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Tabakovic and Grgic EURASIP Journal onWireless Communications andNetworking (2016) 2016:45 DOI 10.1186/s13638-016-0536-1

RESEARCH Open Access

Cognitive radio frequency assignment withinterference weighting and categorizationZeljko Tabakovic1* and Mislav Grgic2

Abstract

Cognitive radio is one of the technologies promoting flexible and efficient use of radio frequency spectrum, thussolving spectrum scarcity problem. Frequency assignment is an integral part of the cognitive radio spectrummanagement and a critical point of success or failure of the cognitive radio concept. In this paper, cognitive radiofrequency assignment with a novel interference weighting and categorization is proposed, as an extension of thesolution to the graph coloring problem. In our approach, the edge weights quantifying the interference potential areappended to the conflict graph, co- and adjacent channel interference are treated, and dynamically changing locallists of blocked frequencies are included. We propose the improved cognitive radio saturation metric for the dynamicvertex ordering and to introduce interference categorization which will reduce the communication overhead. Usingthe proposed model, resource manager can quantify individual interference components, as well as aggregateinterference from multiple users, resulting in more knowledgeable frequency decisions. Generalization of theproposed model is suggested. The suggested generalization consists of the selection of the central frequency andoptimal bandwidth to be used, according to the user requirements. We have developed interference-sensitivealgorithms for minimizing the interference and maximizing the throughput, both in centralized and distributedimplementation. The results show significant reduction of the interference, improved spectrum efficiency, andincrease in network throughput, comparing to the benchmark algorithms.

Keywords: Cognitive radio, Frequency assignment, Resource allocation, Graph coloring, Spectrum management,Dynamic spectrum access, Interference modeling

1 IntroductionThe future market demand for the wireless broadbandservices, internet of things, machine to machine commu-nications, and wireless data offload requires the deploy-ment of the next generation wireless networks, whichwill need a rapid and a more flexible access to the radiofrequency spectrum. Since radio frequencies are a lim-ited natural resource, which cannot be saved for thefuture use or transferred from underused to overloadedareas, efficient usage of the frequencies has become oneof the major concerns of the industry, governments,and scientific research. As a result of these researchefforts, many different proposals for better and moreefficient usage of the radio frequencies have emerged.One of the promising technologies, which could make

*Correspondence: [email protected], Croatian Regulatory Authority for Network Industries, Roberta F.Mihanovica 9, 10000 Zagreb, CroatiaFull list of author information is available at the end of the article

a big paradigm shift towards the future wireless net-works, is a cognitive radio (CR) technology. CR is intro-duced in [1, 2] and refers to intelligent radio commu-nications system employing technology that allows thesystem to obtain knowledge of its operational environ-ment, using technology to learn from the environmentand dynamically adjust its operational parameters andprotocols [3].Problem addressed. CR frequency assignment repre-

sents the core of the cognitive radio process, since itsunique features, along with reconfigurability and learn-ing, make the cognitive radio what it is. The frequencyassignment (FA) problem in wireless communicationsis well-studied, due to the extensive research of FA inmobile radio networks, wireless mesh networks, broad-casting networks, or in military applications [4–6]. Mostof these studies do not consider primary-secondary spec-trum sharing nor the dynamic availability of the spectrumdue to the presence of primary users. Taking a deeper look

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Tabakovic and Grgic EURASIP Journal onWireless Communications and Networking (2016) 2016:45 of 24

into these research approaches, we can deduce that thecognitive radio FA has many unique and specific features,which makes CR unsuitable for transposition of the sameFA models and algorithms from other types of wirelessnetworks.Task of the frequency assignment in the CR context

is to select the best available radio frequency spectrumto satisfy user’s communication needs, while avoidingcausing harmful interference to the primary users (PUs)and minimizing influence to the other concurrent sec-ondary users (SUs) sharing the same frequency band.Since the spectrum opportunities used for dynamic spec-trum access in CR are limited in both time and space,CR has to be very fast and pragmatic in using theavailable spectrum bands. Suboptimal but fast converg-ing and robust solutions are preferred in relation tothe optimal one which usually requires extensive datasets and too much time to obtain results. Having thisin mind, we can present basic characteristics of FAin CR:

• CR has to operate as a secondary service onnon-interfering, non-protection basis, alongsideother services using the same frequency band.

• CR has to work non-intrusively, has to protect PUs,and vacate the spectrum in case of a PU appearance.

• CR FA has to be fast, adaptive and easy to implementand does not necessarily have to provide an optimalFA.

• CR FA has to re-initiate and re-converge in cases ofthe quality degradation due to a dynamic changes inthe radio channel or SU and PU activation.

• CR FA has to allocate the channels and also thespectrum fragments of a different bandwidth.

• CR FA has to work with the limited information in anenvironment with either cooperative or selfish SUs.

• CR FA has to be flexible, applicable in centralized anddistributed manner.

• CR FA has to assign frequencies continuously andsequentially when a part of the PUs and SUs arealready operating.

• CR FA has to be applicable in the heterogeneouswireless environment with the different classes of thedynamic spectrum access, different userrequirements, and different protection requirements.

Our contributions. Our paper is focusing on the FAcomponent of the dynamic spectrum management inthe CR context. The problem of quantifying the inter-ference using interference weighting and categorizationin CR FA process, as well as CR FA algorithms with anumerical measure of interference levels between SUsas described in this paper, have not been previouslyaddressed to the best of our knowledge. The FA in

the CR networks presented in this paper is formulatedas a variation of the graph coloring problem with thedynamic vertex ordering, where specific CR features areincluded. In this paper, the special attention is grantedto the modeling and control of the interference. Numer-ical quantification of the interference is enabled with theinclusion of the conflict graph edge weights represent-ing co- and adjacent channel interference between theSUs. We have developed the centralized and distributedalgorithms with interference minimization and through-put maximization as objectives. Specifically, the contribu-tions and novelty of this paper can be summarized in thefollowing:

• The extension of the CR network conflict graph with:

– Introduction of the continuous value edgeweights quantifying the potential level of co-and adjacent channel interference betweenSUs

– Incorporation of the influence of the adjacentchannel interference by introducing anadditional layer in the conflict graph

• Introduction of the SU interference categorizationfor interference susceptibility of the FA algorithms,while reducing the communication overhead

• The proposal of the spectrum fragments assignmentwith the identification of the central frequency andoptimal bandwidth for the CR transmissions

• Introduction of a new saturation metric for adynamic sorting of the vertices in the process of thesequential FA, taking into consideration the channellimitations due to the PU transmissions as hardconstraints and a level of the interference from theadjacent assigned CRs as soft constraints

• The proposal and evaluation of the interferencesensitive FA algorithms with the objective of:

– Minimal total CR network interference– Maximal CR network throughput with

consideration of the network interference as acomprehensive metric

In our paper, the condition of not causing harmful inter-ference to the active PUs is a hard constraint, whichhas to be respected and cannot be violated by any FAplan. This is realized by the list of the blocked chan-nels at each SU. Each SU has its own local list of theblocked channels, which is dynamically changed in timeand space as the PUs frequency usage pattern con-stantly changes. The soft constraints are conditions whichcan be violated in the FA process if there is no betterchoice of the channel. The violations of the soft con-straints are penalized by the FA algorithm, resulting in


the deterioration of the objective function. The objec-tive function takes into consideration the interferenceamong SUs and the throughput achieved by the SUtransmissions.Our work differs from the previous works on the graph

coloring-based CR networks FA in several aspects: thelevel of the interference between the SUs and between theSUs and PUs are numerically quantified using both thecontinuous and discrete weights; the influence of the co-channel and adjacent channel interference are considered;all individual interference contributions and cumulativeinterference values are monitored in the course of FAprocess. Proposed FA algorithms use this unique fea-ture of the numerical quantification of the interference toprecisely control and assign frequencies that have min-imal interference influence in relation to other users.The advantages of the proposed interference sensitiveFA strategy are numerous. It significantly reduces theinterference in the CR networks, fully protects the PUs,reduces the frequency reuse distance between the CRusers, improves spectrum usage efficiency, and increasesthe overall networks throughput with the available radiospectrum.Paper organization. The rest of the paper is organized

in the following way. Section 2 presents the overviewof the previous research along with the comparison andmain differences with respect to our paper. In Section 3,we formulate a CR network FA problem, present thesystem model and propose a novel framework for theinterference sensitive FA in the CR. In Section 4, an inter-ference estimation model used in the algorithm designis elaborated, characterization and categorization of co-and adjacent channel interference is introduced, anddetermination of weighting coefficients is elaborated. Wedescribe the phases of the proposed FA algorithms, sat-uration metric, and coloring label with the objective ofinterference minimization and throughput maximizationand the transmit power control strategy in Section 5.In Section 6, considerations of the centralized and dis-tributed implementation of the FA algorithms are dis-cussed. In Section 7, generalization to the frequencyand bandwidth spectrum assignment are proposed, aswell as implementation consideration in practical CRsystems. In Section 8, we present an evaluation of theproposed algorithms’ performance in the simulated envi-ronment of the PU and CR networks. Finally, we concludethe paper and outline the key results of this paper inSection 9.

2 Related workSpectrum management is technical, procedural, and pol-icy approach to the planning, coordination, and manag-ing the use of the electromagnetic spectrum as a lim-ited resource. The CR spectrum management functions

have some specific capabilities, since the CR networksare focusing on the secondary access and spectrum shar-ing, while protecting the PUs and minimizing inter-ference with the other SUs. An insightful overview ofthe spectrum management in the CR networks is pre-sented in [7, 8]. The problem of the FA is commonlysolved using different heuristic methods, the graph the-ory, game theory, or linear programming. In the FAmodeled as a the graph coloring problem, the task isto color all the nodes of the graph with the mini-mum number of colors, in a way that no two adja-cent nodes (nodes connected with an edge) have thesame color [4–6]. A comprehensive analysis of the fre-quency assignment in the CR networks can be foundin [9, 10].The comparisons of the different target objectives, the

approaches for the FA, and the used methods for theselected previous works presented in this section are sum-marized in Table 1. A deeper discussion on the insightsof the related work and the main differences with respectto this paper are presented below. In [11], the authorspropose a spectrum decision framework determining aset of spectrum bands taking into account the appli-cation requirements and dynamic nature of spectrumbands. For the real time applications, authors proposespectrum decision with the objective of total capacity vari-ance minimization, while for the best effort applicationsobjective is network capacity maximization. The authorspropose a new metric for calculating the capacity of aCR user, namely, the expected normalized capacity of auser taking into account network switching delay. Thisspectrum switching delay includes the time intervals forthe spectrum decision process in the base station, signal-ing for establishing new channels and the RF front-end

