A

Seminar Report

On

Optimisation in Spectrum Assignment for Cognitive Radio Networks

In partial fulfilment of requirements for the degree of

MASTER OF TECHNOLOGY

In

ELECTRONICS AND COMMUNICATION ENGINEERING

(With Specialization in Communication Systems)

SUBMITTED BY:

Payal Agarwal

UNDER THE GUIDANCE OF:

Dr. Debashis Ghosh

Associate Professor

E & C E Department

IIT Roorkee

DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

INDIAN INSTITUTE OF TECHNOLOGY ROORKEE

ROORKEE – 247667 (INDIA)

AUGUST, 2014

i

ABSTRACT

Recent developments and research have shown significant underutilization of licensed

spectrum. Cognitive radios offer the promise of being a technology innovation that will

enable the future wireless world. They are fully programmable wireless devices that can

sense their environment and dynamically adapt their transmission waveform, channel access

method, spectrum use, and networking protocols as needed for good network and application

performance. The key challenges faced and optimised assignment approaches in spectrum

assignment to secondary users (cognitive radios) are being discussed in this seminar.

ii

TABLE OF CONTENTS

Abstract ....................................................................................................................................... i

Table of Contents ....................................................................................................................... ii

List of Figures .......................................................................................................................... iii

1. Introduction ........................................................................................................................ 1

2. Cognitive Radio Networks ................................................................................................. 3

3. Spectrum assignment parameters ....................................................................................... 6

4. Spectrum assignment optimisation approaches ................................................................. 8

4.1 Capacity Optimisation ................................................................................................. 8

4.2 Sum Rate Optimization ............................................................................................. 10

4.3 SINR Balancing......................................................................................................... 15

4.4 Joint Rate and Power Optimization ........................................................................... 16

5. Conclusion ....................................................................................................................... 20

6. References ........................................................................................................................ 21

iii

LIST OF FIGURES

Fig 2.1 : Functionalities of cognitive radio[1]

3

Fig 2.2 : Spectrum sensing [2]

4

Fig 4.1: Secondary user transmission in deeply faded environment [15].

9

Fig 4.2 : Capacity under peak received-power constraint vs. α [15]

10

Fig. 4.3 : The system model with K no. of secondary links and N no. of primary

links with single transmitting and receiving antennas. SIMO-MAC model

has the base station with Nr receive antennas [18].

13

1

1. INTRODUCTION

Over the years, the radio spectrum is allocated to users by the government agencies in a rigid

manner having exclusive rights to use that spectrum. But the Federal Commission for

Communications (FCC) of US [3] has stated that average duty cycle of the most useable

spectrum is only 40%. With the increasing number of users especially in developing

metropolitan cities this fixed assignment scheme is not able to serve the user requirements.

So, to increase utilization of the spectrum, unlicensed(secondary) users should fit in the

unused portions called “white spaces” in the licensed spectrum i.e use the spectrum when

licensed user(primary user) is idle or interference is within the tolerable limits.

Cognitive radio is a promising technique to solve the issue of spectrum underutilization. It is

basically an intelligent wireless communication system which measures, analyses and adapt

according to the environment while keeping a check on the interference with the primary

user. They are fully programmable devices which have flexibility to operate on different

frequency bands with different modulation schemes. The basic limiting factor in secondary

use of spectrum is the interference caused by secondary user transmission and environment

because interference directly affects the reception capabilities and reduces the transmission

rate [4][5].

Spectrum assignment [6] refers to acquiring the best available spectrum to meet user

communication requirements. The function includes spectrum analysis and then selecting the

band according to user requirements. A cognitive radio should make best use of the available

resources or the ones it has identified for itself and should be able to adapt to the new found

resources. Various operating parameters and transmission parameters need to be continuously

analysed so that the best combinations of parameters might be obtained to maintain the QoS.

A number of optimization techniques have been used to find the optimal resource allocation

parameters. A MAC protocol is proposed in [7] that utilize multiple channels to improve the

cognitive radio network throughput and overall system utilization. Secondary user

transmission can be opportunistic spectrum access (overlay) or shared spectrum access

(underlay) [8] depending upon the system requirements and hardware/cost constraints. IEEE

802.22 [9] was the first proposed standard for wireless networks based on CR techniques.

