The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)

A TWO-PHASE CHANNEL AND POWER ALLOCATION SCHEME FOR

COGNITIVE RADIO NETWORKS

Anh Tuan Hoang and Ying-Chang Liang

Institute for Infocomm Research

21 Heng Mui Keng Terrace, Singapore 119613

{athoang, ycliang}@i2r.a-star.edu.sg

ABSTRACT

We consider a cognitive radio network in which a set of base

stations make opportunistic unlicensed spectrum access to

transmit data to their subscribers. As the spectrum of in-

terest is licensed to another (primary) network, power and

channel allocation must be carried out within the cognitive

radio network so that no excessive interference is caused to

any primary user. For such a cognitive network, we propose

a two-phase channel/power allocation scheme that improves

the system throughput, defined as the total number of sub-

scribers that can be simultaneously served. In the first phase

of our scheme, channels and power are allocated to base sta-

tions with the aim of maximizing their total coverage while

keeping the interference caused to each primary user below a

predefined threshold. In the second phase, each base station

allocates channels to their active subscribers based on a max-

imal bipartite matching algorithm. Numerical results show

that our proposed resource allocation scheme yields signifi-

cant improvement in the system throughput.

I. INTRODUCTION

The traditional approach of fixed spectrum allocation to li-

censed networks leads to spectrum underutilization. In re-

cent studies by the FCC, it is reported that there are vast tem-

poral and spatial variations in the usage of allocated spec-

trum, which can be as low as 15% [3]. This motivates the

concepts of opportunistic unlicenced spectrum access that

allows secondary cognitive radio networks to opportunisti-

cally exploit the underulized spectrum. In fact, opportunistic

spectrum access has been encouraged by both recent FCC

policy initiatives and IEEE standadization activities [4, 6].

On the one hand, by allowing opportunistic spectrum ac-

cess, the overall spectrum utilization can be improved. On

the other hand, transmission from cognitive networks can

cause harmful interference to primary users of the spectrum.

Therefore, important design criteria for cognitive radio in-

clude maximizing the spectrum utilization and minimizing

the interference caused to primary users.

In this paper, we consider a cognitive radio network that

consists of multiple cells. Within each cell, there is a base

station (BS) supporting a set of fixed users called customer

premise equipments (CPEs). We consider the downlink sce-

nario. The spectrum of interest is divided into a set of non-

overlapping channels. Each CPE can be either active or idle

and a BS needs exactly one channel to serve each active CPE.

The spectrum is licensed to a set of primary users (PUs). For

the cognitive radio network, two operational constraints must

be met:

• the total amount of interference caused by all oppor-

tunistic transmissions to each PU must not exceed a pre-

defined threshold,

• for each CPE, the received signal to interference plus

noise ratio (SINR) must exceed a predefined threshold.

We define the system throughput as the total number of active

CPEs that can be simultaneously served.

Note that in order to implement the above system, there

should be a mechanism for secondary users, i.e., BSs and

CPEs, to sense the spectrum and detect the presence of pri-

mary users. This is a challenging problem and is beyond the

scope of this paper. Here, we simply assume that the posi-

tions and operating channels of all PUs are known.

We propose a Two-phase Resource Allocation (TPRA)

scheme that improves the system throughput and can be im-

plemented with a reasonable complexity. In the first phase of

our scheme, channels and power are allocated to BSs with

the aim of maximizing their total coverage while keeping

the total interference caused to each PU below a predefined

threshold. The coverage of a particular BS is the number of

CPEs that can be supported by the BS using at least one of

its allocated channels. In the second phase of TPRA, each

BS allocates channels within its cell so that the number of

active CPEs served is maximized. This is done by solving a

related maximal bipartite matching problem. Numerical re-

sults show that our proposed TPRA scheme yields significant

improvement in the system throughput.

Works on channel allocation in cognitive radio networks

include [10] and [11]. In [10], Wang and Liu consider a prob-

lem of opportunistically allocating licensed channels to a set

of cognitive base stations so that the total number of channel

usages is maximized. In [11], Zheng and Peng consider a

problem similar to [10]. However, they introduce a reward

function that is proportional to the coverage areas of base

stations and also allow the interference effect to be channel

specific. Both problems in [10] and [11] are studied based on

graph-coloring frameworks.

