Marco Di Renzo Paris-Saclay University Laboratory of Signals and - - PowerPoint PPT Presentation

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On System-Level Analysis and Optimization of Large-Scale Networks

(modeling, experimental validation, and hints for optimization)

Marco Di Renzo

Paris-Saclay University Laboratory of Signals and Systems (L2S) – UMR8506 CNRS – CentraleSupelec – University Paris-Sud Paris, France marco.direnzo@l2s.centralesupelec.fr

WiOpt – RAWNET 2017 Paris, France - May 15, 2017

H2020-MCSA H2020-MCSA

5G-PPP – 5G Network Vision

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5G-PPP 5G Vision Document, “The next-generation of communication networks and services”, March

• 2015. Available: http://5g-ppp.eu/wp-content/uploads/2015/02/5G-Vision-Brochure-v1.pdf.

5G-PPP – 5G Network Vision

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5G-PPP 5G Vision Document, “The next-generation of communication networks and services”, March

• 2015. Available: http://5g-ppp.eu/wp-content/uploads/2015/02/5G-Vision-Brochure-v1.pdf.

The 5G (Cellular) Network of the Future

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 Buzzword 1: Densification 1.

Access Points (Network Topology, HetNets)

2.

Radiating Elements (Large-Scale/Massive MIMO)

 Buzzword 2: Spectral vs. Energy Efficiency Trade-Off 1.

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 Scarcity 1.

Cognitive Radio and Opportunistic Communications

2.

mmWave Cellular Communications

 Buzzword 4:Software-Defined, Centrally-Controlled, Shared,Virtualized 1.

SDN, NFV, Network Resource Virtualization (NRV)

Why Network Densification is So Important ?

5

• M. Dohler, R. W. Heath Jr., A. Lozano, C. Papadias, R. A. Valenzuela, “Is the PHY Layer Dead?”, IEEE

Communications Magazine, Vol 49, No 4, pp. 159‐165, April 2011.

… Increase in Capacity Over the Last Decade …

This Talk: System-Level Analysis and Optimization

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 Stochastic Geometry for Modeling and Optimizing Cellular

Networks

• Why do we need Stochastic Geometry ?
• Can Stochastic Geometry model practical network deployments ?
• How to use Stochastic Geometry for performance evaluation ?
• Hints for system-level optimization …

 Cellular “applications”: Not covered in this talk

• HetNets
• Massive MIMO
• mmWave cellular
• Relaying
• Wireless power transfer & renewable energy sources
• etc… etc…

Hints for System-Level Optimization – Caching

7

By courtesy of Ejder Bastug (CentraleSupelec)

The Caching Problem… in general but simple terms…

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Let a realization of base station locations Let a realization of mobile terminal locations Estimate the data to be cached Place the data in the caches Associate the mobile terminals to the caches such that a utility function is optimized subject to some constraints

To be Presented Today at WiOpt - CCDWN 2017

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The Caching Problem: System-Level Formulation

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Let a realization of base station locations Let a realization of mobile terminal locations Let the base station locations be distributed as… Let the mobile terminal locations be distributed as…

Questions: (by taking into account the network topology)

1) Optimal density of base stations that maximizes the area spectral efficiency ? 2) Given the density of base stations, the optimal density of caches ? 3) Given the density of base stations, the interplay between density & size of caches ? 4) Optimal user association in the presence of caches ? 5) …

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Modeling Cellular Networks – In Industry

The NTT DOCOMO 5G Real-Time Simulator

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

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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

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 Conventional approaches to the analysis and design of

cellular networks (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 Technical

Journal, Dec. 1947. http://www.privateline.com/archive/Ringcellreport1947.pdf.

Modeling Cellular Networks – In Academia

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 Conventional approaches to the analysis and design of

cellular networks (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 Technical

Journal, Dec. 1947. http://www.privateline.com/archive/Ringcellreport1947.pdf.

Reality vs. Abstraction Modeling

The Conventional Grid-Based Approach

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Probe mobile terminal Macro base station

The Conventional Grid-Based Approach

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Probe mobile terminal Macro base station

   

 

 

   

 

 

 

w 2 1 1 1 1

, B log 1 SINR ,

i i

r r r C r  

The Conventional Grid-Based Approach

17

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

 

2 2

SINR

• agg

P h r I r







 

 

2 \ agg i i i BS

I r P h r 

 

 

       

cov 2 2

CCDF P Pr SINR Pr ...