Research in dynamic spectrum assignment methods is challenging because of the complexity

of radio propagation in this context and the main goal of the research is to reduce uncertainty

2

in deployed systems, so the risk of interfering with existing users is reduced to an acceptable

and quantifiable level. Heuristic algorithms, game theory approach, linear programming

problems are being formulated for spectrum assignment.

Organisation of the Report

The report is organized into 5 sections:

Section 2: Provides an introduction to cognitive radio systems.

Section 3: Provides an overview of channel assignment parameters.

Section 4: Specific spectrum optimisation algorithms from recent research papers are

discussed.

Section 5: This section concludes the report and suggests future work which can be done.

3

2. COGNITIVE RADIO NETWORKS

A definition given by Haykin in [1] is stated as, “A Cognitive Radio, an intelligent wireless

communication system, that is aware of its surrounding environment and uses methodology

of understanding by building to learn from the environment and adapt its internal states to

statistical variations in the incoming RF signal by making corresponding changes in certain

parameters in real time with two primary objectives in mind.

1. Highly reliable communication.

2. Efficient utilization of the radio spectrum. ”

Cognitive radios have the capability to increase spectrum capacity, to inter-operate, coexist

and work together seamlessly with the existing communication system. They are adaptable

for its transmission power, modulation schemes and error corrections which helps provide

better link quality.

CRN ARCHITECTURE

CRNs, equipped with the intrinsic capabilities of CR, are the secondary user network whose

components do not have the license to access any frequency band.

Fig 2.1.Functionalities of cognitive radio[1]

4

Primary users are the pre-existing users and have exclusive rights to the licensed band. Both

infrastructure and ad hoc networks can be deployed in CRNs, with components of CR users,

CR base stations. The secondary user data transmission, when primary user is transmitting,

keeping the interference levels in control is called underlay network. Data transmission only

when the primary user is idle is called overlay network [8]. IEEE 802.22 [9] was the first

proposed standard for wireless networks based on CR techniques. This standard uses the TV

bands for transmission while keeping the interference to licensed user in control. Cognitive

radio networks involve four main functions:

1. Spectrum sensing:

Sensing [2] includes measuring which frequencies are being used, when they are used,

estimating the location of transmitters and receivers. Results from sensing the environment

can be used to determine radio settings.

Fig.2.2: Spectrum sensing [2]

2. Spectrum Management

CR users select the best available channel to meet their communication requirements.

Interference to primary users is the key factor kept in check while assigning spectrum to the

secondary user. Quality of service of both secondary users and primary users should be met.

Secondary users content for spectrum allocation once a spectrum hole is identified. Number

of adjacent channels is checked for spectrum holes to identify the bandwidth available for

5

secondary user transmission [7]. Many approaches are being proposed to manage spectrum

assignment in cognitive radio networks.

3. Spectrum Mobility

Unlicensed users when sense the primary user’s demand for the channel, they should

immediately vacate the channel for primary user’s use due to its priority without interfering

with its transmission. All other secondary users should also be informed to not to sense the

channel as it is busy. So, cognitive radio should keep monitoring the channel while

transmitting to identify any interference due to primary user to maintain a seamless

communication. On-going secondary user transmission can be allocated some other spectrum

to continue its transmission.

4. Spectrum sharing

Multiple secondary users content for the access to the licensed band. A fair spectrum

scheduling method among coexisting cognitive users is required. Spectrum access can also be

prioritized among the secondary users by using priority algorithms which must satisfy the

transmission requirements of secondary users.

6

3. SPECTRUM ASSIGNMENT PARAMETERS

To maximize the performance of a CRN, major challenge is to reduce interference that is

caused to PUs, as well as interference among SUs. Interference results in additional noise at

the receiver and lowers the Signal to Interference plus Noise Ratio (SINR), which in turn

reduces transmission rate of the wireless interfaces, higher packet delay and lower received

throughput. In the absence of interference, a link should provide its maximum capacity,

which depends on the available transmission rates and corresponding delivery ratios. Other

main issue is the power assignment to SUs. Power at transmitter is controlled to keep in

check the interference. Some of few parameters which are to be considered while spectrum

assignment is listed below [10]:

1. Interference

Most important requirement is to minimize interference caused to PUs due to SU

transmission in underlay system and also to minimize interference between SUs. PUs should

have seamless communication going without the interference of secondary users. Data rate

can be increased at SU and PU if the interference is kept in within tolerable limits.