There are two significant differences between our work

and [10] and [11]. Firstly, instead of looking at the total

number of channel usages or the coverage area of base sta-

tions, we are interested in the number of subscribers that are

actually served. While doing so, we take into account the

fact that subscribers are not always active. Secondly, a major

drawback of the works in [10, 11] lies in their oversimpli-

fied binary interference model, which is based on whether

or not the coverage areas of two base stations overlap. This

is unrealistic and does not capture the aggregate interference

effects when multiple transmissions simultaneously happen

on one channel. Our model overcomes this by considering

the interference effects based on received SINR.

The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)

0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000

PU

BS

CPE

Figure 1: Deployment of a cognitive radio network.

Works on channel-allocation/power-control problems that

model interference effects based on received SINR include

[2] and [7]. The objective of [2] is to maximize spectrum

utilization while that of [7] is to minimize total transmit

power to satisfy the rate requirements of all links. How-

ever, [2] and [7] do not consider the scenario of opportunistic

spectrum access and there is no issue of protecting primary

users. In a broader context, our work is related to the class

of power control problems for interfering transmission links

with SINR constraints [1,5,9]. In fact, similar to [1,5,9], we

use Perron-Frobeniuos theorem to check the feasibility of a

particular channel allocation.

The rest of this paper is organized as follows. In Section

II., we introduce our system model and the control prob-

lem. In Section III., we present the TPRA scheme. Numeri-

cal results showing the performance of our proposed control

scheme will be discussed in Section IV.. Finally, in Section

V., we conclude the paper and outline the future research.

II. PROBLEM DEFINITION

A. System Model

We consider an opportunistic spectrum access scenario de-

picted in Fig. 1. The spectrum of interest is divided into Kchannels that are licensed to a primary network of M primary

users (PUs). In the same area, a cognitive radio network is

deployed. This cognitive network consists of B cells. Within

each cell, there is a base station (BS) serving a number of

fixed customer premise equipments (CPEs) by opportunisti-

cally making use of the K channels. Channel allocation and

power control must be applied to the cognitive radio network

to ensure that each PU experiences an acceptable level of in-

terference.

Let N denote the total number of CPEs. We consider the

downlink scenario in which data are transmitted from BSs

to CPEs. Moreover, we assume that each CPE is only ac-

tive and requires data transmission with probability pa, 0 <pa ≤ 1. Assuming that a BS needs exactly one channel to

serve each active CPE, we define the system throughput as

the total number of active CPEs that can be simultaneously

served. Our objective then is to find a channel/power allo-

cation scheme that achieves good average system throughput

while appropriately protecting all primary users.

B. Operational Requirements

1) SINR Requirement for CPEs

For the sake of brevity, we use the phrase ”transmission to-

ward CPE i” to refer to the downlink transmission from the

BS serving CPE i toward CPE i.Let Gc

ij be the channel power gain from the BS serving

CPE j to CPE i on channel c. Let P ci denote the transmit

power for the transmission toward CPE i on channel c, 0 ≤P c

i ≤ Pmax. If channel c is not assigned for the transmission

toward CPE i, then P ci = 0. The SINR at CPE i is given by:

γci =

GciiP

ci

No +∑N

j=1,j 6=i GcijP

cj

, ∀i ∈ {1, 2, . . .N}, (1)

where No is the noise power spectrum density of each CPE.

For reliable transmission toward CPE i, we require that

γci ≥ γ. (2)

In practice, γ can be the minimum SINR required to achieve

a certain bit error rate (BER) performance at each CPE.

2) Protecting Primary Users

Let Πc denote the set of all PUs that use channel c and let

Gcpi be the channel gain from the BS serving CPE i to PU p

on channel c. We require that, for each PU, the total interfer-

ence from all opportunistic transmissions does not exceed a

predefined threshold ζ, i.e.,

N∑

i=1

P ci Gc

pi ≤ ζ, ∀p ∈ Πc, ∀c ∈ {1, 2, . . .K}. (3)

C. Feasible Assignments

Before moving on, let us address the question of whether it is

feasible to assign a particular channel c simultaneously to a

set of transmissions toward m CPEs: (i1, i2, . . . im). Here,

feasibility means there exists a set of positive transmit power

levels P c = (P ci1

, P ci2

, . . . P cim

)T such that all the SINR con-

straints of the m CPEs are met while the interferences caused

to PUs do not exceed the acceptable threshold.