Table 1 Summary of FA problem solutions presented in relatedwork

Ref. Objective Approach Method

[11] Throughput/ Centralized single ch Linear integervariance optimization

[12] Power/total Distributed / centralized Graph theorythroughput

[13] Fairness/throughput Centralized multi ch Graph theory

[14] Node connectivity/ Local Heuristicinterference algorithm

[15] Throughput surplus Distributed / centralized Nash bargaining /game theory

[16] Fairness/QoS Distributed list coloring Graph theory

[17] Fairness Local multi ch Graph theory / heuristic

[18] Throughput Macro BS femtocell Graph coloring

[19] Interference Wireless mesh Graph coloring

[20] Interference/power Distributed Game theory


reconfiguration. The dynamic resource management forthe spectrum decision is elaborated including admissionand decision control. The authors propose centralizedspectrum management using linear integer optimizationmethod with a single channel assignment. Two phase CRnetwork power control and channel allocation is proposedin [12]. In the first phase, distributed power updatingprocess is employed in order to maximize the coverageof the CR network, while assuring that the signal-to-interference-plus-noise ratio (SINR) constraints at all PUreceivers are met. In the second phase, a centralized chan-nel allocation scheme based on weighted bipartite graphmatching is used. The objective of the channel assignmentis the maximization of the total network throughput whileprotecting the PUs. Both, uplink and downlink scenarios,are investigated with distributed and centralized imple-mentation. The authors consider a cellular CR networkwith base and terminal stations, where the interferencebetween the SUs are not considered. Contrary to this, inour approach, the SUs protect the PUs using the local listof blocked channels, the interference between the SUs ismeasured with conflict edge weights, and FA algorithmsconsider the interference quantification in the frequencydecisions. In [13], the FA problem for the opportunis-tic spectrum access is investigated. The authors proposea novel FA approach using color-sensitive graph color-ing. The authors present a solution of the graph coloringproblem using the sequential coloring with a vertex label-ing. The vertex labeling is based on the channel capacitydivided by the vertex degree, giving priority to the mostvaluable vertices. Based on those premises, the authorspropose coloring algorithms with an objective of maximalcumulative reward, maximal minimal reward, and maxi-mal proportional fairness. Results of the simulations showimprovement of the network performance in through-put and in interference reduction compared to the otheralgorithms. In [13], the authors use binary edge conflictgraph and interference free channel assignment. In ourproposal, the interference is continuous or have discretecharacteristic values. The FA algorithms allow the inter-ference with matching network penalty. In [14], localizedefficient channel assignment in the CR networks is pro-posed with a goal to maximize node connectivity after theFA, which is important for packet delivery. Partition ofthe network into two-level trees, conflict resolution strat-egy and trimming of nonessential links are proposed. Twobasic localized algorithms and an advanced localized algo-rithm for the FA are presented. In assigning, the priorityis given to the nodes with a higher link degree. Node-link-based algorithm with Hungarian method of maximalmatching has almost twice the broadcast reachable nodesand assigned link rate, compared to the basic algorithms.As opposed to our approach, in the proposed model,the CR throughput is not considered, all channels have

the same performance, there is no transit power control,and the interference range is the same as the commu-nication range. In [15], the authors consider cooperativecognitive radio networks and propose the resource allo-cation in an OFDMA-based CR network with the SUsrelaying data of the PUs. A new flexible channel coop-eration (FLEC) design of the PU and SU cooperationis proposed. In the first time slot, PUs transmit to SU.In the second time slot, the SUs transmit to the pri-mary BS. A game theory Nash bargaining-based solutionfor relay and subchannel assignment, as well as strategyoptimization and power control, is considered. Central-ized and distributed algorithms are proposed and showthroughput improvement comparing to the conventionalchannel cooperation model. Distributed bargaining algo-rithm converges within 20 iterations, while centralizedalgorithm proves to be impractical due to the slow con-vergence. Consequently, the authors propose a heuristicmethod for the centralized problem. In [16], the authorspropose a graph coloring-based fair channel allocationfor base stations self-coexistence in the CR networks.The proposed solution is different from our approach inthe following: each base station has a list of the avail-able channels with equal characteristics and throughput.Graph representation of the system employs a binaryinterference model between the base stations. The pro-posed model allows operation of the CR networks withthe different traffic requirements and guarantees the cer-tain quality of service (QoS). Depending on the accesscategory and priorities for the different packets, qualitymetric and share of the resources is determined. Sim-ulation results show fairness improvement in terms ofbandwidth allocation ratio and faster convergence thantraditional list multi-coloring algorithm. An opportunis-tic distributed channel graph coloring algorithms for thespectrum access in dynamic spectrum access networks ispresented in [17]. Maximum spectrum packing algorithmuses the local topology information of one-hop neighborsassigning a channel to the node with the highest degree.The algorithm ensures that all the SUs obtain one colorand some SU’s multiple colors. The algorithm assigns thecolor to the node with the highest degree and also enablesassigning multiple colors to some nodes, thus improv-ing overall spectrum efficiency. The improved heuristicwith probabilistic color selection using truncated geomet-ric distribution based on node degree ranking reducesthe algorithm termination time. In probabilistic heuris-tic, the SUs request different channels with the probabilitythat depends on the relative degree of the SU and itsone-hop neighbors, reducing the possibility of two userscontend for the same frequency. Random backoff is usedto resolve the contentions of the same degree users dur-ing channel access. The performance of the algorithmis tested on randomly generated Bernoulli graphs with


specified graph density. Comparing to our approach, pro-posed model does not consider the protection of the PUsand only simple binary conflict graphs are consideredwithout interference susceptibility in the FA. In [18], theauthors consider downlink resource allocation for hybridmacro/femtocell LTE-advanced network. Both macro andfemto base stations have the CR functionalities. The crosstier interference is reduced by using the cross-cognitionscheme, where base stations have higher priority in uti-lizing its licensed spectrum and lower priority in oppor-tunistically utilizing non-licensed spectrum. The largestdegree first based graph coloring algorithm is applied forthe frequency block assignment reducing intra-tier inter-ference between the femtocell nodes. Simulation resultsshow increased throughput of the CR femtocell networkcompared to non-spectrum shared macro-femto cell net-work and improved interference mitigation of the graphcoloring resource allocation compared to the randomresource allocation. The problem of the FA to the com-munication links in the multi-hop wireless mesh networkswith the objective of minimizing overall network interfer-ence is addressed in [19]. In the proposed mesh network,router nodes have multiple radio interfaces. The authorspropose a centralized algorithm based on the heuristicTabu search technique, where in the first phase, randominitial FA solution is improved using the iterative algo-rithm with Tabu list, and in second phase, the algorithmeliminates remaining interface constraints. Distributedalgorithm is based on a greedy heuristic algorithm forMax K-cut problem of the constrained graph optimiza-tion, where algorithm chooses frequency which producesthe largest decrease in the local interference. The authorsalso propose an extension of the model with considerationof the non-orthogonal channels and non-uniform nodetraffic useful for practical implementation. The empiricalevaluation on randomly generated network graph showsthat proposed algorithms perform close to lower boundsestablished by the semi-definite and integer linear pro-gramming. However, compared to the approach presentedin this paper, the authors assume quasi-static assignmentof the channels, all channels are not available for theFA to all users, binary interference model is assumed insimulations, and finally, there is no sharing between theprimary and the secondary users. In [20], a game theoreticapproach for the distributed channel selection and powerallocation in the cognitive radio networks is investigated.Proposed algorithm enforces the cooperation betweenthe SUs in order to reduce the energy consumption andto find Nash equilibrium. Game theory model fits wellwith the cognitive FA problem because the spectrumdecision of one of the SU influences the performanceof neighboring SUs. Potential game formulation and no-regret learning model have been presented as a solutionto the channel allocation problem. The influence of the

cooperation on observed SINR and power consumptionis investigated. Results show that the proposed iterativealgorithm converges to a pure strategy Nash equilibriumsolution.So far, all the work done on the CR networks graph

coloring FA employed simplistic binary co-channel inter-ference model in order to assign frequencies and opti-mize utility function [10, 12–14, 16–19]. As we know,the interference control and management are of utmostimportance for the spectrum sharing and efficient spec-trum management in the CR systems. The CR FA algo-rithms have to deal with the mutual interference fromco-channel or adjacent channel transmissions, which maycause significant performance degradation. Nevertheless,in the existing work, it was not possible to assess, quantify,or compare interference influence of the CR frequencyselection on the neighboring SUs, nor to share spec-trum between users when the interference exists, but itis bearable. Also, the adjacent channel interference wasmainly neglected. To alleviate this deficiency, we pro-pose a novel conflict graph model and algorithms withinterference weighting and categorization, which enableinterference sensitive frequency decisions, better interfer-ence control, and quantitative estimation of the individualcomponents, as well as the calculation of the cumulativeinterference at the neighboring users. As a result, the pro-posed FA in the CR is performed with the interferencesensitivity, achieving the efficient spectrum utilization,while enabling reliable transmissions.

3 The proposed FA frameworkThe CR spectrum management task is to achieve efficientwireless communications without causing a harmful inter-ference or service interruptions. The CR spectrum man-agement functions have some specific capabilities sincethe CR networks are focusing on the secondary access andspectrum sharing, while protecting the PUs and minimiz-ing interference to the other SUs. A functional overviewof the CR spectrum management framework is shown inFig. 1. It consists of four major steps:

• Spectrum sensing. A CR user can only utilizetemporary unused parts of the spectrum. Therefore,CR should monitor the available spectrum bands,collect the information on the spectrum use, andidentify possible spectrum holes and theircharacteristics.

• Spectrum decision. Based on the spectrum availabilityinformation acquired through the spectrum sensing,policy guidelines, user requirements, and registry ofthe spectrum use, CR characterizes radio frequencyspectrum possible for various models of the dynamicspectrum access. In the spectrum decision, CR or thecentralized entity determines the carrier frequency,


Rad

io e

nviro

nmen

t

REGISTRY POLICIES

CR SPECTRUM MANAGEMENT

SensingSpectrumDecision

DSA

Action at

Eventet

Reward rt

State st

Learning

USER REQ

Fig. 1 CR spectrum management framework

channel bandwidth, transmission power, modulation,coding, communication technology, together withother operational, and technical parameters used forthe CR operation.

• Dynamic spectrum access (DSA). The CRreconfigures its technical parameters in line with theselected operational technical parameters andoperates in order to satisfy its primary goal ofsuccessful communication with a required QoS.

• Learning. Since CR is operating in heterogeneousradio environment with different user characteristics,different requirements and many parametersdetermining its environment and performance, CRhas to adapt to the constantly changing environment,observe performance of its operation, and has toadapt its spectrum decision function usingreinforcement learning.

The process of assigning frequencies to the CR users aspart of the spectrum decision step is of crucial importancefor the CR network functioning and represents a focalpoint of the efficient radio spectrum use, distinguishingthe CR from other wireless communications systems.

