Maximizing Spectrum Utilization ofCognitive Radio Networks Using

Channel Allocation and Power ControlAnh Tuan Hoang and Ying-Chang Liang

Institute for Infocomm Research - 21 Heng Mui Keng Terrace, Singapore 119613Email: {athoang, ycliang}@i2r.a-star.edu.sg

Abstract— We consider a cognitive radio network in which a setof base stations make opportunistic unlicensed spectrum accessto transmit data to their subscribers. As the spectrum of interestis licensed to another (primary) network, power and channelallocation must be carried out within the cognitive radio networkso that no excessive interference is caused to any primary user.We are interested in spectrum-allocation/power-control schemesthat maximize the spectrum utilization of the cognitive networkwhile appropriately protecting primary users. While doing so, thecontrol schemes must also meet the required signal to interferenceplus noise ratio (SINR) of each subscriber of the cognitivenetwork. This problem can be formulated as a linear mixed (0-1)integer programming. Due to the high complexity in obtainingoptimal spectrum-allocation/power-control schemes, we proposea suboptimal scheme that can be obtained at lower complexitywhile still achieving good spectrum utilization. This suboptimalscheme is constructed based on the idea of a dynamic interferencegraph that captures the interfering effects. Numerical studies ofour control scheme are presented.

I. INTRODUCTION

The traditional approach of fixed spectrum allocation tolicensed networks leads to spectrum underutilization. In recentstudies by the FCC, it is reported that there are vast temporaland spatial variations in the usage of allocated spectrum, whichcan be as low as 15% [1]. This motivates the concepts of op-portunistic unlicenced spectrum access that allows secondarycognitive radio networks to opportunistically exploit the un-derulizized spectrum. In fact, opportunistic spectrum accesshas been encouraged by both recent FCC policy initiativesand IEEE standadization activities [2], [3].

On the one hand, by allowing opportunistic spectrum access,the overall spectrum utilization can be improved. On the otherhand, transmission from cognitive networks can cause harmfulinterference to primary users of the spectrum. Therefore,important design criteria for cognitive radio include maximiz-ing the spectrum utilization and minimizing the interferencecaused to primary users.

In this paper, we consider a cognitive radio network thatconsists of multiple cells. Within each cell, there is a basestation (BS) that supports a set of fixed wireless subscriberscalled customer premise equipments (CPEs). The spectrum ofinterest is divided into a set of non-overlapping channels. Toserve each CPE, a BS needs to use exactly one of the availablechannels. The spectrum is actually licensed to a set of primaryusers (PUs). For the cognitive radio network, two operationalconstraints must be met:

• the total amount of interference caused by all opportunis-tic transmissions to each PU must not exceed a predefinedthreshold,

• for each CPE, the received signal to interference plusnoise ratio (SINR) must exceed a predefined threshold.

We define the system utilization as the total number ofCPEs that can be supported while meeting the above twoconstraints. We are interested in spectrum-allocation/power-control schemes that maximize the utilization of the cognitiveradio network.

We note that in order to implement such a system, thereshould be a mechanism that enables secondary users (BSsand CPEs) to sense the spectrum and detect the presence ofprimary users. This is a challenging problem in itself and isbeyond the scope of this paper. Here, we simply assume thatthe positions and operating bandwidth of all PUs are known.

The utilization maximizing problem can be structured asa linear mixed (0-1) integer programming. As solving for anoptimal solution is NP-hard, we propose a heuristic channel-allocation/power-control scheme. This heuristic is based onthe concepts of a dynamic interference graph that captures notonly the pair-wise but also aggregate interference effects whenmultiple transmissions happen simultaneously on one channel.Numerical results are obtained to study the performance of ourproposed algorithm.

