values of λ˜ S /λM , by using (47) and (48).

Fig. 8. MBS coverage in AoM Vs SBS-AU densities λν,S and λ˜ ν,S in AoM , by using (12), (19), (30) and (48).

Fig. 7. MBS coverage in AoM Vs SBS-AUs density λ˜ ν,S , in AoM , by using (30) and (48).

Fig. 9. MBS coverage in AcM Vs MBS-AU density λν,M in AcM , by using (29) and (47).

can be observed from the figure that avoiding SBSD near MBS leads to improved coverage due to lower interference. Fig. 6 presents coverage probabilities against different values of λ˜ S /λM while using the expressions of (47) and (48). For this particular set-up, analysis is performed on the U located both in AcM and AoM . The figure shows that the U experiences better coverage in AcM as compared with AoM due to close MBS proximity. Moreover, the coverage probabilities decrease in both AcM and AoM with increase in the value of βM due to reduced MBS user associations. In addition, increasing the value of λ˜ S /λM lowers the coverage performance due to increased interference caused by the higher SBS density in MBS-EA. In Fig. 7, coverage probabilities are compared against different values of SBS-AUs density, λ˜ ν,S , in AoM . The figure assumes (i) RFA with SM, and (ii) No-RFA with SM, by using (30) and (48), respectively. Moreover, the results are derived for βM = −15 dB (shown in the lower set of plots) and −10 dB (shown in the upper set of plots), as depicted in the figure. The results show that increasing the values of λ˜ ν,S leads to lower network performance due to increased interference. It can be observed form the figure that βM = −15 dB spurs network coverage as compared with βM = −10 dB due to improved user associations with MBS. Moreover, SM with RFA employment leads to improved MBSEA coverage due to lower network interference by the proposed model. Furthermore, increasing the values of λS /λM gives rise to reduce coverage due to increased network interference. Fig. 8, shows coverage probabilities against different values of SBS-AUs densities λν,S and λ˜ ν,S , in AoM . The figure considers the following network scenarios: (i) RFA with SM, (ii) No-RFA with

Fig. 10. MBS coverage in AcM , and in AoM Vs MBS density λM , by using (29) and (30).

SM, (iii) RFA with UM, and (iv) No-RFA with UM, by using (12), (19), (30) and (48), respectively. The results show that RFA with SM outperforms other network scenarios due to better interference mitigation provided by CO-SBSD and RFA. Additionally, the figure indicates that higher values of λν,S and λ˜ ν,S merely cause any coverage degradation of MBS-EU. This is due to RFA where different tiers use distinct frequency bands but in reverse fashion. Fig. 9 demonstrates coverage probabilities against different values of MBS-AUs density λν,M , in AcM . The figure considers, (i) RFA with SM and (ii) No-RFA with SM, using (29) and (47), respectively.

12

M.S. Haroon, Z.H. Abbas, F. Muhammad et al. / Physical Communication 38 (2020) 100908

Fig. 11. Coverage difference (%) based on the values obtained in Fig. 3.

Moreover, the results are derived for βM = −10 dB (shown in the upper set of plots) and 0 dB (shown in the lower set of plots). The results show that increasing the values of λν,M reduces network performance due to increased interference. It can be observed form the figure that βM = −10 dB spurs coverage as compared with βM = 0 dB as more users get associated with MBS. Moreover, the figure indicates that as we use separate bands for DL and UL communications, the higher values of λν,M do not change MBS-EU coverage. Fig. 10 shows MBS coverage in AcM , and in AoM , against different values of MBS density λM while assuming SM. The plots are obtained for βM = −10 dB, −5 dB and 0 dB while using (29) and (30). The results signify the fact that the U experiences better MBS coverage in AcM than in AoM for being in close proximity of MBS. Moreover, it can be observed from the result that decrease in the value of βM leads to improved MBS coverage. This is because more users get the coverage by being associated with MBS. Similarly, the result shows that increasing λM reduces network coverage due to high MBS-I. Furthermore, this result shows that the proposed SM model along with RFA leads to improved coverage performance due to better interference management and efficient resource utilization. In Fig. 11, we compute coverage difference (%) based on the values of coverage probabilities obtained in Fig. 3. In this figure, we compute coverage probability difference between SM and UM, with and without RFA employment. The figure demonstrates that in both the scenarios, a maximum of 70% coverage difference improvement is obtained for the values of βM equal to −19 dB, −17 dB and −15 dB, due to improved MBS-EU coverage.