3.1 Problem formulation and systemmodelIn this paper, we are focusing on the FA component of theCR spectrum management. We will interchangeably usethe following terms: radio links and vertices, frequenciesand colors, interference and edges, cognitive radio andsecondary user. The problem of the FA in the CR networkscan be informally described as follows: given a set of thetransceivers with the CR capabilities, a network of the PUtransceivers with the administrative licenses and priorityaccess rights to the radio frequency spectrum, and prede-fined constrained number of the frequencies, we wish toefficiently assign radio frequencies to the CR users. TheCR FA has to satisfy the following requirements:

• CR self-goal: successfully transmit as muchinformation as possible with required QoS

• CR network goal:

– Minimizing the total network interference– Maximizing the network throughput

• Requirements towards other users: not to causeexcessive interference with the operating PUs, to keepthe CRmutual interference under the reasonable limitand to efficiently share the radio frequency spectrum

The FA problem in the wireless communications canbe modeled as a graph-theoretical problem by defin-ing an undirected conflict graph describing the inter-ference relations and assigning frequencies by coloringvertices. The graph coloring problem is known to beNP-complete problem [21] and therefore computation-ally hard. Although any given solution of the NP-completeproblem can be verified in the polynomial time, there is noknown efficient way to find the optimal solution. Also, thetime required to solve the problem increases very quicklyas the size of the problem grows. For example, 3.16 mil-lion years are needed to find a solution to the FA problemusing brute force search approach for 20 terminals and 10frequencies with 1 μs per solution [6]. Considering thebasic characteristics of the FA in the CR already men-tioned, and the computational complexity of finding anoptimal solution, we are directing towards the use of theheuristic method for solving this problem. Although theheuristic algorithm leads to a suboptimal solution, it pro-vides a reasonably good solution in the limited time, whichworks well in the practical applications of the assigningfrequencies to the CR SUs.In this paper, the CR FA is modeled as a graph coloring

problem using novel dynamic vertex ordering, interfer-ence weighting, and categorization. To illustrate the con-cept presented in this paper, an example of the dynamic


spectrum access scenario is depicted in Fig. 2, withthe corresponding communication and conflict graph.The communication graph represents the communicationlinks between the radio transceivers, while conflict graphshows possible interference between the radio links. Inthe communication graph, the PU and SU transceivers arerepresented as the vertices, while communication linksbetween radio transceivers are represented by communi-cation graph edges. In the communication graph shownin Fig. 2, PU network is illustrated as two base stationsserving a set of PUs, establishing the primary links, whileCR network deployed in the same area is representedby a set of CR links {A, B, . . . , I}. The circles illustrate

the service zones of the PU networks. The correspond-ing conflict graph is shown in Fig. 2, where the verticesrepresent the CR communication links with a dynami-cally changing local list of blocked frequencies due to PUtransmissions. In the same figure, the edges show possibleinterference occurrences where co- and adjacent channelinterference levels are proportional to the edge weightscoefficients.Let us assume there are five available frequencies repre-

sented by numbers, which are opportunistically availableto the CR operation. Since the PU and the CR networksshare the same radio frequency band, the frequenciestemporarily used by PUs cannot be utilized by the CR

a {1,2}

b {4,5}

AB

C

D

E

F

G

H

I

*

*

*

* *

*

*

*

*

*

*

**

*

*

*

**

communication graph

A {}B {1,2}

C {4,5}

D {}

E {1,2}F {1,2,4,5}

G {4,5}

H {1,2,4,5} I {4,5}

10.1 wco = 0.2

wco = 0.6

wadj=0.05

wadj=0 wco = 0.9

wadj=0.1

wco = 0.5

0.02

wco = 0.4wadj=0.03

wco = 0.3

wadj=0.001

wco = 0.2wadj=0

wco = 0.2wadj=0

wco = 0.1

wadj=0

conflict graph

Fig. 2 Communication and conflict graph illustration. The figure shows example of dynamic spectrum access scenario with correspondingcommunication and conflict graph


users if they are in the interference range, and there-fore, those channels are blocked for corresponding CRlink indicated by the corresponding blocked channels list.For the CR link, B channels {1, 2} cannot be used dueto the possible interference with the service area of thePU base station a, for the CR link C channels {3, 4} areblocked, for the CR link F channels {1, 2, 4, 5} are blocked,etc. The conflict edges represent the potential interfer-ence between the CR links with two edge weights peredge indicating co-channel and adjacent channel interfer-ence potential. In Fig. 2, the edge between the CR linkA and CR link B has weights of 1 for co-channel and0.1 for the adjacent channel, indicating very high interfer-ence potential between those links, and therefore, thoselinks cannot use the same channel. The edge betweenthe CR link C and CR link D has a conflict weight of0.6/0.05 indicating a medium interference potential andthe edge between CR link B and CR link F has a weightof 0.2/0 indicating a low co-channel interference and noadjacent channel interference. This indicates the possibil-ity for sharing the channel. The existence of the conflictgraph edges and the corresponding weights depends onthe propagation channel characteristics and the antennadiscrimination between the CR link pairs analyzed. Forexample, between the CR link A and CR link E, thereis no edge because the terrain obstacle prevents possi-ble interference path and corresponding links can usethe same channel without danger of the mutual harm-ful interference. Practical implementation of constructingconflict graph and determining its weights is elaborated inSection 7.2.In our work, we abstract the CR network topology

into the communication graph G = (V,E) as a generalundirected graph over the set of network transceivers rep-resented by the vertices V and PU or CR links representedby the edges E in Fig. 2. The FA channel selection con-straints and potential interference between the radio linksare represented by a conflict graph Gc = (Vc,Eco,Eadj),where Vc is set of conflict graph vertices, and Eco and Eadjare co-channel and adjacent channel conflict edges withassociated interference potential quantified by the edgeweights wco and wadj. Using the described model, the FAproblem can then be further formulated as a completefrequency assignment of the CR network represented bya conflict graph Gc = (Vc,Eco,Eadj). The spectrum ofinterest is divided in M frequencies represented by con-strained set of the radio frequencies F = {1, ..,M}, andthe dynamically changing local set of blocked frequenciesprotecting the PU transmissions represented by Bv. Usingthe abovementioned notation, frequency assignment is agraph coloring function f : (Gc,Bv,Wco,Wadj) → F , suchthat the objective function is maximized. To facilitate fur-ther discussion, we will use the notation and acronyms asdefined in Table 2.

Table 2 Important notation and acronyms

Notation Description

Gc = (Vc, Eco, Eadj

)Conflict graph with vertices Vc and edges Eco, Eadj

F = {1, ..,M} Set ofM available frequencies

Bv List of blocked frequencies at CRv due to PUhard constraints

Wco ={wcovi vj

}∈ [0, 1] Set of co-channel continuous interference

weight coefficients

Wadj ={wadjvi vj

}∈ [0, 1] Set of adjacent channel continuous

interference weight coefficients

NPU,NSU Number of primary and secondary users

hPUi′

PUi hSUk′PUi Channel coefficients between PU Tx i′ , SU Tx k′ ,

and PU Rx i

hSUk′

SUl hPUj′

SUl Channel coefficients between SU Tx k′ , PU Tx j′ ,and SU Rx l

PRx_SUl_D, PRx_SUl_I Desired received signal strength and interferingreceived signal strength at the lth SU

PTx_PUm′ , PTx_SUl′ Transmitting power atm′th PU and l′th SU

Svi Saturation metrics label

Colvi Vertex coloring argument

Acronyms Description

CR Cognitive radio

FA Frequency assignment

PU, SU Primary user, secondary user

Tx, Rx Transmitter, receiver

QoS Quality of service

CminSumInt Centralized minimum cumulative networkinterference FA algorithm

CMaxSumCap Centralized interference sensitive maximumthroughput FA algorithm

DminInt Distributed minimum interference FA algorithm

DMaxCap Distributed interference sensitive maximumthroughput FA algorithm

3.2 Framework overviewThe CR FA task is to assign the frequencies to the SUswhen and where they request access to the spectrum, toassign new frequencies to the CR users when co- or adja-cent channel PU transmission occurs in the interferencerange, or when the quality of service reduces below therequested threshold. As a result of that, we are facing withthe task of assigning frequencies in a partially coloredgraph. In that respect, the FA is a continuous process, asit is not possible to assign frequencies and optimize color-ing to the entire CR network at the same moment. Thereis a need to constantly assign and re-assign frequencies toactive SUs. If the PU reactivates, new SU appears, or sig-nal level drops due to dynamic characteristics of the radiochannel, the FA process has to be re-initiated and chan-nel allocation has to re-converge for the SUs influenced bythese changes.


Based on the system model described in Section 3.1,we have developed a novel framework for assigning thefrequencies in the CR environment. In the prepara-tory step, input data and the CR technical parametersare determined, including available frequencies, com-patibility criteria, CR coverage area, and the interfer-ence potential. In the second step, the CR adjacency,interference levels, and weights are estimated, followedby communication and the conflict graph construc-tion determining whether the CRs can share radio fre-quencies. In the CR FA step, an iterative process isperformed consisting of labeling and ordering of theCRs, selecting the next transmitter to assign the fre-quency, and selecting the frequency maximizing networkobjective.In the previous research of the CR FA application of

graph coloring, the interference model assumed the con-flict edges to be binary variables representing the interfer-ence or no-interference occurrence. The adjacent channelinterference was not taken into account since the chan-nels were assumed to be orthogonal. In the proposed FAframework, the CR network conflict graph illustrated inFig. 2 is extended with the novel features:

• The local list of the blocked frequencies Bv associatedwith each conflict graph vertex representingfrequencies which cannot be used by CR

• Two layers of edges in conflict graph taking intoconsideration co-channel interference Eco andadjacent channel interference Eadj

• Continuous interference weight coefficientsWco andWadj associated to the conflict graph co-channel andadjacent channel edges incorporating quantificationof possible interference between adjacent verticescorresponding to the interference “strength”

• The categorization of the interference weightsreducing communication overhead

Since the CR user has to protect and not cause theinterference to the licensed PUs, each CR keeps its ownlist of blocked frequencies and the FA algorithm avoidsselecting the channels causing harmful interference to thePUs which are temporarily operating in the close vicin-ity of the observed CR. As the PUs frequency usage isconstantly changing, the list of the blocked channels atthe CR is dynamically updated using the spectrum sens-ing, the geo-location database or some other method ofthe spectrum awareness. In the proposed approach, theFA is interference sensitive, as the edges have associatedco-channel and adjacent channel weights determining thelevel of the interference between the vertices. In thispaper, we are proposing the algorithms which can be cate-gorized under the sequential graph coloring class of algo-rithms with a saturation degree dynamic vertex ordering.

This class of algorithms was first introduced by Brélaz[22] as saturation largest first algorithm known underthe name Degree of saturation algorithm (DSATUR). InDSATUR algorithm, the vertices are ordered by a decreas-ing order of saturation, where the saturation degree isdetermined as a number of different colors to which avertex is adjacent. In [13], color-sensitive graph color-ing is used where dynamic vertex ordering is determinedusing labeling based on channel capacity divided by vertexdegree and selecting most valuable SU to assign frequen-cies first (CR link contributing the most to the networkthroughput).In our approach, we are also using labeling and dynamic

SUs ordering to determine the prioritization of assigningfrequencies to the CR users, but with the different sat-uration metric and network objectives compared to theexisting literature on graph coloring FA. We are selectingthe most difficult SUs to assign frequencies first using aspecially designed CR saturation metric. Proposed novelCR saturation metric is determined as a level of freedomin selecting the frequency for the SU, taking into consid-eration channel limitations due to local PUs transmissionsand a level of interference from adjacent assigned SUsas a combination of hard and soft frequency assignmentconstraints. The saturation metric is calculated using theinterference weight coefficients. In this paper, we areproposing two different FA problem solutions with objec-tive functions determined as minimal total network inter-ference and as maximal throughput with the interferencesusceptibility.Taking into account the CR network topology, we are

considering centralized FA where centralized resourcemanager optimizes frequency use on the network orcluster level, and distributed FA where the selectionof the frequencies is performed on a level of CR andits neighboring nodes. More detailed algorithm descrip-tion and the mathematical formulation of the satura-tion metrics and objective functions are provided inSections 5 and 6.