Works on channel allocation in cognitive radio networkswith opportunistic spectrum access include [4] and [5]. In[4], Wang and Liu consider a problem of opportunisticallyallocating unused licensed channels to a set of cognitivebase stations so that the total number of channel usagesis maximized. The authors then formulate this problem asa graph-coloring problem and propose a number of greedyheuristics for channel allocation. In [5], Zheng and Pengconsider a problem similar to [4]. However, they introducea reward function that is proportional to the coverage areasof base stations and also allow the interference effect to bechannel specific. Again, the problem is studied based on agraph-coloring formulation. The main drawback of the worksin [4], [5] lies in their oversimplified binary interferencemodel, which is simply based on whether or not the coverageareas of two base station overlap. This is unrealistic and doesnot capture the aggregate interference effects when multipletransmissions simultaneously happen on one channel. Weovercome this by considering the interference effects based

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Fig. 1. Deployment of a cognitive radio network.

on SINR. As we do that, the problem can not be viewed as astandard graph-coloring problem anymore. However intuitiveideas behind some greedy graph-coloring algorithms can stillbe exploited.

Works on channel-allocation/power-control problems thatmodel interference effects based on the SINR include [6] and[7]. The objective of [6] is to maximize spectrum utilizationwhile that of [7] is to minimize total transmit power to satisfythe rate requirements of all links. However, [6] and [7] do notconsider the scenario of opportunistic spectrum access andthere is no issue of protecting primary users.

In a broader context, our work is related to the class ofpower control problems for interfering transmissions with theobjective of guaranteeing SINR constraints [8]–[11]. In fact,similar to [8]–[11], we use Perron-Frobeniuos theorem tocheck the feasibility of a particular channel allocation.

The rest of this paper is organized as follows. In SectionII, we introduce our system model and then define the controlproblem together with its objective. In Section III, we presentour channel-allocation/power-control algorithm. Numerical re-sults showing the performance of our proposed control schemewill be discussed in Section IV. Finally, we conclude the paperin Section V and outline some future research directions.

II. PROBLEM DEFINITION

A. System Model

We consider the following opportunistic unlicensed spec-trum access scenario. The spectrum of interest is dividedinto K channels. These channels are licensed to a primarynetwork consisting of M primary users (PUs). In the samearea, a secondary cognitive radio network is deployed. Thiscognitive network consists of B cells. Within each cell, thereis a base station (BS) serving a number of fixed customerpremise equipments (CPEs) by opportunistically making useof the K channels. As the K channels are licensed only toM primary users, channel allocation and power control mustbe applied to the cognitive radio network to ensure that eachof the M PUs experiences an acceptable level of interference.This scenario is depicted in Fig. 1.

Let N denote the total number of CPEs in the cognitiveradio network. We consider the downlink situation in which

data are transmitted from BSs to CPEs. Assuming that aBS needs exactly one channel to serve each CPE, we definethe spectrum utilization as the total number of CPEs served.Our objective then is to maximize the spectrum utilization ofthe cognitive radio network while appropriately protecting allprimary users. We will discuss the requirements for reliablecommunications between BSs and CPEs and how PUs areprotected next.

B. Operational Requirements

1) SINR Requirement for CPEs:Note that in our downlink scenario, each CPE is served by

one fixed BS. Therefore, for the sake of brevity, we use thephrase ”transmission toward CPE i” to refer to the downlinktransmission from the BS serving CPE i toward CPE i.

Let Gcij be the channel power gain from the BS serving CPE

j to CPE i on channel c, Gcij includes all path loss and fading

effects. Let P ci denote the transmit power for the transmission

toward CPE i on channel c. If channel c is not assigned forthe transmission toward CPE i, then P c

i = 0. The SINR atCPE i is given by:

γci =

GciiP

ci

No +∑N

j=1,j �=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 regarded as the minimum SINR to achievea 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 interferencefrom all opportunistic transmissions (BSs toward CPEs) doesnot exceed a predefined tolerable threshold ζ, i.e.,

N∑i=1

P ci Gc

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

C. Maximizing Spectrum Utilization

Let aci be a binary variable denoting whether or not channel

c is assigned to the transmission toward CPE i. In particular, aci

equals one if channel c is assigned to the transmission towardCPE i and is zero otherwise. Similar to [6], we can state theproblem of maximizing the total number of CPEs served asthe following linear mixed (0-1) integer programming.

