iot interference modelling and experimental validation
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Laurent Clavier
IOT INTERFERENCE
MODELLING AND
EXPERIMENTAL
VALIDATION
Laurent Clavier
IOT INTERFERENCE
MODELLING AND
EXPERIMENTAL
VALIDATION
5G and mMTC (IoT) β Increasing number of Devices
3CONTEXT
12/10/2021INTERFERENCE IN IOT NETWORKS
4CONTEXT
Coexistence is a major concern as more devices begin to operate on unlicensed bands. Many
networks share the same bandwidth but PHY/MAC layer characteristics or application requirements may
differ;
Different networks will be uncoordinated, it is difficult to assess for a given network in real time its
impact on another (i.e., interference).
12/10/2021INTERFERENCE IN IOT NETWORKS
1. MODELING
INTERFERENCE
2. MEASURING
INTERFERENCE
3. HANDLING
INTERFERENCE
SOMMAIRE
1. MODELING
INTERFERENCE
2. MEASURING
INTERFERENCE
3. HANDLING
INTERFERENCE
SOMMAIRE
What is interference?
Collection of other transmitters using
the same frequency band at the same
time (from the same networks but not
necessarily).
I= ΟπβΞ¦π‘ππ,π‘
βπ
2βπ,π‘π₯π,π‘
Channel PHY layer
Source: x(t)Destination: y(t)
All the contributions add at the destination.
7MODELING INTERFERENCE
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Brief state of the art
Common approach: interference is modelled by a Gaussian random process.
Problem:
β when the number of interferers is large but there are dominant interferers
In many cases, the interference pdf exhibits a heavier tail than what is predicted by
the Gaussian model.
β impulsive interference: Middleton Class A, Gaussian-mixture, generalized
Gaussian, Laplace, a-stable...
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πΌ =
π=1
β
ππβπ2βππ₯π =
π=1
β
ππβπ2 π§π,π + ππ§π,π
From a Poisson Point Process
Mapping theorem: ππ2 is a 1D-PPP with intensity Ξ»π
Lepage Series representation of SaS random variables
π = ππ + πππ is an isotropic 4/h-stable and
ππ΅ = π ππͺππΌ
βππΌ π‘ ππππ
ππΌ
πΌπ
9MODELING INTERFERENCE
12/10/2021INTERFERENCE IN IOT NETWORKSM. Egan et al., βWireless communication in dynamic
interference,β GLOBECOM 2017.
a-stableβ’ Parametric : 4 parameters: a, in ]0,2], is the characteristic exponent (how
impulsive), b the skewness, dispersion, location.
β’ Gaussian is a special case
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-30
-15
0
15
30
Time
Am
plitu
de
a-stable noise
(a=1.5, d=0.5)
-30
-15
0
15
30
Time
Am
plitu
de
Gaussian noise
(a=2, d=1)
0
0.25
0.5
Probability density function
-5 0 50
0.01
0.02Zoom on tails
Heavy
tail
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11MODELING INTERFERENCE
Model validity
12
Introducing access policy.
To make it βsimpleβ: One user access a Frequency block with probability p.
The access policy can introduce dependence
between different blocks. How can we model it?
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How to introduce dependence?
Traditionally
β’ Finite second order moments
β’ Correlation coefficient is an adapted concordance measure
ππ,π =πΈ π β ππ πΈ π β ππ¦
ππππBut:
β’ Not adapted to impulsive interference (and especially a-stable distributions)
β’ Do not allow to model tail dependence (simultaneous strong samples in the
same vector)
As a consequence we are interested in other dependence
models allowing more flexible concordance measures.
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Multivariate a-stable models exist⦠but are difficult to handle (intractable distribution
function).