2. Power

Power of SU user is bounded by the upper bound due to hardware limitations. Also SU

cannot transmit power at very high level as it will interfere with the PUs transmission.

3. Spectral efficiency

Our objective while assigning secondary users channel is to maximize spectrum utilization.

Proper selection of channel window for a SU and how many SU can be allowed access at a

particular time is important. In multi-radio multi-channel SUs the complexity can be very

high.

4. Throughput

Throughput maximisation of user or network is required in certain networks. While

maximising throughput interference should be kept in check and unfairness should be

avoided.

7

5. Fairness

Every SU should have fair chance to access the channel and throughput should be optimised

fairly. Otherwise less no of SU can be accommodated and the spectrum deficiency problem

will not be solved.

6. Delay

Delay includes the time taken for sensing the channel for spectrum hole then contenting for

channel assignment. Various schemes are proposed in MAC layer. Minimising total end to

end delay is of importance because more is the delay more is the spectrum utilised for control

signalling and less data transmission. Also switching delay should be small so that when PU

claims back the spectrum SU should vacate the channel immediately to avoid interference at

the primary user.

7. Price

Network operators assign channels to SUs targeting at maximizing their own revenue. Each

SU selects the channel according to the price of the channel and taking into account the

reward for accessing this channel. SUs need to have a priori knowledge for the cost of each

spectrum band or they should dynamically question the spectrum owners, which induces

delays.

8. Outage probability

An outage is declared when the received SIR falls below a given threshold often computed

from a BER requirement. Outage probability is of great importance in multi hop transmission

over unreliable links and is an important quality of service parameter.

8

4. SPECTRUM ASSIGNMENT OPTIMISATION APPROACHES

Optimal resource allocation solutions subject to QoS constraints, minimum rate requirements

for secondary users, and interference constraints for primary users is required. Problem

formulation done can be both convex and non-convex depending upon the objective function

and associated constraints. Various iterative algorithms which aim at finding the optimal

solution for the given constraints are discussed.

4.1 Capacity Optimisation

Throughput/rate maximization is a very common criterion for channel assignment schemes in

CRNs. The objective is to maximize either the throughput of each individual SU or the total

network throughput, based on constraints [11] maximum transmission power for each SU on

each channel and the maximum interference at primary user. Capacity of channel is an

important parameter used to define the system throughput.

In the infrastructure model [6], the uplink transmissions from the K secondary users (SUs) to

the secondary base station (S-BS) are usually modelled by a multiple-access channel (MAC),

while the downlink transmissions from the S-BS to different SUs are modelled by a broadcast

channel (BC). For the MAC, the equivalent baseband transmission can be represented as

y= ∑ kxk + z (4.1.1)

where Hk M×Nk denotes the channel from the kth SU to S-BS, k=1,…., K, Nk is the number

of antennas at the kth SU; y M×1 denotes the received signal at the S-BS, M is the number

of antennas at S-BS; xk CN

k×1

is the transmitted signal of the kth SU; and z CM×1

is the

noise received at S-BS. xk’s are assumed to be independent over k. The optimal transmit

covariance to achieve the cognitive radio point-to-point MIMO channel capacity for single

secondary link under the peak transmit power constraint at the SU and peak interference

power constraint at the receiver can be represented [12]:

log det(I + HSHH)

Subject to,Tr(S) ≤ P

Tr(GjS

) ≤ Гj j=1, … , J

(4.1.2)

Where, S is the transmit covariance matrix, P is the SU peak power constraint, Gj is the

realisation of the channel from the SU to the jth primary user(PU) and Гj is peak interference

power constraint for the jth PU. The above problem (4.1.2) is a convex optimisation problem

which can be solved using interior point method [13][14].

9

In a fading environment, due to deeply faded signal of secondary user received by the

primary user, secondary user can increase its capacity by increasing its transmission power

[15].

