System-Level Analysis of Cellular Networks Marco Di Renzo

1

System-Level Analysis of Cellular NetworksMarco Di RenzoParis-Saclay University

Laboratory of Signals and Systems (L2S) – UMR8506CNRS – CentraleSupelec – University Paris-Sud

Paris, [email protected]

Course on Random Graphs and Wireless Commun. Networks Oriel College, Oxford University, UK, Sep. 5-6, 2016

H2020-MCSA

5G-PPP – 5G Network Vision

25G-PPP 5G Vision Document, “The next-generation of communication networks and services”, March2015. Available: http://5g-ppp.eu/wp-content/uploads/2015/02/5G-Vision-Brochure-v1.pdf.

5G-PPP – 5G Network Vision

35G-PPP 5G Vision Document, “The next-generation of communication networks and services”, March2015. Available: http://5g-ppp.eu/wp-content/uploads/2015/02/5G-Vision-Brochure-v1.pdf.

The 5G (Cellular) Network of the Future

4

Buzzword 1: Densification1. Access Points (Network Topology, HetNets)2. Radiating Elements (Large-Scale/Massive MIMO)

Buzzword 2: Spectral vs. Energy Efficiency Trade-Off1. Shorter Transmission Distance (Relaying, Femto, D2D)2. Total Power Dissipation (Single-RF MIMO, Antenna Muting)3. RF Energy Harvesting, Wireless Power Transfer, Full-Duplex

Buzzword 3: Spectrum Scarcity1. Cognitive Radio and Opportunistic Communications2. mmWave Cellular Communications

Buzzword 4: Software-Defined, Centrally-Controlled, Shared, Virtualized1. SDN, NFV, Network Resource Virtualization (NRV)

This Lecture: System-Level Analysis of 5G Networks

5

Stochastic Geometry for Modeling Cellular Networks Why do we need Stochastic Geometry ? Can Stochastic Geometry model practical network deployments ? How to use Stochastic Geometry for performance evaluation ? Quick survey of recently proposed mathematical approaches…

Cellular “applications”: Not covered in this lecture HetNets Massive MIMO mmWave cellular Relaying Wireless power transfer etc… etc…

Why? - Densification of Base Stations (your parents net)

6

Why? - Densification of Base Stations (your kids net)

7

8

Modeling Cellular Networks – In IndustryThe NTT DOCOMO 5G Real-Time Simulator

DOCOMO 5G White Paper, “5G Radio Access: Requirements, Concept and Technologies”, July 2014.

9

Life of a 3GPP Simulation Expert (according to Samsung)

Charlie Zhang, Simons Conference on Networks and Stochastic Geometry, October 2015, Austin, USA.

Modeling Cellular Networks – In Academia

10

Conventional approaches to the analysis and design of cellularnetworks (abstraction models) are: The Wyner model The single-cell interfering model or dominant interferers model The regular hexagonal or square grid model

D. H. Ring and W. R. Young, “The hexagonal cells concept”, Bell Labs TechnicalJournal, Dec. 1947. http://www.privateline.com/archive/Ringcellreport1947.pdf.

Modeling Cellular Networks – In Academia

11

Conventional approaches to the analysis and design of cellularnetworks (abstraction models) are: The Wyner model The single-cell interfering model or dominant interferers model The regular hexagonal or square grid model

D. H. Ring and W. R. Young, “The hexagonal cells concept”, Bell Labs TechnicalJournal, Dec. 1947. http://www.privateline.com/archive/Ringcellreport1947.pdf.

Realityvs.

AbstractionModeling

The Conventional Grid-Based Approach

12Probe mobile terminalMacro base station



w 211 1

0 01, B log 1 SINR ,i ir rrC r


14

… Signal-to-Interference-Plus-Noise Ratio (SINR) …

2

20

SINR o oagg

P h rI r

0

20

\agg i i

i BSI r P h r

cov2

20

CCDF P Pr SINRPr ...o o

agg

T T TP h r TI r



w 222 2




w 233 3



17

0 0 0

0

, 1

w 21

1E , ,1 B log 1 SINR ,

i

N ni ir n

nnN

i

nr

n

rr r r

r

C C

r

CN

N


18

Simple enough… So, where is the issue?