• agg

T T T P h r T I r







                

The Conventional Grid-Based Approach

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Probe mobile terminal Macro base station

   

 

 

   

 

 

 

w 2 2 2 2 2

, B log 1 SINR ,

i i

r r r C r  

The Conventional Grid-Based Approach

19

Probe mobile terminal Macro base station

   

 

 

   

 

 

 

w 2 3 3 3 3

, B log 1 SINR ,

i i

r r r C r  

The Conventional Grid-Based Approach

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Simple enough… So, where is the issue? The answer: …this spatial expectation cannot be computed mathematically…  

 

 

0 ,

E ,

i

i r r

C C r r 

The Conventional Grid-Based Approach

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 

 

 

 

0 ,

E ,

i

i r r

C C r r 

   

 

 

   

 

 

 

1 1 w 2

1 , 1 B log 1 SINR ,

n i n N n N n n n i

C r r N r N r

 

  

 

… spatially-average metrics are difficult to be formulated in mathematical terms … ↓ Monte Carlo Approximations (N → ∞)

The Conventional Grid-Based Approach: (Some) Issues

 Advantages:

• Dozens of system parameters can be modeled and tuned in such

simulations, and the results have been sufficiently accurate as to enable the 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…)

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Let’s Change the Abstraction Model, Then…

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Regular deployment

Let’s Change the Abstraction Model, Then…

24

Regular deployment Random deployment (PPP)

Stochastic Geometry Based Abstraction Model

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 A RANDOM SPATIAL MODEL for Ultra-Dense Heterogeneous

Cellular Networks (HetNets):

• K-tier network with BS locations modeled as independent marked

Poisson 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 less

regular BSs placements for lower tiers (femto, etc.)

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

• f ultra-dense HetNets

An Emerging (Tractable) Approach

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Stochastic Geometry: Well-Known Mathematical Tool

27

Stochastic Geometry: Sophisticated Statistical Toolboxes

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Stochastic Geometry: Sophisticated Statistical Toolboxes

Poisson vs. Non-Poisson Point Processes

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• Y. J. Chun, M. O. Hasna, A. Ghrayeb, and M. Di Renzo, “On modeling heterogeneous wireless networks

using non-Poisson point processes”, [Online]. Available: http://arxiv.org/pdf/1506.06296.pdf.

Matern Hard-Core PP

Take a homogeneous PPP and remove any pairs of points that are closer to each other than a predefined minimum distance R

The PPP: Does it Make Sense?

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

PPP-based Abstraction

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How It Works (Downlink – 1-tier)

Probe mobile terminal PPP-distributed macro base station

PPP-based Abstraction

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How It Works (Downlink – 1-tier)

Probe mobile terminal PPP-distributed macro base station

PPP-based Abstraction

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How It Works (Downlink – 1-tier)

Probe mobile terminal PPP-distributed macro base station

PPP-based Abstraction

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How It Works (Downlink – 1-tier)

Probe mobile terminal PPP-distributed macro base station Intended link

   

 

 

   

 

 

 

w 2 1 1 1 1

, B log 1 SINR ,

i i

r r r C r  

PPP-based Abstraction

35

How It Works (Downlink – 1-tier)

Probe mobile terminal PPP-distributed macro base station Intended link

   

 

 

   

 

 

 

w 2 2 2 2 2

, B log 1 SINR ,

i i

r r r C r  

PPP-based Abstraction

36

How It Works (Downlink – 1-tier)

Probe mobile terminal PPP-distributed macro base station Intended link

   

 

 

   

 

 

 

w 2 3 3 3 3

, B log 1 SINR ,

i i

r r r C r  

PPP-based Abstraction

37

 

 

 

 

   

 

 

   

 

 

 

0 ,

1 w 2 1

E , the following is not needed anymore 1 , 1 B log 1 SINR ,

i

i r n i n i N N r n n n n

C C C N N r r r r r r

 

    

 

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

… On Abstraction Modeling …

38

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

39

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

 Methodology:

Is This Abstraction Model Accurate?

40

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

 Methodology:

• Actual base station locations from OFCOM (UK)

OFCOM: London “London Bridge area”

Is This Abstraction Model Accurate?

41

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

 Methodology:

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

ORDNANCE SURVEY: London “London Bridge area”

Is This Abstraction Model Accurate?

