Performance Analysis of
Coexisting Secondary Users
in Heterogeneous Cognitive
Radio Network
Xiaohua Li
Dept. of Electrical & Computer Engineering
State University of New York at Binghamton
Binghamton, NY 13902, USA
Email: [email protected]
1
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
2
Outline
1.
2.
3.
4.
5.
6.
Introduction
System model
MMB for hetero-CRN and throughput analysis
SoR-LFP for CRN throughput optimization
Simulations
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

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?
7
2. System Model

Consider CRN with 𝐼 secondary users (SU)
and 𝐾 channels

Channel available probability 𝜃𝑘 , SU offered load
𝛼𝑖
8

CRN SU’s four basic working modes
k
k
 Spectrum sensing: duration Tsi , SNR threshold 
si



Spectrum access (data packet transmission):
duration Tdik , max transmission power 𝑃𝑖
k
Idling: duration Twi
k
T
Channel switching: duration ci
9
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
y (n)  Pi h s (n) 
k
i
 
k
i
k
k
ii i
I

j 1, j  i
Pi k | hiik |2
I

j 1, j  i
K
f jk Pjk | h kji |2  ik 2
0   Pi k  Pi
k 1
f jk Pjk h kji s j (n)  vik (n)
I
,
R   Ri
i 1
10
3. CRN Model and
Throughput Analysis

Markov model bank (MMB)



A separate Markov chain for each user
3𝐾 + 1 states in each separated Markov chain
Users & Markov chains connected implicitly by
k
q
transitional probability si
 sik : prob. of spectrum sensing
 dik : prob. of data transmission
 wik : prob. of ideling
 ci : prob. of channel switching
qsik : prob. of channel sensed available
11

Essential idea of MMB


 A1




b
Reduce complexity of Markov chains, put all
complexity into a transitional probability  good
for feasible & efficient analysis of mutual
interference
Steady-state probability
AK
b
 1
A k   qsik
1  qsik
a1   x1  0 
   
    
a K   x K  0 
   
1  ci   0 
  sik 
0
 
1 0  , x k    dik 
 wik 
0 1
 
1
K



K
 ci
1
K  2

1 1  qsi


1
 sik 
K


1
K

2

1 1  q

si



k
 (1  qsi )

12

Transitional probability evaluation
 1
k
k
k
qsi   k i P[ si   si ]   k i P  k 2
 i

P |h | f  

j 1, j  i

k k k
q
sj Tsi Tdj
k
k
Bernoulli Random variable f j : P[ f j  1]  k k
Qi Q j

I
k
j
k 2
ji
k
j
k
si
Mutually-coupled transitional probabilities can be
calculated by root-finding algorithms
13

CRN throughput

Each user throughput:
k k
q
k
k
siTdi
Ri    di E[log(1   i )]   k E[log(1   ik )]
k 1
k 1 Qi
K

K
Overall throughput:
I
R   Ri
i 1
14
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


Lm
I
R  max{ Pk }   i  log 1 
i

i 1
1




Pi k | hiik |2

I
k
k 2
k 2 
Pj | h ji |  i 

j 1, j  i

Lm
s.t.
k
k
P

P
,
P
 i i i  0.
1

where
Pi k : transmission power of user i in channel k
Cm  {k1 ,
, k Lm }: set of available and only available channels
16

Reformulate into Sum-of-Ratios Linear
Fractional Programming (SoR-LFP)

aTi z m 
R  max z m   i  log 1  T
 , s.t. Bz m  1, z m  0
i 1
1
 bi z m  1 
I

Lm
where
T
k
k
 P1k1
P1 Lm
PIk1
PI Lm 
zm  
, ,
, ,
, ,
 : normalized transmit power
P1
PI
PI 
 P1
ai , bi , B: corresponding vectors and matrix

Some existing algorithms can be modified to solve
this optimization
17

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
5. Simulations
Random Network,
Path-loss model,
Random PU act.,
SU load 0.9
Gap between CRN achieved throughput and the optimal
CRN throughput. Analysis results are accurate.
19
Random Network,
Path-loss model,
Random PU act.,
Random SU load
CRN throughput increases with number of channels and number of SU.
Analysis expressions are accurate & efficient for large heterogeneous CRN.20
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
21