Monte Carlo Simulation

Monte Carlo simulation started in the 1940s for the purpose of testing engi-

neering systems subjects to real behaviour [87]. It is a broad class of computa-

Attach to Cell BSs Locations Assign Radio Resources Throughput Signal Power Calculation SINR Calculation Scheduler Users Locations Communication Network

Figure 3.2: A typical Monte Carlo simulation for cellular communication sys- tem.

results. When planning a wireless network, design must be proved to work

for a wide variety of scenarios that depend mainly on the number of users

and their locations [88]. Monte Carlo simulation is typically used to generate

these users and their locations. The network performance is then evaluated

and optimised.

As Figure 3.2 shows a typical Monte Carlo simulation structure for cel-

lular communication system. The main random variables are: users’ locations,

BSs locations, network traffic and channel conditions.

By knowing the locations of BSs and UEs, the received signal power

and SINR can be calculated using the propagation and pathloss model. The

channel throughput highly depends on the receive SINR by using the Shannon

3.2.1

Statistical Pathloss Model

The signal strength of an electromagnetic wave would result from a line-of-

sight path through free space, with no obstacles nearby to cause reflection or

diffraction, which is defined in “Standard Definitions of Terms for Antennas”,

IEEE Std 145-1983, as “The loss between two isotropic radiators in free space,

expressed as a power ratio.” Free-space path loss (FSPL) is proportional to

the square of the distance between the transmitter and receiver.

P LFS = 4πrf c 2 (3.1)

wheref is the signal frequency (in Hz), r is the distance from the transmitter (in m), andc is the speed of light in a vacuum.

The statistical Pathloss Model approach includes two components: an

estimate of the median path loss and a random component that depends upon

the physical features of the local terrain. The measurement of the field strength

in various environments is a function of the distance r, and from the trans- mitter to the receiver motivates a simple propagation model for median path

loss having the form:

PR PT

= λ

α (3.2)

Where PR is the received power, PT is the transmission power,λ represents a

gain that is related to the frequency and antenna gains, andα is the pathloss distance exponent typically rangesfrom 2 to 5 depending on the environment

Table 3.1: Example Path-loss exponents Environments α Free space 2 Flat rural 3 Rolling rural 3 Suburban rural 3.5

Dense urban, skyscrapers 4.5

shown in Table 3.2.1.

3.2.2

Ray Tracing by Wireless InSite

The simulation is based on the software Wireless InSite1, which is a suite of ray-tracing models and high-fidelity electromagnetic solvers for the analysis

of site-specific radio propagation and wireless communication systems. The

Shooting and Bouncing Ray method (SBR) is used to find the propagation

paths from the transmitters to the receiver points [89], [90]. A dense grid of

geometric bouncing optics rays representing the transmission electromagnetic

wave is shooting into the propagation medium and follow the rays bounce,

reflection off materials, diffraction off materials and penetrate through mate-

rials. These rays interact with environmental features (dielectric constant of

obstruction material, obstruction size shape and location, location of trans-

mitter and receiver) and make their way to receivers. In this simulation, the

maximum number of reflections for each single ray is 30 and the maximum

number of diffractions is 5. The SBR for the number of ray paths is more than

2 interactions, image method for Ray paths is within 2 interactions.

However, the Monte Carlo simulation strongly depends on the known

UEs or BSs locations for a particular network. If the UEs locations change

Table 3.2: Symbol Notation

Symbol Definition Parameter Value

γ link SINR Bandwidth 20 MHz

m source D2D UE Transmit Frequency 2.1 GHz DL

m0 destination D2D UE macro-BS Number 19

j Relay D2D UEs CC UE Number/BS 120

o nearest BS D2D UE Number/BS 150

H fading gain Environment Ottawa City

σ2 AWGN power Propagation Model 3GPP UMi [91]

λ pathloss constant UE Distribution PPP

PBS BS transmission power ζ -6 dB

PD2D D2D transmission power AWGN Power -132 dBm

ζ SINR threshold BS Antenna Height 45 m

R max. D2D trans. distance D2D User Height 1.5 m

rj,j0 average hop distance P_BS 40 W

rSPR

j,j0 average hop distance for SPR P_D2D 0.1 W

rIAR(_j,j0 i) average hop distance for IAR ΛD2D 400/km2

KSPR,IAR number of hops Wall Loss 20 dB

RBS BS coverage range Traffic Model full buffer

Ψ Macro-BSs coverage size Multi-path Fading Rayleigh

ΛD2D available D2D density Fading Variance 6 dB

Λ0_D2D co-frequency D2D density Macro-BSs coverage 1650 m

or the network structure changes, the simulation model would be changed.

Stochastic Geometry is a general analytical model that applies for all cellular

networks’ realizations. The simulation parameters and symbols are defined in

Table 3.2.