SBSs result in lower deployment cost and reduced interference leading to an improved network performance. As a future work, decoupled user association can be employed in conjunction with the proposed model to achieve better coverage performance. Moreover, different path loss exponents can be considered for MBS and SBS to model a more realistic HetNet. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment A part of this paper has been published in the 28th International Telecommunication Networks and Applications Conference (ITNAC’2018), University of New South Wales, Sydney, Australia [1]. Appendix A. Proof of (10) The Laplace transform of the interference from MBS-tier in DL is obtain as L DL

I φM ,AcM

(s) = EI DL

(

[

φM ,AcM

D

exp −Iφ L ,Ac s M

M

)] |s=rMα βM

5. Conclusion

⎡ In this paper, Stienen’s cell based CO-SBSD is investigated as compared with uniform-SBSD in HetNet, where according to 5G, SBSs are densely overlaid in the MBS coverage area. The proposed model is analyzed with and without RFA employment. Coverage probabilities of MBSs are evaluated both in AcM and AoM with emphasis on MBS-EUs performance. Analytical and simulation results show improvement in MBS-EUs coverage by employing the proposed model. Moreover, the results depict improved coverage for the U in AcM as compared with the U in AoM due to better SIR reception. The results further demonstrate that by increasing λM , λS , λ˜ S , λν,M , λν,S and λ˜ ν,S reduces network performance due to increased interference. Furthermore, Stienen’s cell based CO-SBSD along with RFA outperforms rest of the simulations scenarios in terms of coverage probability due to reduced interference as a result of fewer SBSD . From operators perspective, fewer

= EI D L

φM ,AcM

,|hj |

⎛

⎣exp ⎝−s

φM ,AcM

∏ ,|hj |

⎣

φM ,AcM

⎤ ( ) −α α ⎦ exp −|hj |βM rM rj

j∈φM

⎡ = EI D L

∏ ⎣

⎤ ( ) α −α ⎦ E|hj | exp −|hj |βM rM rj

j∈φM

⎡ = EI D L

φM ,AcM

|hj |rj−α ⎠⎦

j∈φM

⎡ = EI D L

⎞⎤ ∑

⎢∏ ⎣ j∈φM

⎤ 1 1 + βM

⎥ ( r )−α ⎦ j rM

M.S. Haroon, Z.H. Abbas, F. Muhammad et al. / Physical Communication 38 (2020) 100908

⎛ ⎜ ⎜ ⎜ (a) ⎜ ≈ exp ⎜−2π λM ⎜ ⎜ ⎝

∫

d1

rj drj

( 1+

⎜ ⎜ ⎜ ⎜ (b) ⎜ 2/α ≈ exp ⎜−π λM βM rM2 ⎜ ⎜ ⎜ ⎝

(c )

≈exp

⎛

∫

β

β

1/α M rM

⎠

⎞2

⎛

y′

⎝

1/α

βM rM

⎠

∫

⎛

⎟ ⎟ ⎟ ⎟ )α ⎟ ⎟ ⎟ ⎠

⎜ ⎜ ⎜ ⎜ 2/α 2/α = exp ⎜−πλν,S η1 βM rM2 ⎜ ⎜ ⎝

⎞2

d1

⎝

(2−α) α

rj 1/α M rM

y′

⎛

(

⎞

⎞ = exp

( 2 F1

∞

⎛

d1

⎞2

⎝

(η1 βM )1/α rM

⎠

⎟ ⎟ ⎟ du ⎟ α/2 ⎟ 1 + (u) ⎟ ⎟ ⎠

−λν,S πη1 βM d(12−α) rMα × α/2 − 1

(

⎟ ⎟ ⎟ ⎟ du ⎟ ⎟ 1 + (u)α/2 ⎟ ⎟ ⎟ ⎠

13

⎞

1, 1 − 2/α, 2 − 2/α, −βM η1

(

rM

)α ) )

d1

.

