1.
Priyadarshi Mukherjee
Electronics and Telecommunication Engineering Department
Indian Institute of Engineering Science and Technology.
Shibpur, Howrah.
West Bengal, India.
priyadarshi.m004@gmail.com

2.
Outline
 Introduction to Cognitive Radio Networks (CRNs)
 Research Issues in CRNs
 Resource Allocation in CRNs
 Power Allocation Problems in Single User CRNs
 Power Allocation Problems in Multiuser CRNS
 Joint Channel and Power Allocation Problem in Multiuser CRNS
 Power Allocation Problem in Relay based CRNs
 Joint Channel and Power Allocation Problem in Relay based
CRNs
 Joint Channel and Power Allocation Problem in OFDM-Based
CRNs with Relay
 Recent Trends in Resource Allocation in CRNs

3.
Why Cognitive Radio?
According to a FCC report [1], a large portion of the
licensed spectrum of various agencies remains underutilized.
The concept of Cognitive Radio is introduced as a method
to improve the spectrum utilization.
Fig 1: Spectrum Usage [2]

4.
Introduction to Cognitive Radio
Networks(CRNs)
 Cognitive Radio
- Termed formally introduced by Joseph Mitola [3].
- “Radio that includes a transmitter in which operating
parameters such as frequency range, modulation type or
maximum output power can be altered by software.“
 Allows the unlicensed users to dynamically and
opportunistically access the “under-utilized" licensed bands.

5.
Introduction to CRNs (Contd…)
In order to access “under-utilized” licensed bands dynamically
and opportunistically, Cognitive Radio has to:
 identify the spectrum opportunities (idle frequency bands) in
spatial and frequency domain.
 or use the licensed spectrum with transmit power constraint so
that the interference created by secondary users is below the
tolerable limit.

6.
The Basic Cognitive Cycle
Fig 2: Basic Cognitive Cycle [4]

7.
Characteristics of CRNs
 Cognitive capability
 Ability to capture or sense the information from its radio
environment and allows to identify and select the portion of
the spectrum that are unused at a specific time or location.
 Reconfigurability
 Dynamically programmable capability according to radio
environment to transmit and receive on a variety of
frequencies.

8.
Terminology
 Primary user(PU): users have license to use a certain
frequency spectrum.
 Secondary user(SU): devices/ users that able to sense and
adapt licensed users allocated spectrum.
 Spectrum hole: a frequency band licensed to a PU but not
utilized by that user at a particular time and at a specific
geographic location.

9.
Detection of Spectrum Holes
In the context of detection of the presence of spectrum
holes, the spectrum has been classified into three predominant
types [4]:
 Black spaces: occupied by high-power “local” interferers some of the
time.
 Grey spaces: partially occupied by low-power interferers.
 White spaces: free of RF interferers except for ambient noise, made up of
natural and artificial forms of noise.

10.
Some Research Issues on CRNs
 Spectrum Sensing and Dynamic Spectrum Management
 Transmission Power Control
 Spectrum Allocation
 Routing in Multi-hop CRNs
 Link Scheduling
 Group and Link Management
 OFDM in Cognitive Radio

11.
Resource Allocation in CRNs
Based on local information on the spectrum band, CR users
need to determine the communication resources intelligently.
Each CR user tries to utilize spectrum resource as much as
possible.
Two main issues in Resource Allocation:
 Power Allocation
 Channel Allocation

12.
Resource Allocation in CRNs
(Power and Channel Allocation)
Without relay With relay
Single Users Multiple Users Single Relay Multiple Relays
Dual Hop Multi Hop
Fig 3: Classification of Resource Allocation Problem in
CRNs (based on network architecture)

13.
Power Allocation Problem in Single User
CRNs
 In power allocation, mainly the transmission power of the CR
user is adjusted by considering co-channel (or inter-user)
interference.
 Power allocation is based on the PU activities in its
transmission, not to violate the interference constraints.
 Of late, power allocation in cognitive radio network is being
related to OFDM for certain advantages.