arg maxac

i∈{0,1}

K∑c=1

N∑i=1

aci (4)

subject to: K∑c=1

aci ≤ 1, ∀i ∈ {1, 2, . . . N}, (5)

GciiP

ci − γ

N∑j=1,j �=i

GcijP

cj − γNo ≥ (ac

i − 1)δ, (6)

m∑i=1

P ci Gc

pi ≤ ζ, ∀p ∈ Πc, (7)

0 ≤ P ci ≤ Pmax, ∀i ∈ {1, 2, . . . N}. (8)

In (6) δ is a relatively large constant. We note that the aboveproblem is NP-hard, therefore, instead of going for an optimalsolution, we are interested in heuristic algorithms that canprovide good performance.

D. Feasible Assignments

Before moving on to present different channel-allocation/power-control algorithms in Section III, let us dealwith the question of whether it is feasible to assign a particularchannel c simultaneously to a set of transmissions toward mCPEs: (i1, i2, . . . im). Here, feasibility means there exists aset of positive transmit power levels P c = (P c

i1, P c

i2, . . . P c

im)T

such that all the SINR constraints of the m CPEs are metwhile the interferences caused to PUs do not exceed theacceptable threshold.

If we define an m × 1 vector U c as:

U c =(

γNo

Gci1i1

,γNo

Gci2i2

, . . .γNo

Gcimim

)T

(9)

and an m × m matrix F c as:

F crs =

{0, if r = sγGc

iris

Gcirir

, if r �= s, r, s ∈ {1, 2 . . . m} , (10)

then it can be verified that the SINR constraints of m CPEs(i1, i2, . . . im) can be written compactly as:

(I − F c)P c ≥ U c. (11)

From the Perron-Frobenious theorem [8]–[10], (11) has a pos-itive component-wise solution P c if and only if the maximumeigenvalue of F c is less than one. In that case, the Pareto-optimal transmit power vector is

P c∗ = (I − F c)−1U c. (12)

Here Pareto-optimal means that if P c is a positive powervector that satisfies (11), then P c ≥ P c∗ component-wise.Due to this fact, the following 2-step procedure can be usedto check the feasibility of assigning a particular channel c tothe transmissions toward the set of CPEs (i1, i2, . . . im).

Two-step Feasibility Check:

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

defined in (10) is less than one. If not, conclude that theassignment is not feasible, otherwise, continue at Step 2.

• Step 2: Using (12) to calculate the Pareto-optimal trans-mit power vector P c∗. Then, check if P c∗ satisfies theconstraints for protecting PUs in (7) and the maximumpower constraints in (8). If yes, conclude that the assign-ment is feasible and P c∗ is the power vector that shouldbe used. Otherwise, the assignment is not feasible.

III. CHANNEL-ALLOCATION/POWER-CONTROL

ALGORITHMS

As has been mentioned, we are interested in channel-allocation/power-control heuristics that achieve good perfor-mance and can be obtained at lower complexity than theoptimal algorithm. Note that the objective is to maximizethe number of CPEs served while guaranteeing protection tolegacy primary users. We focus on centralized control algo-rithms in which all channel-allocation/power-control decisionsare determined offline before being signaled to BSs and CPEs.Although there has been a great interest in distributed powercontrol for wireless interference networks [8]–[11], distributedcontrol is not suitable for control a secondary cognitive system.This is because with distributed/online algorithms, it is notpossible to give absolute protection to primary users.

A. Main Algorithm: Dynamic Graph Based

In this section, for the sake of brevity, when a channel c isallocated to the transmission toward CPE i, we simply say that”channel c is allocated to CPE i”. Our proposed algorithmstarts with no CPEs being assigned any channel. It thenallocates a channel to one CPE at a time, until either all CPEsare served, or there is no more feasible channel assignment.At each step, channel assignment and power control must becarried out so that all CPEs that have been allocated channelsin prior steps are protected.