42

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

 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 terminal Base station (outdoor) Base station (rooftop) NLOS LOS NLOS

2-state: the location of MTs and BSs and the location/shape of buildings determine LOS/NLOS conditions 1-state: all links are either in LOS or NLOS regardless of the topology

Practical Example of Blockage Model (3GPP)

43

... statistically modeling of blockages using LOS/NLOS links …

Mobile terminal Base station NLOS LOS 3GPP

The London Case Study

44 O2 + Vodafone O2 Vodafone Number of BSs 319 183 136 Number of rooftop BSs 95 62 33 Number of outdoor BSs 224 121 103 Average cell radius (m) 63.1771 83.4122 96.7577

The London Case Study

45

The London Case Study

46

The London Case Study

47

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

The London Case Study

48

PPP Accuracy: 2-State Channel Model

O2+VODAFONE O2 VODAFONE

The London Case Study (6/8)

49

 1-State vs. 2-State Channel Models:

• Only LOS  Worse coverage, as interference is enhanced
• Only NLOS  In-between, as interference is reduced but probe link gets worse
• LOS and NLOS  More realistic: we can model it with stochastic geometry

The London Case Study (7/8)

50

Omni-Directional vs. 3GPP Radiation Patterns

The London Case Study (8/8)

51

• M. Di Renzo, W. Lu, and P. Guan, “The Intensity Matching Approach: A Tractable Stochastic Geometry

Approximation to System-Level Analysis of Cellular Networks”, IEEE Trans. Wireless Commun., Sep. 2016.

100 200 300 400 500 600 700 800 900 1000 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Rcell [m] Rate [bps/Hz] 3GPP link state

• nly LOS
• nly NLOS

* With blockages (LOS+NLOS)

 Standard model (LOS): r-αl

• Standard model (NLOS): r-αn

towards interference-limited

… This Changes The Story, Let’s go Back to 2011 …

52

• J. G. Andrews, F. Baccelli, and R. K. Ganti, “A Tractable Approach to Coverage and Rate in Cellular

Networks”, IEEE Trans. Commun., vol. 59, no. 11, pp. 3122–3134, Nov. 2011.

Why Is This Modeling Approach So Accurate?

53 O2 + Vodafone O2 Vodafone Number of BSs 319 183 136 Number of rooftop BSs 95 62 33 Number of outdoor BSs 224 121 103 Average cell radius (m) 63.1771 83.4122 96.7577

Intrigued Enough? On Experimental Validation…

54

• W. Lu and M. Di Renzo, “Stochastic Geometry Modeling of Cellular Networks: Analysis, Simulation and

Experimental Validation”, ACM Int. Conf. Modeling, Analysis and Simulation of Wireless and Mobile Systems, 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 and

Experimental Validation”, IEEE Int. Workshop on Measurement and Networking (M&N) – Special Session on Advances in 5G Wireless Networks, Oct. 12-13, 2015.

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

55

… understanding the basic math …

r

i

r

BS

 

cov

P Pr SINR T  

 

2 2

SINR

• agg

P h r I r







 

 

2 \ agg i i i BS

I r P h r 

 

 

 

2 cov 2

P Pr ...

• agg

P h r T I r







             

is a PPP 

i

BS

How It Works: The Magic of Stochastic Geometry (2/5)

56

… understanding the basic math …

   

 

 

 

 

 

 

 

 

  



 

2 cov 2 2 2 1 2 1 , 2 1 1

P Pr Pr E exp E exp MGF

agg agg

• agg
• agg
• agg
• I

r r r

• I

r

P h r T I r h I r P Tr I r P Tr P Tr P Tr

    

   

    

                    

 

2 ~exp

• h



 

 

MGF E

X sX X

s e          

How It Works: The Magic of Stochastic Geometry (3/5)

57

… understanding the basic math …

 

  



 

 

  



 

2 1 1 cov 2 1 1

P E exp MGF exp MGF PDF

agg agg

r

• I

r r I r

T P r P Tr T P P T d

   

     

    

   



How It Works: The Magic of Stochastic Geometry (3/5)

58

… understanding the basic math …

 

  



 

 

  



 

2 1 1 cov 2 1 1

P E exp MGF exp MGF PDF

agg agg

r

• I

r r I r

T P r P Tr T P P T d

   

     

    

   



Trivial so far… where is the magic?