(52)

U

λM π βM d1 rM 2 2 , 2 − , −βM 2 F1 1, 1 − α/2 − 1 α α

(

(

rM

Here, η1 =

)α )

d1

Pν,LS D PML

−

U

, where Pν,LS is the SBS transmit power in UL .

Appendix C. Proof of (26) ′ (2−α) α rM My

λM πβ α/2 − 1

(

1, 1 −

2 F1

2

α

,2 −

2

α

, −βM

(

rM

)α ))

y′

.

(51)

where Step (a) is obtained ( using PGFL )2 of PPP [3], Step (b) is rj and Step (c) is obtained obtained by substituting u = 1/α βM rM by Gauss-hypergeometric approximation of Step (b) [28].

LDDL

I φM ,AcM

(s) = EI DL

φM ,AcM

,|h|

= EI DL

φM ,AcM

I φν,S ,AoM

L UL I

φν,S ,AoM

(

(s) = EI UL

φν,S ,AoM

⎡ = EI U L

φν,S ,AoM

,|hk |

s=

⎣exp ⎝−s

φν,S ,AoM

⎤ ∏ ) ( α −α ⎦ ⎣ exp −|hk |βM η1 rM rk

∏

φν,S ,AoM

φν,S ,AoM

L′ D L

I φM ,AcM

(s) = E DL

(

[

I φM ,AcM

⎣

⎡

⎤ ( ) α −α ⎦ E|hk | exp −|hk |βM η1 rM rk

= EI D L

φM ,AcM

k∈φS

⎡ = EI U L

.

(53)

D

exp −Iφ L ,Ac s M

M

)]⏐⏐ ⏐ α ⏐ ri βM s=

,|hj |

⎢∏ ⎣ k∈φS

1 + βM η1

⎛ ⎜ ⎜ ⎜ ⎜ = exp ⎜−2π λν,S ⎜ ⎜ ⎝

∫ d1

= EI D L

⎥ ( r )−α ⎦

∞

⎣exp ⎝−s ⎡

1

φM ,AcM

k

rM

∏ ,|hj |

⎣

⎟ ⎟ ⎟ rk drk ⎟ ( )α ⎟ ⎟ rk ⎟ 1+ 1/α (η1 βM ) rM ⎠

= EI D L

φM ,AcM

∑

φM ,AcM

−α ⎠⎦

|hj |rj

⎤ ( ) α −α ⎦ exp −|hj |βM rM rj

∏ ⎣

⎤ ( ) α −α ⎦ E|hj | exp −|hj |βM rM rj

j∈φM

⎡ = EI D L

D PML

j∈φM

⎡ ⎞

⎞⎤

⎛ j∈φM

⎤

⎢∏ ⎣ j∈φM

⎤ 1 1 + βM

D

PML

k∈φS

⎡ = EI U L

ψ )1/2 ( ∆−2 + ψ 2

I φM ,AcM

k∈φS

,|hk |

)1/2 + ψ2 )α )−1

The Laplace transform of the interference from MBS-tier in DL , L′ D L (s), is obtained as

U

PS L |hk |rk−α ⎠⎦

⎡ = EI U L

∆−2

( )1/2 ∆−2 + ψ 2 )α )−1

Appendix D. Proof of (27)

⎞⎤ ∑

(

ψ

(

)α )]