At each step, we construct an interference graph thatrepresents the interference between pairs of unserved CPEs.Moreover, this interference graph must also take into accountthe aggregate interference caused by transmissions that havebeen allocated channels in previous steps. This means ourinterference graph dynamically changes during the process ofchannel allocation. This is the major difference between ourapproach and the approach that constructs a fixed interferencegraph once at the beginning of the channel allocation process[6]. We name our approach Dynamic Graph Based and theapproach in [6] Fixed Graph Based.

To implement the Dynamic Graph Based approach, at eachstep, for each unserved CPE i, we calculate its degree corre-sponding to a channel c and prior channel-allocation matrixAsgn, as follows.

• Deg(i, c, Asgn) = ∞ if it is not feasible to assign chan-nel c to user i while keeping all prior assignments. Thefeasibility can be checked using the two-step procedurepresented at the end of Section II-D.

• If it is feasible to assign channel c to CPE i, thenDeg(i, c, Asgn) is the total number of unserved CPEsthat can not be assigned channel c anymore when thischannel is assigned to CPE i. Note that we only countthose unserved CPEs that can use channel c here.

The algorithm then picks a CPE-channel pair [i∗, c∗] thatminimizes Deg(i, c, Asgn) and assigns channel c∗ to CPE i∗.The channel assignment matrix Asgn and the set of unservedCPEs UnSrv are then updated and the process is repeated.The pseudo-codes for our algorithm are given in Algorithm 1.

Algorithm 1 Dynamic Graph Based

1: Asgn(i, c) ← 0, UnSrv ← {1, 2, . . . N}2: loop3: [i∗, c∗] ← arg min

i∈UnSrv, cDeg(i, c, Asgn)

4: if Deg(i∗, c∗, Asgn) = ∞ then5: break6: end if7: Asgn(i∗, c∗) ← 1, UnSrv ← UnSrv \ {i∗}8: if UnSrv = ∅ then9: break

10: end if11: end loop12: return Asgn

Note that our approach of picking a CPE with the minimumdegree to assign a channel is similar to the minimum-degreegreedy heuristic in graph-coloring theory [12].

B. Other Algorithms

1) Power-based Algorithm:In [7], Kulkarni et al. consider a problem of allocating

subchannels to multiple interfering links so that their raterequirements are met while the total transmit power is min-imized. Here, a SINR requirement is also set for each link.In [7], a power-based subchannel allocation algorithm isproposed. The general procedure is the same as our algorithmpresented in the above section. The only difference is that,at each step, the degree of CPE i on channel c is set equalto the total transmit power of all the nodes. We term thisapproach Min Trans Power. In Section IV, we also considerthe performance of another power-based algorithm calledMin Interf Power. This algorithm, at each step, allocates achannel to an unserved CPE such that the total interferencepower at all PUs and CPEs is minimized.

2) Random Algorithm:We also consider a simple random channel-

allocation/power-control algorithm as follows. A channel isassigned to one CPE at a time. At each step, we randomlypick an unserved CPE i and a channel c. We then check ifit is feasible to assign channel c to CPE i while keeping allprevious channel assignments using the Two-step FeasibilityCheck (Section II-D). If it is so, assign channel c to CPEi. Otherwise, another pair of unserved CPE and channel israndomly picked again. The algorithm stops when all CPEshave been served, or when there is no more feasible channelassignment.

IV. NUMERICAL RESULTS AND DISCUSSION

A. Simulation Model

The system model used in our numerical studies is asfollows. We consider a square service area of size 1000 ×1000m in which a cognitive radio network is deployed. Theservice area is further divided into B adjacent squares, eachof size 1000/

√B × 1000/

√Bm. We set B = 4, 9, 16.

A BS is deployed at the center of each cell to serve CPEs

within the cell. The total number of CPEs is N = 40. Thetotal number of PUs is M = 5 → 40. All CPEs and PUsare randomly deployed across the entire service area with auniform distribution. A sample network is shown in Fig. 1.