How It Works: The Magic of Stochastic Geometry (3/5)

59

… understanding the basic math …

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

 

  



 

 

  



 

2 1 1 cov 2 1 1

P E exp MGF e M xp GF PDF

agg agg

r

• I

r r I r

T P r P Tr T P P T d

   

     

    

   



How It Works: The Magic of Stochastic Geometry (4/5)

60

… understanding the basic math …

 

2 \ agg i i i BS

I r P h r 

 

 

The aggregate other-cell interference constitues a Marked PPP, where the marks are the channel power gains

 

 

2

PDF 2 exp

r 

   

The PDF of the closest-distance follows from the null probability of spatial PPPs    

MGF ...

agg

I r

s 

The MGF of the aggregate other- cell interference follows from the Probability Generating Functional (PGFL) of Marked PPPs

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

61

… understanding the basic math …

   

   

 

 

 

 

 

2 2 2

2 , \ 2 \ 2

MGF E exp E E exp exp 2 1 E exp

agg i i i

i i I r h i BS i i h i BS i i i i h r

s s P h r sP h r sP h d

  

   

       

                                         

  

 

PGFL 

available in closed-form in papers

Stochastic Geometry in Formulas (Poisson Nets)…

62

   

 

  



 

 

  



   

 

   

 

 

 

2

cov 2 1 1 cov 2 1 1 2 2

P 1 P E exp MGF MGF MGF exp 2 1 E e PDF P xp e DF e x x p 2 p

agg g i agg a g

r

• I

r i i i i I r h r r r I r

x C dx x x x P r P xr x P P x d s sP h d

    

            

        

                   

  

So Powerful and Just Two Lemmas Need to be Used…

63

64

Some References



• M. Di Renzo, C. Merola, A. Guidotti, F. Santucci, and G. E. Corazza, “Error Performance of

Multi–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 Cellular

Networks 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 the

Analysis 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 Error

Probability 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 Cellular

Networks 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 MIMO

Cellular 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-Hop

AF Relaying in a Poisson Field of Interferers at the Destination”, IEEE Trans. Veh. Technol., vol. 64, no. 4, pp. 1620-1628, June 2015.

Some References



• M. Di Renzo, “Stochastic Geometry Modeling and Analysis of Multi-Tier Millimeter Wave

Cellular 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-Level Analysis/Optimization of Relay-Aided Downlink Cellular Networks”, IEEE Trans. Commun., vol 63, no. 11, pp. 4063-4085, Nov. 2015.



• M. Di Renzo and P. Guan, “Stochastic Geometry Modeling, System-Level Analysis and

Optimization 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 with

Simultaneous Wireless Information and Power Transfer: Stochastic Geometry Modeling”, IEEE

• Trans. Vehicular Technol., IEEE Early Access.



• F. J. Martin-Vega, G. Gomez, M. C. Aguayo Torres, and M. Di Renzo, “Analytical Modeling of

Interference Aware Power Control for the Uplink of Heterogeneous Cellular Networks”, IEEE

• Trans. Wireless Commun., IEEE Early Access.



• Y. Deng, L. Wang, M. Elkashlan, M. Di Renzo, and J. Yuan, “Modeling and Analysis of Wireless

Power Transfer in Heterogeneous Cellular Networks”, IEEE Trans. Commun., IEEE Early Access.



• T. Tu Lam, M. Di Renzo, and J. P. Coon, “System-Level Analysis of SWIPT MIMO Cellular

Networks”, 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 Stochastic

Geometry Approximation to System-Level Analysis of Cellular Networks”, IEEE Trans. Wireless Commun., IEEE Early Access.

65

The Intensity Matching (IM) Approach

A Complete Mathematical Framework for System-Level Analysis

 M. Di Renzo, W. Lu, and P

. Guan, “The Intensity Matching Approach: A Tractable Stochastic Geometry Approximation to System-Level Analysis of Cellular Networks”, IEEE Trans. Wireless Commun., Sep. 2016.

• 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 of

BSs and MTs

• …

66

Our Proposed Tractable Approach for Poisson Networks

67

• M. Di Renzo, W. Lu, and P. Guan, “The Intensity Matching Approach: A Tractable Stochastic Geometry

Approximation to System-Level Analysis of Cellular Networks”, IEEE Trans. Wireless Commun., Sep 2016.

IM Approach: How To Efficiently Model Blockages

68

Why Modeling Blockages is so Important ?

