5G: The Quest for Cell-less Cellular Networks Martin Haenggi Dept. - - PowerPoint PPT Presentation

5G: The Quest for Cell-less Cellular Networks

Martin Haenggi

• Dept. of Electrical Engineering

University of Notre Dame Notre Dame, IN

2014 Communication Theory Workshop May 26, 2014 Work supported by: U.S. NSF (CNS 1014932 and CCF 1216407)

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 1 / 37

Overview

Menu

Overview

Bird’s view of cellular networks The HIP model and its properties Comparing SIR distributions: The crucial role of the mean interference-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

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 2 / 37

Introduction The big picture

Big picture

Frequency reuse 1: A single friend, many foes

−4 −3 −2 −1 1 2 3 4 −4 −3 −2 −1 1 2 3 4

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 3 / 37

Introduction The big picture

A walk through a single-tier cellular network

−4 −3 −2 −1 1 2 3 4 −4 −3 −2 −1 1 2 3 4

−3 −2 −1 1 2 3 −6 −4 −2 2 4 6 8 10 12 SIR (no fading) x SIR (dB)

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 4 / 37

Introduction The big picture

Coverage at 0 dB

−4 −3 −2 −1 1 2 3 4 −4 −3 −2 −1 1 2 3 4

−3 −2 −1 1 2 3 −6 −4 −2 2 4 6 8 10 12 SIR (no fading) x SIR (dB)

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 5 / 37

Introduction The big picture

SIR distribution

−3 −2 −1 1 2 3 −25 −20 −15 −10 −5 5 10 15 SIR (with fading) x SIR (dB)

For ergodic models, the fraction of the curve that is above the threshold θ is the ccdf of the SIR at θ: ps(θ) ¯ FSIR(θ) P(SIR > θ) It is the fraction of the users with SIR > θ if users are uniformly distributed.

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 6 / 37

HIP model Definition

The HIP baseline model for HetNets

The HIP (heterogeneous independent Poisson) model

−2 −1.5 −1 −0.5 0.5 1 1.5 2 −2 −1.5 −1 −0.5 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.

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 7 / 37

HIP model Definition

The HIP (heterogeneous independent Poisson) model

−2 −1.5 −1 −0.5 0.5 1 1.5 2 −2 −1.5 −1 −0.5 0.5 1 1.5 2 −2 −1.5 −1 −0.5 0.5 1 1.5 2 −2 −1.5 −1 −0.5 0.5 1 1.5 2

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

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 8 / 37

HIP model Basic result

Basic result for downlink

Assumptions: A user connects to the BS that is strongest on average, while all

• thers interfere.

Homogeneous path loss law ℓ(r) = r −α and Rayleigh fading. Result for α = 4: ps(θ) = P(SIR > θ) = ¯ FSIR(θ) = 1 1 + √ θ arctan √ θ . Remarkably, this is independent of the number of tiers, their densities, and their power levels. So as far as the SIR is concerned, we can replace the multi-tier HIP model by an equivalent single-tier model. (For bounded path loss laws, this does not hold.)

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 9 / 37

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?

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 10 / 37

Comparing SIR Distributions

Comparing SIR distributions

Two distributions

−15 −10 −5 5 10 15 20 25 0.2 0.4 0.6 0.8 1 SIR CCDF θ (dB) P(SIR>θ) baseline scheme improved scheme

How to quantify the improvement?

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 11 / 37

Comparing SIR Distributions Vertical comparison

The standard comparison: vertical

−15 −10 −5 5 10 15 20 25 0.2 0.4 0.6 0.8 1 SIR CCDF θ (dB) P(SIR>θ) baseline scheme improved scheme

At -10 dB, the gap is 0.058. Or 6.4%. At 0 dB, the gap is 0.22. Or 39%. At 10 dB, the gap is 0.15. Or 73%. At 20 dB, the gap is 0.05. Or 78%. Or use the gain in P(SIR ≤ θ)?

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 12 / 37

Comparing SIR Distributions Horizontal comparison

A better choice: horizontal

−15 −10 −5 5 10 15 20 25 0.2 0.4 0.6 0.8 1 SIR CCDF θ (dB) P(SIR>θ) G G G G baseline scheme improved scheme

Use the horizontal gap instead. This SIR gain is nearly constant

• ver θ in many cases.

If the improvement is due to better BS deployment, it is the deployment gain. ps = P(SIR > θ) ⇒ ps = P(SIR > θ/G). Can we quantify this gain?

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 13 / 37

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 and

• users. 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−α

k

• =
• E

R Rk α .

