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Performance Analysis of Coexisting Secondary Users in Heterogeneous Cognitive Radio Network

Xiaohua LiDept. of Electrical & Computer EngineeringState University of New York at Binghamton

Binghamton, NY 13902, USAEmail: xli@binghamton.edu

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Major Contributions: Develop a framework to analyze the

throughput performance of heterogeneous cognitive radio networks (CRN) Develop Markov Model Bank (MMB) to

model heterogeneous CRN and to derive its throughput

Advantage: Feasible to analyze mutual interference among all users in large heterogeneous CRN

Formulate sum-of-ratios linear fractional programming (SoR-LFP) to derive theoretically optimal CRN throughput

Work as a benchmark for evaluating the optimality of practical CRN

Outline

1. Introduction2. System model3. MMB for hetero-CRN and throughput

analysis4. SoR-LFP for CRN throughput optimization5. Simulations6. Conclusions

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1. Introduction

CRN reuses spectrum white spaces CRN sense spectrum for spectrum white

spaces, access the spectrum white spaces secondarily, and vacate the spectrum when primary users come back

Heterogeneous CRN Choose spectrum sensing/access strategies

freely Choose transmission parameters and

spectrums freely Flexible software implementation

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How do different CRN users coexist with each other? Need to analyze the performance of CRN

under heterogeneous setting CRN performance analysis is

challenging Mostly done by simulation rather than

analysis Limited analysis results are for simplified

&homogeneous CRN, or for small CRN with a few users only

Optimal performance is unknown: a long-standing challenge

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We focus on CRN throughput analysis Throughput: product of time spent in

successful data transmission and capacity of the channel used in this transmission

Each CRN user’s throughput, overall CRN throughput

Need to consider CRN operation modes, and mutual interference among all the CRN users

Throughput optimization: assign transmission power optimally to available channels for maximum throughput

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Objectives: Develop a way to analyze CRN throughput

under practical strategies and mutual interference

Look for theoretically optimal CRN throughput

Challenges: large CRN with many different mutually

interfering users How to take the unique CRN

characteristics into modeling and analysis?

How to derive optimized/ideal throughput?

2. System Model

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Consider CRN with secondary users (SU) and channels Channel available probability , SU offered

load

CRN SU’s four basic working modes Spectrum sensing: duration SNR threshold Spectrum access (data packet

transmission): duration , max transmission power

Idling: duration Channel switching: duration

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ksiT k

si

kdiT

kwiT k

ciT

SU’s transmission power in each channel Practical: Use max power, one channel each

time Theoretical: distribute power among all

channels Basic equations for SU

Signal, SNR, sum throughput

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1

0K

ki i

k

P P

1,

2

2 2 1

1,

( ) ( ) ( ) ( )

| |,

| |

Ik k k k k k ki i ii i j j ji j i

j j i

k k Ik i iii iI

k k k k ij j ji i

j j i

y n P h s n f P h s n v n

P hR R

f P h

3. CRN Model andThroughput Analysis Markov model bank (MMB)

A separate Markov chain for each user states in each separated Markov chain Users & Markov chains connected

implicitly by transitional probability

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: prob. of spectrum sensing

: prob. of data transmission

: prob. of ideling

: prob. of channel switc

: prob. of channel sensed available

hing

ksi

kdi

ksi

kwi

ci

q

ksiq

Essential idea of MMB Reduce complexity of Markov chains, put all

complexity into a transitional probability good for feasible & efficient analysis of mutual interference

Steady-state probability

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11 1

1 0

1 1 0

1 0 ,

1 0 1

KK K

ci

ksi

k kk si k di

k ksi wi

q

q

xA a 0

xA a 0

b b

A x

1

1

12

1

1

12 (1 )

1

ci K

si

ksi K

ksi

si

K

Kq

K qq

Transitional probability evaluation

Mutually-coupled transitional probabilities can be calculated by root-finding algorithms

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1,

1[ ] | |

Bernoulli Random variable : [ 1]

Ik k k k k k ksi k i si si k i j ji j sik

j j ii

k k ksj si djk k

j j k ki j

q P P P h f

q T Tf P f

Q Q

CRN throughput Each user throughput:

Overall throughput:

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1 1

[log(1 )] [log(1 )]k kK K

k k ksi dii di i ik

k k i

q TR E E

Q

1

I

ii

R R

4. CRN Throughput Optimization

Assume fully cooperated users to jointly optimize their transmission powers in all channels Objective function: max sum throughput of

all users Used as a benchmark for evaluation of CRN

throughput performance

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Formulation of the optimization problem

where

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2

{ }221 1

1,

1

| |max log 1

| |

s.t. , 0.

m

ki

m

k kLIi ii

i IPk k kij ji i

j j i

Lk ki i i

P hR

P h

P P P

1

in channel

{ , , }: set

: transmission power

of available and o

of

nly

u

available channels

ser

mm

k

L

iP i k

C k k

Reformulate into Sum-of-Ratios Linear Fractional Programming (SoR-LFP)

where

Some existing algorithms can be modified to solve this optimization

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1 1

max log 1 , s.t. ,1

m

m

TLIi m

i m mTi i m

R

z

a zBz 1 z 0

b z

1 11 1

1 1

: normalized transmit powe, , , , , ,

: corresponding vectors and matri, x

r

,

L Lm mTk kk k

I Im

I I

i i

P P P P

P P P P

z

a b B

Sum-of-ratios linear fractional programming A global optimization problem that has

many applications and has stimulated decades of research

Generally non-convex. But under some constraints, many successful algorithms have been developed to solve it

Some such algorithm can be revised to solve our throughput-formulated problem

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5. Simulations

Gap between CRN achieved throughput and the optimal CRN throughput. Analysis results are accurate.

Random Network,Path-loss model,Random PU act.,SU load 0.9

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CRN throughput increases with number of channels and number of SU. Analysis expressions are accurate & efficient for large heterogeneous CRN.

Random Network,Path-loss model,Random PU act.,Random SU load

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6. Conclusions

Developed a framework to evaluate the throughput performance of CRN Develop Markov Model Bank (MMB) to

model CRN operations and analyze CRN throughput

Accurate & efficient expressions for large heterogeneous CRN

Formulate Sum-of-Ratios Linear Fractional Programming (SoR-LFP) to find the optimal CRN throughput

Optimize non-convex expressions of sum of capacities