0 0 0

0

, 1

w 21


i

N ni ir n

nnN

i

nr

n

rr r r

r

C C

r

CN

N


19

Simple enough… So, where is the issue?The answer:

…this spatial expectation cannot be computed mathematically…

0 0 0

0

, 1

w 21


i

N ni ir n

nnN

i

nr

n

rr r r

r

C C

r

CN

N

The Conventional Grid-Based Approach: (Some) Issues Advantages:

Dozens of system parameters can be modeled and tuned in suchsimulations, and the results have been sufficiently accurate as to enablethe evaluation of new proposed techniques and guide field deployments Limitations:

Actual coverage regions deviate from a regular grid Mathematical modeling and optimization are not possible. Any elegant

and insightful Shannon formulas for cellular networks? The abstraction model is not scalable for application to ultra-dense

HetNets (different densities, transmit powers, access technologies, etc…)

20

Let’s Change the Abstraction Model, Then…

21

Regulardeployment

Let’s Change the Abstraction Model, Then…

22

Regulardeployment

Randomdeployment

(PPP)

Stochastic Geometry Based Abstraction Model

23

A RANDOM SPATIAL MODEL for Heterogeneous CellularNetworks (HetNets): K-tier network with BS locations modeled as independent markedPoisson Point Processes (PPPs) The PPP model is surprisingly good for 1-tier as well (macro BSs):lower/upper bound to reality and trends still hold The PPP model makes even more sense for HetNets due to lessregular BSs placements for lower tiers (femto, etc.)

Stochastic Geometry emerges as a powerful tool for theanalysis, design and optimization

of ultra-dense HetNets

An Emerging (Tractable) Approach

The PPP: Does it Make Sense?

24

Additive White Gaussian Noise. Does it? Independent and Identically Distributed Rayleigh Fading. Does it? etc…

Beyond the PPP: Possible, but Math is More Complicated

25Y. J. Chun, M. O. Hasna, A. Ghrayeb, and M. Di Renzo, “On modeling heterogeneous wireless networksusing non-Poisson point processes”, IEEE Commun. Mag., submitted. [Online]. Available:http://arxiv.org/pdf/1506.06296.pdf.

Matern Hard-Core PPTake a homogeneous PPP and remove any pairs of points that are closer to each other

than a predefined minimum distance R

PPP-based Abstraction

26

How It Works (Downlink – 1-tier)

Probe mobile terminalPPP-distributed macro base station


27




28




29



Intended link

w 211 1



30



Intended link

w 222 2



31



Intended link

w 233 3



32

0 0 0

0

, 1

w 21


i

N ni ir n

nnN

i

nr

n

rr r r

r

C C

r

CN

N


33

Are you kidding me? ... What makes it different?

0 0 0

0

, 1

w 21


i

N ni ir n

nnN

i

nr

n

rr r r

r

C C

r

CN

N


34

Are you kidding me? ... What makes it different?The answer:

…this spatial expectation can be computed mathematically…

0 0 0

0

, 1

w 21


i

N ni ir n

nnN

i

nr

n

rr r r

r

C C

r

CN

N

… On Abstraction Modeling …

35

George Edward Pelham Box (18 October 1919 – 28 March 2013)

StatisticianFellow of the Royal Society (UK)

Director of the Statistical Research Group (Princeton University)

Emeritus Professor(University of Wisconsin-Madison)

“…all models are wrong, but some are useful…”

Is This Abstraction Model Accurate?

36OFCOM: http://stakeholders.ofcom.org.uk/sitefinder/sitefinder-dataset/ORDNANCE SURVEY: https://www.ordnancesurvey.co.uk/opendatadownload/products.html

Methodology:



Methodology: Actual base station locations from OFCOM (UK)

OFCOM:London“London

Bridge area”



Methodology: Actual base station locations from OFCOM (UK) Actual building footprints from ORDNANCE SURVEY (UK)

ORDNANCESURVEY:London“London

Bridge area”



Methodology: Actual base station locations from OFCOM (UK) Actual building footprints from ORDNANCE SURVEY (UK) Channel model added on top (1-state and 2-state with LOS/NLOS)

Mobile terminalBase station (outdoor)Base station (rooftop)NLOS

LOS

NLOS

2-state: the location of MTs and BSsand the location/shape of buildingsdetermine LOS/NLOS conditions1-state: all links are either in LOS orNLOS regardless of the topology

An Example of Blockage Model (3GPP)

40

... Impact of LOS/NLOS …

Mobile terminalBase station

NLOS

LOS

3GPP

The London Case Study (1/7)

41

O2 + Vodafone O2 VodafoneNumber of BSs 319 183 136

Number of rooftop BSs 95 62 33Number of outdoor BSs 224 121 103Average cell radius (m) 63.1771 83.4122 96.7577


42


43


44

PPP Accuracy: 1-State Channel Model

O2+VODAFONE O2 VODAFONE

OFCOM: Actual base station locations, (actual building footprints), actual channels PPP: Random base station locations, (actual building footprints), actual channels


45

PPP Accuracy: 2-State Channel Model

O2+VODAFONE

O2 VODAFONE


46

1-State vs. 2-State Channel Models: Only LOSWorse coverage, as interference is enhanced Only NLOS In-between, as interference is reduced but probe link gets worse LOS and NLOSMore realistic: we can model it with stochastic geometry


47

Omni-Directional vs. 3GPP Radiation Patterns

Why Is This Modeling Approach So Accurate?