Fig 4.1 : secondary user transmission in deeply faded environment[15].

Let g0 and g1 represents the instantaneous channel gains from the secondary transmitter to the

primary and secondary receivers, respectively. Both gains are assumed to be stationary and

unit-mean. Assuming that transmitter should have perfect knowledge of g0 as well as g1and

constraints are placed at receiver side, so there are no constraints on transmitted power [15],

the channel capacity upper bound is evaluated. Assuming g0 and g1 to be independent of each

other, Q is the maximum average interference power that the primary user can tolerate at its

receiver, P and B are the transmitted power and the total available bandwidth, respectively

and N0 is the power spectral density of the AWGN noise at the secondary receiver, the

channel capacity is evaluated in [15], for an AWGN channel with unit mean channel gains

that means P=Q,

Cawgn = B log(1+α) (4.1.3)

Where, α = Q/N0B is the average signal-to-noise ratio (SNR) for the AWGN channel and

=1/(λ0N0B)

For Log normal shadowing [16,17] assuming g0 = and g1 = , where X0 and X1 are two

independent zero mean Gaussian random variables with equal variance. Capacity can be

evaluated as [15]:

10

Clognormal = B[

( 1+ erf

)) +

] (4.1.4)

For a Rayleigh fading channel [17] both g0 and g1 are exponentially distributed with unit

mean. Capacity can be evaluated as [15]

Crayleigh = Blog (1+γ0(α)) (4.1.5)

Where γ0(α) is the solution of γ0 −log(1+ γ0)=α for the given value of α.

For a Nakagami-m fading channel [17] capacity can be evaluated as [15]

Cnakagami = B log [1+γ0(α))− γ0(α)/(1+γ0(α))2 ] (4.1.6)

Where γ0(α) is the solution of

=α for the given value of α.

Fig 4.2 : Capacity under peak received-power constraint vs. α [15]

From the above graph it can be observed that

Clognormal>Crayleigh>Cnakagami>C AWGN

4.2 Sum Rate Optimization

Using the same system model as mentioned above for single secondary user without fading

environment, for multiple secondary users Pk denotes the peak transmit power for the kth

SU.

11

For this MIMO-MAC link jointly optimizing SU transmit covariance matrices to maximize

their weighted sum-rate subject to power and interference problem can be expressed as [6]:

∑ log |

∑

∑

|

s. t. Tr(Sk) ≤ Pk , k= 1,………,K

∑ (GkjSk

) ≤ Гj, j=1, … , J

(3)

Where, >0 are user rate weights. The optimal decoding order of users at the S-BS to

maximize the weighted sum-rate is in accordance with the reverse user index [6].It can be

verified that it is a convex optimization problem over Sk’s. Thus, it can be solved by an

interior- point-method-based algorithm [13].

Transmission from secondary base station to secondary users is a broadcast channel and

system can be represented as [6]

yk=

x + zk, k =1,….. , K (4)

Where, yk CNk×1

is the received signal at the kth SU, x CM×1

is the transmitted signal from S-

BS, is the channel from the S-BS to the kth SU and zk C

Nk×1 is the receiver noise of the

kth

SU. The weighted sum rate maximization problem for the broadcast channel can be

represented as [6]

∑ log |

∑

∑

|

s. t. ∑

≤ P

Tr (Fj ∑

) ≤ Гj, j=1, … , J

(4.2.3)

Where Qk CM×M

is the covariance matrix for the transmitted signal of S-BS to the kth SU,

k=1, .. , K;

are the given user rate weights; and P is the transmit power constraint for the

secondary base station. Assuming that, , in the optimal encoding order of users for

DPC to maximize the weighted sum-rate is in accordance with the user index [6]. Above

problem is non-convex because the objective function is non-concave over Qk’s for K > 2. To

transform the non-convex MIMO-BC problem into a convex MIMO-MAC problem a “BC-

MAC duality” relationship is proposed in [6], which can be solved by efficient convex

optimization techniques such as the interior point method.

