Stability Analysis in a Cognitive Radio System with Cooperative Beamforming

Outline System Model System Analysis Numerical Results Conclusion

Stability Analysis in a Cognitive RadioSystem with Cooperative Beamforming

Reference: Karmoose, Mohammed, Ahmed Sultan, and Moustafa Youssef. "Stability analysis in acognitive radio system with cooperative beamforming." Wireless Communications and Networking

Conference (WCNC), 2013 IEEE. IEEE, 2013.

Mohamed Seif1, and Abdelrahman Youssef1

1Wireless Intelligent Networks Center (WINC), Nile University, Egypt

June 22, 2015

Mohamed Seif, and Abdelrahman Youssef Nile University

Stability Analysis in a Cognitive Radio System with Cooperative Beamforming 1


Outline

1 Outline

2 System ModelNetwork ModelSensing and Beamforming

3 System AnalysisQueue Service RatesStability Analysis

4 Numerical ResultsNumerical Results

5 ConclusionConclusion




Outline

•System Model

•System Analysis

M. Seif

•Numerical Results

•Conclusions

A. Youssef




Network Model

Network Model

Pair of a SU are communicating inthe presence of 2 PUs, eachequipped with one antenna

K (decode and forward) relays areworking together forming a virtualantenna array (VAA)

Functions of relays:

1 Enhance the throughput of SUnetwork

2 Null the interference on PUnetwork

TX RX

1

2

K

TX RX

Secondary User Network

Primary User Network

Figure: CRN model




Sensing and Beamforming

Sensing and Beamforming

SU-TX senses the occupancy of PUactivity

1 If PU is idle:

ws =√

PsHs∣∣Hs ∣∣

2 If PU is active:

ws =√

Ps(I−φ)Hs

√

HHs (I−φ)Hs

TX RX

1

2

K

TX RX



Figure: CRN model




Queue Service Rates

A. Primary User Service Rate

1 Secondary user’s queue is empty:pout,p = Pr{Pp ∣Hp ∣

2< βp} = 1 − exp(βp

Pp)

Then, primary service rate is 1 − pout,p

2 Secondary user’s is nonempty and the primary user is detected:This event happens w.p. (1 − pmd)Pr{Qs ≠ 0}Then, primary service rate is 1 − pout,p

3 Secondary user’s queue is nonempty and the primary user ismisdetected:

This event happens w.p. pmdPr{Qs ≠ 0}Then, primary service rate is 1 − pout,pThe relays mistakenly don’t employ the nullingbeamforming vectorpmd

out,p = Pr{ Pp ∣Hp ∣2

∣HHspwa∣+1 < βp}




Queue Service Rates



2< βp} = 1 − exp(βp

Pp)


2 Secondary user’s is nonempty and the primary user is detected:This event happens w.p. (1 − pmd)Pr{Qs ≠ 0}









Queue Service Rates



2< βp} = 1 − exp(βp

Pp)










Queue Service Rates



2< βp} = 1 − exp(βp

Pp)










Queue Service Rates


The mean service rate for PU is:

µp = (1 − pout,p)(Pr{Qs = 0} + (1 − pmd )Pr{Qs ≠ 0}) + (1 − pmdout,p)(pmd Pr{Qs ≠ 0})




