Green Telecom & IT Workshop: Marceau greentouch

Impact on Coverage and Capacity of Reduced
Transmit Power in Cellular Networks

Marceau Coupechoux∗
TELECOM ParisTech (INFRES/RMS) and CNRS LTCI
∗

Joint work with Jean-Marc K´lif (Orange Labs) and Fr´d´ric Marache
e e e
(Orange Labs)

Green Telecom and IT Workshop, Indian Institute of Science, Bangalore

4 April 2012

M. Coupechoux (TPT) Limiting Power Transmission 4 April 2012 1 / 20

Outlines

Interference Model
Outage Probabilities
Interference Factor Analysis
Noise and Power Analysis
Applications
Conclusion


Interference Model

Interference Model: SINR

Figure: Interference model.

SINR is a central parameter for performance evaluation:

∗ Su
γu = .
α(Iint,u − Su ) + Iext,u + Nth


Interference Model

Interference Model: Output Power

Other-cell interference factor: fu = Iext,u /Iint,u

j=b Pj gj,u
fu =
Pb gb,u

Transmitted power for mobile u: Pb,u = Su /gb,u
∗
γu
Pb,u = ∗
(αPb + fu Pb + Nth /gb,u ).
1 + αγu

Total BS output power:
γu∗
Nth
Pcch + u 1+αγu gb,u
∗
Pb = γu
∗ .
1− u 1+αγu∗ (α + fu )



Outage Probabilities: Generic Expression

For n MS with a single service:
n−1
(n) 1−ϕ
Pout = Pr Tu > − nα ,
β
u=0

where ϕ = Pcch /Pmax , β = γ ∗ /(1 + αγ ∗ ) and

Tu = fu + hu .

Two terms appear:
The OCIF: fu and
Nth
A noise factor: hu = Pmax gb,u .



Outage Probabilities: Without Shadowing

The outage probability is now (Gaussian approx.):
1−ϕ
(n) β − nµT − nα
Pout = Q √ .
nσT

where:

µT = µf0 + µh0
2 2 2
σT = σf0 + σh0 + 2E[f0 h0 ] − 2µf0 µh0

Means and standard deviations are taken over the uniform distribution
of MS on the cell area.



Outage Probabilities: With Shadowing

The outage probability is now:
1−ϕ
(n) β − nMT − nα
Pout = Q √ ,
nST

where:

MT = Mf + Mh ,
2
ST 2
= Sf2 + Sh + 2E[fu hu ] − 2Mf Mh ,

Means and standard deviations are taken both over the shadowing
variations and mobile location.


Interference Analysis

Interference Analysis: Fluid Model
Interfering BS are approximated by a continuum of BS.
Each elementary surface zdzdθ at distance z from u contains
ρBS zdzdθ BS and contributes with ρBS zdzdθPb Kz −η to the
interference.

Rnw Continuum of
base stations

Rc

2Rc

Figure: Cellular network approximation.




Discrete sum is approximated by
an integral: First BS ring

Cell boundary Network boundary

2π Rnw −ru
Iext,u = ρBS Pb Kz −η zdzdθ ru 2Rc - ru

0 2Rc −ru BS b MS u
Rnw - ru
(1)
If network size is large:
η
2πρBS ru
f0 = (2Rc − ru )2−η . Figure: Integration limits for interference
η−2 computation.
(2)




Figure: Interference factor vs. distance to the BS; comparison of the ﬂuid model
with simulations on an hexagonal network with η = 2.7, 3, 3.5, and 4.



Interference Analysis: Without Shadowing

OCIF is obtained from the ﬂuid model:
2πρBS r η
f0 = (2Rc − r )2−η .
η−2
We integrate over the cell area:
η
24−η πρBS Rc
2 Re
µf 0 = 2 F1 (η − 2, η + 2, η + 3, Re /2Rc ).
η2 − 4 Rc

where 2 F1 (a, b, c, z) is the hypergeometric function, whose integral
form is given by:
1
Γ(c) t b−1 (1 − t)c−b−1
Z
2 F1 (a, b, c, z) = dt,
Γ(b)Γ(c − b) 0 (1 − tz)a

The same for σf0 (can be expressed in closed-form using 2 F1 ).



Interference Analysis: With Shadowing

At a distance ru , fu can be approx. by a log-normal RV with
Fenton-Wilkinson → mf and σf .
We then integrate RV fu over the cell area:
Re Re
2 s 2 /2 2r
Mf = E[fu |r ]pr (r )dr = f0 (r )J(r , σ)e a f
2
dr ,
0 0 Re
Re Re
2s2 2r
E fu2 = E fu2 |r pr (r )dr = (f0 (r )J(r , σ))2 e 2a f
2
dr .
0 0 Re

2 2 2 2 −1
2
where J(ru , σ) = e a σ /2 L(ru , η)(e a σ − 1) + 1 and
f0 (ru ,2η)
L(ru , η) = f0 (ru ,η)2



Noise and Power Analysis: Without Shadowing

Nth
This is a simple case since: hu = h0 = −η
Pmax Kru
Mean and standard deviation over MS locations:
η
2Nth Re
µh0 =
Pmax K (η + 2)
2η 2
Re Nth
σh0 = .
η+1 Pmax K