4 Interferencemodeling and characterization4.1 Interference modelModeling and estimation of the mutual interference are ofvital importance for exploiting the potential of the radiospectrum band to the full extent, while keeping the inter-ference under control and below level causing the net-work performance deterioration. Since the interference isthe primary limiting factor influencing the performanceof the CR networks, we have built our FA model withthe interference susceptibility. The determined level ofinterference is a basis for the interference weighting andcategorization used in the proposed FA algorithms. Chan-nel model for the co-existing PUs and cognitive SUs isillustrated in Fig. 3. The figure shows one PU transmitter-


PU Tx1'

PURx1

SUTx2'

SURx2

SUTx1'

SURx1

XPU1' XSU2'

XSU1'

ZSU1

YSU1

ZPU1ZSU2

YSU2

YPU1

hSU1SU1'

hSU2SU1'

hPU1SU1'

hSU2PU1'

hSU1PU1'

hPU1PU1'

hSU1SU2'

hPU1SU2'

hSU2SU2'

Fig. 3 Channel model for scenario of co-existing PUs and SUs

receiver pair (PU Tx1’ - PU Rx1) and two SU transmitter-receiver pairs (SU Tx1’ - SU Rx1, SU Tx2’ - SU Rx2). Thereceived signal at Rx is noted by Y, transmitted signal fromTx is noted by X and Z is the noise. Lines between Txand Rx represent TX-Rx channel paths, where each Txis connected to all receivers with corresponding channelcoefficients h. We assume that the quasi-static fading ispresent, and the channel coefficients between users areconsidered to be independent random variables. Channelcoefficients take into consideration the total loss of theradio link between the transmitter and the receiver, as wellas the antenna gain and the propagation effects (e.g., largescale fading due to the shadowing and small scale fadingdue to the multipath).The signal received at the PU or at the SU can be

represented with a sum of: the desired received signal,interfering received signal, and the noise. Signal receivedat ith PU and signal received at lth SU is a superpositionof various components and can be expressed as

YPUi = hPUi′

PUi XPUi′ +NPU∑

j′=1,j′ �=ihPUj

′PUi XPUj′

+NSU∑k′=1

hSUk′

PUi XSUk′ + ZPUi, (1)

YSUl = hSUl′

SUl XSUl′ +NPU∑j′=1

hPUj′

SUl XPUj′

+NSU∑

k′=1,k′ �=ihSUk

′SUl XSUk′ + ZSUl, (2)

where XPUi′ is the signal from PU transmitter i′, XSUl′ isthe signal from SU transmitter l′, hPUi′PUi denotes the chan-nel coefficient between PU transmitter i′ and PU receiver

i, hSUk′PUi is the channel coefficient between SU transmit-

ter k′ and PU receiver i, hSUl′SUl is the channel coefficientbetween SU transmitter l′ and SU receiver l, hPUj

′SUl is the

channel coefficient between PU transmitter j′ and SUreceiver l, NPU is the number of PUs, and NSU is thenumber of SUs, as illustrated in the Fig. 3. ZPUi and ZSUlrepresent additive white Gaussian noise at the PU receiveri and SU receiver l with the variances σ 2

PUi and σ 2SUl.

The desired received signal strength represents thepower of the useful signal received at the SU receiver fromthe wanted SU transmitter contributing to the informa-tion data flow. The interfering received signal strength isthe superposition of all received interfering signals at theinput of the same SU receiver. Accordingly, we can expressthe desired received signal strength PRx_SUl_D, and inter-fering received signal strength PRx_SUl_I at SU receiverl as

PRx_SUl_D =∣∣∣hSUl′SUl

∣∣∣2 PTx_SUl′ , (3)

PRx_SUl_I =NSU∑

k′=1,k′ �=l

∣∣∣hSUk′SUl

∣∣∣2 PTx_SUk′ + σ 2SUl

+NPU∑m′=1

∣∣∣hPUm′SUl

∣∣∣2 PTx_PUm′ , (4)

where PTx_PUm′ , PTx_SUl′ , and PTx_SUk′ are PU and SU

transmitting powers, and∣∣∣hSUl′SUl

∣∣∣2 and∣∣∣hPUm′

SUl

∣∣∣2 are thewanted and interfering channel gain coefficients. Receivedinterfering power PRx_SUl_I takes into account the interfer-ence received from PUs, interference from other SUs onco-channel, and adjacent channel operating in the inter-ference range of the corresponding SU and the noise. Allthose interferences add up to the cumulative interference,which reduces quality and reliability of the SU link. Sim-ilarly, we can calculate the desired received signal, andinterfering received signal at the PU, which is omitted forbrevity.The SU throughput is proportional to the normalized

ergodic channel capacity, which is defined as the maxi-mum achievable rate averaged over all fading blocks andit can be expressed as

C (SINR) = max E[log2

(1 + F−1 (1 − ε) SINR

)], (5)

where F(x) = P(∣∣∣hSUk′

SUl

∣∣∣2 > x)

is the complemen-

tary cumulative distribution function of SU channel gain∣∣∣hSUk′SUl

∣∣∣2, ε is an error probability of the secondary trans-missions, and SINR is the desired signal-to-interference-plus-noise ratio at the SU receiver. If the SU channelgain is below minimal threshold level x, no useful datatransmission can be obtained between the SU transmitter


and receiver. In Eq. (5), the theoretical relation betweenSU throughput and an ergodic channel capacity for thefading channel is shown. In the numerical simulationin Section 8, we assume that SU system utilizes M-aryquadrature amplitude modulation (M-QAM) and we usethe approximation (19) for SU throughput. Additionally,in the simulation, we have set up the upper limit of theachievable individual SU throughput in order to avoidunfair spectrum usage between the SUs.

4.2 Weighting coefficients characterizationSince all of the channel parameters and fading statis-tics between interfering nodes are generally unknown tothe SUs, it would be demanding to implement full net-work interference model. On the other hand, reliable andprecise interference estimation is important for construct-ing the CR conflict graph needed for the FA algorithmimplementation. Therefore, to encompass the sensitivityto the potential levels of the interference in the process ofassignment of the frequencies to the SUs, we propose theclassification of the interference in four categories. Thisenables an efficient practical implementation of the FAprotocol with control and quantification of the interfer-ence levels, while not adding too much of an additionalburden to the network communication overhead. Con-sidering the spectrum sharing between the SUs, for eachinterfering path between SUswe designate co-channel andadjacent channel conflict edge and introduce associatedinterference weights determining the level of the potentialinterference between the corresponding SUs as follows:

wco = pco · wi , wadj = padj · wi, (6)

where wco and wadj are co- and adjacent channel inter-ference edge weights, pco and padj are co- and adjacentchannel penalties, and wi is the nominal edge weight.Co- and adjacent channel interference edge weights are

the network penalties for violation of the soft FA con-straints in the neighboring vertex, resulting in the deterio-ration of the objective function used for the optimizationof the FA process. The channel penalties pco and padj rep-resent the portion of the CR transmitter power whichis absorbed by the CR receiver on the same or adjacentchannel. Generally, channel penalty is calculated as thereduction of the interference power caused by the filtershape of the transmitter spectrum density mask and thereceiver selectivity mask or it can be measured. As we areanalyzing network with a predefined set of frequenciesand aligned channel bandwidths, in network simulation inSection 8, we assume that the channel penalties are pre-defined and have the constant values. The nominal edgeweight wi corresponds to the channel coefficient includ-ing propagation loss, antenna gain, and discriminationbetween the SU Tx and SU Rx under the consideration.

We propose to classify level of the potential interfer-ence in four main categories (harmful—high interfer-ence; disturbing—medium-high interference; annoying—medium-low interference; permissible—low interference)and assign the corresponding conflict edge weight coef-ficients wi ∈ {0; 0.4; 0.7; 1}. To classify the potentialinterference in the appropriate category, a value of thepotential interference between the SU Tx and Rx is com-pared with the cumulative probability density functionof the average received interference power between theSUs. The cumulative probability density function (cdf )is empirically determined from the previous spectrumsensing measurements in the frequency band under con-sideration. On the basis of this comparison, it is identifiedto which category out of four this potential interferencebelongs and the characteristic value of the nominal edgeweight factor is assigned for the identified interferencecategory. Proposed values for the categorization of thenominal edge weights are calculated by evaluating the cdfof the average received interference power between theSUs. Interference cdf is divided into four non-overlappingareas and a median cumulative probability value for eacharea is calculated. Channel weights representing each cat-egory are calculated as the ceiling round up (roundedoff to the higher value) for the edge weight coefficients(0.4; 0.7; 1) and as floor round up for edge weight coeffi-cient (0). Specific weights for four different categories ofthe interference are chosen in such way that the possibleharmful interference between SUs is emphasized.We havetested proposed algorithms with the variation of the val-ues of discrete interference weights, and the results showsimilar behavior as the algorithms with a small variationof the nominal network weight coefficients representingfour categories.This novel interference categorization allows the intro-

duction of the susceptibility of the FA protocol to the levelof the interference, taking into account the probabilisticnature of the received signal as described above, as well aspossible interference estimation errors.To illustrate the used model of the interference classifi-

cation, Fig. 4 shows the criteria for the forming of a list ofblocked channels Bv, depending on ameasured level of thePU signal at the corresponding SU. IPU is the level of theinterference from PUs transmissions at the observed fre-quency measured on the SU terminal. If the value of IPUis above the threshold of the receiver interference limit,the said frequency cannot be temporarily used for the SUtransmissions, since it may cause harmful interference tothe PUs in the vicinity of the SU terminal. The frequency isincluded in the dynamic list of the blocked channels at thisSU. If IPU is below the threshold, the interference is smalland SU can share the frequency with the PUs with appro-priate transmission power. Probability density function ofthe received interfering signal is shown in the middle of


Fig. 4 Categorization of interference for FA in CR networks. The criteria for forming list of blocked channels is shown on the left side. Classificationand quantification of SU interference is shown on the right side

Fig. 4. In the right side of Fig. 4, a proposed categorizationof the SU interference corresponding to SU interferencelevel, edge weights coefficients, and their binary codingis shown. ISU is the level of the measured interferencefrom the SU transmissions, used for determining the SUadjacency and the conflict edge weights. The SUs edgeweights are used for quantitative estimation of the inter-ference in the process of the assigning frequencies. In sucha way, we can make more knowledgeable frequency deci-sions and control individual interference components aswell as aggregate interference from multiple users duringthe FA process. In the proposed FA algorithms, we usethe continuous edge weights in the interval [ 0, 1], or thediscrete weight values as shown in Fig. 4. The protocolfor determining the SUs adjacency and the conflict graphedge weights is elaborated in Section 6.

5 Interference sensitive FA algorithmsThe proposed FA in the CR networks is based on theefficient heuristic based algorithms that can run reason-ably fast and provide a good quality solution. In thispaper, non-uniform traffic on the different communica-tion links and frequencies, weighted interference model,and non-orthogonal channels are considered based on theCR networks specifics.

