1
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: [email protected]
2
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
3
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
4
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
5
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
6
7
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
8
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
9
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
10
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
11
: 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
12
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
13
22
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:
14
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
15
Formulation of the optimization problem
where
16
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
17
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
18
19
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
20
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
21
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