48

O2 + Vodafone O2 VodafoneNumber of BSs 319 183 136

Number of rooftop BSs 95 62 33Number of outdoor BSs 224 121 103Average cell radius (m) 63.1771 83.4122 96.7577

Intrigued Enough?

49W. Lu and M. Di Renzo, “Stochastic Geometry Modeling of Cellular Networks: Analysis, Simulation andExperimental Validation”, ACM Int. Conf. Modeling, Analysis and Simulation of Wireless and MobileSystems, Nov. 2015. [Online]. Available: http://arxiv.org/pdf/1506.03857.pdf.

… Further Information and Case Studies …

How It Works: The Magic of Stochastic Geometry (1/5)

50

… understanding the basic math …

0rir0BS

covP Pr SINR T

2

20

SINR o oagg

P h rI r

0

20

\agg i i

i BSI r P h r

2

cov 20

P Pr ...o oagg

P h r TI r

is a PPP

iBS


51


0 0

0 0

2cov 2

02 2 1

02 1

0,

2 1 1

P Pr

PrE exp

E exp MGF

agg

agg

o oagg

o agg o

agg oI r r

r o oI r

P h r TI rh I r P Tr

I r P Tr

P Tr P Tr

2 expoh

MGFE

XsX

X

se


52


0 0

00

2 1 1cov

2 1 10

P E exp MGFexp MGF PDF

agg

agg

r o oI r

rI r

T P r P TrT P P T d


53


0 0

00

2 1 1cov

2 1 10

P E exp MGFexp MGF PDF

agg

agg

r o oI r

rI r

T P r P TrT P P T d

Trivial so far… where is the magic?


54


Trivial so far… where is the magic?Stochastic Geometry provides us with themathematical tools for computing, in closed-form,the MGF and the PDF of the equation above

0 0

00

2 1 1cov

2 1 10

P E exp MGFe Mxp GF PDF

agg

agg

r o oI r

rI r

T P r P TrT P P T d


55


0

20

\agg i i

i BSI r P h r

The aggregate other-cell interference

constitues a Marked PPP, where themarks are the channel power gains

02PDF 2 expr The PDF of the closest-distance

follows from the null probability ofspatial PPPs

0MGF ...aggI r s The MGF of the aggregate other-cell interference follows from theProbability Generating Functional(PGFL) of Marked PPPs


56


20

0

20

20

2, \

2\

2

MGF E exp

E E exp

exp 2 1 E exp

agg i

i

i

i iI r h i BS

i ihi BS

i i i ihr

s s P h r

sP h r

sP h d

PGFL available in closed-form in papers

So Powerful and Just Two Lemmas Need to be Used…

57

Error Probability: From Link-Level…

58

S AWGN DBPSK ML

0

0 0222 0

22 0

21BEP erfc221 1exp exp2 2sin2 b

b b

bE N

E EQN NE Nt dt d

Error Probability: …to System-Level Analysis

59

A. Single-Input-Single-Output Transmission over Nakagami-m FadingB. Spatial Multiplexing MIMO Transmission over Rayleigh Fading – Optimal DemodulationC. Single-Input-Multiple-Output (SIMO) Transmission over Rayleigh FadingD. Orthogonal Space-Time Block Coding (OSTBC) Transmission over Rayleigh FadingE. Spatial Multiplexing MIMO Transmission over Rayleigh Fading – Worst-CaseF. Zero-Forcing (ZF) MIMO Receiver over Rayleigh FadingG. Zero-Forcing MIMO Precoding over Rayleigh Fading

60

Three New and General Mathematical Tools1. Average Rate: The MGF-Based Approach

M. Di Renzo, A. Guidotti, and G. E. Corazza, “Average Rate of Downlink HeterogeneousCellular Networks over Generalized Fading Channels – A Stochastic Geometry Approach”,IEEE Trans. Commun., vol. 61, no. 7, pp. 3050–3071, July 2013.

2. Average Error Probability: The EiD-Based Approach M. Di Renzo and W. Lu, “The Equivalent–in–Distribution (EiD)–based Approach: Onthe Analysis of Cellular Networks Using Stochastic Geometry”, IEEE Commun. Lett.,vol. 18, no. 5, pp. 761-764, May 2014. M. Di Renzo and W. Lu, “Stochastic Geometry Modeling and Performance Evaluation ofMIMO Cellular Networks by Using the Equivalent-in-Distribution (EiD)-BasedApproach”, IEEE Trans. Commun., vol. 63, no. 3, pp. 977-996, March 2015.

