an overview of resource allocation problem in cognitive radio networks

Priyadarshi Mukherjee

Electronics and Telecommunication Engineering Department

Indian Institute of Engineering Science and Technology.

Shibpur, Howrah.

West Bengal, India.

[email protected]

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

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]

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.

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.

The Basic Cognitive Cycle

Fig 2: Basic Cognitive Cycle [4]

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.

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.

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.

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


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


(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)

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.

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



for the secondary link



for the link from PU-Tx to

SU-Rx



for the link from SU-Tx to

PU-Rx

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

pgEC

pps

sss

0

20

1logmaxNPg

pgEC

pps

sss

ps

Assuming the noise

(n) to be AWGN,

i.e. n ~ CN(0,N0).

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. Eps≤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. Egspps≤Qav (6)

Qpeak: peak interference power constraint.

Qav: average interference power constraint .

E. : expectation opn.

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

20

1logmaxNPg

pgEC

pps

sss

ps

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.

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 rN

Pg ppp

p

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 rNpg

Pg

ssp

ppp

c

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

20

1logmaxNPg

pgEC

pps

sss

ps

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.

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.

m ax

mQ

Boltzmann’s constant

Interference temperature limit.

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.


(11)

N

iN

ijj

jj

ii

gp

gppC

1

,1

22 1log

noise and the

interference from the

licensed users.

)(max0

pCp


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 ,...,1ip

NihH

1

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.

pCp 0

max

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.

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.

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.

Problem FormulationLet

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)


(16)

N

n nk

nknknkk

BN

gPBC

1 0

2 1log

assignment of channel n to user k,ϵ 0,1

Cnknk P 0,10

max

K

k

N

nnk

nknknk

K

k

kBN

gPBCC

1 10

21

1log

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 continuousand discrete variables and thus belongs to the class of mixedinteger programming.

N

n

knk kPP1

available power budget

Cnknk P 0,10

max

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)nK

k nk 11

Cnknk P 0,10

max

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.

Cnknk P 0,10

max

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.

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].

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

1pGpG

out

th

eP


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 Ppp1

transmit power of source s

transmitted power of n th relay

available power budget

a

N

n

mrn Thpn

1

Ta, Tb: interference power

threshold levels on m and n,

respectively.

hij: the link gain

between node i and j.

transmit power constraint

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].

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].


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.

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].

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

mss

mm

thout

mmgP

NP

1 ,,

0exp1

ss

mmg ,

mmP ,

N

mss

mm

th

mmgP

N

1 ,,

0

N

mss

mm

th

Pmm

mm gP

N

1 ,,

0

0,

min

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 PPm

1

,

N

m

PU

sp

mm TgPm

1

,

channel gain from the mth

relay to the PU

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

mss

mm

th

Pmm

mm gP

N

1 ,,

0

0,

min

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]


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.

System ModelAn 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 Δfbandwidth.

The relay is assumed to be half-duplex, thus receiving and transmitting in two different time slots.

cognitive relayR

cognitive source

S

primary receiver

cognitive destination

D

obstacle

Fig. 12: Cooperative relay cognitive radio network [11].

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,1logmin2

1),(

k

RD

k

RD

j

SR

j

SR HPHPkjR

)( k

RD

j

SR PP

)( k

RD

j

SR HH

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

kjtPP

kjRtkj

kRD

jSR 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

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 PP1

N

j

R

k

RD PP1

N

j

th

j

SP

j

SR IP1

N

j

th

k

RP

k

RD IP1

N

j

kj

N

k

kj ktjt1

,

1

, ,1;,1

)( j

RP

j

SP

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

kjtPP

kjRtkj

kRD

jSR 1 1

,,0,0

),(max,

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].

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.

Recent Trends in Resource Allocation in CRNs

(contd…)

Joint spectrum sensing and throughput

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.

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.

Questions

PU-Rx

CU Base Station CR

Interference link

System Model

Fig. 6: System Model with 1 PU and N CRs

Subcarrier interference factorAssuming 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

ssii

fT

fTTPf

i

i

Bd

Bd

iiiii PdffGPdIi

i

2/

2/

)(,

spectral distance between ith

subcarrier and the PU bandbandwidth occupied by PU

Channel gain between ith

subcarrier and PU