E[f0 h0 ] involves an hypergeometric function but can be computed
with:
Re
2Nth πρBS
E[f0 h0 ] = r 2η (2Rc − r )2−η pr (r )dr .
Pmax K (η − 2) 0



Noise and Power Analysis: With Shadowing

Thermal noise factor is now: hu = h0 /Ab = h0 10−ξb /10 .
2 σ 2 /2
And so: Mh = µh0 E 10−ξb /10 = µh0 e a (the same for Sh ).
fu hu (both terms are not ind.) can be approx. at a given distance r
by a log-normal RV using Fenton-Wilkinson.
We then integrate over the cell area:
Re
E[fu hu ] = E[fu hu |r ]pr (r )dr
0
2 2 Re
4πρBS Nth e 3a σ /2
= 2
r 2η+1 (2Rc − r )2−η dr .
Pmax KRe (η − 2) 0

Again, this can be expressed in closed-form using 2 F1 .


Applications

Applications: Scenarios

Common parameters: CDMA network, γ ∗ = −19 dB, W = 5 MHz,
α = 0.6, ϕ = 0.2, N0 = −174 dBm/Hz.
Urban and rural scenarios:

Table: Propagation parameters
K (2 GHz) K (920 MHz) σ (dB) t η Rc
Urban 4.95 10−4 6.24 10−3 6 0.5 3.41 1 Km
Rural 0.88 4.51 4 0.5 3.41 5 Km


Applications

Applications: Capacity
Urban (R =1Km) Rural (R =5Km)
c c
7 0.45

6
0.4
∗
We set Pout = 5%
0.35

5 For a given Pmax ,
MS density ρ MS [MS/Km ]
2

0.3

4
nMS is the max nb.
0.25

of MS such that
3 0.2
∗
Pout < Pout
0.15
2 2
ρMS = nMS /πRe
0.1

1
0.05
f=920 MHz f=920 MHz
f=2000 MHz f=2000 MHz
0 0
0 5 10 15 20 25 30 35 40 45 0 10 20 30 40 50
Maximum output power Pmax [dBm] Maximum output power Pmax [dBm]

Effect of Freq. ↑: K ↓, fu is unchanged, hu ↑
Effect of Rural deployment: Rc ↑ so more power is needed per MS
but K ↑ and σ ↓. Cell range increase has a dominant influence.


Applications

Applications: Coverage
Urban (R =1Km) Rural (R =5Km)
c c
1.1 5.5
∗
Pout = 1 or 5%
1
5
ρMS is ﬁxed for
rural and urban
0.9
4.5
920 MHz

Coverage range [Km]
0.8
Cov. range Re is 4

variable 0.7
920 MHz
2 GHz
2 GHz

3.5

For given Pmax , we 0.6

3
look for Re such 0.5

∗
that Pout < Pout 2.5
0.4 f=920 MHz, target outage = 5%
f=2000 MHz, target outage = 5%
2
0 5 10 15 20 25 30 0 5 10 15 20
Maximum output power Pmax [dBm] Maximum output power Pmax [dBm]

When Pmax ↓, Re ↓ because less MS can be served and average power
per MS should decrease.
A small degradation of QoS allows an important power reduction in
rural

Applications

Applications: Should we neglect noise ?
Urban
0.1 0.1
Rural
∗
Pout = 5%
f=920 MHz
f=2000 MHz
Noise neglected

0.09 0.09
Pmax = 43 dBm
nMS is ﬁxed such
0.08 0.08
∗
that Pout = Pout
Outage probability

when noise is
0.07 0.07
neglected.
0.06 0.06 We then compute
Pout while
0.05 0.05
considering noise.
0.5 1 1.5 2 2.5 3 1 2 3 4 5 6 7 8 9 10
Half inter−BS distance Rc [Km] Half inter−BS distance Rc [Km]

Noise neglected ⇒ Pout doesn’t depend on K , frequency, Rc
(homothetic networks).
Noise cannot be neglected for Rc > 1 Km in urban and Rc > 7 Km in
rural at 2 GHz (if we accept 0.5% error).

Applications

Applications: Power Density and Densiﬁcation
∗
Pout = 5% Urban
0.5

MS density 0.45
f=2000 MHz
f=920 MHz

constant 0.4

Full coverage is 0.35

Power density [W/Km ]
2
assumed 0.3

For a given Rc , 0.25

Pmax is such that
0.2

∗
Pout < Pout
0.15

0.1

Power density is 0.05
2
Pmax /πRe 0
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
Half inter−BS distance Rc [Km]

At 2 GHz, 11% more BS means half power density.
Deploying small and femto cells are good means of reducing
electromagnetic pollution provided that transmission power is
optimized.

Conclusion

Conclusion

This work analyzes interference, noise and outpout power in cellular
networks and their impact on outage.
Fluid model provides a simple formula for the OCIF.
Integrations are done both over shadowing variations and MS
locations.
Slight QoS degradation implies much lower output powers (rural).
Slight increase of BS nbr implies much lower power densities (2GHz).


Green Telecom & IT Workshop: Marceau greentouch

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