3. Coverage Probability: The Gil-Pelaez-Based Approach M. Di Renzo and P. Guan, “Stochastic Geometry Modeling of Coverage and Rate ofCellular Networks Using the Gil-Pelaez Inversion Theorem”, IEEE Commun. Lett., vol.18, no. 9, pp. 1575–1578, September 2014.

Average Rate of Cellular Networks: The Scenario

61

Downlink – 1-tier (the paper deals with HetNets)


Useful link

Average Rate of Cellular Networks: Problem Statement

62

0

02

agg

agg\BS

E ln 1 SINR E ln 1N

b bb

PgR II Pg d

2 02

agg02 exp E ln 1

N

PgR dI

63

The Rate in Terms of the Coverage: Sketch of the Proof

SINR0

SINR cov SINR SINR

SINR SINR0 0SINR

SINR0 0

SINR0

E ln 1 SINR ln 1Integration by parts , 1

1ln 1 1 111 11 1ln 1

1y

R x f x dxF x P x F x F x

x F x F x dxxF xF x dx dxx x

y xF e dy

Pcov-based Approach: State-of-the-Art

64J. G. Andrews, F. Baccelli, and R. K. Ganti, “A Tractable Approach to Coverage and Rate in CellularNetworks”, IEEE Trans. Commun., vol. 59, no. 11, pp. 3122–3134, Nov. 2011.

Bottom Line: Mathematically tractable and insightful for Rayleigh fading Closed-form expressions for special cellular setups (always forRayleigh fading) Intractable multi-fold integrals for fading channels different fromRayleigh

The Enabling Result

65K. Hamdi, “A Useful Lemma for Capacity Analysis of Fading Interference Channels”, IEEE Trans.Commun., vol. 58, no. 2, pp. 411–416, Feb. 2010.

The Enabling Result: Sketch of Proof


MGF-based Approach: The Main Theorem

68M. Di Renzo, A. Guidotti, and G. E. Corazza, “Average Rate of Downlink Heterogeneous CellularNetworks over Generalized Fading Channels – A Stochastic Geometry Approach”, IEEE Trans. Commun.,vol. 61, no. 7, pp. 3050-3071, July 2013.

Note: The “inner integral” can be solved in closed-form with the aidof the Meijer G-function and the Mellin-Barnes theorem. Proposedefficient numerical methods for this computation

On the Computation of TI(·)

69M. Di Renzo, A. Guidotti, and G. E. Corazza, “Average Rate of Downlink Heterogeneous CellularNetworks over Generalized Fading Channels – A Stochastic Geometry Approach”, IEEE Trans. Commun.,vol. 61, no. 7, pp. 3050-3071, July 2013.

It can be computed in closed-form for the most common fadingchannel models No need of computing an infinite summation and the derivatives ofthe MGF of the interference An example: Composite Nakagami-m fast-fading with Log-Normalshadowing

Simple Mathematical Expressions for Special Setups

70

Dense cellular networks:

Interference-limited cellular networks:

High-SNR regime:

ASEP of Ad-Hoc Networks: The Scenario

71

Probe/intended receiverPPP-distributed interferers

Useful link

Useful transmitter at a fixed distance cell association is neglected

Interfering link

72

ASEP of Ad-Hoc Networks: Problem Statement 2 * *

0 0 0 AGGDecision Useful AWGN AggregateMetric Signal Interference

Λ U 2 Re N 2Re I

PPP

1 2AGG AGGI I 2 ,

I

di I I I I Ibi i

Z B G S S bd

11 ,1,cos 2

E exp exp0,4

I

II I

I

bI I I

bB B I

bI I

B S b bM s sB sG CN

M. Di Renzo, C. Merola, A. Guidotti, F. Santucci, G. E. Corazza, “Error Performance of Multi–AntennaReceivers in a Poisson Field of Interferers – A Stochastic Geometry Approach”, IEEE Trans. Commun.,vol. 61, no. 5, pp. 2025–2047, May 2013.

73

Stable Distribution (α=2 Gaussian, β=0 SαS)

74

Stable Distribution (α=2 Gaussian, β=0 SαS)

75

ASEP of Ad-Hoc Networks: Methodology


2 * * 1 20 0 0

Decision Useful AWGNMetric AggregateSignal InterferencEquivalent AWGNconditioning upon

e

Λ U 2 Re N 2Re

IB

I IB G

STEP 1: The frameworks developed without interference can be applied by conditioning upon BI

STEP 2: The conditioning can be removed either numerically or analytically (we did it analytically)

76

ASEP of Ad-Hoc Networks: The Result 2 * *

0 0 0 AGGDecision Useful AWGN AggregateMetric Signal Interference

Λ U 2 Re N 2Re I

PPP

1 2AGG AGGI I 2 ,

I

di I I I I Ibi i

Z B G S S bd

0

12

2 0 30

1ASEP E 1 sinrp

I

m N

BI

K dK N K B


ASEP of Cellular Networks: The Scenario

77

Probe mobile terminalPPP-distributed interfering macro base stations

Useful link (r0)

