coverage analysis of hetnets with base station cooperation ......coverage analysis of hetnets with...

Coverage Analysis of HetNets with

Base Station Cooperation and Interference Cancellation

Martin Haenggi

Dept. of Electrical Engineering

University of Notre Dame

Notre Dame, IN, USA

2014 HetNet Workshop

June 16, 2014

Work supported by:U.S. NSF (CNS 1014932 and CCF 1216407)

M. Haenggi (Univ. of Notre Dame) Coverage of HetNets 06/16/2014 1 / 46

Coverage Analysis of HetNets withBase Station Cooperation and Interference Cancellation:

Why the Waist-to-Hip Ratio is Essential

Martin Haenggi

Dept. of Electrical Engineering

University of Notre Dame

Notre Dame, IN, USA

2014 HetNet Workshop

June 16, 2014

Work supported by:U.S. NSF (CNS 1014932 and CCF 1216407)


Content

Contents

Coverage


Content

Small cells

A small cell.


Content

Cell-ular user

A cell phone.

No noise

This is a completely noise-less talk.


Overview

Menu

Overview

Bird’s view of cellular networks

The HIP model and its properties

Comparing SIR distributions: The crucial role of the meaninterference-to-signal ratio (MISR)

MISR gain due to BS silencing and cooperation

DUI: Diversity under interference

General BS cooperation

Back to modeling: Inter- and intra-tier dependence

Conclusions


Introduction The big picture

Big picture

Frequency reuse 1: A single friend, many foes

−4 −3 −2 −1 0 1 2 3 4−4

−3

−2

−1

0

1

2

3

4



A walk through a single-tier cellular network

−4 −3 −2 −1 0 1 2 3 4−4

−3

−2

−1

0

1

2

3

4

−3 −2 −1 0 1 2 3−6

−4

−2

0

2

4

6

8

10

12SIR (no fading)

x

SIR

(dB

)



Coverage at 0 dB

−4 −3 −2 −1 0 1 2 3 4−4

−3

−2

−1

0

1

2

3

4

−3 −2 −1 0 1 2 3−6

−4

−2

0

2

4

6

8

10

12SIR (no fading)

x

SIR

(dB

)



SIR distribution

−3 −2 −1 0 1 2 3−25

−20

−15

−10

−5

0

5

10

15SIR (with fading)

x

SIR

(dB

)

For ergodic models, the fraction of the curve that is above the threshold θis the ccdf of the SIR at θ:

ps(θ) , F̄SIR(θ) , P(SIR > θ)

It is the fraction of the users with SIR > θ if users are uniformly distributed.


HIP model Definition

The HIP baseline model for HetNets

The HIP (homogeneous independent Poisson) model

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

Start with a homogeneous Poisson point process (PPP). Here λ = 6.Then randomly color them to assign them to the different tiers.


HIP model Definition

The HIP (homogeneous independent Poisson) model

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

Randomly assign BS to each tier according to the relative densities. Hereλi = 1, 2, 3. Assign power levels Pi to each tier.This model is doubly independent and thus highly tractable.


HIP model Basic result

Basic result for downlink

Assumptions:

A user connects to the BS that is strongest on average, while allothers interfere.

Homogeneous path loss law ℓ(r) = r−α and Rayleigh fading.

Result for α = 4:

ps(θ) = P(SIR > θ) = F̄SIR(θ) =1

1 +√θ arctan

√θ.

Remarkably, this is independent of the number of tiers, their densities, andtheir power levels.So as far as the SIR is concerned, we can replace the multi-tier HIP modelby an equivalent single-tier model.(For bounded path loss laws, this does not hold.)


HIP model Basic result

Properties of the HIP model

For the unbounded path loss law:

E(S) = ∞ and E(SIR) = ∞ due to the proximity of the strongest BS.

E(I ) = ∞ for α ≥ 4 due to the proximity of the strongest interferer.

The first two properties are not restricted to the Poisson model.

Remarks

Per-user capacity improves with smaller cells, but coverage does not.(Unless the interference benefit from inactive BSs kicks in.)