ψ

U

PML

⎛

(

(

= 1 + βM

( )]⏐⏐ [ UL exp −Iφ ,Ao s ⏐⏐ r α β ν,S M M M

D

1 + βM

φM ,AcM

D

PML

exp −|h|βM

,|h|

= EI DL

s=

)] −α

(

( Similarly, the Laplace transform of the interference from SBSAUs in UL , L UL (s), is obtain as

M

)]⏐ ⏐ α ⏐ r βM M

exp −sPML |h|D

[ Appendix B. Proof of (13)

M

(

[

D

exp −Iφ L ,Ac s

φM ,AcM

= EI DL

(

[

⎥ ( r )−α ⎦ j rM

14

M.S. Haroon, Z.H. Abbas, F. Muhammad et al. / Physical Communication 38 (2020) 100908

⎛

⎞

⎜ ∫ ∞ ⎜ = exp ⎜ − 2 π λ M ⎜ R◦ (∆−1 −ψ ) ⎝ ⎛ ⎜ ⎜ ⎜ ⎜ 2/α 2 2 = exp ⎜ ⎜−π λM βM ψ R◦ ⎜ ⎜ ⎝ ( = exp

v dv

( 1+

Appendix F. Proof of (43)

⎟ ⎟ )α ⎟ ⎟ ⎠

v 1/α

The Laplace transform of the interference from MBS-tier in DL , L′ D L (s) is obtained as I φM ,AcM

βM ψ R◦

⎞

∫

L′ D L

∞

⎛

R ⎜ ◦ ⎝

α

( λM π βM ψ ∆−1 − ψ − α/2 − 1

(

I

∆−1 − ψ

) ⎞2 ⎟ ⎠

1/α

βM ψ R ◦ )2−α 2 R◦

⎟ ⎟ ⎟ ⎟ du ⎟ α/2 ⎟ 1 + (u) ⎟ ⎟ ⎠

φM ,AcM

(s) = EI DL

= EI D L

φM ,AcM

,|hj |

φM ,AcM

2 F1

1, 1 − 2/α, 2 − 2/α, −βM

(

ψ ∆−1 − ψ

)α ) )

.

(54)

,|hj |

⎣

φM ,AcM

⎞⎤ ∑

D PML

−α ⎠⎦

|hj |rj

⎤ ( ) α −α ⎦ exp −|hj |βM rM rj

⎣

⎤ ) ( α −α ⎦ rj E|hj | exp −|hj |βM rM

j∈φM

⎤

⎡ Appendix E. Proof of (28) The Laplace transform of interference from SBS-AUs in UL , L UL (s), is obtained as

= EI D L

φM ,AcM

I˜ φν,S ,AoM

L UL I˜

φν,S ,AoM

(s) = EI UL

φ˜ ν,S ,AoM

= EI UL

φ˜ ν,S ,AoM

,|hk |

( )]⏐⏐ [ UL exp −I ˜ s ⏐⏐ r α β M φν,S ,AoM i s=

1 + βM

⎥ ( r )−α ⎦ j rM

⎛

U

∑

U PS L

⎛

−α ⎠⎦

|hk |rk

exp −|hk |βM η1 Rα◦ rk−α ⎦

(

⎣

)

k∈φ˜ S

⎡ = EI UL

φ˜ ν,S ,AoM

⎤ ∏ ( ) ⎣ E|hk | exp −|hk |βM η1 Rα◦ rk−α ⎦

= EI UL

φ˜ ν,S ,AoM

⎤ k∈φ˜ S

1 1 + βM η1

⎥ ( r )−α ⎦ k

2 F1

R◦

v dv v

∞

R◦ (1−ψ)

( 1+

⎛ ⎜ ⎜ ⎜ ⎜ 2/α 2 2 ˜ = exp ⎜ ⎜−π λν,S (η1 βM ) ψ R◦ ⎜ ⎜ ⎝

⎛

⎛

R ⎜ ◦ ⎝

( −1 ) ⎞2 ∆ −ψ ⎟ 1/α

1, 1 − 2/α, 2 − 2/α, −βM

(

1, 1 − 2/α, 2 − 2/α, −βM η1

⎠

ψ ∆−1 − ψ

)α ))

.