5.1 Algorithm descriptionIn a proposed model, we have a predefined set of frequen-cies F = {1, ..,M} and the task is to assign frequencies toall SUs requesting network access, taking into considera-tion the network interference. The SU is not allowed touse any of the frequencies which could cause noticeable

interference to the PU network, determined by the spec-trum awareness and expressed with a set of blocked chan-nels Bv. If there are no available channels in the spectrumpool, SU’s request is rejected or transferred to anotherspectrum band. In our approach, the SUs connected withthe conflict graph edge (i.e., interfering each other) canshare the same frequency or an adjacent frequency, butwith a corresponding penalty, which is proportional toa level of the mutual interference calculated as a prod-uct of the nominal edge weights and co-/adjacent channelpenalty. Having this quantitative metric, resource man-ager selects the frequencies with a minimal interferencecontribution towards the other users. Proposed FA algo-rithms consist of four main phases with specific tasks ineach phase as follows:

• Phase 1. FA preparation:

– Establish the list of the blocked channels at allSUs.

– Determine the SU transmitting power for eachavailable channel at all SUs.

– Calculate the SU throughput for each availablechannel at all SUs.

– Establish a conflict graph edges and determinethe interference weights for co-channel andadjacent channel transmissions.

– Interference categorization.

• Phase 2. Selecting the next SU to assign frequency:

– Label the non-assigned SUs using specific CRFA saturation metric.


– Dynamically order the SUs with decreasingsaturation score.

– Select the SU with the highest saturationmetric to assign frequency as the next SU toprocess.

• Phase 3. Assigning frequency to the selected SU:

– Calculate objective function for each availablefrequency at the selected SU.

– Select and assign frequency maximizingobjective function at the selected SU.

• Phase 4. CR FA performance evaluation and conflictgraph update:

– Calculate interference, throughput, andthroughput variance for all SUs.

– Determine the overall network performanceand update conflict graph.

The initial SU transmitting power for each availablechannel at SUs is determined in a way that SU doesnot cause harmful interference to the closest PU usingthis channel and that the minimal required SINR atthe SU user is achieved. In the following phases,the SU calculated transmitting power per channel isupdated using power control ratio parameter. The detailsof the power control mechanism are described inSection 5.3, while establishing the list of blocked chan-nels, calculation of the conflict graph edge weights,and its categorization are performed as described inSection 4.2.We propose the centralized and distributed algorithms

with the objective of minimizing the cumulativeCR network interference and with the objective ofmaximizing the network throughput, as shown inTable 3.

5.2 Saturation metric labeling and coloringThe proposed algorithms process and assign frequenciesto the SUs requiring spectrum access in a sequence wherein each iteration step the most difficult SU is selected.Most difficult SU is the vertex with the smallest choiceof channels determined by the saturation metric. Thesaturation metrics label Svi is calculated as

Table 3 Summary of proposed FA algorithms

Objective

Implementation Minimal interference Maximal throughput

Centralized CminSumInt CMaxSumCap

Distributed DminInt DMaxCap

Svi =∑vi∈Vc

Bvi +∑

f ∈ F , vj∈ Vc

Eco vi vj · xvj · wcovi vj

+∑

f ∈ F , vk∈ Vc

Eadj vi vk · xvk · wadjvi vk, (7)

where Bvi are blocked frequencies, which cannot be usedat the SU vi, Eco vi vj, and Eadj vi vk are co- and adjacentchannel edges indicating the interference between theSUs, wco

vi vj and wadjvi vk are the conflict edge weights deter-

mining the interference potential of the adjacent SUs, xvjand xvk are variables indicating that the adjacent SUs havethe frequency assigned. All the vertices are sorted in thedecreasing order of the saturation label. The vertex withthe largest label is selected for coloring. Saturation met-rics score is changing in each iteration step due to thecontinuous process of the assigning frequencies to theSUs, and therefore, the order of the SUs also dynamicallychanges. In the assignment phase, the selected SU is col-ored with a color which contributes themost to the systemutility function. Here, we investigate the different algo-rithms with the objective of the minimal interference andmaximal throughput.

5.2.1 Minimum cumulative network interference FAThe proposed algorithm is minimizing the total networkinterference while taking into account co-channel andadjacent channel interference. Vertex coloring is per-formed according to

Colvi = argmin [α + β] , (8)α =

∑vj∈ Eco vi vj

wcovi vj · xvj, (9)

β =∑

vk∈ Eadj vi vk

wadjvi vk · xvk, (10)

where α and β are co- and adjacent channel cumulativeinterference at the adjacent vertices. In coloring, the algo-rithm is selecting the frequency which contributes theleast to the cumulative network interference. Having theinterference represented by edge weights, the individualinterference contributions can be quantified and the levelof total network interference can be controlled.

5.2.2 Interference sensitivemaximum throughput FAThe FA is performed using a comprehensive coloringargument that integrates the interference and throughput.The proposed algorithm is maximizing the total networkthroughput while taking into account co-channel andadjacent channel interference. The coloring argument iscalculated as

Colvi = argmax[ ∑

Cf vi · xvi∑vi∈Vc Bvi + α + β

], (11)


where Cf vi is the SU throughput at frequency f. The SUthroughput is calculated using Eq. (5), and its value canbe between 0 and the maximum available throughput perSU. This value is set to 16 Mbit/s in the numerical simula-tion in Section 8. The coloring is done with the preferencegiven to the frequencies having the highest throughput,while having the minimal influence to the rest of the SUnetwork.

5.3 Transmit power controlThe proposed transmit power control strategy is basedon the balancing of the SU transmit power level betweenminimal required to satisfy QoS requirements and maxi-mal permissible level in order to avoid interference withthe PUs. In order to minimize the interference to theother concurrent SUs, it is recommended to maintain thetransmission power level at a minimum, while ensuringan adequate signal quality at the receiving end. Minimumrequired transmit power is determined by adjusting thepower level until the targeted SINR at the SU receiver issatisfied. Maximum acceptable transmit power is estab-lished by considering the permissible interference at thePUs.The initial SU power is calculated using the path loss

estimation determined by spectrum sensing of the PUs as:

PTx_SU = PTx_C − PRx_C + SR − LA + PRx_SU_I, (12)

where PTx_SU is the initial SU transmit power, PTx_C is thepredetermined transmitted power of the common pilotchannel, PRx_C is the measured power of the commonpilot channel at the SU receiver, LA is the additional gain,loss, and tolerances, SR is the required SINR, and PRx_SU_Iis the interfering power. The initial power level is used forthe initial communication between SU terminals and as astarting power level for the process of adaptive adjustingof the transmitter power. Instant transmit power of thesecondary user is determined as

PTx_SU ={PTx_SU_R if PTx_SU_M ≥ PTx_SU_R

0 if PTx_SU_M < PTx_SU_R

}, (13)

where PTx_SU_M is the maximal acceptable transmit powerand PTx_SU_R is the required transmit power. The max-imal acceptable transmit power represents the maximalallowed power of the cognitive SU in order to satisfythe interference constraints, as illustrated in Fig. 4, andis determined by the spectrum sensing of the PU at theSU location. The required transmit power is the trans-mit power level just strong enough to satisfy SINR forobtainable throughput at the SU receiver. The compari-son of the measured SINR at the SU receiver with therequired SINR determines the SU transmit power controlratio for the transmit power adjustment. The new mini-mum required transmit power is obtained by multiplying

presentminimum required transmit power with the trans-mit power control ratio RTPC as follows:

PTx_SU_R (t + 1) = PTx_SU_R (t)RTPC. (14)

A possible implementation of the proposed adaptivetransmit power control strategy using fuzzy logic powercontroller is described in [23].

6 Centralized and distributed algorithm6.1 Centralized FA algorithmThe centralized network resource manager has the advan-tage of collecting all the relevant information and usingmore complex processing engines. It can, therefore, pro-vide an overall better solution. The centralized algorithmcan keep track of the CR user mobility, achieving con-tinuous connectivity of the established CR session. Pseu-docode of the centralized FA algorithm is presented inFig. 5.In each iteration, the centralized algorithm calculates

the saturation metrics of all unassigned vertices. In orderto detect the most difficult vertex to process first, thevertices are sorted and vertex with the largest saturationmetrics is selected. For the selected SU, coloring is per-formed with the frequency which maximizes the objec-tive function. In CminSumInt algorithm, the frequency isselected on the basis of the minimal interference caused

Fig. 5 Centralized FA algorithm. The figure shows pseudo code ofproposed centralized algorithm


to the adjacent vertices. In CMaxSumCap algorithm, theselected frequency maximizes the comprehensive met-ric that integrates both interference and throughput.The centralized solution requires an additional commu-nication overhead to collect and distribute informationbetween the vertices. In that respect, the common com-munication channel and protocol are necessary. Also, thecentralized solution is sensitive to the potential failures ofthe central entity, which can result in the discontinuities ofthe FA in the CR networks. In the cluster topology, the CRnetwork is subdivided in a number of geographically dis-tinguished clusters. Each cluster uses a different resourcemanager and an independent algorithm determining thenext SU to assign frequency using the saturation metriclabel and frequency assignment maximizing the networkobjective.In order to determine the complexity of the algorithm, it

is essential to determine the number of iterations neededfor the algorithm to terminate. The number of itera-tions in the centralized algorithm is bounded by O(NSU),where NSU is the number of the secondary users request-ing access to the CR network. Since the single vertexcoloring can be completed in O(M) where M is the num-ber of available frequencies, the overall complexity of theproposed centralized algorithm is O(NSUM).

6.2 Distributed FA algorithmThe distributed algorithm finds a local objective, butit results in a more robust, flexible, faster and lesscommunication demanding implementation. Proposeddistributed algorithm works on a vertex level andeach vertex only has the local information, which iscommunicated between the adjacent incident vertices.Pseudocode of the distributed FA algorithm is shownin Fig. 6.The algorithm initializes and the SU requesting fre-

quency access calculates its own saturation metrics label.Vertex saturation label and set of blocked frequencies arecommunicated to other adjacent non-assigned verticesrequesting access to the same frequency band. In order toavoid transmission collision, contention window for thetransmission backoff time is calculated as a random valuein the interval [0, window], where the window is calcu-lated as 1/Svi. On the basis of the exchanged informationon the local vertex saturation metric, ordering of the ver-tex coloring is determined. Vertex with a local maximumsaturation score is selected first to color, and then it selectsa frequency with the maximum contribution to the objec-tive function. Selected frequency is then communicatedto the adjacent vertices and the list of assigned frequen-cies is updated. Subsequently, new saturation labeling isperformed and the next vertex to color is determined.Each iteration of the single vertex coloring can be com-

pleted in O(M) where M is the number of the available

Fig. 6 Distributed FA algorithm. The figure shows pseudo code ofproposed distributed algorithm

frequencies. The number of the iterations in the dis-tributed algorithm is bounded by O(�), where � is amaximum degree of a vertex in the conflict graph. Theoverall complexity of the proposed distributed algorithmis O(�M). The complexity of the distributed algorithm isNSU/� times smaller compared to the centralized algo-rithm, indicating that the distributed algorithm is simplerand converges faster.