Question: How to boost coverage?⇒ Non-Poisson deployment⇒ BS silencing⇒ BS cooperation

How to quantify the improvement in the SIR distribution?


Comparing SIR Distributions

Comparing SIR distributions

Two distributions

−15 −10 −5 0 5 10 15 20 250

0.2

0.4

0.6

0.8

1SIR CCDF

θ (dB)

P(S

IR>

θ)

baseline schemeimproved scheme

How to quantify the improvement?


Comparing SIR Distributions Vertical comparison

The standard comparison: vertical

−15 −10 −5 0 5 10 15 20 250

0.2

0.4

0.6

0.8

1SIR CCDF

θ (dB)

P(S

IR>

θ)


At -10 dB, the gap is 0.058. Or 6.4%.

At 0 dB, the gap is 0.22. Or 39%.



Or use the gain in P(SIR ≤ θ)?


Comparing SIR Distributions Horizontal comparison

A better choice: horizontal

−15 −10 −5 0 5 10 15 20 250

0.2

0.4

0.6

0.8

1SIR CCDF

θ (dB)

P(S

IR>

θ)

G

G

G

Gbaseline schemeimproved scheme

Use the horizontal gap instead.

This SIR gain is nearly constantover θ in many cases.

If the improvement is due to betterBS deployment, it is the deploymentgain.

ps = P(SIR > θ) ⇒ ps = P(SIR > θ/G ).

Can we quantify this gain?


Comparing SIR Distributions The horizontal gap

Horizontal gap at probability p

The horizontal gap between two SIR ccdfs is

G (p) ,F̄−1

SIR2(p)

F̄−1SIR1

(p), p ∈ (0, 1),

where F̄−1SIR is the inverse of the ccdf of the SIR, and p is the target success

probability.We also define the asymptotic gain (whenever the limit exists) as

G , G (1) = limp→1

G (p).

Relevance

We will show that

G is relatively easy to determine.

G (p) ≈ G for all practical p.


Comparing SIR Distributions ISR

The ISR

Definition (ISR)

The interference-to-average-signal ratio is

ISR ,I

Eh(S),

where Eh(S) is the desired signal power averaged over the fading.

Comments

The ISR is a random variable due to the random positions of BSs andusers. Its mean MISR is a function of the network geometry only.

If the desired signal comes from a single BS at distance R , ISR = IRα.

If the interferers are located at distances Rk ,

MISR , E(ISR) = E

(

Rα∑

hkR−αk

)

=∑

E

(

R

Rk

)α

.



Relevance of the ISR

−30 −25 −20 −15 −10 −5 0

10−3

10−2

10−1

100

SIR CDF (outage probability)

θ (dB)

P(S

IR<

θ)

Gasym


pout = P(hR−α < θI ) = P(h < θ ISR)

For exponential h and θ → 0,

P(h < θ ISR | ISR) ∼ θ ISR,

thus P(h < θ ISR) ∼ θE(ISR).

So the asymptotic gain is

G , E(ISR1)/E(ISR2) .

So the gain is the ratio of the two MISRs.

How accurate is the asymptotic gain for non-vanishing θ?



The ISR for the HIP model

For the (single-tier) HIP model, we need to calculate the MISR

E(ISR) = E

(

Rα1

∞∑

k=2

R−αk

)

=

∞∑

k=2

E

(

R1

Rk

)α

,

where Rk is the distance to the k-th nearest BS.The distribution of νk = R1/Rk is

Fνk (x) = 1 − (1 − x2)k−1, x ∈ [0, 1].

Summing up the α-th moments E(ναk ), we obtain (remarkably)

E(ISR) =2

α− 2.

This is the baseline E(ISR) relative to which we measure the gain.For α = 4, it is 1. Hence pout(θ) = FSIR(θ) ∼ θ, θ → 0.