Tagged macro base station at a random distance cell association is NOT neglected

Interfering link

78

ASEP of Cellular Networks: Problem Statement 2 * *

0 0 0 0 0 AGG 0Decision Useful AWGN AggregateMetric Signal Interference

Λ U 2 Re N 2 Re Ir r r

P 0P P

AGG 0 AGG 0I I ???id r

dibi i

Zr rd

Q1: What is the distribution of IAGG ?Q2: Can we develop an Equivalent-in-Distribution (EiD)

representation of IAGG for arbitrary r0>0 ?M. Di Renzo and W. Lu, “The Equivalent-in-Distribution (EiD)-based Approach: On the Analysis ofCellular Networks Using Stochastic Geometry”, IEEE Commun. Lett., vol. 18, no. 5, pp. 761-764, May 2014.

79

EiD-based Approach: Main Results (1/2)

M. Di Renzo and W. Lu, “The Equivalent-in-Distribution (EiD)-based Approach: On the Analysis ofCellular Networks Using Stochastic Geometry”, IEEE Commun. Lett., vol. 18, no. 5, pp. 761-764, May 2014.

80

EiD-based Approach: Main Results (2/2)

M. Di Renzo and W. Lu, “The Equivalent-in-Distribution (EiD)-based Approach: On the Analysis ofCellular Networks Using Stochastic Geometry”, IEEE Commun. Lett., vol. 18, no. 5, pp. 761-764, May 2014.

81

ASEP of Cellular Networks: Methodology

M. Di Renzo and W. Lu., “Stochastic Geometry Modeling and Performance Evaluation of MIMO CellularNetworks by Using the Equivalent-in-Distribution (EiD)-Based Approach”, IEEE Trans. Commun., vol.63, no. 3, pp. 977-996, March 2015.

2 * *0 0 0

Decision Useful AWGNMetric Signal AggregateInt

1 21

erfer

Equivalent AWGNconditioning upon

ence

1 , 2 , ,

Λ U 2 Re N 2Re

I I I

I Iq

B B B

B q G q

STEP 1: The frameworks developed without interference can be applied by conditioning upon BI(1), BI(2), …, BI(∞)

STEP 2: The conditioning can be removed either numerically or analytically (we did it analytically)

82

EiD-based Approach: The MIMO Case

A. Single-Input-Single-Output Transmission over Nakagami-m FadingB. Spatial Multiplexing MIMO Transmission over Rayleigh Fading – Optimal DemodulationC. Single-Input-Multiple-Output (SIMO) Transmission over Rayleigh FadingD. Orthogonal Space-Time Block Coding (OSTBC) Transmission over Rayleigh FadingE. Spatial Multiplexing MIMO Transmission over Rayleigh Fading – Worst-CaseF. Zero-Forcing (ZF) MIMO Receiver over Rayleigh FadingG. Zero-Forcing MIMO Precoding over Rayleigh Fading

83

EiD-based Approach: The MIMO Case (Approx.)

Coverage/Rate of Cellular Networks: The Scenario

84

Probe mobile terminalPPP-distributed interfering macro base stations

Useful link (r0)

Tagged macro base station at a random distance

Interfering link

85

Coverage/Rate of Cellular Networks: Problem Statement

86

The Rate in Terms of the Coverage: Sketch of the Proof

SINR0

SINR SINR0 0SINR

SINR0 0

SINR0

E ln 1 SINR ln 1Integration by parts

1ln 1 1 111 11 1ln 1

1Integration by parts...again...

y

R x f x dx

x F x F x dxxF xF x dx dxx x

y xF e dy

87

Gil-Pelaez Based Approach

0

1 1CDF Im exp CF2X X XdF x x j x

M. Di Renzo and P. Guan, “Stochastic Geometry Modeling of Coverage and Rate of Cellular NetworksUsing the Gil-Pelaez Inversion Theorem”, IEEE Commun. Lett., vol. 18, no. 9, pp. 1575–1578, Sep. 2014.