Queue Service Rates

B. Secondary User Service Rate

1 Primary Queue is empty and the secondary user detects thechannel to be vacant:

This case happens w.p. (1 − pfa)Pr{Qp = 0}pout,s = Pr{Ps ∣∣Hs ∣∣

2< βs}

2 Primary queue is empty and the secondary user finds thechannel busy:

This case happens w.p. pfaPr{Qp = 0}

pfaout,s = Pr{∣HH

s wp ∣2< βs}

3 Primary queue is nonempty and the secondary user detectsprimary activity:

This case happens w.p. (1 − pmd )Pr{Qp ≠ 0}

pdout,s = Pr{

∣HHs wp ∣

2

Pp ∣Hps ∣2+1< βs}

4 Primary queue is nonempty and the secondary user misdetectsprimary activity:

This case happens w.p. pmd Pr{Qp ≠ 0}, pdout,s = Pr{ Ps ∣∣Hs ∣∣

2





Queue Service Rates




2< βs}



pfaout,s = Pr{∣HH

s wp ∣2< βs}



pdout,s = Pr{

∣HHs wp ∣

2




2





Queue Service Rates




2< βs}



pfaout,s = Pr{∣HH

s wp ∣2< βs}



pdout,s = Pr{

∣HHs wp ∣

2




2





Queue Service Rates




2< βs}



pfaout,s = Pr{∣HH

s wp ∣2< βs}



pdout,s = Pr{

∣HHs wp ∣

2




2





Queue Service Rates


The mean service rate for SU is:

(pout,s(1 − pfa) + pfaout,spfa)Pr{Qp = 0} + (Pd

out,s(1 − pmd ) + pmdout,spmd )Pr{Qp ≠ 0}




Stability Analysis

Stability Analysis

Our main objective is to characterizethe stability region defined as theset of arival pairs (λp, λs)

Since Qp and Qs are interactingtogheter and their direct analysis isitractable

The concept of dominant systems

TX RX

1

2

K

TX RX



Figure: CRN model




Stability Analysis

Stability Analysis

In a multiqueue system, the system is stable when all queuesare stable. We can apply Loynes’theorem to check the stability

TheoremIf the arrival process and the service process of a queue are strictlystationary, and the mean service rate is greater than the mean arrivalrate of the queue, then the queue is stable, otherwise it is unstable.




Stability Analysis

Stability Analysis

In a multiqueue system, the system is stable when all queuesare stable. We can apply Loynes’theorem to check the stability

TheoremIf the arrival process and the service process of a queue are strictlystationary, and the mean service rate is greater than the mean arrivalrate of the queue, then the queue is stable, otherwise it is unstable.




Stability Analysis

Stability Analysis using Dominant Systems

In order to analyze the interacting queues, we employ theconcept of dominant systems.

In a dominant system a user transmits dummy packets if itsqueue is empty

Since, we have two users, we can construct two dominantsystems




Stability Analysis








Stability Analysis








Stability Analysis

I. First dominant system

The primary transmitter sends dummy packets when its queue isempty

Whereas, the secondart transmitter behaves as it would in theoriginal system

Pr{Qp = 0} = 0

µpds = (pd

out,s(1 − pmd) + pmdout,spmd)




Stability Analysis




Pr{Qp = 0} = 0

µpds = (pd





Stability Analysis




Pr{Qp = 0} = 0

µpds = (pd





Stability Analysis



Whereas, the secondary transmitter behaves as it would in theoriginal system

Pr{Qs = 0} = 1 − λs

µpds

µpdp = (1 − pout,p) −

λs

µpds

pmd(pmdout,p − pout,p)




Stability Analysis


The stability region on the first dominant system is given by theclosure of the rate pairs (λp, λs)

max λp = µpdp s.t. λs < µ

pds ,Ps ≤ Pmax

Same manner for the second dominant system ,

Stability region of the original system is the union of the twodominant system (Theorem)




Stability Analysis




pds ,Ps ≤ Pmax






Stability Analysis




pds ,Ps ≤ Pmax






Numerical Results

Simulation Results




Numerical Results

Simulation Results




Numerical Results

Simulation Results

Figure: Optimal secondary transmit power versus λs for the firstdominant system




Numerical Results

Simulation Results




Numerical Results

Simulation Results




Numerical Results

Simulation Results

Figure: Optimal secondary transmit power versus λp for the seconddominant systems




Numerical Results

Simulation Results




Numerical Results

Simulation Results




Conclusion

Conclusion

A CRN is considered which consists of a single primary and asingle secondary links.

The secondary transmitter utilizes a set of dedicated relays byapplying beamforming techniques to null out secondarytransmission at the primary receiver

Studying the stability region of the queues with sensing errortaken into account

We resorted to the concept of dominant systems in order todecouple the interacting queues




Conclusion

Conclusion








Conclusion

Conclusion








Conclusion

Conclusion








Conclusion

Thank You!



Engineering

Stability Analysis in a Cognitive Radio System with Cooperative Beamforming