Optimum Location of Power Beacons in Massive Wireless Power
Networks
Osmel Martínez*, Onel López*, Hirley Alves*, Samuel Montejo-Sánchez†, Matti Latva-aho*
*University of Oulu, Centre for Wireless Communications, 6G Flagship, Oulu, Finland
†Programa Institucional de Fomento a la I+D+I, Universidad Tecnológica Metropolitana, Santiago 8940577, Chile
{osmel.martinezrosabal, onel.alcarazlopez, hirley.alves, matti.latva-aho}@oulu.fi, smontejo@utem.cl
Energy harvesting is a promising technology that allows to low-power
devices to replenish their batteries by collecting radio frequency (RF)
energy from the surrounding environment.
Fig. 2 Available average power at
worst position ( 𝑚𝑖𝑛.𝑗 𝔼[𝜉𝑗𝑅𝐹 ] ) in
the circle area for different
number of PBs, using 𝑅 = 100𝑚,
and 𝛾 = 3 . As a benchmark
(lbound) we also show the case
when just one PB is radiating
from the circle center with total
power 𝑁𝑃𝑇 .
Deployment of dedicated power beacons (PBs) is being considered as
an efficient solution to improve the energy availability in wireless
powered networks.
We investigate the minimum number of PBs and their deployment to
meet a maximum energy outage Quality of Service (QoS) constraint.
• 𝑚𝑖𝑛.𝑗 𝔼[𝜉𝑗𝑅𝐹 ]
increases
with the number of
distributed PBs.
Optimal PBs' positions are determined by maximizing the average
incident power for the worst location since no information about sensors'
positioning is given.
• IPMs
improve
convergence
as
decreases.
the
𝑘
What if we impose
QoS guarantees wrt.
powering
the
devices?
SYSTEM MODEL AND ASSUMPTIONS
Fig. 1 The system model comprises a
set of PB deployed in a circular area of
radius 𝑅, to charge wirelessly a sensor
network, using 𝑀 antennas each.
Fig. 3 Solutions of 𝐏𝟏 . Energy
outage probability versus number
of antennas (𝑀) for 𝑅 = 50𝑚 and
𝛾 = 3. We set 𝜉𝑡ℎ = −22𝑑𝐵𝑚.
PROBLEM FORMULATION
What is the impact
of
the
distancedependent loss in
the solution of 𝐏𝟏?
With P1 we aim to clarify: what is the minimal number of PBs that
does achieve the energy outage requirement?
• Interior-point methods (IPMs) based on logarithmic barrier function
assuming 𝑚𝑖𝑛.𝑗 𝔼 𝜉𝑗𝑅𝐹 ≈ lim
𝑥→−∞
1
|𝒟|
𝒟
𝑗=1
𝜉𝑗𝑅𝐹
𝑘 1/𝑘
Fig. 4 Solutions of 𝐏𝟏. Minimum
number of PBs (𝑁𝑚𝑖𝑛 ) as a
function of the outage probability
𝑝 for 𝑅 ∈ {50,100}𝑚 and 𝛾 = 3.
We set 𝜉𝑡ℎ = −22𝑑𝐵𝑚.
.
• Particle Swarm Optimization (PSO).
• Genetic Algorithms (GA).
NUMERICAL RESULTS AND DISCUSSION
𝑅𝐹
𝑚𝑖𝑛.𝑗 𝔼[𝜉𝑗 ]
- The average harvested energy
increases with the number of
distributed PBs and overcome the case when just one PB is radiating from
the circle center with total power 𝑁𝑃𝑇 .
- Due to the lack of closed-form for the distribution of 𝜉𝑗𝑅𝐹 , Monte Carlo
simulations are used to find the outage probability as a function of 𝑀 in 𝐏𝟏,
showing that the number of PBs have a greater impact than 𝑀.
- Dominant impact of the distance-dependent loss leads to fluctuations in
𝑁𝑚𝑖𝑛 as the radius increases.
SELECTED REFERENCES
Fig. 2 Heat map of the available average power in the circle area for different number of PBs, using 𝑅 =
100𝑚, 𝛾 = 3, and 36000 sensors distributed in evenly spaced circumferences as a function of each
radius. The black crosses represent the solutions found via IPMs.
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