88

Gil-Pelaez Approach: Coverage Probability

89

Gil-Pelaez Approach: Average Rate

90

Gil-Pelaez Approach: Interference-Limited Scenario

91

Gil-Pelaez Approach: Gamma-Distributed Power-Gains (1/3)Relevant for studying MIMO cellular networks over Rayleigh fading

92

Gil-Pelaez Approach: Gamma-Distributed Power-Gains (2/3)Closed-form approximations

93

Gil-Pelaez Approach: Gamma-Distributed Power-Gains (3/3)Closed-form approximations: Performance trends

94

Useful References M. Di Renzo, C. Merola, A. Guidotti, F. Santucci, and G. E. Corazza, “Error Performance ofMulti–Antenna Receivers in a Poisson Field of Interferers – A Stochastic Geometry Approach”,IEEE Trans. Commun., vol. 61, no. 5, pp. 2025–2047, May 2013. M. Di Renzo, A. Guidotti, and G. E. Corazza, “Average Rate of Downlink Heterogeneous CellularNetworks over Generalized Fading Channels – A Stochastic Geometry Approach”, IEEE Trans.Commun., vol. 61, no. 7, pp. 3050–3071, July 2013. M. Di Renzo and W. Lu, “The Equivalent–in–Distribution (EiD)–based Approach: On theAnalysis of Cellular Networks Using Stochastic Geometry”, IEEE Commun. Lett., vol. 18, no. 5,pp. 761-764, May 2014. M. Di Renzo and P. Guan, “A Mathematical Framework to the Computation of the ErrorProbability of Downlink MIMO Cellular Networks by Using Stochastic Geometry”, IEEE Trans.Commun., vol. 62, no. 8, pp. 2860–2879, July 2014. M. Di Renzo and P. Guan, “Stochastic Geometry Modeling of Coverage and Rate of CellularNetworks Using the Gil-Pelaez Inversion Theorem”, IEEE Commun. Lett., vol. 18, no. 9, pp.1575–1578, September 2014. M. Di Renzo and W. Lu, “End-to-End Error Probability and Diversity Analysis of AF-Based Dual-Hop Cooperative Relaying in a Poisson Field of Interferers at the Destination”, IEEE Trans.Wireless Commun., vol. 14, no. 1, pp. 15–32, January 2015. M. Di Renzo and W. Lu, “Stochastic Geometry Modeling and Performance Evaluation of MIMOCellular Networks by Using the Equivalent-in-Distribution (EiD)-Based Approach”, IEEE Trans.Commun., vol. 63, no. 3, pp. 977-996, March 2015. M. Di Renzo and W. Lu, “On the Diversity Order of Selection Combining Dual-Branch Dual-HopAF Relaying in a Poisson Field of Interferers at the Destination”, IEEE Trans. Veh. Technol., vol.64, no. 4, pp. 1620-1628, June 2015.

Useful References M. Di Renzo, “Stochastic Geometry Modeling and Analysis of Multi-Tier Millimeter WaveCellular Networks”, IEEE Trans. Wireless Commun., vol. 14, no. 9, pp. 5038-5057, Sep. 2015. W. Lu and M. Di Renzo, “Stochastic Geometry Modeling and System-LevelAnalysis/Optimization of Relay-Aided Downlink Cellular Networks”, IEEE Trans. Commun., vol63, no. 11, pp. 4063-4085, Nov. 2015. M. Di Renzo and P. Guan, “Stochastic Geometry Modeling, System-Level Analysis andOptimization of Uplink Heterogeneous Cellular Networks with Multi-Antenna Base Stations”,IEEE Trans. Commun., IEEE Early Access. M. Di Renzo and W. Lu, “System-Level Analysis/Optimization of Cellular Networks withSimultaneous Wireless Information and Power Transfer: Stochastic Geometry Modeling”, IEEETrans. Vehicular Technol., IEEE Early Access. F. J. Martin-Vega, G. Gomez, M. C. Aguayo Torres, and M. Di Renzo, “Analytical Modeling ofInterference Aware Power Control for the Uplink of Heterogeneous Cellular Networks”, IEEETrans. Wireless Commun., IEEE Early Access. Y. Deng, L. Wang, M. Elkashlan, M. Di Renzo, and J. Yuan, “Modeling and Analysis of WirelessPower Transfer in Heterogeneous Cellular Networks”, IEEE Trans. Commun., IEEE EarlyAccess. T. Tu Lam, M. Di Renzo, and J. P. Coon, “System-Level Analysis of SWIPT MIMO CellularNetworks”, IEEE Commun. Lett., IEEE Early Access. T. Tu Lam, M. Di Renzo, and J. P. Coon, “System-Level Analysis of Receiver Diversity in SWIPT-Enabled Cellular Networks”, IEEE/KICS J. Commun. & Networks, IEEE Early Access. M. Di Renzo, W. Lu, and P. Guan, “The Intensity Matching Approach: A Tractable StochasticGeometry Approximation to System-Level Analysis of Cellular Networks”, IEEE Trans. WirelessCommun., IEEE Early Access. 95

The Intensity Matching (IM) ApproachA Complete Mathematical Framework for System-Level Analysis

M. Di Renzo, W. Lu, and P. Guan, “The Intensity MatchingApproach: A Tractable Stochastic Geometry Approximation toSystem-Level Analysis of Cellular Networks”, IEEE Trans.Wireless Commun., IEEE Early Access. Realistic path-loss model with LOS/NLOS conditions Arbitrary shadowing and fading General antenna-array radiation pattern Multi-tier topology with practical cell association Realistic traffic load models as a function of the densities ofBSs and MTs …

96

IM Approach: Why So Many Details are Needed?