Gains due to Deployment and Cooperation Deployment gain

Deployment gain

−20 −15 −10 −5 0 5 100.3

0.4

0.5

0.6

0.7

0.8

0.9

1PPP and square lattice, α= 3.0

θ (dB)

P(S

IR>

θ)

PPPsquare latticeISR−based gain

−20 −15 −10 −5 0 5 100.3

0.4

0.5

0.6

0.7

0.8

0.9

1PPP and square lattice, α= 4.0

θ (dB)P

(SIR

>θ)

PPPsquare latticeISR−based gain

For the square lattice, the gap (deployment gain) is quite exactly 3dB—irrespective of α! For α = 4, psq

s = (1 +√

θ/2 arctan√

θ/2)−1.

For the triangular lattice, it is 3.4 dB. This is the maximum achievable.


Gains due to Deployment and Cooperation BS silencing

BS silencing: neutralize nearby foes

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4


Gains due to Deployment and Cooperation BS silencing

Gain due to BS silencing (or interference cancellation) for HIP model

Let ISR(!n)

be the ISR obtained when the n strongest (on average)interferers are silenced.For HIP,

E(ISR(!n)

) =2Γ(1 + α/2)

α− 2

Γ(n + 2)

Γ(n + 1 + α/2).

For α = 4, in particular,

E(ISR(!n)

) =2

n + 2.

So the gain from silencing n BSs is simply

Gsilence = 1 +n

2.


Gains due to Deployment and Cooperation Interference cancellation

Remarks on interference cancellation

The gain from successive canceling interferers is highest if transmittersare clustered.

For a non-homogeneous Poisson model with intensity functionλ(x) = a‖x‖b , b ∈ (−2, α− 2), the closer b to −2, the better.

If small-cell BSs are clustered due to high user density or ifclosed-access femtocells exist, SIC is promising.

Probability of decoding k-th strongest transmitter if k − 1 havealready been decoded, for arbitrary fading:

For θ ≥ 1 : Pk =1

θkβΓ(1 + kβ)(Γ(1 − β))k,

where β = (2 + b)/α ∈ (0, 1).


Gains due to Deployment and Cooperation BS cooperation

BS cooperation: turn nearby foes into friends

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Cooperation for worst-case users

SIR at Voronoi vertices with cooperation

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4

At these locations (×), the user isfar away from any BS, and thereare two interfering BS at thesame distance.

In the Poisson model,

F̄×

SIR(θ) =F̄ 2

SIR(θ)

(1 + θ)2.

With BS cooperation from the 3equidistant BSs, for α = 4,

F̄×,coop

SIR (θ) = F̄ 2SIR(θ/3) =

(

1 +√

θ/3 arctan(√

θ/3))

−2

.



SIR at Voronoi vertices with cooperation

−20 −15 −10 −5 0 5 100

0.2

0.4

0.6

0.8

1SIR CCDF for PPP, α=4

θ (dB)

P(S

IR>

θ)

general userworst−case, no coop.worst−case, 3−BS coop.

Without cooperation,E(ISR) = 4 (for α = 4).

With 3-BS cooperation, theSIR performance is slightlybetter for the worst-case usersthan the general users, andE(ISR) = 2/3.

So the gain from 3-BScooperation is 6, or 7.8 dB.

Can we approximate the SIR distribution using the ratio of the two MISRs?



Using the ISR approximation

−20 −15 −10 −5 0 5 100

0.2

0.4

0.6

0.8

1SIR CCDF for PPP, α=4

θ (dB)

P(S

IR>

θ)

general userworst−case, no coop.worst−case, 3−BS coop.shifted by E(ISR) ratio

For worst-case users withn ∈ {1, 2, 3} BSs cooperating,

E(ISR) =4 + (3 − n)(α− 2)

n(α− 2).

So for n = 3, the ratio of the twoMISRs is

Gcoop =MISR

MISRcoop

= 3 +3

2(α− 2).


Diversity Definition

DUI: Diversity under interference

Decreasing the variability in the SIR

The shift along the θ axis preserves the variability in the SIR.The variability can be decreased by increasing the diversity.

Definition (DUI)

The diversity under interference is defined as

d , limθ→0

log pout(θ)

log θ.

Hencepout(θ) = FSIR(θ) = Θ(θd).