14.
System Model
PU-Tx gpp PU-Rx
gps
gsp
SU-Tx gss SU-Rx
Figure 4: A simple CR network system model[4].
Assumptions:
 PU and SU links share the same narrow-band frequency for transmission.
 All channels involved are assumed to be independent block fading (BF) channels.
 The additive noises at PU-RX and SU-RX are assumed to be CN(0, N0).
instantaneous channel
power gain at fading state ν
for the primary link
instantaneous channel
power gain at fading state ν
for the secondary link
instantaneous channel
power gain at fading state ν
for the link from PU-Tx to
SU-Rx
instantaneous channel
power gain at fading state ν
for the link from SU-Tx to
PU-Rx

15.
Objective Function
Assuming that
 transmitted signals are Gaussian in nature [6],
the ergodic capacity of the SU link is defined [5] as
(1)
where
 Pp : constant power transmitted by PU-Tx.
 ps: instantaneous transmit power of SU-Tx.
 E{.}: expectation
The objective function is:
(2)


















0
2 1log'
NPg
pg
EC
pps
sss



















0
2
0
1logmax
NPg
pg
EC
pps
sss
ps
Assuming the noise
(n) to be AWGN,
i.e. n ~ CN(0,N0).

16.
Constraints in Power Allocation
Mainly 2 types of power constraints [6] exist:
A. Transmit power constraint.
(i) peak transmit power constraint, i.e. ps≤ Ppeak (3)
(ii) average transmit power constraint, i.e. E{ps}≤Pav (4)
Ppeak: peak transmit power constraint.
Pav : average transmit power constraint.
B. Interference power constraint.
(i) peak interference power constraint (PIP), i.e. gspps≤ Qpeak (5)
(ii) average interference power constraint (AIP), i.e. E{gspps}≤Qav (6)
Qpeak: peak interference power constraint.
Qav: average interference power constraint .
E{.} : expectation opn.

17.
Problem Formulation
The problem thus formulated:
from equation (2)
s.t
C1: transmit power constraint, from equation (3)/(4)
C2: interference power constraint, from equation (5)/(6)
This above problem has been solved [6] by convex optimization.



















0
2
0
1logmax
NPg
pg
EC
pps
sss
ps

18.
Numerical Result
Fig 5: Capacity under both the peak power constraints vs.
transmit power constraint (Ppeak ) [6].
As can be seen in the plot, in spite
of Ppeak increasing gradually,
capacity does NOT increase
monotonically, but saturate at some
point of time in the presence of the
interference constraints.

19.
Constraint based on PU Outage
 Instead of applying the conventional interference power
constraint, a constraint based on the maximum tolerable outage
probability for the PU [5] may also be considered.
 Given target transmission rate ro, SU being absent, the
transmission outage probability of the PU is
(7)












 0
0
2 1logPr r
N
Pg ppp
p

20.
Constraint based on PU Outage (contd…)
 But when SU is active, the transmission outage probability of the
PU becomes
(8)
 To protect the PU, additional outage probability of PU caused by
SU transmission should not be larger than Δε.
εc − εp ≤ Δε. (9)
• Equation (9) is termed as the PU outage loss constraint.


















 0
0
2 1logPr r
Npg
Pg
ssp
ppp
c

21.
Problem Formulation
The ergodic capacity of the SU can be obtained by solving the
following problem:
from equation (2)
s.t. C1: transmit power constraint, from equation (3)/(4)
C2: εc − εp ≤ Δε. from equation (9)
This problem has been solved [5] by applying convex
optimization.



















0
2
0
1logmax
NPg
pg
EC
pps
sss
ps

22.
Power Allocation Problem in Multiuser
CRNs
 Till this point of time, the scenario where multiple CUs exist,
have not been highlighted upon.
Hence the quality of service (QoS) requirement of CUs
could not be guaranteed.
 Thus, power allocation in multiuser CRNs is of much more
practical importance.

23.
System Model
 The uplink of a single cell of a CRN is considered [7] with N
unlicensed users.
 A network with one licensed receiver is considered, having a
maximum interference tolerance .
 The maximum interference tolerance (Qmax) is calculated [7] as
Qmax= ξ Tmax
 The network is modeled as interference channels, where
gi: path gain between base station (BS) and user equipment (UE) i.
max
mQ
Boltzmann’s constant
Interference temperature limit.