69

100 200 300 400 500 600 700 800 900 1000 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Rcell [m] Rate [bps/Hz] 3GPP link state

• nly LOS
• nly NLOS

* With blockages (LOS+NLOS)

 Standard model (LOS): r-αl

• Standard model (NLOS): r-αn

towards interference-limited

… This Changes The Story, Let’s go Back to 2011 …

70

• J. G. Andrews, F. Baccelli, and R. K. Ganti, “A Tractable Approach to Coverage and Rate in Cellular

Networks”, IEEE Trans. Commun., vol. 59, no. 11, pp. 3122–3134, Nov. 2011.

The Problem (e.g., Computing the Shannon Rate)

71

Key Observation: The Intensity Measure is Essential

72

 Proposed approach/approximation:

• No attempt for simplifying the expression of the rate is made
• The intensity measure is approximated with another intensity measure

that is more suitable for mathematical analysis

 What is it needed ?

• An approximated intensity measure suitable for mathematical analysis
• A criterion for computing, from the exact intensity measure, the set of its

constituent parameters

73

… the approach (e.g., 3-ball case) …

 Practical blockage models are approximated by using a multi-ball model  The related parameters are computed using the “intensity matching” criterion

d1 d3 d2

 

         

1 1 1

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

with 1 1,2, ,

n n n n n n

N d d d d S S S d d n S

p r q r q n N

  

  

   

 

1 

  



 

    



 

 

2 actual approx max max LOS,NLOS, LOS,NLOS,

minimize ln 0, ln 0,

S S

S S F

x x

   

                            

 

 

Rationale of the IM Approach: Multi-Ball Approximation

Main Result: Tractable Expression of the Rate

74

IM Approach: Experimental Validation

75

Simplified Expressions in Four Regimes

76

• M. Di Renzo, W. Lu, and P. Guan, “The Intensity Matching Approach: A Tractable Stochastic Geometry

Approximation to System-Level Analysis of Cellular Networks”, IEEE Trans. Wireless Commun., Sep. 2016.

2 5 10 25 50 100 300 1000 0.5 1 1.5 2 2.5 3 3.5 Rcell [m] Rate [bps/Hz]

Very Dense Dense Sparse Very Sparse

Mathematical Proof of Performance

77

• M. Di Renzo, W. Lu, and P. Guan, “The Intensity Matching Approach: A Tractable Stochastic Geometry

Approximation to System-Level Analysis of Cellular Networks”, IEEE Trans. Wireless Commun., Sep. 2016.

New Insights for System-Level Optimization

78

• M. Di Renzo, W. Lu, and P. Guan, “The Intensity Matching Approach: A Tractable Stochastic Geometry

Approximation to System-Level Analysis of Cellular Networks”, IEEE Trans. Wireless Commun., Sep. 2016.

2 5 10 25 50 100 300 1000 0.5 1 1.5 2 2.5 3 3.5 Rcell [m] Rate [bps/Hz]

Depends on the density of blockages Depends on the base station load

… final thoughts …

79

The Role of Stochastic Geometry

80

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

January 2014.

Stochastic Geometry for Commun. – Bottom Line

81

 Stochastic geometry provides us with suitable mathematical models

and appropriate statistical methods for studying and optimizing heterogeneous (future deployments) cellular networks

 It is instrumental for identifying subsets of

candidate (feasible, relevant) solutions based on which finer-grained simulations can be conducted, thus significantly reducing the time and cost of optimizing complex communication networks

 Its application to cellular network designs, however, necessitates to

abandon conventional and comfortable assumptions

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

 Relying upon adequate approximations to avoid oversimplifying the

system model is not an option. CAUTION is, however, mandatory.

Stochastic Geometry for Cellular Nets – YouTube Video

82

https://youtu.be/MB8IvOYYvB0

Thank You for Your Attention

Marco Di Renzo, Ph.D., H.D.R.

Chargé de Recherche CNRS

Editor, IEEE Communications Letters Editor, IEEE Transactions on Communications Editor, IEEE Transactions on Wireless Communications Distinguished Lecturer, IEEE Communications Society Distinguished Lecturer, IEEE Veh. Technol. Society

Paris-Saclay University Laboratory of Signals and Systems (L2S) – UMR-8506 CNRS – CentraleSupelec – University Paris-Sud 3 rue Joliot-Curie, 91192 Gif-sur-Yvette (Paris), France E-Mail: marco.direnzo@l2s.centralesupelec.fr Web-Site: http://www.l2s.centralesupelec.fr/perso/marco.direnzo

• ETN-5Gwireless (H2020-MCSA, grant 641985)
• ETN-5Gaura (H2020-MCSA, grant 675806)

Two European Training Networks on 5G Wireless Networks