Presentation of the paper "Optimizing the Number of Samples for Multi-Channel Spectrum Sensing" at the IEEE International Conference on Communications (IEEE ICC 2015)

1. IEEE ICC, 8-12 June 2015
Saud Althunibat, Yung Manh Vuong & Fabrizio Granelli
University of Trento
Trento, Italy.
“Optimizing the Number of Samples for
Multi-Channel Spectrum Sensing “

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Outline
Conclusions
Throughput maximization setup
Problem Statement
Introduction : Cognitive Radio
Interference minimization setup
State of the art
Simulation Results
Energy minimization setup

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Cognitive Radio
• Cognitive Radio targets the problem of spectrum
scarcity by dynamically exploiting the underutilisation of
the spectrum among the operators.
• Operation: Access the spectrum of another system,
called “primary system”, with minimum interference
and without impact on the QoS of the primary system.

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Spectrum Sensing
Aims at identifying the instantaneous
spectrum status to use the unoccupied
portions.
High sensing requirements should be
satisfied to avoid interference.
Usually performed in a collaborative
approach, called collaborative spectrum
sensing (CSS).

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The problem
• Our main problem is the high resource
consumption (including time and energy)
during spectrum sensing stage.
• Why ?
Continuous process.
Large number of users.
Large number of channels.
Large amount of information.

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State of the art
• Several approaches:
• Reducing the number of sensing users.
• Reducing the number of reporting users
(confidence voting).
• Reducing the number of sensed channels.
• Clustering.
• Optimizing the fusion rule.
• Gamy theory.

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Contributions
• In this work we optimize the number of
samples to be collected from each channel
in a multi-channel spectrum sensing.
• Different setups have been considered:
oThroughput Maximization
oInterference Minimization
oEnergy Minimization

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Throughput Maximization Setup
… (1)
• For L channels, the average achievable throughput can
be expressed as follows:
Where
 P0 : the probability that the channel is idle.
 R: the data rate.
 Tt : the transmission time.
 Pfi : the false-alarm probability of the ith channel.

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Throughput Maximization Setup
…(2)
• The throughput maximization problem with a constraint
on the total number of samples (ST) can be expressed
as follows:
• Notice that Pfi is a function of Si (the no. of samples)
as follows:

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Throughput Maximization Setup
…(3)
• The problem can be solved using Lagrange method as
follows:
• Which can be approximated as follows:

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Interference Minimization Setup
…(1)
• As the interference occurs in the missed-detection case,
it can be modeled for L channels as follows:
Where
 P1 : the probability that the channel is busy.
 Pt : the transmit power.
 Tt : the transmission time.
 Pdi : the detection probability of the ith channel.

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Interference Minimization Setup
…(2)
• The Interference minimization problem with a
constraint on the total number of samples (ST) can be
expressed as follows:
• Notice that Pdi is a function of Si (the no. of samples)
as follows:

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Interference Minimization Setup
…(3)
• The solution is also can be approximated using the
same procedure:

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Energy Minimization Setup …(1)
• The energy consumed in sensing L channels can be
expressed as follows:
Where
 Ps : the sensing power.
 fs : the transmission time.

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Energy Minimization Setup …(2)
• The energy minimization problem with a constraint on
the achievable throughput can be formulated as follows
:
where DT is the lowest acceptable throughput

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Energy Minimization Setup …(3)
• Similarly, the optimal no. of samples collected form the
ith channel can be approximated as follows

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• Once two channels have
equal noise variance (σ ),
the same no. of samples
should be collected from
both.
• If the noise variance is
larger than detection
threshold (λ) , the number
of samples is zero.
• For a maximum throughput,
if the channel has a noise
variance more than the
detection threshold, it
should not be sensed.
Simulation Results …(1)
Optimal no. of samples versus the noise variance
of the 3rd channel (σ2
1 =0.45, σ2
2 =0.65)

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• If the sum of the noise and
signal variances of two
different channels is equal,
the same no. of samples
should be collected from
both.
• For a minimum interference,
if the channel has a sum of
noise and signal variances
less than the detection
threshold, it should not be
sensed.
Simulation Results …(2)
Optimal no. of samples versus the sum of the
noise and signal variances of the 3rd channel .

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• If the noise variance of
two different channels is
equal, the same no. of
samples should be
collected from both.
• For a minimum energy
consumption, if the
channel has a noise
variance more than the
detection threshold, it
should not be sensed.
Simulation Results …(3)
Optimal no. of samples versus the noise variance
of the 3rd channel .

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Conclusions
• Optimization of the number of samples from each channel in multi
channel spectrum sensing is addressed.
• Three different setups have been considered:
• Throughput maximization with a constraint on the total number of
samples.
• Interference minimization with a constraint on the total number of
samples.
• Energy minimization with a constraint on the achievable throughput.
• Approximated solutions have been proposed for the optimal number
samples to be collected from each channel for each setup.

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Conclusions
• Mathematical and simulation results allow to conclude that:
• For maximum throughput, if the channel has a noise variance
higher than the detection threshold, it should not be sensed.
• For minimum interference, if the channel has a sum of noise
and signal variances lower than the detection threshold, it
should not be sensed.
• For minimum energy consumption, if the channel has a noise
variance higher than the detection threshold, it should not be
sensed.

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Thanks for your kind attention!
Fabrizio Granelli
granelli@disi.unitn.it