If we define an m × 1 vector U c as:

U c =

(

γNo

Gci1i1

,γNo

Gci2i2

, . . .γNo

Gcimim

)T

(4)

and an m × m matrix F c as:

F crs =

{

0, if r = sγGc

iris

Gc

irir

, if r 6= s, r, s ∈ {1, 2 . . .m}, (5)

then the SINR constraints of m CPEs (i1, i2, . . . im) can be

written compactly as:

(I − F c)P c ≥ U c. (6)

From the Perron-Frobenious theorem [1,5,9], (6) has a posi-

tive component-wise solution P c if and only if the maximum

eigenvalue of F c is less than one. In that case, the Pareto-

optimal transmit power vector is:

P c∗ = (I − F c)−1U c. (7)

The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)

Here Pareto-optimal means that if P c is a positive power vec-

tor that satisfies (6), then P c ≥ P c∗ component-wise. Due

to this fact, the following 2-step procedure can be used to

check the feasibility of assigning a particular channel c to

the transmissions toward the set of CPEs (i1, i2, . . . im).

Two-step Feasibility Check:

• Step 1: Check if the maximum eigenvalue of F c defined

in (5) is less than one. If not, the assignment is not

feasible, otherwise, continue at Step 2.

• Step 2: Using (7) to calculate the Pareto-optimal trans-

mit power vector P c∗. Then, check if P c∗ satisfies the

constraints for protecting PUs in (3) and the maximum

power constraints, i.e. P c∗ ≤ Pmax. If yes, conclude

that the assignment is feasible and P c∗ is the power vec-

tor to use. Otherwise, the assignment is not feasible.

If it is feasible to assign channel c to the transmis-

sions toward CPEs (i1, i2, . . . im), we simply say the set

(i1, i2, . . . im) is feasible on channel c.

III. TWO-PHASE RESOURCE ALLOCATION

A. Motivations

We are interested in channel/power allocation schemes that

can simultaneously serve a good number of active CPEs

while protecting all PUs from excessive interference. To pro-

tect PUs, all BSs have to coordinate their transmit powers on

each channel. That requires a global control mechanism. On

the other hand, CPEs in the network can switch between ac-

tive and idle states frequently. In that case, it is preferable

that changes in CPEs’ states are dealt with locally, within

each cell. This will reduce the amount of recalculations and

signaling/updates involved. These observations motivate our

Two-Phase Resource Allocation (TPRA) scheme.

B. The Two-Phase Resource Allocation Scheme

1) Phase 1 - Global Allocation:

In this phase, channels and transmit powers are allocated to

BSs so that the interference caused to each PU is below a

tolerable threshold. At the same time, we aim to cover as

many CPEs as possible. When talking about coverage here,

we do not care whether a CPE is active or idle. That will be

taken care of in the second phase of the TPRA scheme.

Consider a particular channel c. For each BS, the higher

power it transmits on c, the more CPEs it can cover. How-

ever, the higher the transmit power of the BS, the more in-

terference it causes to PUs and other cells. This interference

reduces the number of CPEs that can be covered using chan-

nel c in other cells.

We note that it is extremely hard to fully characterize the

above dual effects of varying base stations transmit powers

on the number of CPEs being covered in the whole network.

Therefore, we rely on the following intuition for making our

channel/power allocation decisions. A BS that is near any PU

using channel c should only transmit at low power to reduce

interference. On the other hand, a BS that is faraway from

all PUs using channel c can transmit at higher power. Each

BS can use a set of channels on which it can transmit at high

power to cover faraway CPEs. The same BS can use a set of

channels on which it can only transmit at low power to cover

nearby CPEs.