97


Mobile terminalBase station

NLOS

LOS

3GPP

Modeling Blockages: A Practical Example

98

… the mmWave case study …T. S. Rappaport et al. “Millimeter wavechannel modeling and cellular capacityevaluation”, IEEE JSAC, June 2014.Accurate statistical characterizationof the mmWave channel based onthe measurements conducted byresearchers at NYU-WIRELESS:1. Path-loss model2. Shodowing model3. LOS/NLOS/outage link state4. Directional beamforming5. Beamsteering errors6. Multi-tier topology7. Different cell associations


99



100

... Impact of LOS/NLOS on network densification (fully-loaded) …


101

... Impact of LOS/NLOS (fully-loaded) …

0 100 200 300 400 500 600 700 800 900 10000.2

0.40.60.8

11.2

1.41.61.8

2

Rcell [m]

Rate [

bps/H

z]

3GPP link stateonly LOSonly NLOS

Current assumption

(for tractability)in stochastic

geometry modeling(99.99%

of papers)


102

... Impact of Load of Base Stations …

Resource Blocks Resource Blocks

Inactive for these resource blocksBlocked


103

... Impact of Load of Base Stations …

2 5 10 25 50 1000

0.5

1

1.5

2

2.5

3

Rcell [m]

Rate [

bps/H

z]

full loadpractical load, NRB=1practical load, NRB=4practical load, NRB=8


104

... Impact of Antenna Directionality …

-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180-15

-10

-5

0

5

10

Azimuth in degrees

Gain i

n dB

Omni-directional3GPP antenna pattern

Omni-directional antennas

Directional antennas


105

... Impact of Antenna Directionality …

2 5 10 25 50 1000123456789

10

Rcell [m]

Rate [

bps/H

z]

Omni-directional3GPP antenna pattern


106

... Sub-Linear Trend of the Area Spectral Efficiency = λ∙Rate …RATE ASE

Intrigued Enough? On Experimental Validation…

107

W. Lu and M. Di Renzo, “Stochastic Geometry Modeling of Cellular Networks: Analysis, Simulation andExperimental Validation”, ACM Int. Conf. Modeling, Analysis and Simulation of Wireless and MobileSystems, Nov. 2015. [Online]. Available: http://arxiv.org/pdf/1506.03857.pdf.W. Lu and M. Di Renzo, “Stochastic Geometry Modeling of mmWave Cellular Networks: Analysis andExperimental Validation”, IEEE Int. Workshop on Measurement and Networking (M&N) – SpecialSession on Advances in 5G Wireless Networks, Oct. 12-13, 2015.

108

… the approach (e.g., 3-ball case) … Practical link-state models are approximated using a multi-ball model The related parameters are computed using the “intensity matching” criterion

d1

d3

d2

1 11

3 , ,,1 LOS,NLOS,...

with 1 1, 2, ,n n n nn n

N d d d dS S Sd dn Sp r q r q n N

1

2actual approx

max maxLOS,NLOS, LOS,NLOS,

minimize ln 0, ln 0,S SS S Fx x

Rationale of the IM Approach: Multi-Ball Approximation

Rationale of the IM Approach: Multi-Ball Approximation

109

Why Matching the Intensity Measures ? Consider the general association criterion as follows:

Ф is a (non-homogeneous) PPP of BSs with density λ(r) = λ*p(r)l(r) denotes the path-loss functionΥ is a random variable that accounts for all random variables that are takeninto account for cell association except for the distance (e.g., shadowing)

Based on the displacement theorem of PPPs, the set Ψ is a PPP in R+ whoseintensity measure is the following:

0BS is chosen as the of the set minimum ,n

n

l r n

0

0

0, 2 Pr 0,

2 E Pr 0,

l rx x p r rdr

l r x p r rdr

110

Since the intensity measure is now known and Ψ is still a PPP, the coverageprobability can be formulated, after some algebra, as follows:

LOS

NLOS

2,LOS LOS

cov LOS NLOS LOS LOS2LOS

2,NLOS NLOS

LOS LOS NLOS NLOS2NLOS

2,LOS

2

P E Pr Pr

E Pr Pr

Pr

ol

agg

ol

agg

o

agg

P h l T l l l lI l

P h l T l l l lI lP h x T xI x

NLOS LOS

LOS NLOS

0

2,NLOS

20

CCDF PDF

Pr CCDF PDF

l l

ol l

agg

x x dx

P h y T y y y dyI y

LOSLOS LOS LOS NLOS NLOS NLOS NLOSmin minl l r l l r

Rationale of the IM Approach: Multi-Ball ApproximationWhy Matching the Intensity Measures ?