Diversity Diversity for HIP model

Diversity for HIP model

−40 −30 −20 −10 0

10−4

10−3

10−2

10−1

100

Outage for PPP with Nakagami fading, m=[1 2 5 ∞ ]

θ (dB)

P(S

IR<

θ)

m=1m=2m=5no fading

−20 −15 −10 −5 0 5 100.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1PPP with Nakagami fading, m=[1 2 5 ∞ ]

θ (dB)P

(SIR

>θ)

m=1m=2m=5no fading

For a PPP with Nagakami-m fading, d = m.


Diversity SIR gain

SIR gain with diversity

If the fading distribution satisfies Fh(x) ∼ axm, x → 0, (Nakagami fading)

pout(θ) ∼ aθmE(ISRm).

The diversity order is m—if the m-th moment of the ISR is finite.

The asymptotic gain is

G (m) =

(

E(ISRm

1 )

E(ISRm

2 )

)1/m

≈ G (1).

For the PPP, all moments of the ISRm

are finite.

For a large class of mixing motion-invariant point process models, themoments E(ISR

m) exist, and all outage curves have the same slope. The

exact necessary conditions have not been established.


Diversity SIR gain

Deployment gain for Nakagami fading

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0.4

0.5

0.6

0.7

0.8

0.9

1SIR CCDF, α=4, Nakagami fading, m= 2

θ (dB)

P(S

IR>

θ)

PPPsquare latticeISR−based approx

−15 −10 −5 0 5 100.3

0.4

0.5

0.6

0.7

0.8

0.9

1SIR CCDF, α=4, Nakagami fading, m= 5

θ (dB)

P(S

IR>

θ)

PPPsquare latticeISR−based approx


General BS sharing

General BS sharing

Fluid sharing of BS resources

Take a non-increasing function f : R+ 7→ R+.

Let (r1, r2, r3) be the triplet of distances to the 3 nearest BSs.

s = f (r1) + f (r2) + f (r3)

Allocate resources according to f (ri )/s from BS i .

Example:• f (r) = r−α. For α → ∞, this is the non-sharing (hard) scheme.• f (r) ≡ 1: BS sharing with equal powers.


Amorphous networks

Towards amorphous networks

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No BS sharing

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BS sharing with α = 4


Amorphous networks

"SIR walk"

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4

BS sharing with α = 4

−3 −2 −1 0 1 2 3−10

−5

0

5

10

15

20

25

xS

IR (

dB)

SIR (no fading)

without BS sharingwith BS sharing

SIR improvement atequal total power consumption

This BS sharing framework can be reversed for the uplink in a natural way.There is hope that such a fluid BS sharing model is tractable.


Cellular network modeling

Back to modeling

Introducing dependencies

BS of one tier are not placed completely independently (intra-tierdependence).

BS of different tiers are not placed independently, either (inter-tierdependence).

Intra-tier dependence

The HIP model is conservative since it places BSs arbitrarily close to eachother.In actual deployments, it is unlikely to have two BSs very close, so the BSsform a soft-core or hard-core process. In other words, the BSs process isrepulsive.Repulsion can be quantified using the pair correlation function g(r). Forthe PPP, g(r) ≡ 1. For a repulsive process, g(r) < 1.



Adjusting to population density

−6 −4 −2 0 2 4 6−6

−4

−2

0

2

4

6

A single tier with density adjusted according to the population density tokeep the average number of (active) users per cell constant.



Two-tier models

−6 −4 −2 0 2 4 6−6

−4

−2

0

2

4

6

Small cells for urban regions−6 −4 −2 0 2 4 6

−6

−4

−2

0

2

4

6

Overlay with small cells

Either way, there is intra- and inter-tier dependence.


Cellular network modeling The Ginibre point process

The Ginibre model

Realizations of PPP and the Ginibre point process (GPP) on b(o, 8)

−5 0 5

−5

0

5

PPP with n=65

−5 0 5−8

−6

−4

−2

0

2

4

6

81−GPP with n=64

The GPP exhibits repulsion—just as BSs in a cellular network.Its pair correlation function is g(r) = 1 − e−r2 .



The Ginibre point process

The GPP is a motion-invariant determinantal point process.