Based on the above intuition, we propose the following

procedure to allocate channels/powers to BSs. We process

K channels one at a time. For channel c, let Γcpb denote the

channel gain from base station b to primary user p and define:

Γc∗b = max

p∈Πc{Γc

pb}. (8)

We do the following:

• Sort the base stations in the ascending order of Γc∗b , i.e.,

form (b1, b2, . . . bB) where Γc∗bn

≤ Γc∗bm

, ∀1 ≤ n <m ≤ B. The base stations will be processed one at a

time in this order.

• For base station bn, determine a particular CPE inthat bn should cover. This is done as follows. Given

the set (i1, i2, . . . in−1) of CPEs being covered by

(b1, b2, . . . bn−1), let Vcn be the set of all CPEs in the

cell of bn such that (i1, i2, . . . in−1, i) is feasible on

channel c (see the two-step feasibility check in Section

II-C.). Then in is the CPE that has the weakest channel

gain from bn, i.e.,

in = arg mini∈V c

n

{Gcii} (9)

It can happen that the set Vcn is empty. Then, with some

little abuse of notation, we set in = 0 to indicate that no

CPE is covered by bn.

• After processing all BSs in the order b1, b2, ...bB , we

obtain a set of CPEs (i1, i2, . . . iB). Using (7), deter-

mine the transmit power to serve each of these CPEs,

i.e., (P ci1

, P ci2

, . . . P ciB

).

• Finally, based on (P ci1

, P ci2

, . . . P ciB

), determine the N ×K coverage matrix C, where C(i, c) = 1 indicates that

CPE i can be served by the corresponding BS on chan-

nel c. This can be checked based on (2).

It can happen that when sorting BSs based on Γc∗b , there are

ties among BSs. In that case, the BSs with less number of

CPEs covered so far (can be checked from coverage matrix

C) will be processed first.

2) Phase 2 - Local Allocation

Based on the coverage matrix C obtained in the first phase,

channel allocation can be carried out within each cell, in a

manner independent to what happens in the rest. The proce-

dure is as follows.

• First, determine all active CPEs in the cell.

• Next, form a bipartite graph that represents the coverage

of the cell. This is done by representing the set of active

CPEs as a set of vertices, which are connected to an-

other set of vertices representing the available channels.

Note that an edge exists between the vertex representing

CPE i and the vertex representing channel c if and only

if C(i, c) = 1. This is demonstrated in Fig. 2.

• Now, the problem of maximizing the number of active

CPEs served is equivalent to the problem of maximiz-

ing the number of disjoint edges in the resulting bipar-

tite graph. Two edges in a graph are disjoint if they do

not share any end. This is called the maximal bipartite

matching problem.

The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)

CPEs Channels

1

3

2

4

1

3

2

Figure 2: Representing the coverage within one cell as a bi-

partite graph. Edges with the same color represent the same

channel.

There are a host of algorithms for finding the maximal

matching of a bipartite graph. In this paper, we obtain maxi-

mal bipartite matching based on Berge’s Theorem of finding

alternating augmenting paths [8].

C. Other Channel/Power Allocation Schemes

To relatively evaluate the performance of our proposed

TPRA scheme, let us consider the following other resource

allocation schemes.

1) Random Allocation

In this so called Random scheme, the two-phase approach

is still followed. However, the decisions in each phase are

made in random manners.

In the first phase, for each channel c, the base stations

are processed one at a time following a random order, e.g.,

(b1, b2, . . . bB). For base station bn, instead of picking a CPE

to cover according to (9), we just arbitrarily choose any CPE

i with i ∈ Vcn.

In the second phase, for each cell, no maximal bipartite

matching is carried out. Instead, active CPEs in the cell are

processed one at a time according to a randomly chosen or-

der. For each active CPE, we assign the first free channel.

This continues until all active CPEs of the cell are served or

no more channel is available.

2) Non-overlapping Allocation

In this scheme, the K channels are first partitioned into Bdisjoint groups, each consists of ⌊K/B⌋ channels. Each of

the base stations is then assigned one group of channels to

support its active CPEs. Channel groups are formed and as-

signed as follows. Pick an arbitrary order of the base stations,

e.g., (b1, b2, . . . bB), and let them to choose their ⌊K/B⌋channels one at a time in this order. This means bn can-

not pick the channels chosen by b1, b2, . . . bn−1. Among all

channel left, each of the channel c chosen by bn must satisfy:

Γc∗bn

< Γc∗bm

, ∀1 ≤ n < m ≤ B. (10)

Each BS can assign channels to its active CPEs based on

the simple allocation procedure of the Random scheme dis-

cussed above. We call this the Non-overlapping Channel Al-

location (NOCA) scheme.