7 Generalizations and implementation7.1 Central frequency and bandwidth CR spectrum

assignmentIn the proposed FA, we assume fixed set of the channelswith predetermined bandwidth and channel separation.In general, the problem of the FA in the CR networksshould include not only the identification of the centralfrequency but also the optimal bandwidth to be usedaccording to the service requirements of the SUs. Gener-ally, spectrum holes can be of the various bandwidth and


frequency separation, and CR devices by definition shouldbe able to use these spectrum opportunities. The ques-tion of the assigning spectrum fragments of the differentsizes is still an open area in research of the CR FA [10]. Inthis section, we present the generalization of the proposedmodel of the FA in order to relax input assumptions of thefixed channel division, to an implementation consideringbandwidth and central frequency decision. This general-ization is quite useful in the practical deployments of theCR systems.The proposed solution of the central frequency and

bandwidth assignment for the CR consists of the followingsteps: the admission control, the bandwidth reservation,and the spectrum assignment. In the admission con-trol, the spectrum management system has to determineweather the new incoming CR communication requestcan be accepted or the request is queued. Fair spectrumbandwidth BSUi, which could be assigned to the SUi iscalculated as

BSUi = CSUr_iBfree∑NSUj=1 CSUr_ j

, (15)

where CSUr_i and CSUr_j are the requested throughputs ofSU i and SU j and Bfree is the available idle spectrum inthe frequency band considered and not currently used byPUs.The SUi request is accepted, if the achievable through-

put in the bandwidth which can be assigned to the SU cansupport the minimal sustainable throughput needed forsatisfying the service requirements for the SU as:

ackSUi ={1 if CSUa = BSUi · cSINR ≥ CSUs_i0 if CSUa = BSUi · cSINR < CSUs_i

}, (16)

where ackSUi is the binary acceptance variable, CSUa isthe achievable SU throughput, cSINR is the normalizedchannel throughput of the SU with observed SINR andCSUs_i is the minimal sustainable throughput. AchievableSU throughput of the SU is calculated using Eq. (5) or byapproximation Eq. (19) in case of M-QAM.For the bandwidth reservation, we propose to use MSA

algorithm of the spectrum aggregation presented in [24].The MSA algorithm is utilizing the worst spectrum bandwhich can barely satisfy the bandwidth requirements BSUiof the SU in consideration relating to all unassigned SUs.In MSA algorithm, the SUs are sorted by the bandwidthrequirements and the idle spectrum is sorted by the avail-able bandwidth of the spectrum regions. For the band-width reservation, the MSA algorithm firstly chooses theSU with the highest bandwidth requirements and try toassign the spectrum region with the least available band-width. The reservation continues in the decreasing orderof SU’s bandwidth requirements and ascending order ofthe available spectrum regions, until all users are assignedor there is no available spectrum.

The spectrum assignment phase can use proposed algo-rithms for the CR FA presented in this paper without theneed for modification. In the preparatory phase, general-ization of the interference weighting to include interfer-ence potential between the spectrum fragments is pro-posed. As we assign discontinuous spectrum regions ofthe different bandwidths to SUs, we have to extend thedefinition of the spectrumweights to be able to accommo-date the evaluation of the level of the interference betweenthe SUs. For each interfering path between the SUs, wedesignate the conflict edge and introduce the associatedinterference weight wE determining the level of potentialinterference between corresponding SUs as follows:

wE = pE · wN0, (17)

where pE is the conflict edge channel penalty and wN0 isthe nominal edge weight. The nominal edge weight wN0corresponds to the channel coefficient including propaga-tion loss, antenna gains, and discrimination between theSU Tx and SU Rx under the consideration. It is deter-mined as described in Section 4. The conflict edge channelpenalty pE represents the portion of the SU transmitterpower which is absorbed by the SU receiver. It is calcu-lated as the reduction of the interference power caused bythe filter shape of the transmitter spectrum density maskand the receiver selectivity mask as follows:

pE =∫ fh

flSSUTx

(f) · SSURx

(f − �f

) · df , (18)

where SSUTx is the Tx signal’s power distribution acrossthe frequency spectrum, SSURx is the SU receiver filter fre-quency response, f is the frequency, fl and fh are lowerand higher limits of the frequency band in consideration,and �f = ∣∣fTx0 − fRx0

∣∣ is the spectrum gap between theSU Tx and Rx center frequency. If �f = 0, both Tx andRx are operating at the same central frequency and we arecoming to the special case of co-channel penalty.

7.2 Implementation considerationsThe CR networks utilizing algorithms with the objectiveof the minimal total network interference (CminSumInt,DminInt) are more suitable for the user scenarios wherethere exists a large number of SUs and scarcity of theavailable frequencies, requiring reliable but not very datademanding communications. The real-world applicationsof CR networks with this objective function could be thewireless sensor networks, the radiometers in the smartgrid networks, the medical body area network devicesfor monitoring, diagnosing or treating of the patients, theutility companies’ telemetry networks, location services inthe search and rescue applications, different machine tomachine communications, backup system for the emer-gency networks, and the military communications in thehostile interference environment. The CR networks using


algorithms with the objective of the maximal through-put with the interference susceptibility (CMaxSumCap,DMaxCap) are more appropriate for the capacity orientedapplications encompassing different scenarios includinginternet connectivity, cellular networks, and TV whitespace applications. The real-world applications could bethe cellular networks data offload, realizing femtocells inthe cellular networks, the best effort wireless hotspots, thelocal internet connectivity, the internet of things applica-tions, the public protection and disaster relief networksrealizing communication between the emergency respon-dents and the public safety agencies, and the wirelesscameras video transfer.The FA in the CR is an event-based functionality and

continuously re-iterated process. In a given moment intime, frequencies for only part of the active SUs have to beassigned.When the PU appears, all active SUs in the inter-ference range have to move to the new spectrum bands[11]. This event triggers re-initiation of the FA process formultiple SUs. When new SU appears in the CR network,it needs to be assigned frequency for its transmissions.Similarly, when the quality of the SU transmissions dete-riorates due to dynamic channel conditions, the SU wantsto switch to a better frequency. In those cases, the processof a single frequency selection is initiated.The network protocol for determining the conflict

graph edges and corresponding weights can be as follows.Each of the active SUs interchangeably transmits SU IDand test message on the common communication chan-nel, while all other SUs are temporarily monitoring thechannel and receiving. The test message and default trans-mission parameters of the SU are known to all of the SUsin the same geographic area. By monitoring the receivedsignal strength, each of the SUs can determine its adjacentSU transceivers and categorize the interference potentialwith the corresponding interference category (harmful,disturbing, annoying, permissible). Accordingly, each SUcan construct a local conflict network graph with edgescorresponding to all of the received SUs transmissionsand associated weighting coefficient proportionate to thereceived signal strength. In the centralized implementa-tion, these network weights are then communicated to thecentral spectrum management entity, which constructsthe network graph and assigns frequencies. The imple-mentation of the protocol determining network conflictgraph and corresponding weights is easy to implementand it can be coded by only 2 bits. Since determining ofthe conflict graph edges and corresponding weights addsadditional communication overhead to the CR communi-cation, it is rational to construct the conflict graph andperform weight determining protocol only when needed.In the case of the stationary SU, the weight determiningprotocol should be performed at the time of the estab-lishing the network or when some change in the network

configuration or propagation parameters occurs, whilein the case of moving SUs, the weight determining pro-tocol should be performed more often. This could bedetermined by a network policy and triggered when theCR terminals determine the increased probability level ofdropped or severely disturbed transmissions.

8 Numerical results and discussion8.1 Simulation setupIn order to evaluate the performance of the proposed FAalgorithms, we have implemented the stochastic simula-tion of the primary and the CR network. In the setup of thestochastic simulation, we assumed that the area under testis a square with dimensions of 30 km× 30 km.We consid-ered the SU Tx−Rx pairs that co-exist with a cellular PUnetwork in a configuration similar to the one illustratedin Fig. 2. PU network consists of a number of base sta-tions covering a circular area around them. CR networkconsists of NSU short range secondary links which accessradio spectrum opportunistically in the same area. Thefrequency band considered is 2000 MHz, and availablefrequencies are consisting of the group of 15 to 25 chan-nels with a channel bandwidth of 3.5MHz. The number ofthe PUs active in the area under test is between 15 and 40;the number of the SU links requesting frequency accessis between 10 and 50. The whole spectrum is consideredto be open for an opportunistic spectrum access scenario,meaning the SUs can use any channel on the condition ofnot causing harmful interference to the PU network. Wesummarize the simulation parameters in Table 4.PU network model. In the simulation, we considered the

network of the PU base stations, each of them operatingon one channel, which has to be protected by all SUs inthe corresponding interference range. We have randomlyplaced a number of PUs in a given area. For simplicity, weassumed that the PUs have a constant Tx power of 43 dBm

Table 4 Simulation parameters

Parameter Value

Area under test 30 km × 30 km

Number of PUs (NPU) 15–40

Number of SUs (NSU) 10–50

Frequency band 2000 MHz

Channel bandwidth 3.5 MHz

Number of frequencies (M) 15–25

PU transmission range (dPU) 10 km

SU transmission range (dSU) 1–4 km

PU interference range 20 km

SU interference range 2–8 km

Modulation M-QAM M = [4, 16, 32, 64]

Maximal SU throughput (64 QAM) 16 Mbit/s


and omnidirectional antenna radiation pattern. Each oneof the PUs is defined as an information source, which canbe in two distinctive states: an active state in which PUconstantly generates information packets and requests fordata transmission or in a passive state in which PU is notactive as an information source. The PU entity is modeledas a two state Markov birth-death process with birth rateα and death rate β . Since each user arrival is independent,transition follows the Poisson arrival process.CR network model. Cognitive secondary system co-

exists in the same area with a primary system usingopportunistic radio spectrum access. The SU transmitterand receiver pairs are uniformly randomly generated inthe analyzed area. The distance between SU Tx and SURx is set between 1 and 4 km. In order to test proposedalgorithms in a difficult sharing environment with manyinterference cases and for simplicity reasons, we assumethat SUs also have an omnidirectional antenna radiationpattern. The SU adjusts its transmitting power in order toavoid generating interference with the active PUs on thesame frequency. The SU Tx power is limited to a maximalvalue of PSUMAX = 27 dBm, and it can have any contin-uous value in the interval [ 0,PSUMAX]. The SU Tx poweris calculated for each available channel using the trans-mit power strategy as described in Section 5.3. For thechannels which are included in the local list of blockedchannels Bv, the SU TX power is set to 0 because they can-not temporarily be used. In the simulation, we assumedthat the SUs use square M-QAM with Grey bit mapping,without losing the generality of the proposed algorithms.For the calculation of the SU throughput in simulation,we used the approximation in [25], tight within 1 dB forM ≥ 4 and BER ≤ 10−3 as

C (SINR) ≈ BWchlog2

[1 + SINR

−ln(5BER

)/1.6

], (19)

where C (SINR) is the throughput, BWch is the channelbandwidth, SINR is the wanted signal to interference plusnoise ratio at the SU receiver and BER = 10−3 is thetarget bit error rate. The SINR at each SU differs anddepends on the channel used, obtainable SU Tx power,distance to SU Rx, and sum of all interference from otherSUs. The maximal throughput of the individual SU is setto 16 Mbit/s, using 64-QAM modulation, as an upperlimit of the achievable individual SU throughput. For eachSU, the list of blocked channels is established, compar-ing calculated distance between the PU and SU with thePU interference range. If the distance is smaller than theinterference range, this channel cannot be used at the SU.The corresponding channel is included in the SU list ofblocked channels Bv in order to protect PU transmissions.This list for each SU is dynamically updated with each iter-ation of the FA algorithm. In the simulation, the SU edges

and their corresponding co-channel and adjacent channelweights are calculated from the level of overlapping ofinterference ranges of the SUs as follows:

wco = pco · wi , wadj = padj · wi, (20)

wi =

⎧⎪⎪⎨⎪⎪⎩

1 if dSUiSUj < 2dST2dST−dSUiSUj

2(dSI−dST

) + 1 if 2dST ≤ dSUiSUj ≤ 2dSI

0 if 2dSI < dSUiSUj

⎫⎪⎪⎬⎪⎪⎭ , (21)

where dSUiSUj is the distance between SUi and SUj, dST is theSU transmission range, dSI is the SU interference range,pco is the co-channel penalty set to 1, padj is the adjacentchannel penalty set to 0.1. Interference is classified in fourcategories as described in Section 4.2.Methodology. The three parameters, the number of the

available frequencies M, the number of the secondaryusers NSU, and the number of the active primary usersNPU are tunable in the ranges shown in Table 4. Each time,we change one of the parameters in the tuning range andthen compare the algorithms using the following metrics:

• Average throughput per SU (Mbit/s): the ratio of thecumulative CR network throughput over the numberof active SUs

• Average interference per SU: the ratio of thecumulative interference of all interference sourcesover the number of active SUs

• SU throughput fairness: Jain’s fairness index as ameasure of the throughput distribution of all of theactive SUs in the CR network

Instead of using the cumulative network values, we usethe average throughput and average interference as a met-ric, to be able to compare the results of the simulationswith different input parameters. The higher the averagethroughput per SU, the better the result. A smaller aver-age interference indicates that the algorithm is better inrespect of protecting the other users and more efficientin the spectrum usage. The fairness of the proposed algo-rithms is measured using Jain’s fairness index (JFI) [26]calculated as

JFI (x1, x2, . . . , xn) =(∑n

i=1 xi)2

n∑n

i=1 x2i, (22)

where n is the number of the SU and xi is the quantity ofresources (i.e., throughput in our case) allocated to eachuser i. The value of JFI varies from 1/n representing poorfairness to 1 representing excellent fairness. Typically, sys-tems with JFI larger than 0.5 are considered to provide agood fairness of the resource distribution.On the basis of the simulated PU and CR network, we

assign frequencies to each of the requesting SUs, using


centralized and distributed FA algorithms under investi-gation. As a benchmark algorithm, we use the centralizedand distributed version of CollaborativeMax Sum Reward(CSUM) algorithm presented in [13], with a difference ofassigning only one frequency per CR. As the performanceof graph coloring depends on the conflict graph topology,we test algorithms on a large number of different networksfor each setup of the input parameters, in order to havenetwork neutral performance results. Each deploymentof the PUs and SUs produces different network topologyand a different corresponding conflict graph. All simula-tions are repeated 500 times with the selected set of inputparameters. In each iteration, the new set of PUs and CRTx-Rx pairs are generated, frequencies are assigned to thePUs, transmit power and throughput are calculated forall SUs, communication and conflict graph is constructedwith corresponding interference weighting and catego-rization. After that, the process of assigning frequencies toall SUs is performed with the proposed algorithms and theexperimental performance of the algorithms is comparedto the benchmark algorithms. The results are averaged toreduce the influence of the network topology or simula-tions variance on the network performance and presentedresults.

8.2 Overall FA algorithms resultsIn this section, we analyze and present the performanceof the FA algorithms in a simulated environment of thePU and CR network. Figure 7 shows the cumulative distri-bution function F(x) of the average interference level andaverage throughput per individual SU for 2000 iterationsof the FA process with the same input parameters.The CR network using centralized interference mini-

mizing algorithm (CminSumInt) for assigning frequenciesresults in the lowest interference with the other concur-rent users but also results in a lower individual throughputreward comparing to other algorithms. Throughput max-imization algorithm (CMaxSumCap), on the other hand,outperforms all other analyzed algorithms taking intoaccount the achieved SU throughput but causes moreinterference with the other users compared to a mini-mum interference algorithm. Figure 7 also shows tradeoffof the average interference level and the average through-put for the proposed algorithms. Using cumulative CRnetwork interference minimization as the objective forFA also results a downturn in the lower level of averagethroughput compared to the algorithm using throughputmaximization as the objective. For example, for the 90 %of the SUs in the network utilizing CminSumInt algo-rithm, the average interference level is below 0.4, while theaverage throughput is higher than 8 Mbit/s. On the otherside, for the 90 % of the SUs in the network using CMax-Cap algorithm, the average interference is below 0.7, andthe average throughput is higher than 10.2 Mbit/s. The

0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.2

0.4

0.6

0.8

1

Average Interference Level

F(x

)

CminSumInt

CMaxSumCap

CSUM

7 8 9 10 11 12 13 140

0.2

0.4

0.6

0.8

1

Average Throughput (Mbit/s)

F(x

)

CminSumInt

CMaxSumCap

CSUM

Fig. 7 Cumulative distribution functions of average interference leveland throughput (NoPU = 25, NoSU = 40,M = 15)

cumulative distribution functions in Fig. 7 show that label-ing and coloring rules have been appropriately selected toachieve the minimal interference and maximal through-put objective. In the analyzed case, the network usingCSUM algorithm have 2.5–3.5 times larger average levelof interference per user compared to the network usingCminsumInt algorithm. Introducing the interference sen-sibility in the proposed FA algorithms with co-channeland adjacent channel interference modeling, edge weightscoefficients, and interference categorization significantlycontribute to the algorithm efficiency related to inter-ference reduction compared to benchmark CSUM algo-rithm, which employs binary interference model.Figure 8 shows the convergence time required by the

centralized and distributed algorithms to perform the FA,depending on the number of the SUs, for a network with25 active PUs and 15 frequencies. As the number of SUsaccessing the FA system increases, the time required toassign the frequencies to all SUs also increases. The con-vergence time for the centralized algorithm grows muchfaster than for the distributed algorithm and also showsa non-linear increase related to the number of SUs. Onthe other side, the distributed algorithm converges muchfaster than the centralized algorithm and shows a lineardependence on the number of SUs. The centralized algo-rithm has the higher complexity, since more iterations are


10 20 30 40 500

5

10

15

20

25

Number of SUs

Con

verg

ence

tim

e (m

s)

Centralized

Distributed

Fig. 8 Convergence time for centralized and distributed algorithm.The figure shows performance metrics of proposed centralized anddistributed algorithm

needed compared to the distributed algorithm. The dis-tributed algorithm performs local optimization involvingadjacent vertices, and the FA process is done in parallelby the several SUs. As a result, differences in convergencetimes between algorithms become more significant whenthe number of the SUs increases. For the network with50 SUs, the distributed algorithm is two times faster thanits centralized counterpart. As we can see from Figs. 11and 12, proposed centralized algorithms outperform dis-tributed algorithms, but the time for calculating the FAscheme for all SUs is much longer. As a result, for biggernetworks having more than hundred of SUs, usage of thecentralized algorithms would become impractical. Due tothe longer convergence time, the SUs would be in a situa-tion of missing some of the spectrum opportunities (e.g.,short temporal spectrum holes). We can conclude that,for the smaller CR networks, or for longer lasting spec-trum opportunities (e.g., TVwhite spaces), the centralizedalgorithm is more suitable. On the other side, distributedalgorithms would be a better choice for the bigger SU net-works and spectrum band with more dynamic changes inthe frequency availability.

8.3 Centralized FA algorithms performanceThe performance of the centralized FA algorithms in theCR networks is presented in Figs. 9 and 10.Figure 9 shows the average throughput per SU, the

average interference per SU, and the throughput fairnessdepending on the number of the frequencies, for the net-work with 25 active PUs, 40 SUs, and other simulationparameters according to Table 4. It can be seen that theaverage throughput per SU steadily increases with theincrease of a number of the available frequencies. CMax-SumCap algorithm reaches maximum throughput per SU,

which is set at 16 Mbit/s with a frequency pool of 23channels. In order to achieve an average throughput of13 Mbit/s per SU, a network with CMaxSumCap algo-rithm uses 16 frequencies, with CSUM algorithm uses18 frequencies and with CminSumInt uses 22 frequencieswhich is 35 % more than the best performing algorithm.The average interference per SU is decreasing with alarger number of the available frequencies, since the samenumber of SUs is distributed in a larger frequency pool,resulting in a lower number of SUs per frequency andtherefore lower mutual interference. If the average mutualinterference per SU is limited to 0.1, the CR network with40 SUs and CminSumInt algorithm can operate with 16frequencies. The network with CMaxSumCap algorithmneeds more than 18 frequencies and network with CSUMalgorithm needs at least 23 frequencies. If the number offrequencies is set to 20, it can be observed that the averageinterference is below 0.05 for CMaxSumCap and Cmin-SumInt algorithms, while it is 0.22 for CSUM algorithm(i.e., 4.5 times larger). This clearly shows the benefits ofthe interference weighting and categorization on the net-work performance. A comparison of throughput fairnessshows that the algorithms have Jain’s fairness index largerthan 0.8, meaning that algorithms provide a good fairnessof network resources. As the number of available frequen-cies increases, fairness also increases. From Fig. 9, weconclude that the SU networks using CMaxSumCap andCSUM algorithms have excellent fairness. The networkusing CminsumInt algorithms has a higher discrepancy inthe SU throughput, but nevertheless, it is still satisfactory.Figure 10 shows the average throughput per SU, the

average interference per SU and the throughput fairnessdepending on the number of SUs in the CR network with25 active PUs, and the available pool of 15 frequencies.The average throughput decreases, and the interferenceincreases with an increasing number of secondary usersin the CR network. Intuitively, when we set the CR net-work area and available frequencies, while the number ofSUs increases, there are more conflicts between SUs, sincethe distance between the interfering SUs is decreasing.Consequently, there is a smaller choice of the available fre-quencies, frequencies are more saturated, the SINR perSU is decreasing, and an average throughput per userdecreases. If an average interference per SU is set to0.2, the CR network with 15 frequencies using CSUMalgorithm can accommodate 22 SUs, the network usingCMaxSumCap algorithm can accommodate 33 SUs, andthe network using CminSumInt algorithm can accommo-date 42 SUs. Therefore, the results show that networkusing CMaxSumCap can accommodate almost two timesmore users than the network using CSUM algorithm. TheCR network with 30 SUs using CminSumInt algorithmhas a very low average interference of 0.03, comparingto 0.14 for the network using CMaxSumCap algorithm


15 20 2510

11

12

13

14

15

16

Number of frequencies

Ave

rage

thro

ughp

ut (

Mbi

t/s)

15 20 250

0.1

0.2

0.3

0.4

0.5

0.6


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rage

inte

rfer

ence

leve

l CminSumInt

CMaxSumCap

CSUM

CminSumInt

CMaxSumCap

CSUM

15 20 250.75

0.8

0.85

0.9

0.95

1


SU

thro

ughp

ut fa

irnes

s (J

FI)