111

void probability th.CCDF exp 0, PDF CCDFSS S Sl l ld d

2,

2,

2,

,LOS,2

, , ,,

2, , ,

PGF

N OS

L,

, L

2

MGF ; MGF ;MGF ;E exp

E E e

MGF ;

xp

exp 1 E exp

agg

QQ k Q

agg ag

Q Q

g

k

Q

g

Q

k

a gI SI Q S

k Q k Q k Q Skh

k Q k Q k Q Sk h

k Q

S I

h

I Sw lw P h l l l

w P h l l l

w P l

l

h

w l w l w

1

1

1

0,

0,QS

Q

ld dl l

l dl

Rationale of the IM Approach: Multi-Ball ApproximationWhy Matching the Intensity Measures ?

Intrigued Enough? On Mathematical Modeling…

112M. Di Renzo, W. Lu, and P. Guan, “The Intensity Matching Approach: A Tractable Stochastic GeometryApproximation to System-Level Analysis of Cellular Networks”, IEEE Trans. Wireless Commun., to appear.

The Intensity Matching Approach: Main Takes


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Very Dense

Dense SparseVery Sparse



2 5 10 25 50 100 300 10000

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Rcell [m]

Rate

[bps/H

z]

Depends on the density of blockages

Depends on the base station load

What the IM Approach Allows Us to Model…?


… General Cell Association Criteria

117

… shortest distance …


118

… highest average received power with shadowing …


119

… smallest path-loss with LOS/NLOS links …


120

… two-tier biased smallest path-loss …

… Practical Blockage Models

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… Practical Load Models

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… Practical Load Models

123

… Practical Radiation Patterns

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… Relevant Key Performance Indicators

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… Proof of Several Performance Trends

126

… Proof of Several Performance Trends

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Rcell [m]

Rate

[bps/H

z]

Depends on the density of blockages

Depends on the base station load

… Experimental Validation

128

Beyond the PPP-Based Modeling: The α-Ginibre PP

129


130I. Nakata and N. Miyoshi, “Spatial stochastic models for analysis of heterogeneous cellular networks withrepulsively deployed base stations”, Research Reports on Mathematical and Computing Sciences (ISSN1342-2804), Oct. 2013, B-473.

The Road Ahead: IM Approach for non-Poisson Nets

133

… Cauchy determinantal point process (spatially-repulsive) …

SINR [dB]

Solid lines: Simulations with RMarkers: Proposed approximationDashed lines: Poisson networks

… final thoughts …

134

The Role of Stochastic Geometry in Communications

135S. Mukherjee: “Analytical Modeling of Heterogeneous Cellular Networks”, Cambridge University Press,January 2014.

The Renaissance of (Network) Communication Theory

136PLENARY PANEL: “The Impact of Communication Theory on Technology Development: Is the BestBehind us or Ahead?”, IEEE Communications Theory Workshop, May 2010.

… IEEE TCOM Nov. 2011 – now …

Bottom Line

137

Stochastic geometry provides suitable mathematical models andappropriate statistical methods to study and analyze heterogeneous(future deployments) cellular networks It is instrumental for identifying subsets of candidate (feasible,relevant) solutions based on which finer-grained simulations can beconducted, thus significantly reducing the time and cost of optimizingcomplex communication networks Its application to cellular network designs, however, necessitates toabandon conventional and comfortable assumptions

Poisson (complete spatially random) modeling Simplistic path-loss models Simplistic transmission schemes …

Relying upon adequate approximations to avoid oversimplifying thesystem model is not an option. CAUTION is, however, mandatory.

The System-Level Side of 5G – YouTube Video

138https://youtu.be/MB8IvOYYvB0

Thank You for Your Attention

Marco Di Renzo, Ph.D., H.D.R.Chargé de Recherche CNRS (Associate Professor)Editor, IEEE Communications LettersEditor, IEEE Transactions on CommunicationsDistinguished Lecturer, IEEE Veh. Technol. SocietyDistinguished Visiting Fellow, RAEng-UKParis-Saclay UniversityLaboratory of Signals and Systems (L2S) – UMR-8506CNRS – CentraleSupelec – University Paris-Sud3 rue Joliot-Curie, 91192 Gif-sur-Yvette (Paris), FranceE-Mail: [email protected]: http://www.l2s.centralesupelec.fr/perso/marco.direnzo

ETN-5Gwireless (H2020-MCSA, grant 641985)An European Training Network on 5G Wireless Networkshttp://cordis.europa.eu/project/rcn/193871_en.html (Jan. 2015, 4 years)

System-Level Analysis of Cellular Networks Marco Di Renzo

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