Stability Analysis in a Cognitive Radio System with Cooperative Beamforming

Motivation and Related Work System and Data Models Problem Insights and Formulation Queue Service Rates Stability analysis using dominant systems

Stability Analysis in a Cognitive Radio Systemwith Cooperative Beamforming

Mohammed Karmoose1 Ahmed Sultan1 Moustafa Youseff2

1Electrical Engineering Dept, Alexandria University

2E-JUST

Mohammed Karmoose, Ahmed Sultan, Moustafa Youseff Alex. Univ.

Stability Analysis in a Cognitive Radio System with Cooperative Beamforming


Agenda

1 Motivation and Related Work

2 System and Data Models

3 Problem Insights and Formulation

4 Queue Service Rates

5 Stability analysis using dominant systems




Motivation and Related Work

Queuing analysis in CRNs to study the stability of the primaryand secondary networks

Shortcomings of such models: no time-frequency sharingbetween primary and secondary networks

Cooperative beamforming to increase the available spectrumopportunities for the secondary networks

No queuing analysis to characterize the stability regions ofsuch systems

Our goal: study a CR scenario in which cooperativebeamforming is enabled for the secondary network, and obtainthe stability region of the system for the primary andsecondary network




System and Data Models

Primary Network:

Single link (Tx-Rx pair)

Primary transmit power Pp

Infinite buffer Qp - Bernoulliarrival R.P with mean λ

Noise at the receiversCN ∼ (0, 1)

SU - Tx SU - Rx

PU - Tx PU - Rx

R 1

R 2

R K

K Relaying Nodes

H p

H psH sp1

H sp2 H spK

H s1

H s2

H sK

Figure: System Model





Secondary Network:

Single link (Tx-Rx pair)

Relay-assisted transmission (Krelays) operating in adecode-and-forward fashion

Relays are close to the secondarysource

Power control on totaltransmitted power by all relays(Ps ≤ Pmax

Infinite buffer Qs - Bernoulliarrival R.P with mean λs

Noise at the receiversCN ∼ (0, 1)

SU - Tx SU - Rx

PU - Tx PU - Rx

R 1

R 2

R K

K Relaying Nodes

H p

H psH sp1

H sp2 H spK

H s1

H s2

H sK






Channel Conditions:

Small pathloss between secondarysource and relays (error freecommunications)

Imperfect sensing of primarytransmission

Channel between relays andreceivers are CN ∼ (0, 1)

Slow fading (channel constantover many time slots)

SU - Tx SU - Rx

PU - Tx PU - Rx

R 1

R 2

R K

K Relaying Nodes

H p

H psH sp1

H sp2 H spK

H s1

H s2

H sK






System Operation:

Perfect channel estimation atrelays based on transmitted ARQs

Channel estimations are reportedto secondary transmitter(negligible time)

PU packets are sensed bysecondary transmitter - imperfectsensing (pmd and pfa

SU - Tx SU - Rx

PU - Tx PU - Rx

R 1

R 2

R K

K Relaying Nodes

H p

H psH sp1

H sp2 H spK

H s1

H s2

H sK






Secondary transmitter computesrequired beamforming weights

Secondary data packet is sent torelays which decode perfectly(beamforming vector included inthe header)

Time required for relay receptionand decoding is negligible

SU - Tx SU - Rx

PU - Tx PU - Rx

R 1

R 2

R K

K Relaying Nodes

H p

H psH sp1

H sp2 H spK

H s1

H s2

H sK






If PU is detected

wp =√Ps

(I − Φ)Hs√HH

s (I − Φ)Hs

If PU is not detected

wa =√Ps

Hs

||Hs||.

SU - Tx SU - Rx

PU - Tx PU - Rx

R 1

R 2

R K

K Relaying Nodes

H p

H psH sp1

H sp2 H spK

H s1

H s2

H sK





Problem Insights and Formulation

If sensing was pefect: PU will not be aware of the secondarytransmitter. What would only limit its achievable service rate(µp) is the channel conditions between PU Tx-Rx

If sensing is not perfect: SU can unintentionally interfere withPU transmission, reducing achievable service rate of primaryuser

For the SU: Two factors govern its achievable service rate(µp):

1 Channel conditions between relays and secondary destination2 The rate at which PU uses the channel (i.e., λp and µp)




Problem Insights and Formulation

Problem Formulation

Stability for a queue is achieved iff λ < µ

We try to find the stability region of the system (the regionsof λp and λs for which the two queues are stable), i.e.:

λp < µp

λs < µs




Queue Service Rates

Primary Queue: If secondary queue is empty OR secondary queueis not empty and PU is detected:

pout,p = Pr{Pp|Hp|2 < βp} = 1− exp(−βpPp

)

If secondary queue is not empty and PU is misdetected:

pmdout,p = Pr

{ Pp|Hp|2

|HHspwa|2 + 1

< βp

}Service rate:

µp = (1− pout,p)(Pr{Qs = 0}+ (1− pmd)Pr{Qs 6= 0}

)+ (1− pmd

out,p)pmdPr{Qs 6= 0}




Queue Service Rates

Secondary Queue:PU queue is emptyAND not detected:

pout,s = Pr{Ps||Hs||2 < βs}

PU queue is emptyAND detected (false alarm):

pfaout,s = Pr{|HHs wp|2 < βs}

PU queue is not emptyAND detected:

p(d)out,s = Pr

{ |HHs wp|2

Pp|Hps|2 + 1< βs

}PU queue is not emptyAND misdetected:

pmdout,s = Pr

{ Ps||Hs||2

Pp|Hps|2 + 1< βs

}µs =

(pout,s (1− pfa) + pfaout,s pfa

)Pr{Qp = 0}

+(p(d)out,s(1− pmd) + pmd

out,s pmd

)Pr{Qp 6= 0}




Stability analysis using dominant systems

Continuing analysis is hard to interacting queues

We use the concept of “dominance”: We assume two auxiliarysystems

1 Primary queue is dominant (sends dummy packets when queueis empty)

2 Secondary queue is dominant (sends dummy packets whenqueue is empty)

It is proven that the union of the stability regions of bothsystems is exactly the stability region of the original system





Primary dominant queue:

Pr{Qp = 0} = 0

µpds =(p(d)out,s(1− pmd) + pmd

out,s pmd

)Secondary queue does not depend on the state of primaryqueue (channel stationarity is guaranteed). We apply Little’s

theorem(Pr{Qs = 0} = 1− λs

µpds

)µpdp = (1− pout,p)− λs

µpdspmd

(pmdout,p − pout,p

)





Effect of changing Ps:

On secondary rate: Increasing Ps increases µpdsOn primary rate:

Increasing Ps increases interference on the primary receiverwhen misdetection occursIncreasing Ps helps SU empty its queue faster and evacuatesthe channel

The impact of both effects depend on λs and µpdp

Optimization problem over Ps to maximize µpdp

max.Ps

λp = µpdp s.t. λs < µpds , Ps ≤ Pmax






0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

P s

µ s

pd

1st Dominant System

P s

range for Q s

stability (λs = 0.35)

Figure: Pp = 1, K = 4, pmd = 0.1, pfa = 0.01, βp = βs = 1 andPmax = 2.






0 0.5 1 1.5 20.354

0.356

0.358

0.36

0.362

0.364

0.366

0.368

0.37

P s

µ p

pd

1st Dominant System

λs = 0

λs = 0.1

λs = 0.35






Secondary dominant queue:

Pr{Qs = 0} = 0

µsdp = (1− pout,p) (1− pmd) + (1− pmdout,p)pmd

Primary queue does not depend on the state of secondaryqueue (channel stationarity is guaranteed). We apply Little’s

theorem(Pr{Qp = 0} = 1− λp

µsdp

)

µsds =λpµsdp

(p(d)out,s(1− pmd) + pmd

out,s pmd − pout,s (1− pfa)

− pfaout,s pfa

)+(pout,s (1− pfa) + pfaout,s pfa

)Mohammed Karmoose, Ahmed Sultan, Moustafa Youseff Alex. Univ.




Effect of changing Ps:

On primary rate: Increasing Ps decreases µsdpOn secondary rate:

Increasing Ps enhances SINR of secondary transmission andincrease µsd

s

Increasing Ps interferes with primary transmission - PU willoccupy the channel for longer times which decreases µsd

s

The impact of both effects depend on λp and µsds

Optimization problem over Ps to maximize µsds

max.Ps

λs = µpds s.t. λp < µpdp , Ps ≤ Pmax






0 0.5 1 1.5 20.34

0.345

0.35

0.355

0.36

0.365

0.37

P s

µ p

sd

2nd Dominant System

P s

range for Q p

stability (λp = 0.35)







0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

P s

µ s

sd

2nd Dominant System

λp = 0

λp = 0.1

λp = 0.35

λp = 0.36






Stability region of the original system:

0 0.2 0.4 0.6 0.8 10

0.5

1

λ s

λ p

Stability region of the 2nd dominant system

Stability region of the 1st dominant system

0 0.2 0.4 0.6 0.8 10

0.5

1

λ s

λ p

Stability region of the systemwith two interacting queues

Figure: K = 4, pmd = 0.1, pfa = 0.01, βp = βs = 1 and Pmax = 2.





Stability region of the original system:

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

λ s

λ p

Stability region of the systemwith two interacting queues (P

p = 10)

Stability region of the systemwith two interacting queues (P

p = 1)

Figure: Pp = 1, 10, K = 4, pmd = 0.1, pfa = 0.01, βp = βs = 1 andPmax = 2.




Thank you

For any questions, feel free to contact the author atm h [email protected]



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Stability Analysis in a Cognitive Radio System with Cooperative Beamforming