3) Allocation Based on An Interference Graph

In [2], Behzad and Rubin propose the power control schedul-

ing algorithm (PCSA) that improves the system throughput

while also guaranteeing the SINR constraints of all trans-

mission links. In the PCSA scheme, an interference graph,

10 15 20 25 30 35 40 45 50 55 6010%

20%

30%

40%

50%

60%

70%

80%

90%

100%

No. of primary users

% o

f C

PE

s c

ove

red

TPRANOCARandomPCSA

Figure 3: Percentage of CPEs being covered vs no. of PUs.

No. of BSs = 4, no. of CPEs = 300, no. of channels = 16.

which captures the pairwise interference effects among all

transmissions, is first constructed. After that, the prob-

lem of channel allocation to maximize the number of non-

interfering links can be converted into the problem of finding

a maximum independent set of the interference graph.

In Section IV., we will test the performance of PCSA un-

der two scenarios. In the first scenario, we reapply the algo-

rithm every time there is a change in state of any CPE. We

call this PCSA G (PCSA Global). In the second scenario,

we apply the algorithm to the whole network once, and after

that, the changes in CPEs’ states are only dealt with locally.

We call this PCSA L (PCSA Local).

IV. NUMERICAL RESULTS AND DISCUSSION

A. Simulation Model

We consider a square service area of size 1000 × 1000m in

which a cognitive radio network is deployed. The service

area is further divided into B = 4 adjacent cells, each is a

square of size 500 × 500m. A BS is deployed at the center

of each cell to serve CPEs within the cell. The total number

of CPEs is N = 300 and each CPE is active with probability

pa = 0.1. We vary M , the total number of PUs, from 10to 60. All CPEs and PUs are randomly deployed across the

entire service area with a uniform distribution. A sample

network is shown in Fig. 1.

The number of channels available is K = 16. We assume

a free-space path loss model with the path-loss exponent of

4. We assume that each PU randomly picks and uses one of

the K channels. The noise power spectrum density at each

CPE is No = 100dBm. The required SINR for each CPE is

15dB. The maximum tolerable interference for each PU is

90dBm. For each BS, the maximum transmit power on each

channel is Pmax = 50mW .

B. Performance Analysis

As the number of active CPEs served is closely related to

how many CPEs in the network are covered, let us look at

the percentage of CPEs being covered first. In Fig. 3, we plot

the percentage of CPEs being covered versus the number of

PUs when four schemes TPRA, NOCA, Random, and PCSA

are employed. As expected, when the number of PUs in-

creases, the coverage of each of the four schemes decreases.

The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)

10 15 20 25 30 35 40 45 50 55 600

5

10

15

20

25N

o. of active C

PE

s s

erv

ed

No. of primary users

PCSA_GTPRANOCARandomPCSA_L

Figure 4: Number of active CPEs being served versus no. of

PUs. No. of BSs = 4, no. of CPEs = 300, probability of a

CPE being active = 0.1, no. of channels = 16.

The coverage of TPRA is best because in this scheme (first

phase), we deliberately seek to cover faraway CPEs. On the

other hand, the coverage of PCSA is worst. This is because

when using the interference graph approach, PCSA tends to

only cover nearby CPEs to minimize interference. The cov-

erage of NOCA is close to that of TPRA. This is because in

NOCA scheme, base stations employ non-overlapping chan-

nel groups and therefore, can transmit at high power to reach

faraway CPEs. The coverage of Random scheme is signif-

icantly worse than that of TPRA, but still much better than

that of PCSA.

Next, in Fig. 4, we plot the average number of active

CPEs served versus the number of PUs for TPRA, NOCA,

Random, and PCSA G and PCSA L. Clearly, as PCSA G is

allowed to respond globally to changes in CPEs’ states, its

performance outperforms the rest. We present the through-

put of PCSA G here just to show what can be achieved if we

can tolerate the computational and signaling costs of always

carrying out global control.