(56)

Appendix G. Proof of (45)

R◦ (1 − ψ) 1/α

(η1 βM )

ψ 1−ψ

⎟ ⎟ ⎟ ⎟ du ⎟ α/2 ⎟ 1 + (u) ⎟ ⎟ ⎠

⎞

∞

ψ R◦

⎞2

⎟ ⎟ ⎟ ⎟ du ⎟ α/2 ⎟ 1 + (u) ⎟ ⎟ ⎠

⎠

The Laplace transform for the SBS-tier in DL is obtained by considering the interference from outside the disk B (xo , R◦ (1 − ψ)), L DL (s), is calculated as I˜ o φ S ,A

M

L DL

−λ˜ ν,S π η1 βM ψ α (1 − ψ)2−α R2◦ × α/2 − 1

(

ψ R◦

Here, Step (e) is obtained using PGFL )of PPP [3]. Step (f ) is ( 2 rj obtained by substituting u = . 1/α βM ψ R ◦

⎟ )α ⎟ ⎠

(η1 βM )1/α ψ R◦

∫ ⎝

(

β

⎞

⎞ ∫

rj 1/α M

∞

(

⎛ ⎜ ˜ = exp ⎜ ⎝−2π λν,S

1+

βM ψ R◦ ( ( )2−α 2 R◦ −λM πβM ψ α ∆−1 − ψ = exp × α/2 − 1

k∈φ˜ S

⎡ ⎢∏ ⎣

(

∫

⎜ ⎜ ⎜ ⎜ (f ) 2/α 2 2 ≈ exp ⎜ ⎜−πλM βM ψ R◦ ⎜ ⎜ ⎝

⎤

⎟ ⎟ )α ⎟ ⎟ ⎠

rj drj

⎞⎤

⎣exp ⎝−s

∏

,|hk | φ˜ ν,S ,AoM

⎞

⎜ ∫ ∞ ⎜ ⎜ ≈ exp ⎜−2πλM R◦ (∆−1 −ψ ) ⎝

k∈φ˜ S

= EI UL

2 F1

j∈φM

1

(e)

PML

⎡

(

⎢∏ ⎣

⎛

⎡

= exp

D

j∈φM

∏

= EI D L

s=

j∈φM

∏

= EI D L

M

PML

⎣exp ⎝−s

⎡ (

M

)]⏐⏐ ⏐ α ⏐ r i βM

⎛

⎡

×

D

exp −Iφ L ,Ac s

φM ,AcM

⎡

(

[

I˜ o φ S ,A

(s) = EI DL

φ˜ S ,AoM

M

)α ) )

⎡ .

(55)

= EI D L

φ˜ S ,AoM

[

,|hk |

(

D

exp −I ˜ L

φS ,AoM

s

)]⏐⏐ ⏐ α ⏐ ri βM s=

⎛

⎣exp ⎝−s

D

PML

⎞⎤ ∑ k∈φ˜ S

D PS L

−α ⎠⎦

|hk |rk

M.S. Haroon, Z.H. Abbas, F. Muhammad et al. / Physical Communication 38 (2020) 100908

⎤ ∏ ) ( −α α ⎣ exp −|hk |βM η3 rM rk ⎦ ⎡

= EI DL

φ˜ S ,AoM

,|hk |

k∈φ˜ S

⎤

⎡ ∏

= EI DL

φ˜ S ,AoM

⎣

α rk E|hk | exp −|hk |βM η3 rM

) −α

(

k∈φ˜ S

⎤

⎡ = EI DL

φ˜ S ,AoM

⎦

⎢∏ ⎣ k∈φ˜ S

1 1 + βM η3

⎥ ( r )−α ⎦ k

rM

⎞

⎛ ⎜ ˜ = exp ⎜ ⎝−2π λS

∫

∞ R◦ (1−ψ)

rk drk

( 1+

⎜ ⎜ ⎜ ⎜ = exp ⎜−π λ˜ S (η3 βM )2/α ψ 2 R2◦ ⎜ ⎜ ⎝ ( = exp

( 2 F1

(η3 βM )1/α ψ R◦

∫

⎛

⎟ )α ⎟ ⎠

rk

⎞

∞

⎛

R◦ (1 − ψ)