24.
Objective Function
 Total system capacity based on Shannon formula is described as
(10)
where
 p=(p1,…,pN)T, p1 is transmit power of user i.
The objective function is:
(11)
  
















N
i
N
ijj
jj
ii
gp
gp
pC
1
,1
2
2 1log

noise and the
interference from the
licensed users.
)(max
0
pC
p

25.
Constraints in Power Allocation
 Peak transmit power constraint
, (12)
where
, and : maximum transmit power of
user i.
 Peak interference power constraint
Hp ≤ Qmax, (13)
where
 hi: path gain between user i and the PU-Rx, and
pp 0
 Nppp ,...,1
ip
  NihH 
 1

26.
Problem Formulation
The optimization problem thus formulated:
from equation (11)
s.t.
C1: peak transmit power constraint from equation (12)
C2: peak interference power constraint from equation (13)
This problem is a concave minimization problem with
linear constraints in mathematical programming. So, the branch
and bound algorithm [7] has been used here to search optimal
solutions.
 pC
p 0
max


27.
Joint Channel and Power Allocation
Problems in Multiuser CRNs
 Till now, power allocation was being done assuming that the
channels have been already allocated.
 But to achieve satisfactory performance from a multiuser
multichannel wireless network, such as CRNs, not just power
but joint channel and power allocation provides satisfactory
results.

28.
System Model
A CRN is considered with K users and N channels (both K and N
varying dynamically based on the number of contending users and available
vacant channels) .
AP CR Primary User
Fig. 7: Cognitive Radio Network [8].
 An access point (AP) controls the
transmission of CRs lying within its
range of coverage and also collects
reports about the activities of
primary users (PUs) that CRs may
interfere with.

29.
Assumptions
 The following knowledge [8] is available at the AP:
(i) the set of vacant channels that are not currently utilized
by PUs and are free for CRs to use.
(ii) the power gains of this channel set corresponding to
each of the contending users.
 Channels are assumed to be independent and identically
distributed (IID). The strength of each is assumed to be
Rayleigh distributed.

30.
Problem Formulation
Let
 N0: one-sided noise power spectral density
 B: unit bandwidth
 Pnk: uplink power when channel n is assigned to the user k
Capacity associated with user k (depends on the number of channels assigned) is
(14)
The total sum capacity is:
(15)
The objective function is:
(16)










N
n nk
nknk
nkk
BN
gP
BC
1 0
2 1log


assignment of channel n to user k,ϵ {0,1}
C
nknk P 0,10
max

   








K
k
N
n
nk
nknk
nk
K
k
k
BN
gP
BCC 1 1
0
2
1
1log



31.
Problem Formulation (contd…)
 Sum transmit power constraint
(17)
 The constrained optimization problem is :
from equation (16)
s.t.
C1: sum transmit power constraint from equation (17)
The above optimization problem comprises both continuous
and discrete variables and thus belongs to the class of mixed
integer programming.


N
n
knk kPP
1
available power budget
C
nknk P 0,10
max


32.
Problem Formulation (contd…)
To make the problem tractable, discrete nature of αnk is relaxed
and channel sharing among different users is allowed, i.e. αnk
is allowed to take on continuous values in the range from 0 to 1.
Thus, now the optimization problem is :
from equation (16)
s.t.
C1: sum transmit power constraint from equation (17)
C2: assignment constraint, i.e.
(18)n
K
k nk  1
1
C
nknk P 0,10
max


33.
Problem Formulation
 In this new formulation, channel sharing is allowed among
different users under the condition stated in C2.
 The importance of having αnk in the denominator of C (15)
becomes clear now as αnk can be a fraction (channel sharing).
The methodology used here is to start solving the modified
problem (with channel sharing) and then find the condition that
allows for only 1 user utilization per channel.
Above formulated problem being convex, convex optimization has
been used to solve it.
C
nknk P 0,10
max


34.
Power Allocation Problem in Relay based
CRNs
 In the case of direct communication between SUS and
SUD, transmission power requirement, sometimes, may
exceed the limits of acceptable interference to the PU.
 It may also happen that there exists no direct link between
the source(S) and the destination (D).
To address such problems, the context of relay-based CRNs
is of high practical importance.

35.
System Model
As shown below, a communication system with N relay nodes is
considered. rN
s Ia-b d
Ia-b r1 r3
Ua m n Ub
Ib-a r2
a b
 Ua, Ub : PUs, and their coverage areas are a and b respectively.
 s,d: 2 SUs, which use relays r1 …rN for their communication.
 Ia-b : Idle channel set in a, but busy in b. [Ib-a is just the reverse]
Interference for PUs
Secondary transmission using Cooperative scheme
Fig. 8: N relay nodes used in secondary communication. Source node and relay nodes
are transmit signal with different frequency sets [9].