For ad hoc secondary/CR network [6], channel between secondary user and primary user is as

an interference channel (IC). Assuming that for the kth

secondary link, k=1,…, K, TXsk

12

represents the transmitter and RXsk represents the secondary receiver, although in general a

secondary terminal can be both a transmitter and a receiver. The baseband transmission of the

IC can be represented as

k =Hkk k + ∑ ik i + k , k=1,….,K (4.2.4)

Where k CBk×1

is the received signal at kth

secondary receiver RXsk, with Bk number of

receiving antennas, Hkk CBk×Ak

is the direct-link channel from TXsk to RXsk, Hik CBk×Ai

is the

cross-link channel from TXsi to RXsk, i k, k CAk×1

is the transmitted signal of TXsk, with

Ak number of transmitting antennas and k CBk×1

is the noise at RXsk. Assuming that xk’s are

independent over k. The sum rate maximisation problem can be represented as [6]

∑

log | ∑

|

s. t. Tr(Rk) ≤ Pk , k= 1,………, K

∑ (EkjRk

) ≤ Гj, j=1, …, J

(4.2.5)

Where, Rk CAk×Ak

is the transmit covariance matrix for the kth SU link. Above problem is a

non-convex optimisation problem because the objective function is non-concave. As a result,

there are no efficient algorithms yet to obtain the globally optimal solution for this problem.

A feasible approach to solve is to decompose each of the interference constraints into a set of

interference-power constraints over the K secondary user transmitters [6].

Beamforming is a signal processing technique used to control the directionality of the

transmission and reception of radio signals. When it is included, it enables improvement in

performance, reliability, range and coverage. Sum rate maximisation for a single input

multiple output multiple access channel with joint beamforming and power allocation for the

cognitive radio is discussed.

System Model

Assuming, system model defined in figure 4.3. The SUs communicate with the same base

station (BS) equipped with Nr receive antennas. The signal model can be represented as [18]:

y = Hx+ +z, (4.2.6)

where y is the Nr × 1 received signal vector, H = [h1,···,hK] is the Nr × K channel matrix with

hi representing the channel response for the ith SU to the base station, x is the K × 1 transmit

signal vector whose ith

entry, xi, denotes the signal transmitted from SUi, =[ 1,…….., N ] is

the Nr ×N channel matrix where n is the channel response from the nth PU’s transmitter to

13

the base station, is the N ×1 transmit signal vector from the PUs, and z is the Gaussian

noise vector whose entries are assumed to be independent Gaussian random variables (RVs)

with mean zero and variance σ2. Assuming, the transmit power, pi, of SUi, is subject to a peak

power , i.e., pi ≤ i, i = 1,···,K. Let gn,i be the power gain between SUi to PUn. The

interference power received by PU from all SUs is characterized by p, where

gn=[gn,1,···,gn,K]T and p = [p1,···,pK]

T. Let G=[ g1,...,gN]

T, assuming the channel matrices H,

, and G are fixed during each transmission block and change independently according to

random process from one block to another. The proposed optimisation algorithms are

performed at the base station of the CR network, assuming perfect knowledge of these

metrics at base station [18].

Fig.4.3 :The system model with K no. of secondary links and N no. of primary links with

single transmitting and receiving antennas. SIMO-MAC model has the base station with Nr

receive antennas[18].

The data rate of secondary user is to be maximised to achieve maximum utilisation of the

spectrum for the given SU transmitting power and beamforming vector, subject to constraints

of the transmitting power at SU and interference at primary user. The problem can be

formulated as[18]:

ri

Subject to, pi ≤ , i=1 ,2,...,K

p ≤

, n=1 ,···,N

(4.2.7)

where U is [u1,...,uK] with ui denoting the linear beamforming vector for SUi,

represents

the interference power threshold for PUn and ri is the variable information rate of SUi

corresponding to a channel state (H, ,G).Applying QR decomposition to the channel matrix

14

H of SUs, and defining M as the rank of H, H = QR, where Q=[q1,···,qM] CNr×M

has

orthogonal columns and R CM×K

is an upper triangular matrix with rm,k denoting its (m,k)th

entry. Using equalizer QH to the received signal and using successive interference

cancellation, the channel is decomposed as M independent sub-channels, each associated

with one SU. This receiver can also be viewed as receive beamforming in the sense that the

beamforming vectors are determined by the QR decomposition of the channel matrix H.