Remarkable property: If Φ = {x1, x2, . . .} ⊂ R2 is a GPP, then

{‖x1‖2, ‖x2‖2, . . .} d= {y1, y2, . . .}

where (yk) are independent gamma distributed random variables with pdf

fyk (x) =xk−1e−x

Γ(k); E(yk) = k .

Removing y1 from the process yields the Palm measure.

The intensity is 1/π but can be adjusted by scaling.

The GPP can be made less repulsive by independently deleting pointswith probability 1 − β and re-scaling. This β-GPP approaches thePPP in the limit as β → 0.



The Ginibre point process in action

We would like to model these two deployments:

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360000 380000 400000 420000

1000

0012

0000

1400

0016

0000

Rural Region (75000m x 65000m)

E−W

N−

S

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528000 529000 53000018

0500

1815

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Urban Region (2500m x 1800m)

E−W

N−

S



The Ginibre point process in action

SIR distributions for different path loss exponents:

−10 −5 0 5 10 15 200

0.2

0.4

0.6

0.8

1

SIR Threshold (dB)

Cov

erag

e P

roba

bilit

y

Rural Region

Experimental Data w. α=4Experimental Data w. α=3.5Experimental Data w. α=3Experimental Data w. α=2.5The fitted β−GPP

−10 −5 0 5 10 15 200

0.2

0.4

0.6

0.8

1

SIR Threshold (dB)C

over

age

Pro

babi

lity

Urban Region

Experimental Data w. α=4Experimental Data w. α=3.5Experimental Data w. α=3Experimental Data w. α=2.5The fitted β−GPP

For the rural region, β = 0.2. For the urban region, β = 0.9.


Conclusions

Conclusions

The gain of a deployment/architecture/scheme is best measured asthe horizontal gap relatively to a baseline (e.g., the HIP) model.

The MISR E(ISR) is easy to obtain by simulation, since it does notdepend on the fading. The ISR-based approximation is very accuratefor ps > 3/4, and the gains are quite insensitive to the path lossexponent and the fading statistics.

The DUI "compresses" the SIR distribution. Care is needed due to thecorrelation in the interference across time and space. The existence ofa diversity gain is coupled with the moments of the ISR.

General BS sharing is a promising framework to analyze amorphousnetworks.

Future work should also include models with intra- and inter-tierdependence. The Ginibre point process is promising as a repulsivemodel due to its tractability.


Conclusions

Key Take-away: What matters is the

WAIST-HIP Ratio

MISRHIP

MISRWAIST

WAIST: Wireless Advanced InterferenceSuppression Technique


References

ReferencesM. Haenggi, "The Mean Interference-to-Signal Ratio and its Key Role in Cellular and

Amorphous Networks", arXiv, June 2014.

N. Deng, W. Zhou, and M. Haenggi, "A Heterogeneous Cellular Network Model with

Inter-tier Dependence", GLOBECOM 2014. Submitted.

A. Guo and M. Haenggi, "Asymptotic Deployment Gain: A Simple Approach to

Characterize the SINR Distribution in General Cellular Networks", IEEE Trans. Comm.,

submitted.

G. Nigam, P. Minero, and M. Haenggi, "Coordinated Multipoint Joint Transmission in

Heterogeneous Networks", IEEE Trans. Comm., submitted.

X. Zhang and M. Haenggi., "A Stochastic Geometry Analysis of Inter-cell Interference

Coordination and Intra-cell Diversity", IEEE Trans. Wireless, submitted.

N. Deng, W. Zhou, and M. Haenggi, "The Ginibre Point Process as a Model for Wireless

Networks with Repulsion", IEEE Trans. Wireless, accepted.

X. Zhang and M. Haenggi, "The Performance of Successive Interference Cancellation in

Random Wireless Networks", IEEE Trans. Info. Theory, submitted.

A. Guo and M. Haenggi, "Spatial Stochastic Models and Metrics for the Structure of

Base Stations in Cellular Networks", IEEE Trans. Wireless, Nov. 2013.

See http://www.nd.edu/~mhaenggi/pubs for our publications.


http://www.nd.edu/~mhaenggi/pubs

coverage analysis of hetnets with base station cooperation ......coverage analysis of hetnets with...

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