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 14 / 37

Comparing SIR Distributions ISR

Relevance of the ISR

−30 −25 −20 −15 −10 −5 10

−3

10

−2

10

−1

10 SIR CDF (outage probability) θ (dB) P(SIR<θ) Gasym baseline scheme improved scheme

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) ∼ θ E(ISR). So the asymptotic gain is Gasym E(ISR1)/E(ISR2) . So the gain is the ratio of the two MISRs. How accurate is the asymptotic gain for non-vanishing θ?

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 15 / 37

Comparing SIR Distributions ISR

The ISR for the HIP model

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

• Rα

1 ∞

• k=2

R−α

k

• =

∞

• 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(να

k ), 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.

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 16 / 37

Gains due to Deployment and Cooperation Deployment gain

Deployment gain

−20 −15 −10 −5 5 10 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 PPP and square lattice, α= 3.0 θ (dB) P(SIR>θ) PPP square lattice ISR−based gain −20 −15 −10 −5 5 10 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 PPP and square lattice, α= 4.0 θ (dB) P(SIR>θ) PPP square lattice ISR−based gain

For the square lattice, the gap (deployment gain) is quite exactly 3 dB—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.

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 17 / 37

Gains due to Deployment and Cooperation BS silencing

BS silencing: neutralize nearby foes

−4 −3 −2 −1 1 2 3 4 −4 −3 −2 −1 1 2 3 4

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 18 / 37

Gains due to Deployment and Cooperation BS silencing

Gain due to BS silencing 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.

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 19 / 37

Gains due to Deployment and Cooperation BS cooperation

BS cooperation: turn nearby foes into friends

−4 −3 −2 −1 1 2 3 4 −4 −3 −2 −1 1 2 3 4

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 20 / 37

Gains due to Deployment and Cooperation BS cooperation

Cooperation for worst-case users

SIR at Voronoi vertices with cooperation

−4 −3 −2 −1 1 2 3 4 −4 −3 −2 −1 1 2 3 4

At these locations (×), the user is far away from any BS, and there are two interfering BS at the same distance. In the Poisson model, ¯ F ×

SIR(θ) =

¯ F 2

SIR(θ)

(1 + θ)2 . With BS cooperation from the 3 equidistant BSs, for α = 4, ¯ F ×,coop

SIR

(θ) = ¯ F 2

SIR(θ/3) =

• 1 +
• θ/3 arctan(
• θ/3)

−2 .

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 21 / 37

Gains due to Deployment and Cooperation BS cooperation

SIR at Voronoi vertices with cooperation

−20 −15 −10 −5 5 10 0.2 0.4 0.6 0.8 1 SIR CCDF for PPP, α=4 θ (dB) P(SIR>θ) general user worst−case, no coop. worst−case, 3−BS coop.

Without cooperation, E(ISR) = 4 (for α = 4). With 3-BS cooperation, the SIR performance is slightly better for the worst-case users than the general users, and E(ISR) = 2/3. So the gain from 3-BS cooperation is 6, or 7.8 dB. Can we approximate the SIR distribution using the ratio of the two MISRs?

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 22 / 37

Gains due to Deployment and Cooperation BS cooperation

Using the ISR approximation

−20 −15 −10 −5 5 10 0.2 0.4 0.6 0.8 1 SIR CCDF for PPP, α=4 θ (dB) P(SIR>θ) general user worst−case, no coop. worst−case, 3−BS coop. shifted by E(ISR) ratio

For worst-case users with n ∈ {1, 2, 3} BSs cooperating, E(ISR) = 4 + (3 − n)(α − 2) n(α − 2) . So for n = 3, the ratio of the two MISRs is Gcoop = MISR MISRcoop = 3 + 3 2(α − 2).

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 23 / 37

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 lim

θ→0

log pout(θ) log θ . Hence pout(θ) = Θ(θd).

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 24 / 37

Diversity Diversity for HIP model

Diversity for HIP model

−40 −30 −20 −10 10

−4

10

−3

10

−2

10

−1

10 Outage for PPP with Nakagami fading, m=[1 2 5 ∞ ] θ (dB) P(SIR<θ) m=1 m=2 m=5 no fading −20 −15 −10 −5 5 10 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 PPP with Nakagami fading, m=[1 2 5 ∞ ] θ (dB) P(SIR>θ) m=1 m=2 m=5 no fading

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

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 25 / 37

Diversity SIR gain

SIR gain with diversity

If the fading distribution satisfies Fh(x) ∼ axm, x → 0, (Nakagami fading) pout(θ) ∼ aθmE(ISR

m).

The diversity order is m—if the m-th moment of the ISR is finite. The asymptotic gain is G (m)

asym =

• E(ISR

m 1 )

E(ISR

m 2 )

1/m ≈ G (1)

asym.