⎞2

⎝

(η3 βM )1/α ψ R◦

⎠

⎟ ⎟ ⎟ du ⎟ ⎟ 1 + (u)α/2⎟ ⎟ ⎠

−λ˜ S π η3 βM ψ α (1 − ψ)2−α R2◦ × α/2 − 1

1, 1 − 2/α, 2 − 2/α, −βM η3

(

ψ 1−ψ

)α ) )

.

(57)

D

Here, η3 = in DL .

PS L D PML

D

, where PS L is the power transmitted by SBS-AU

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Muhammad Sajid Haroon received the B.Sc. degree in electronics engineering from the International Islamic University Islamabad, Pakistan, in 2007, and M.S. degrees in electrical engineering from COMSATS Institute of Information Technology, Attock, Pakistan, in 2013. He is currently pursuing his Ph.D. degree at the Ghulam Ishaq Khan Institute of Engineering Science and Technology, Swabi, Pakistan, with a focus on interference management in next generation cellular networks using tools from stochastic geometry, point process theory, and spatial statistics. His research interests include interference mitigation in cellular networks, next generations cellular networks, stochastic processes and digital signal processing. Ziaul Haq Abbas received the M.Phil. degree in electronics from the Quaid-e-Azam University, Pakistan, in 2001, and the Ph.D. degree from the Agder Mobility Laboratory, Department of Information and Communication Technology, University of Agder, Norway, in 2012. He was a Visiting Researcher with the Department of Electrical and Computer Engineering, University of Minnesota, USA in 2012. He is currently an Associate Professor with the Faculty of Electrical Engineering and a co-founding member of the Telecommunications and Networking (TeleCoN) Research Lab at GIK Institute. His research interests include energy efficiency in hybrid mobile and wireless communication networks, 5G and beyond mobile systems, mesh and ad hoc networks, traffic engineering in wireless networks, performance

evaluation of communication protocols and networks by analysis and simulation, quality-of-service in wireless networks, green wireless communication, and cognitive radio. Fazal Muhammad received the B.Sc. and M.Sc. degrees in electrical engineering from the University of Engineering and Technology, Peshawar, Pakistan, in 2004 and 2007, respectively, and the Ph.D. degree in electronic engineering from GIK Institute of Engineering Sciences and Technology, Pakistan in 2017. He is currently working as Assistant Professor and Head of Electrical Engineering Department at City University of Sciences and Information Technology, Peshawar. He is the Secretary of Institutions of Engineers, Pakistan, Peshawar Center. His research interests include heterogeneous cellular networks, cognitive radio networks, and sensor networks. Ghulam Abbas received the B.S. degree in computer science from University of Peshawar, Pakistan, in 2003, and the M.S. degree in distributed systems and the Ph.D. degree in computer networks from the University of Liverpool, U.K., in 2005 and 2010, respectively. From 2006 to 2010, he was Research Associate with Liverpool Hope University, U.K., where he was associated with the Intelligent & Distributed Systems Laboratory. Since 2011, he has been with the Faculty of Computer Sciences & Engineering, GIK Institute of Engineering Sciences and Technology, Pakistan. He is currently working as Associate Professor and Director Huawei Authorized Information and Network Academy. He is a co-founding member of the Telecommunications and Networking (TeleCoN) Research Lab at GIK Institute. Dr. Abbas is a Fellow of the Institute of Science & Technology, U.K., a Fellow of the British Computer Society, and a Senior Member of the IEEE. His research interests include computer networks and wireless and mobile communications.