Thus, only power allocation vector that maximizes the sum-rate is to be determined. In this

case, assuming Gaussian signal inputs equation 4.2.7 can be written as [18],

∑

)

Subject to

pi ≤ , i=1 ,2,...,K

p ≤

, n=1 ,···,N

(4.2.8)

Where, di = |ri,i|2, and

=

2+∑

n nqi is the interference-plus-noise power after

receive beamforming qi is applied. Above represents the sum rate achieved through the zero

forcing – decision feedback equalizer based receiver. If the power constraints are replaced by

a single total power constraint,∑ I ≤ Pmax, then the optimal power allocation achieving the

maximum sum-rate is described by the water-filling principle [19]:

pi =[

] ,i=1 ,···,K,

(4.2.9)

Where, µ is the water level for which the power constraint is satisfied with equality.

a. For a Single PU constraint

For N=1 solution of (17) is given in [18] using lagrangian optimization [7], the power

allocation for SUi is given by

pi =[

]

(4.2.10)

Where, lagrangian coefficients λ ≥0 and νi ≥0 for i =1,…, K

So, the optimal power allocation for SUi can be computed as [18]:

pi {

(4.2.11)

b. Multiple PU constraints

15

Similar to single constraint with the multiple primary user interference constraints [18]

Pi =

{

{ (∑

(∑

)

(4.2.12)

The power is allocated to K SU’s by evaluating if the all the N interference constraints are

satisfied for the given power allocation. If the interference constraint is not satisfied power

for different users is evaluated iteratively.

4.3 SINR Balancing

With required QoS of the primary user, power allocation in a cognitive radio network should

be appropriately determined to optimize the performance metrics of the secondary user,

which can be reflected through signal to interference plus noise ratio (SINR) balancing.

Assuming the same SIMO-MAC system model as in previous section, the output SINR of

SUi after applying beamforming to the received signal vector is given by [18]

SINRi(ui,p) =( pi Riui/(

∑ kRk + σ2INr +∑

n n)ui) (4.3.1)

Where, n is the transmit power of PUn, Ri = hi for i =1 ,···,K, and n = n

for n=1,···,N.

SINR balancing problem is in which the minimal ratio of the achievable SINRs relative to the

target SINRs of the users in the system is maximised under a sum-power constraint. The

problem formulation for the given system is as [18]:

Subject to,

pi ≤ , i=1 ,2,...,K

p ≤

, n=1 ,···,N

(4.3.2)

Where,γi is the pre-set SINR target for the ith

secondary user SUi.

SINR problem statement can be rewritten as

maxU,p min1≤ i ≤K

( )

(5.3.3)

subject to ≤ , l=1,...,N + K

where,

16

= {

and

= {

el defining the lth column of identity matrix.

The SINR balancing problem under a single sum-power constraint is solved in which an

iterative algorithm [8] is adopted. Two steps are involved at each iteration. In the first step,

the beamforming matrix is fixed and optimal vector p is evaluated. In the second step,

corresponding optimal beamforming matrix is evaluated for updated power vector. The

optimal power allocation to balanced SINR is obtained if it satisfies the constraint in above

problem with equality. It can be proved that the multi-constraint problem above can be

completely decoupled into single constraint sub-problems [18].Single constraint sub-problem

can be solved [18] and between the multiple solutions so obtained only one solution will

satisfy the other constraints as well. That will be the globally optimal solution for the given

multi constraint power allocation problem [18].

4.4 Joint Rate and Power Optimization

A joint admission control, rate/power allocation for optimal spectrum sharing in a cognitive

radio network is proposed in [20].An outage is declared when the received SIR falls below a

given threshold (γi) of the ith

secondary user. A violation is declared when the interference at

the primary user is more than maximum tolerable interference (ηj). Assuming that a central

controller in the secondary users’ network has complete information of channel interference

and performs the admission control, and rate/power allocation for secondary links. Rate and

power allocations for the cognitive radios are adjusted so that the interference temperature

limits at the primary receivers are not violated and its QoS requirements are satisfied.