We model an orthogonal frequency division multiple access(OFDMA) system in which the entire bandwidth is dividedinto 48 subcarriers. Each subcarrier is regarded as one channelin our channel-allocation scheme. The fading channel is rep-resented by a six-tap channel, with exponential decay factor.Although there are 48 channels (subcarriers), we assume thatonly a subset of them is considered for used by primary andsecondary users. The number of channels K is set at 4, 8, 16.The path loss exponent is taken to be 4. We assume that eachof the M PUs randomly picks and uses one of the channels.

The noise power spectrum density at each CPE is No =−100dBm. The required SINR at each CPE is 15dB. Themaximum tolerable interference for each PU is 90dBm. Foreach BS, the maximum transmit power on each channel isPmax = 50mW .

B. Performance of Different Algorithms

In Figs. 2, 3, 4, and 5, we plot the number of CPEs servedversus the number of PUs when each of the algorithms Dy-namic Graph Based, Fixed Graph Based, Min Trans Power,Min Interf Power, and Random is employed. Here, 500 in-stances of the network are generated for each scenario in orderto obtain the average performance of each algorithm.

As expected, for all scenarios and all algorithms tested,when the number of PUs increases, the number of CPEssupported decreases. This is because less spectrum is availablefor opportunistic spectrum access.

As can be seen, our Dynamic Graph Based algorithm con-sistently outperforms others. On the other hand, Randomscheme always has the worst performance. The performancegain of the Dynamic Graph Base scheme, with respect to theRandom scheme, is between 5% and 19%.

The performance of three schemes Fixed Graph Based,Min Trans Power, and Min Interf Power are comparable toeach other. When the number of BSs is relatively smallwhile the number of channels is relatively large, there are notmuch gains of using Fixed Graph Based, Min Trans Power,and Min Interf Power, relative to using the Random scheme(Figs. 2 and 3). However, when the number of BSs increaseswhile, at the same time, the number of channels decreases(Figs. 4 and 5), the performance gains of Fixed Graph Based,Min Trans Power, and Min Interf Power, relative to Randomscheme, are more prominent. These effects can be explained asfollows. When the number of BSs is small while the number ofchannels is large, there is not much need to reuse each channel.To put it another way, there are enough channels to compensatefor the sub-optimality effect of random assignment. On theother hand, with more BSs and less channels, there is a realneed in reducing interference so that each channel can bereused, and this can be achieved with Fixed Graph Based,Min Trans Power, and Min Interf Power.

5 10 15 20 25 30 35 4010

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PE

s se

rved

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Fig. 2. Performance in terms of no. of CPEs served versus no. of PUs.No. of BSs = 4, no. of CPEs = 40, no. of channels = 16.

5 10 15 20 25 30 35 4025

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No.

of C

PE

s se

rved

Dynamic GraphMin−Trans−PowerMin−Interf−PowerFixed GraphRandom

Fig. 3. Performance in terms of no. of CPEs served versus no. of PUs.No. of BSs = 9, no. of CPEs = 40, no. of channels = 16.

4 6 8 10 12 14 16 18 2016

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PE

s se

rved

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Fig. 4. Performance in terms of no. of CPEs served versus no. of PUs.No. of BSs = 9, no. of CPEs = 40, no. of channels = 8.

4 6 8 10 12 14 16 18 2012

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of C

PE

s se

rved

Dynamic GraphMin−Trans−PowerMin−Interf−PowerFixed GraphRandom

Fig. 5. Performance in terms of no. of CPEs served versus no. of PUs.No. of BSs = 16, no. of CPEs = 40, no. of channels = 4.

V. CONCLUSIONS

In this paper, we consider the problem of channel-allocation/power-control to maximize the spectrum utiliza-tion of a cognitive radio network that employs opportunis-tic spectrum access. At the same time, a realistic controlframework is formulated to guarantee protection to primaryusers and reliable communications for cognitive nodes. Wepropose a heuristic channel-allocation/power-control algorithmthat is based on constructing a dynamic interference graph.Numerical results are obtained to show the performance gainof our proposed algorithm.

For future research, we are currently extending this workto consider fairness among CPEs. At the same time, a jointnetwork-admission/resource-allocation framework is being de-veloped based on the system model of this paper.

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