For the PPP, all moments of the ISR

m are finite.

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

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

exact necessary conditions have not been established.

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 26 / 37

Diversity SIR gain

Deployment gain for Nakagami fading

−15 −10 −5 5 10 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SIR CCDF, α=4, Nakagami fading, m= 2 θ (dB) P(SIR>θ) PPP square lattice ISR−based approx −15 −10 −5 5 10 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SIR CCDF, α=4, Nakagami fading, m= 5 θ (dB) P(SIR>θ) PPP square lattice ISR−based approx

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 27 / 37

General BS sharing

General BS sharing

Fluid sharing of BS resources

Take a non-increasing function f : R+ → 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.
• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 28 / 37

Cell-less networks

Towards cell-less "cellular" systems

−4 −3 −2 −1 1 2 3 4 −4 −3 −2 −1 1 2 3 4

No BS sharing

−4 −3 −2 −1 1 2 3 4 −4 −3 −2 −1 1 2 3 4

BS sharing with α = 4

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 29 / 37

Cell-less networks

"SIR walk"

−4 −3 −2 −1 1 2 3 4 −4 −3 −2 −1 1 2 3 4

BS sharing with α = 4

−3 −2 −1 1 2 3 −10 −5 5 10 15 20 25 x SIR (dB) SIR (no fading) without BS sharing with BS sharing

SIR improvement at equal 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.

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 30 / 37

Cellular network modeling

Back to modeling

Introducing dependencies

BS of one tier are not placed completely independently (intra-tier dependence). BS of different tiers are not placed independently, either (inter-tier dependence).

Intra-tier dependence

The HIP model is conservative since it places BSs arbitrarily close to each

• ther.

In actual deployments, it is unlikely to have two BSs very close, so the BSs form a soft-core or hard-core process. In other words, the BSs process is repulsive. Repulsion can be quantified using the pair correlation function g(r). For the PPP, g(r) ≡ 1. For a repulsive process, g(r) < 1.

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 31 / 37

Cellular network modeling The Ginibre point process

The Ginibre model

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

−5 5 −5 5 PPP with n=65 −5 5 −8 −6 −4 −2 2 4 6 8 1−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.

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 32 / 37

Cellular network modeling The Ginibre point process

The Ginibre point process

The GPP is a motion-invariant determinantal point process. Remarkable property: If Φ = {x1, x2, . . .} ⊂ R2 is a GPP, then {x12, x22, . . .} 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 points with probability 1 − β and re-scaling. This β-GPP approaches the PPP in the limit as β → 0.

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 33 / 37

Cellular network modeling The Ginibre point process

The Ginibre point process in action

We would like to model these two deployments:

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

360000 380000 400000 420000 100000 120000 140000 160000 Rural Region (75000m x 65000m) E−W N−S

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

528000 529000 530000 180500 181500 Urban Region (2500m x 1800m) E−W N−S

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 34 / 37

Cellular network modeling The Ginibre point process

The Ginibre point process in action

SIR distributions for different path loss exponents:

−10 −5 5 10 15 20 0.2 0.4 0.6 0.8 1 SIR Threshold (dB) Coverage Probability Rural Region

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

−10 −5 5 10 15 20 0.2 0.4 0.6 0.8 1 SIR Threshold (dB) Coverage Probability Urban Region

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

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

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 35 / 37

Conclusions

Conclusions

The gain of a deployment/architecture/scheme is best measured as the horizontal gap relatively to a baseline (e.g., the HIP) model. The MISR E(ISR) is easy to obtain by simulation, since it does not depend on the fading. The ISR-based approximation is very accurate for ps > 3/4, and the gains are quite insensitive to the path loss exponent and the fading statistics. The DUI "compresses" the SIR distribution. Care is needed due to the correlation in the interference across time and space. The existence of a diversity gain is coupled with the moments of the ISR. General BS sharing is a promising framework to analyze cell-less 5G systems. Future work should also include models with intra- and inter-tier

• dependence. The Ginibre point process is promising as a repulsive

model due to its tractability.

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 36 / 37

References

References

• 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, 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.

• M. Haenggi and R. Smarandache, "Diversity Polynomials for the Analysis of Temporal

Correlations in Wireless Networks", IEEE Trans. Wireless, Nov. 2013.

• M. Haenggi, "A Versatile Dependent Model for Heterogeneous Cellular Networks", arXiv,

May 2013. See http://www.nd.edu/~mhaenggi/pubs for our publications.

• M. Haenggi (Univ. of Notre Dame)

Towards cell-less networks 05/26/2014 37 / 37