As can be seen in Fig. 4, our TPRA scheme consis-

tently outperforms NOCA and Random schemes. The gain

of TPRA, relative to NOCA, is higher when the number of

PUs is small. This is because when the number of PUs is

small, there is more chance for channel reuse but NOCA is

not flexible enough to take advantage of that. The gain of

TPRA, relative to Random, is higher when the number of

PUs increases. This is because Random scheme does not

take PUs into account when carrying out allocation. It is also

interesting to see how PCSA performs when it is subject to

the local update constraint, i.e. PCSA L. The throughput of

PCSA L is much worst than all the other schemes. This is

because, as shown in Fig. 3, the coverage of PCSA is very

low compared to that of other schemes.

In Fig. 5, the number of channels is increased from 16 to

24. The performance trends are similar to those of Fig. 4.

We have results for other sets of system parameters and the

trends are also similar to what have been discussed.

V. CONCLUSIONS

In this paper, we consider the problem of channel-

allocation/power-control to maximize the system throughput

10 15 20 25 30 35 40 45 50 55 608

10

12

14

16

18

20

22

24

26

No. of primary users

No. of active C

PE

s s

erv

ed

TPRANOCARandom

Figure 5: Number of active CPEs being served versus no. of

PUs. No. of BSs = 4, no. of CPEs = 300, probability of a

CPE being active = 0.1, no. of channels = 24.

of a cognitive radio network that employs opportunistic spec-

trum access. At the same time, a realistic control framework

is formulated to guarantee protection to primary users and

reliable communications for cognitive nodes.

We propose the TPRA scheme that achieves good sys-

tem performance while can be implemented at reasonable

complexity. Numerical results show that our proposed

scheme achieves significant performance gain, relative to

other schemes.

For future research, we are currently extending this work

to consider fairness among CPEs as well as their QoS. At

the same time, a joint network-admission/resource-allocation

framework is being developed based on the system model of

this paper.

REFERENCES

[1] N. Bambos, S. C. Chen, and G. J. Pottie. Radio link admission algo-

rithms for wireless networks with power control and active link quality

protection. In Proc. of IEEE INFOCOM, Boston, MA, Nov. 1995.

[2] A. Behzad and I. Rubin. Multiple access protocol for power-controlled

wireless access nets. IEEE Transactions on Mobile Computing,

3(4):307–316, Oct.-Dec. 2004.

[3] FCC. Spectrum policy task force report, FCC 02-155. Nov. 2002.

[4] FCC. Facilitating opportunities for flexible, efficient, and reliable

spectrum use employing cognitive radio technologies, notice of pro-

posed rule making and order, FCC 03-322. Dec. 2003.

[5] G. J. Foschini and Z. Miljanic. A simple distributed autonomous

power control algorithm and its convergence. IEEE Transactions on

Vehicular Technology, 42(4):641–646, Apr. 1993.

[6] IEEE 802.22 Wireless RAN. Functional requirements for the 802.22

WRAN standard, IEEE 802.22- 05/0007r46. Oct. 2005.

[7] G. Kulkarni, S. Adlakha, and M. Srivastava. Subcarrier allocation and

bit loading algorithms for OFDMA-based wireless networks. IEEE

Transactions on Mobile Computing, 4(6):652–662, Nov./Dec. 2005.

[8] K. Mehlhorn and S. Naher. The LEDA Platform of Combinatorial and

Geometric Computing. Cambridge University Press, 1999.

[9] D. Mitra. An asynchronous distributed algorithm for power control in

cellular radio systems. In Proceedings of 4th WINLAB Workshop on

Third Generation Wireless Information Networks, Rutgers University,

New Brunswick, NJ, Oct. 1993.

[10] W. Wang and X. Liu. List-coloring based channel allocation for open-

spectrum wireless networks. In Proceedings of IEEE 62nd Vehicular

Technology Conference (VTC’05 Fall), Dallas, Texas, Sep. 2005.

[11] H. Zheng and C. Peng. Collaboration and fairness in opportunistic

spectrum access. In Proceedings of IEEE International Conference on

Communications (ICC’05), Korea, May 2005.