CMaxSumCap

CminSumInt

CSUM

Fig. 9 Centralized FA algorithms’ performance depending on the number of frequencies (NoPU = 25, NoSU = 40,M = 15–25). The figure showsaverage throughput per SU, average interference level per SU, and SU throughput fairness depending on number of frequencies

and 0.37 for the network using CSUM algorithm (i.e.,12 times larger). Due to its greedy nature, fairness of allthree algorithms in Fig. 10 is decreasing with increasingnumber of the SUs accessing the network. CMaxSumCapresults in Jain’s fairness index above 0.9 in whole tun-ing range, while in networks using CminSumInt algorithmfairness is worse due to larger differences in SU’s through-put. Generally, we can conclude that among the studiedalgorithms, the centralized minimum cumulative networkinterference algorithm CminSumInt causes the lowestinterference levels in all investigated scenarios and mostefficiently uses the radio frequency spectrum. The CRnetworks using CminSumInt algorithm have a low harm-ful interference footprint, and therefore, they cause lowinterference pollution of the radio spectrum environment.Having minimized the level of harmful interference tothe SUs and limited interference to the primary network,the largest number of the SUs can be accommodated inthe available radio spectrum space. Therefore, networks

using CminSumInt algorithm provide the most efficientuse of the radio spectrum among the studied algorithms.On the other hand, minimizing interference leads to thegreater differences of the throughput between the SUsas the JFI score is lesser compared to the other studiedalgorithms. Centralized interference sensitive maximumthroughput frequency assignment algorithm CMaxSum-Cap has the highest CR network throughput and excellentfairness among the studied algorithms. Considering that,the CR network using CMaxSumCap algorithm makesthe best self-use of the available radio frequency spec-trum without causing excessive interference to the PUnetwork. Since the CMaxSumCap algorithm is selectingthe frequency with high throughput, causing minimuminterference in the selection phase, it is very efficient infrequency usage. CMaxSumCap algorithm causes moreinterference than CminSumInt algorithm, but it is a well-balanced algorithm, since it distributes throughput morefairly between the users. Both proposed algorithms show

10 20 30 40 500

0.2

0.4

0.6

0.8

1

Number of SUs

Ave

rage

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leve

l CminSumInt

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10 20 30 40 508

10

12

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16

Number of SUs

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rage

thro

ughp

ut (

Mbi

t/s)

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CMaxSumCap

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10 20 30 40 500.7

0.75

0.8

0.85

0.9

0.95

1

Number of SUs

SU

thro

ughp

ut fa

irnes

s (J

FI)

CMaxSumCap

CminSumInt

CSUM

Fig. 10 Centralized FA algorithms’ performance depending on the number of SUs (NoPU = 25, NoSU = 10–50,M = 15). The figure shows averagethroughput per SU, average interference level per SU, and SU throughput fairness depending on the number of SUs


significant reduction of the average interference com-pared to the benchmark binary interference algorithmCSUM. CMaxSumCap algorithm performs better thanthe benchmark algorithm in throughput value, averageinterference, and throughput fairness due to the introduc-tion of a co-channel and an adjacent channel interferencegradation with edge weights and new saturation metricfor dynamic sorting of vertices in the process of frequencyassignment.

8.4 Distributed FA algorithms performanceIn this section, we evaluate the performance of the dis-tributed FA algorithms in the CR networks, as presentedin Figs. 11 and 12. Comparing the distributed algorithmsto their centralized counterparts as a benchmark, dis-tributed algorithms are inferior because they perform alocal optimization only, with the cooperation among theneighboring SUs, while the centralized algorithms tendto objectivize the whole CR network under their control,resulting in an overall better results. However, distributedalgorithms are much faster as shown in Fig. 8, more robustand simpler to implement.Figure 11 shows an average throughput per SU depend-

ing on the number of SUs, the number of frequencies,and the number of PUs for centralized and distributedalgorithms. In the distributed algorithms, the averagethroughput per SU decreases with the increase of thenumber of PUs or SUs, similarly to centralized algorithms.Also, an average throughput per SU increases with a largernumber of available frequencies, due to a lower frequencycongestion. An average SU throughput in the networkof 30 SUs and with 15 frequencies is 14 Mbit/s for dis-tributed CSUM algorithm (D-CSUM), 14.48 Mbit/s forDMaxCap algorithm, and 15 Mbit/s for CMaxSumCapalgorithm. In the environment with 25 active PUs and CRnetwork with 50 SUs, 18 frequencies (17.84) is needed

for CMaxSumCap algorithm, 20 frequencies (19.31) forDMaxCap algorithm, and 21 frequencies (20.95) for D-CSUM algorithm, in case of setting 14Mbit/s for the aver-age throughput. In the CR network with 40 SUs and 19frequencies assigned to 25 PUs, an average throughput forthe CR network using D-CSUM algorithm is 13.1 Mbit/s,for the CR network using DMaxCap is 13.8 Mbit/s andfor the CR network using CMaxSumCap is 14.5 Mbit/s.Comparing an average network throughput per SU, wecan conclude that the distributed algorithm achieves 5 %lower average throughput per user compared to a cen-tralized version of the algorithm with the advantage of afaster algorithm convergence and reduced network com-plexity and communications overhead. The throughputdifference between centralized and distributed algorithmsis not large, but if we sum over a large number ofSUs, the total CR network throughput of the networkwith distributed frequency assignment is lower than theCR network with the centralized frequency assignmentalgorithm.Figure 12 shows an average interference per SU depend-

ing on the number of SUs, the number of frequencies,and the number of PUs for centralized and distributedalgorithms. Having primary network of 25 PUs using 15frequencies, CR network utilizing D-CSUMalgorithm canoperate 23 SUs with an average interference 0.1, CR net-work utilizing DminInt algorithm can handle 40 SUs,and the CR network utilizing CminSumInt algorithm canoperate 47 SUs. The CR network with 50 SUs using adistributed frequency assignment algorithm needs two tothree frequencies more than the CR network using a cen-tralized algorithm, which roughly corresponds to 15 %but significantly less than the SU network using D-CSUMalgorithm. Increasing the number of PUs in the analyzedarea deteriorates the performance of the CR networkbecause the number of available frequencies is reduced

15 20 25 30 35 4011

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10 20 30 40 5011

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Ave

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D−CSUM

Fig. 11 Throughput performance of distributed and centralized FA algorithms (NoPU = 15–40, NoSU = 1–50,M = 15–25). The figure showsaverage throughput per SU depending on the number of SUs, number of frequencies, and number of PUs


15 20 25

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10−1

100


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D−CSUM

15 20 25 30 35 4010

−2

10−1

100

Number of PUs

Ave

rage

inte

rfer

ence

leve

l

CminSumInt

DminInt

D−CSUM

Fig. 12 Interference performance of distributed and centralized FA algorithms (NoPU = 15–40, NoSU = 10–50,M = 15–25). The figure showsaverage interference per SU depending on number of SUs, number of frequencies and number of PUs

due to the fact that SUs cannot operate on the samefrequencies as PUs in the interfering area.From the presented analysis, we can conclude that

the distributed algorithms are less efficient in frequencyassignment compared to their centralized counterparts.On the other hand, the distributed algorithms are sim-pler and easier to implement, since they do not requirean extensive cooperation and communication betweenthe SUs. Taking into account analyzed and presenteddistributed frequency assignment algorithms, we can con-clude that the distributed minimum interference algo-rithm DminInt causes the lowest interference levelsand most efficiently uses the radio frequency spectrumin all investigated distributed scenarios. Considering athroughput performance, distributed interference sensi-tive maximum throughput frequency assignment algo-rithm DMaxCap has the highest CR network throughputand the lowest SUs throughput imbalance among thestudied distributed algorithms.

9 ConclusionsIn this paper, we have formulated and addressed the FAproblem in the CR networks. The FA ensures that theappropriate frequency is selected to satisfy the require-ments of the SUs, while enabling an efficient usage of theradio frequency spectrum. The FA is a crucial functionthat limits the interference between the CR devices andPUs operating in a heterogeneous and dynamic radio envi-ronment. We have treated the FA problem as a graph col-oring problem, while introducing the CR specificity. Wehave introduced the interference susceptibility with a two-layered conflict graph determining the interference poten-tial using co- and adjacent channel edge weights. Theprotection of the PUs is realized with a local dynamicallychanging list of blocked channels in the PUs interference

range. We have proposed the interference characteriza-tion with four categories as an extension to a continuousinterference model. As a generalization of our model, weproposed frequency and bandwidth selection instead ofchannel selection in the FA decision process.We have pre-sented centralized and distributed sequential algorithmsthat can assign channels to the SU communication linksin the CR network with the objective of minimizing net-work interference (CminSumInt, DminInt) and maximiz-ing network throughput (CMaxSumCap, DMaxCap). Thealgorithms use dynamic vertex ordering with CR spe-cific novel saturation metrics, which takes into accountthe frequency limitations due to the PUs activities andinterference potential of the already assigned neighbor-ing SUs determining the degree of freedom in selectingthe frequency. We showed the effectiveness of our algo-rithms in the reducing interference and improving theSU network throughput using the network simulation andperformance evaluation.CminSumInt algorithm minimizes the influence of the

SU to the other PUs and SUs, resulting in 70 % averagereduction of the interference compared to the bench-mark CSUM algorithm. CMaxSumCap maximizes theSU network throughput resulting in 15 % increase ofthe average throughput per SU. CMaxSumCap is a well-balanced algorithm with a good performance in all threeperformance indicators: throughput, fairness, and inter-ference. The CR networks using the FA algorithms withthe interference weighting and categorization can accom-modate almost twice as much CR users compared to thenetworks using algorithms with only binary interferencemodel. Distributed algorithms DminInt and DMaxCapcarrying out local optimization provide benefits compa-rable to a centralized approach. The distributed algo-rithms reduce the computation complexity and have the


faster algorithm convergence and linear increase withthe number of SUs. It is shown that the centralizedalgorithms are more suitable for smaller CR networks,or networks with longer lasting spectrum opportuni-ties, while distributed algorithms are more suitable forthe bigger SU networks and more dynamic spectrumenvironment.We can conclude that the proposed interference weight-

ing and categorization is beneficial to the CR networkperformance, since it is possible to quantify the individ-ual interference components and aggregate interference.This approach results in a significantly reduced mutualinfluence between terminals (2.5–12 times less then withbinary interference model) and more efficient spectrumusage. Based on the proposed interference metric, theresource manager can make more knowledgeable andmore frequency efficient decisions. The downturn of theinterference minimum algorithms is in lower fairness ofthe throughput. This problem is not present in the max-imum capacity algorithms. In future work, the proposedframework can be extended to add a selection of appro-priate frequency band and type of the CR spectrum accessfor multi-band CR operation in heterogeneous environ-ment and to investigate implementation of the fuzzy logicmembership function for the interference categorization.

Competing interestsThe authors declare that they have no competing interests.

AcknowledgementsThe authors would like to thank Dr. Hongjian Sun, the associate editorcoordinating the review of this paper and approving it for publication. Theauthors would also like to express sincere appreciation to the anonymousreviewers and Dr. Ninoslav Majurec from NASA-JPL for their valuablecomments which helped in significantly improving this manuscript.

Author details1HAKOM, Croatian Regulatory Authority for Network Industries, Roberta F.Mihanovica 9, 10000 Zagreb, Croatia. 2Faculty of Electrical Engineering andComputing, University of Zagreb, Unska 3, 10000 Zagreb, Croatia.

Received: 14 July 2015 Accepted: 21 January 2016

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http://dx.doi.org/10.1109/TENCONSpring.2014.6863005

http://dx.doi.org/10.1109/TENCONSpring.2014.6863005

http://dx.doi.org/10.1109/VTCFall.2012.6399054

http://dx.doi.org/10.1007/978-0-387-48945-2_9

http://dx.doi.org/10.1109/IWSSIP.2009.5367794

http://dx.doi.org/10.1109/VETECS.2010.5494044

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