36.
Objective Function
In general, the objective function [9] is:
(19)
where
 Pout: outage probability of the communication system.
Mathematical expression of Pout is different for different relay based CRNS,
depending on whether it is regenerative or non-regenerative.
For instance, for single relay transmission with regenerative relay [vtc 2010],
where (20)
 γth: threshold SNR.
 p1, p2: SU and relay transmit power.
 G1, G2: parameters independent of power.
outPmin







 2211
11
1
pGpG
out
th
eP


37.
Constraints in Power Allocation
 Sum power constraint [9]
(21)
 Transmit power constraint [9]
pn ≤ Pmax : n=1,2,…N (22)
ps ≤ Pmax
 Interference power constraint [9]
pshsn ≤ Tb (23)


N
n
Tns Ppp
1
transmit power of source s
transmitted power of n th relay
available power budget
a
N
n
mrn Thp n
1
Ta, Tb: interference power
threshold levels on m and n,
respectively.
hij: the link gain
between node i and j.
transmit power constraint

38.
Problem Formulation
The constrained optimization problem [9] is :
min Pout from equation (19)
s.t.
C1: sum power constraint from equation (21)
C2: transmit power constraint from equation (22)
C3: interference power constraint from equation (23)
Above formulated problem being convex in nature, convex
optimization has been applied to solve it [9].

39.
Numerical Result
As can be seen in the plot, in
spite of Total power increasing
gradually, outage probability
does NOT decrease
monotonically, but saturate at
some point of time in the
presence of interference
constraints.
Fig 9: Outage Probability vs. Total power [9].

40.
Joint Channel and Power Allocation
Problem in Relay based CRN
 Just like multiuser CRNs,
in relay based CRNs too only power allocation on the
assumption of the channels being already allocated, does not
provide satisfactory result always.
 So to improve performance, in terms of guaranteed QoS for
instance, joint channel and power allocation IS important in
relay based CRNs too.

41.
System Model
The system model shown in figure 10 [10] includes a N-hop CRNs
with linear network topology. PUS PUD
 Source and the relaying nodes (R n) are operating in
full-duplex mode.
 Underlay scenario is considered,
where CUs share their spectra with PUs SU-Tx R 1 RN SU-Rx
simultaneously.
 Available spectrum is divided into N
orthogonal channels to be used by CUs.
 The channels are AWGN, subject to quasi-static fading, i.e. channel gains are random,
although remain constant during a transmission suite from source to destination.
PUS: primary source, PUD: primary destination.
SU-Tx: cognitive transmitter, SU-Rx: cognitive receiver.
Fig 10: System model of relay based multi-hop
CR network [10].

42.
Objective Function
End to end outage probability in Rayleigh fading channel with ‘N’
regenerative relays can be written [10] as
(24)
where
 γth: predetermined SNR threshold
 N0: average noise power at each relay
 : transmission power of the m th relay over channel Ωm .
 : channel gain between two consecutive relays, when channel Ωm is allocated.
Minimizing outage probability is equivalent to minimizing
Thus, the objective function [10] is:
(25)
 









N
m
ss
mm
th
out
mm
gP
N
P
1 ,,
0
exp1

ss
mm
g ,
mm
P ,
 
N
m
ss
mm
th
mm
gP
N
1 ,,
0








 

N
m
ss
mm
th
P
mm
mm gP
N
1 ,,
0
0,
min


43.
Constraints in Joint Channel and Power
Allocation
 Sum power constraint
(26)
PT: maximum transmission power.
 Sum interference power constraint
(27)
TPU: Accumulated interference power threshold (AIPT) at PU.

 
N
m
Tm PP m
1
,

 
N
m
PU
sp
mm TgP m
1
,
channel gain from the mth
relay to the PU

44.
Problem Formulation
The optimization problem is:
from equation (25)
s.t.
C1 :sum power constraint. from equation (26)
C2: sum interference power constraint from equation (27)
The objective function is convex and two constraints are linear.
So, the minimization problem is solved by convex optimization [10].








