A two phase channel and power allocation

A TWO-PHASE CHANNEL AND POWER ALLOCATION SCHEME FORCOGNITIVE RADIO NETWORKS Anh Tuan Hoang and Ying-Chang Liang Institute for Infocomm Research 21 Heng Mui Keng Terrace, Singapore 119613

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

0 100 200 300 400 500 600 700 800 900 1000

0

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 PROBLEMDEFINITION

A System Model

We consider an opportunistic spectrum access scenario

de-picted in Fig 1 The spectrum of interest is divided intoK

channels that are licensed to a primary network ofM primary

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

deployed This cognitive network consists ofB 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 theK 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

LetN 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 probabilitypa, 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 CPEi toward CPE i

LetGc

ij be the channel power gain from the BS serving CPE j to CPE i on channel c Let Pc

i denote the transmit power for the transmission toward CPEi on channel c, 0 ≤

Pc

i ≤ Pmax If channelc is not assigned for the transmission toward CPEi, then Pc

i = 0 The SINR at CPE i is given by:

γc

c

iiPc i

No+PN

j=1,j6=iGc

ijPc, ∀i ∈ {1, 2, N }, (1) whereNois the noise power spectrum density of each CPE For reliable transmission toward CPEi, we require that

γc

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 channelc and let

Gc

pibe the channel gain from the BS serving CPEi to PU p

on channelc We require that, for each PU, the total interfer-ence from all opportunistic transmissions does not exceed a predefined thresholdζ, i.e.,

N

X

i=1

Pc

iGc

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 channelc simultaneously to a set of transmissions towardm CPEs: (i1, i2, im) Here, feasibility means there exists a set of positive transmit power levelsPc= (Pc

i1, Pc

i2, Pc

i m)T such that all the SINR con-straints of them CPEs are met while the interferences caused

to PUs do not exceed the acceptable threshold

If we define anm × 1 vector Ucas:

Uc= γNo

Gc

i1i1

, γNo

Gc

i2i2

, γNo

Gc

i m i m

T

(4) and anm × m matrix Fcas:

Frsc =

(

0, ifr = s

γG c

ir is

G c

ir ir , if r 6= s, r, s ∈ {1, 2 m} , (5) then the SINR constraints ofm CPEs (i1, i2, im) can be written compactly as:

From the Perron-Frobenious theorem [1, 5, 9], (6) has a posi-tive component-wise solutionPcif and only if the maximum eigenvalue ofFc is less than one In that case, the Pareto-optimal transmit power vector is:

Pc∗= (I − Fc)−1Uc (7)

Here Pareto-optimal means that ifPcis a positive power

vec-tor that satisfies (6), thenPc ≥ Pc∗component-wise Due

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

check the feasibility of assigning a particular channelc to

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

Two-step Feasibility Check:

• Step 1: Check if the maximum eigenvalue of Fcdefined

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 vectorPc∗ Then, check ifPc∗satisfies the

constraints for protecting PUs in (3) and the maximum

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

that the assignment is feasible andPc∗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-PHASERESOURCEALLOCATION

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 channelc For each BS, the higher

power it transmits onc, 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 inin-terference

reduces the number of CPEs that can be covered using

chan-nelc 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 channelc should only transmit at low power to reduce

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

all PUs using channelc 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 Γc

pb denote the channel gain from base stationb to primary user p and define:

Γc∗b = max

We do the following:

• Sort the base stations in the ascending order of Γc∗

b , i.e., form (b1, b2, bB) where Γc∗

b n ≤ Γc∗

b m, ∀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 in

thatbn 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 channelc (see the two-step feasibility check in Section II-C.) Theninis the CPE that has the weakest channel gain frombn, i.e.,

in= arg min

i∈V c n

It can happen that the set Vcnis empty Then, with some little abuse of notation, we setin= 0 to indicate that no CPE is covered bybn

• 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.,(Pc

i 1, Pc

i 2, Pc

i B)

• Finally, based on (Pc

i 1, Pc

i 2, Pc

i B), determine the N ×

K coverage matrix C, where C(i, c) = 1 indicates that CPEi can be served by the corresponding BS on chan-nelc This can be checked based on (2)

It can happen that when sorting BSs based onΓc∗

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 matrixC 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 CPEi and the vertex representing channel c if and only

ifC(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 resultmaximiz-ing 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

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 channelc, 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, theK channels are first partitioned into B

disjoint 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 byb1, b2, bn−1 Among all

channel left, each of the channelc chosen by bnmust satisfy:

Γc∗

b n< Γc∗

b m, ∀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%

20%

30%

40%

50%

60%

70%

80%

90%

100%

No of primary users

TPRA NOCA Random PCSA

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 NUMERICALRESULTS ANDDISCUSSION

A Simulation Model

We consider a square service area of size1000 × 1000m in which a cognitive radio network is deployed The service area is further divided intoB = 4 adjacent cells, each is a square of size500 × 500m A BS is deployed at the center

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

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

pa = 0.1 We vary M , the total number of PUs, from 10

to60 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 isK = 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 theK channels The noise power spectrum density at each CPE isNo= 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 isPmax= 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

10 15 20 25 30 35 40 45 50 55 60

0

5

10

15

20

25

No of primary users

PCSA_G TPRA NOCA Random PCSA_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 toleratethe 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 from16 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

8 10 12 14 16 18 20 22 24 26

No of primary users

TPRA NOCA Random

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

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