Optimizing the Number of Samples for Multi-Channel Spectrum Sensing

IEEE ICC, 8-12 June 2015

Saud Althunibat, Yung Manh Vuong & Fabrizio Granelli

University of TrentoTrento, 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 MaximizationoInterference MinimizationoEnergy 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, σ22

=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 Granelligranelli@disi.unitn.it