 

N
m
ss
mm
th
P
mm
mm gP
N
1 ,,
0
0,
min


45.
Numerical Result
Transmission Power (dB)
As can be seen in the plot,
this scheme [10] is comparatively better
than the scheme proposed in [9]
Figure 11: Outage Probability vs. Transmission Power [10]

46.
Joint Channel and Power Allocation
Problem in OFDM-Based CRNs with
Relay
In a cognitive radio environment, spectrum holes come and
go, depending on the availability of subbands as permitted by
licensed users. To deal with this phenomenon and thereby provide
the means for improved utilization of the radio spectrum, a
cognitive radio system must have the ability to fill the spectrum
holes rapidly and efficiently. In other words, cognitive radios have
to be frequency-agile radios with flexible spectrum shaping
abilities. The orthogonal frequency-division multiplexing (OFDM)
modulation scheme can provide the required flexibility, and is
therefore being considered as a good candidate for cognitive radio.

47.
System Model
An OFDM-based relay CRN is considered, as shown in figure 10
[11]
 The CR relay system coexists with the primary system in the same geographical
location.
 There is no direct link between S and D. So, S tries to communicate with D through R.
 The CR system’s frequency spectrum is divided into N subcarriers each having a Δf
bandwidth.
 The relay is assumed to be half-duplex, thus receiving and transmitting in two different
time slots.
cognitive relay
R
cognitive source
S
primary receiver
cognitive destination
D
obstacle
Fig. 12: Cooperative relay cognitive radio network [11].

48.
Objective Function
Let
 In 1st time slot, S connects to R via jth subcarrier and in 2nd slot, R connects to D via kth
subcarrier.
 Ps (PR): maximum total transmission powers that can be used in S (R).
 noise power (σ2)is assumed to be same for all subcarriers.
Transmission rate of jth subcarrier in the source coupled with kth
subcarrier in the relay [11], R(j, k) is
(28)
where
 :power transmitted over the jth (kth) subcarrier in the S-R(R-D) link.
 : jth (kth) subcarrier fading gain over S-R(R-D) link.


















 2222 1log,1logmin
2
1
),(

k
RD
k
RD
j
SR
j
SR HPHP
kjR
)( k
RD
j
SR PP
)( k
RD
j
SR HH

49.
Objective Function (contd…)
Our aim is to maximize the CR system throughput by:
 Optimization of subcarrier pairing.
 Distribution of the available power budgets in S and R between
the subcarrier pairs.
The objective function [11] is:
(29)
 

N
j
N
k
kj
tPP
kjRt
kj
k
RD
j
SR 1 1
,
,0,0
),(max
,
assignment variable.
tj,k= 1, when jth subcarrier is selected in 1st time
slot and kth subcarrier in the 2nd time slot.
0, otherwise.
total number of subcarriers

50.
Constraints in Joint Channel and
Power Allocation
 Source power constraint [11]
(30)
 Relay power constraint [11]
(31)
 Interference power constraint at the 1st and 2nd time slot [11]
; (32)
 Subcarrier pairing constraint [11]
(33)
 : subcarrier interference factor to the PU band from S (R).


N
j
s
j
SR PP
1


N
j
R
k
RD PP
1


N
j
th
j
SP
j
SR IP
1


N
j
th
k
RP
k
RD IP
1
 

N
j
kj
N
k
kj ktjt
1
,
1
, ,1;,1
)( j
RP
j
SP 

51.
Problem Formulation
The optimization problem [11] is formulated as:
from equation (29)
s.t.
C1: source power constraint from equation (30)
C2: relay power constraint from equation (31)
C3: interference power constraint at the 1st and 2nd time slot
from equation (32)
C4: subcarrier pairing constraint from equation (33)
This problem has been solved [11] by applying convex
optimization.
 

N
j
N
k
kj
tPP
kjRt
kj
k
RD
j
SR 1 1
,
,0,0
),(max
,

52.
Numerical Result
As can be seen in the plot, in spite
of interference threshold (Ith)
increasing gradually, capacity does
NOT increase monotonically, but
saturate at some point of time in the
presence of the interference
constraints.
Fig 13: Capacity under both the power constraints vs.
interference threshold (Ith) [11].

53.
Recent Trends in Resource Allocation in
CRNs
 In a highly dynamic environment (as in CRN), finding a
reasonably good solution (i.e., a suboptimal solution) fast enough
is the only practical goal. Otherwise, spectrum holes may
disappear before they can be utilized for communication. In such
a situation, the concept of equilibrium is very important, and here
comes the advantage of using Game Theory in this context.
 Due to this advantage of the very idea of Game Theory , it is now
being quite interestingly used to solve the Resource Allocation
Problems in CRNs. For instance, [12] shows the investigation of
distributed power control for CRNs, based on a cooperative
game-theoretic framework.