As an alternative, we keep the marginal behavior of the stable random variables
and propose a copula to model the dependence structure
Copulas
We can define a copula as follows. Consider a random vector π β π π with a
continuous distribution F. Then to X one can associate a d-copula πΆ: 0,1 π β 0,1defined by:
πΉ π₯1, π₯2, β¦ , π₯π = πΆ πΉ1 π₯1 , β¦ , πΉπ π₯π
Marginals (1D) distributions of ππ
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15MODELING INTERFERENCE
Model validity - K = 4 blocks and N = 2 subcarriers in each block
1. MODELING
INTERFERENCE
2. MEASURING
INTERFERENCE
3. HANDLING
INTERFERENCE
SOMMAIRE
Five distinct locations at street level
within Aalborg
β’ shopping area,
β’ business park,
β’ hospital complex,
β’ industrial area,
β’ residential area.
Measured power measurements on
β’ a frequency grid from 863 to 870 Mhz,
β’ with 7kHz bins,
β’ sampling time was 200 ms,
β’ measurements were conducted during two hours.
17MEASURING INTERFERENCE
12/10/2021INTERFERENCE IN IOT NETWORKSM. Lauridsen et al., βInterference measurements in the European 868
MHZ ISM band with focus on LoRa and Sigfox,β WCNC 2017.
18MEASURING INTERFERENCE
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We focus on a LoRa-like receiver.
β’ Frequency band of 125 MHz (we
aggregate 18 bands of 7 MHz, which
makes 126 MHz bands)
β’ We select a time-frequency window
where interference is stationary.
β’ Resource block: time-frequency area
of 200ms and 126 MHz
How to define impulsiveness? βRareβ events with βlargeβ values
Can be related to βa larger probability of getting very large valuesβ
https://reference.wolfram.com/language/guide/HeavyTailDistributions.html
We can find several ways to define it, one interesting is:
β Heavy Tail (A distribution with a βtailβ that is βheavierβ than an Exponential)
have tails which fail to satisfy the following bound on the complementary
cumulative distribution function ΰ΄€πΉ π₯ = β π > π₯ for any positive real numbers M and t, ΰ΄₯π π β€ π΄πβππ, βπ > π. (log-normal, Weibull, Pareto, a-Stableβ¦)
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Definitely Heavy Tail behavior
-15log(x)
-23 -21 -19 -17-14
-10
-6
-2 Shopping areaa=1.4a=1.6a=1.8a=2
log
(1-F
(x))
20MEASURING INTERFERENCE
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Log-tail test
The idea is to represent the
log of the survival function
π₯π¨π ΰ΄₯π π as a function of
π₯π¨π π . For heavy-tailed
distribution we will obtain a
straight line while for
exponential distributions πΎwill be 0 leading to a very
abrupt fall.
1. MODELING
INTERFERENCE
2. MEASURING
INTERFERENCE
3. HANDLING
INTERFERENCE
SOMMAIRE
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22
Receiver design
We use a LDPC code.
The input of the decorder (Belief Propagation) is based on the log-
likelihood ratio.
In the Gaussian case it is a straight line. In an impusive case it is not !
Gaussian case Stable case
HANDLING INTERFERENCE
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23HANDLING INTERFERENCE
πΏπ,π π₯ = min ππ₯, ππ₯
We approximate the
LLR with a simple
function
This, in fact, does
not depend on the
noise/interference
distribution
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24
Example with a
Middleton class A noise.
β’ Very poor
performance of the
linear receiver
β’ Significant
improvement with the
non linear approach
β’ The approximation
works well
HANDLING INTERFERENCE
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25
But it fails with short
codewords
β’ Estimation problems due
to the impulsive noise
β’ We need to improve the
optimisation case
HANDLING INTERFERENCE
1. MODELING
INTERFERENCE
2. MEASURING
INTERFERENCE
3. HANDLING
INTERFERENCE
SOMMAIRE
27
Main conclusions
Gaussian interference is not always adapted (it depends on the variation of the
interferer set)
Impulsive interference is more complex to model but we can use an a-stable
distribution.
β’ The characteristic exponent (a) is linked to the channel attenuation
β’ The dispersion is linked to the density of users, the PHY layer and the fading
Dependence can in that case be modeled with a t-copula
β’ The degrees of freedom is linked to the probability of access to a resource block
MODELING INTERFERENCE
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