The outage probability for QoS constraints for secondary users and violation probability for

interference constraints for primary users is evaluated in [20]. The secondary user

transmission rate is maximised for joint power and rate for the given constraints. The

problem can be formulated as [20],

∑

Subject to, µi <αγi i=1,…., N

ηj< βIj j=1, …, M

(4.4.1)

17

Rmin

≤Ri≤ Rmax,

i=1,…., N

0 ≤Pi≤ Pmax

i=1,…., N

Where, Ri is data rate at ith SU, Pi is power allocated at ith SU, µi is average SNR at ith SU,

ηjis interference at jth PU, Ij is maximum tolerable interference atjth PU, Rmax

= maximum

data rate at SU, Rmin

= minimum data rate at SU, Pmax

= maximum transmitted power at SU,

for α,β>1 are constants.

Two allocation methods for joint admission control and power/rate allocation for secondary

users are given in [20].

Algorithm 1: one step removal

Step I: Solve the problem (4.4.1) without minimum rate requirements as

Step 1. Initialize α = 1,β =1

Step 2. Solve the joint rate and power allocation problem with current values of α and

β as follows:

∑

Subject to, , ∑

≤ βIj , j= 1,2,…,M

µi < αγi i=1,2,…N

0 ≤Pi≤ Pmax

, i=1,2,…N

(4.4.2)

Where, ∑

represents interference at jth primary user due to secondary

users transmission.

Step 3. Calculate the outage probabilities for SIR and violation probability of

interference as given in [20]. Check whether they are smaller than the maximum

tolerable outage probability (δ(s)

) and violation probability (δ(I)

). If yes, finish;

otherwise go to step 4.

Step 4. Adjust the conservative factors as follows. If only mean channel gains are

available and one or more of the SNR constraints are violated, update

α = α +Δα

If one or more of the interference constraints are violated, update

β = β −Δβ

18

where, Δα and Δβ are small adjustment values.

Step 5. Return to step 2.

Step II: Perform admission control using rate/power allocation solution in step I as follows.

For each secondary link i, compare optimal rate with minimum rate Rmin

. Remove all

secondary links with Ri∗<R

min.

Step III: Solve the rate/power allocation problem again for the remaining set of secondary

links using steps in step I.

Algorithm 2: one-by-one removal

Step I: Solve the above problem without minimum rate requirements as

Step 1. Initialize α = 1,β =1

Step 2. Solve the joint rate and power allocation problem with current values of α and

β as follows:

∑

Subject to, , ∑

≤ βIj , j= 1,2,…,M

µi < αγi i=1,2,…N

0 ≤Pi≤ Pmax

, i=1,2,…N

(4.2.3)

Step 3. Calculate the outage probabilities for SIR and violation probability of

interference as given in [20]. Check whether they are smaller than the maximum

tolerable outage probability (δ(s)

) and violation probability (δ(I)

). If yes, finish;

otherwise go to step 4.

Step 4. Adjust the conservative factors as follows. If only mean channel gains are

available and one or more of the SNR constraints are violated, update

α = α +Δα

If one or more of the interference constraints in are violated, update

β = β −Δβ

where, Δα and Δβ are small adjustment values.

19

Step 5. Return to step 2.

Step II: If the optimal solution in step I is such that all secondary links achieve their

minimum rates, finish. Otherwise, remove one link with the smallest rate.

Step III: Solve the rate/power allocation problem again for the remaining set of secondary

links and go to step II.

Performance evaluation of both the algorithms is done in [20]. Algorithm 1 is

computationally faster than algorithm 2 but performs worse. They can be implemented for

both the instantaneous channel gains and average channel gains.

20

5. CONCLUSION

Cognitive radio networks have got great potential in increasing the utilization of the

spectrum. IEEE 802.22 standard for cognitive radio is also being introduced. This seminar

report provides a brief overview on the challenges and optimization approaches for spectrum

assignment.

It should be noted that there are many hardware constraints involved in having channel state

information beforehand, also delay is introduced in optimisation calculations. Separate

channels may be introduced for control information exchange but that will introduce

hardware and spectrum cost. Capacity and data rate maximisation is done keeping optimum

value of power assigned to secondary users and interference in check. Recent papers

presented in this report have been able to achieve efficient algorithms for spectrum

assignment but it still remains an interesting research problem.

21

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