54.
Recent Trends in Resource Allocation in CRNs
(contd…)
Joint spectrum sensing and throughput

55.
References
 [1] Federal Communications Commission, “Spectrum Policy Task Force ,” Rep. ET Docket no.
02-135, Nov. 2002.
 [2] I. F. Akyildiz, W. Y. Lee, M. C. Vuran, and S. Mohanty, “Next generation/ dynamic
spectrum access/cognitive radio wireless networks: A survey,” Computer Networks, Vol. 50,
pp. 2127–2159, May 2006.
 [3] J. Mitola, “Cognitive radio: An integrated agent architecture for software defined radio,”
Ph.D. dissertation, KTH Royal Inst. of Technol., Stockholm, Sweden, 2000.
 [4] S. Haykin, “Cognitive Radio: Brain-empowered Wireless Communications”, IEEE Journal
on Selected Areas in Communications (JSAC), Vol. 23, No. 2, Feb. 2005, pp. 201-220.
 [5] Xin Kang, Rui Zhang, Ying-Chang Liang, and Hari Krishna Garg, “Optimal Power
Allocation for Cognitive Radio under Primary User’s Outage Loss Constraint, ” IEEE
International Conference on Communication( ICC), pp.1-5, June 2009.
 [6] Xin Kang, Ying-Chang Liang, Arumugam Nallanathan, “Optimal Power Allocation for
Fading Channels in Cognitive Radio Networks under Transmit and Interference Power
Constraints, ” IEEE International Conference on Communication( ICC), pp. 3568 - 3572, May
2008.
 [7] Wei Wang, Tao Peng, Wenbo Wang, “Optimal Power Control under Interference
Temperature Constraints in Cognitive Radio Network,” IEEE Wireless Communications and
Networking Conference(WCNC), pp. 116– 120, March 2007.

56.
References (contd…)
 [8] F. F. Digham, “Joint Channel and Power Allocation for Cognitive Radios” IEEE Wireless
Communications and Networking Conference(WCNC), pp. 882 – 887, April 2008.
 [9] L.K. Saliya Jayasinghe and Nandana Rajatheva, “Optimal Power Allocation for Relay
Assisted Cognitive Radio Networks ,” IEEE 72nd Vehicular Technology Conference (VTC’10-
Fall), pp. 1-5, September 2010.
 [10] Tamaghna Acharya, Swagata Mandal and Santi P. Maity, “Joint Power and Channel
Allocation in Cognitive Radio Ad Hoc Networks,” 5th International Conference on
Communication Systems and Networks (COMSNETS), pp. 1-7, January 2013.
 [11] Musbah Shaat and F. Bader, “Asymptotically Optimal Subcarrier Matching and Power
Allocation for Cognitive Relays With Power and Interference Constraints,” IEEE Wireless
Communications and Networking Conference(WCNC), pp. 663-668, April 2012.
 [12] Chun-Gang Yang, Jian-Dong Li and Zhi Tian, “Optimal Power Control for Cognitive
Radio Networks Under Coupled Interference Constraints: A Cooperative Game-Theoretic
Perspective,” IEEE Transactions on Vehicular Technology, Vol. 59, Issue 4, pp. 1696-1706,
May 2010.
 [13] Timo Weiss, Joerg Hillenbrand, Albert Krohn Friedrich K. Jondral , “Mutual interference
in OFDM-based spectrum pooling systems,” in Vehicular Technology Conference (VTC’04-
Spring), Vol. 4, pp. 1873-1877, May 2004.

57.
Questions

58.
PU-Rx
CU Base Station CR
Interference link
System Model
Fig. 6: System Model with 1 PU and N CRs

59.
Subcarrier interference factor
Assuming an OFDM based CR, the power spectrum density of the ith subcarrier
is [13]
where
 Pi: total transmit power in the ith subcarrier.
 Ts: symbol duration.
The mutual interference introduced by the ith subcarrier to PU [11] is
 The term Ωi is defined as the INTERFERENCE FACTOR of the ith
subcarrier to the PU band.
 
2
sin







s
s
sii
fT
fT
TPf


  i
i
Bd
Bd
iiiii PdffGPdI
i
i
 


2/
2/
)(, 
spectral distance between ith
subcarrier and the PU band
bandwidth occupied by PU
Channel gain between ith
subcarrier and PU