 Research
 Open Access
Cognitive radio frequency assignment with interference weighting and categorization
 Zeljko Tabakovic^{1}Email author and
 Mislav Grgic^{2}
https://doi.org/10.1186/s1363801605361
© Tabakovic and Grgic. 2016
Received: 14 July 2015
Accepted: 21 January 2016
Published: 9 February 2016
Abstract
Cognitive radio is one of the technologies promoting flexible and efficient use of radio frequency spectrum, thus solving spectrum scarcity problem. Frequency assignment is an integral part of the cognitive radio spectrum management and a critical point of success or failure of the cognitive radio concept. In this paper, cognitive radio frequency assignment with a novel interference weighting and categorization is proposed, as an extension of the solution to the graph coloring problem. In our approach, the edge weights quantifying the interference potential are appended to the conflict graph, co and adjacent channel interference are treated, and dynamically changing local lists of blocked frequencies are included. We propose the improved cognitive radio saturation metric for the dynamic vertex ordering and to introduce interference categorization which will reduce the communication overhead. Using the proposed model, resource manager can quantify individual interference components, as well as aggregate interference from multiple users, resulting in more knowledgeable frequency decisions. Generalization of the proposed model is suggested. The suggested generalization consists of the selection of the central frequency and optimal bandwidth to be used, according to the user requirements. We have developed interferencesensitive algorithms for minimizing the interference and maximizing the throughput, both in centralized and distributed implementation. The results show significant reduction of the interference, improved spectrum efficiency, and increase 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 Introduction
The future market demand for the wireless broadband services, internet of things, machine to machine communications, and wireless data offload requires the deployment of the next generation wireless networks, which will need a rapid and a more flexible access to the radio frequency spectrum. Since radio frequencies are a limited natural resource, which cannot be saved for the future use or transferred from underused to overloaded areas, efficient usage of the frequencies has become one of the major concerns of the industry, governments, and scientific research. As a result of these research efforts, many different proposals for better and more efficient usage of the radio frequencies have emerged. One of the promising technologies, which could make a big paradigm shift towards the future wireless networks, is a cognitive radio (CR) technology. CR is introduced in [1, 2] and refers to intelligent radio communications system employing technology that allows the system to obtain knowledge of its operational environment, using technology to learn from the environment and dynamically adjust its operational parameters and protocols [3].
Problem addressed. CR frequency assignment represents the core of the cognitive radio process, since its unique features, along with reconfigurability and learning, make the cognitive radio what it is. The frequency assignment (FA) problem in wireless communications is wellstudied, due to the extensive research of FA in mobile radio networks, wireless mesh networks, broadcasting networks, or in military applications [4–6]. Most of these studies do not consider primarysecondary spectrum sharing nor the dynamic availability of the spectrum due to the presence of primary users. Taking a deeper look into these research approaches, we can deduce that the cognitive radio FA has many unique and specific features, which makes CR unsuitable for transposition of the same FA models and algorithms from other types of wireless networks.

CR has to operate as a secondary service on noninterfering, nonprotection basis, alongside other services using the same frequency band.

CR has to work nonintrusively, has to protect PUs, and vacate the spectrum in case of a PU appearance.

CR FA has to be fast, adaptive and easy to implement and does not necessarily have to provide an optimal FA.

CR FA has to reinitiate and reconverge in cases of the quality degradation due to a dynamic changes in the radio channel or SU and PU activation.

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

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

CR FA has to be flexible, applicable in centralized and distributed manner.

CR FA has to assign frequencies continuously and sequentially when a part of the PUs and SUs are already operating.

CR FA has to be applicable in the heterogeneous wireless environment with the different classes of the dynamic spectrum access, different user requirements, and different protection requirements.

The extension of the CR network conflict graph with:

Introduction of the continuous value edge weights quantifying the potential level of co and adjacent channel interference between SUs

Incorporation of the influence of the adjacent channel interference by introducing an additional layer in the conflict graph


Introduction of the SU interference categorization for interference susceptibility of the FA algorithms, while reducing the communication overhead

The proposal of the spectrum fragments assignment with the identification of the central frequency and optimal bandwidth for the CR transmissions

Introduction of a new saturation metric for a dynamic sorting of the vertices in the process of the sequential FA, taking into consideration the channel limitations due to the PU transmissions as hard constraints and a level of the interference from the adjacent assigned CRs as soft constraints

The proposal and evaluation of the interference sensitive FA algorithms with the objective of:

Minimal total CR network interference

Maximal CR network throughput with consideration of the network interference as a comprehensive metric

In our paper, the condition of not causing harmful interference to the active PUs is a hard constraint, which has to be respected and cannot be violated by any FA plan. This is realized by the list of the blocked channels at each SU. Each SU has its own local list of the blocked channels, which is dynamically changed in time and space as the PUs frequency usage pattern constantly changes. The soft constraints are conditions which can be violated in the FA process if there is no better choice of the channel. The violations of the soft constraints are penalized by the FA algorithm, resulting in the deterioration of the objective function. The objective function takes into consideration the interference among SUs and the throughput achieved by the SU transmissions.
Our work differs from the previous works on the graph coloringbased CR networks FA in several aspects: the level of the interference between the SUs and between the SUs and PUs are numerically quantified using both the continuous and discrete weights; the influence of the cochannel and adjacent channel interference are considered; all individual interference contributions and cumulative interference values are monitored in the course of FA process. Proposed FA algorithms use this unique feature of the numerical quantification of the interference to precisely control and assign frequencies that have minimal interference influence in relation to other users. The advantages of the proposed interference sensitive FA strategy are numerous. It significantly reduces the interference in the CR networks, fully protects the PUs, reduces the frequency reuse distance between the CR users, improves spectrum usage efficiency, and increases the overall networks throughput with the available radio spectrum.
Paper organization. The rest of the paper is organized in the following way. Section 2 presents the overview of the previous research along with the comparison and main differences with respect to our paper. In Section 3, we formulate a CR network FA problem, present the system model and propose a novel framework for the interference sensitive FA in the CR. In Section 4, an interference estimation model used in the algorithm design is elaborated, characterization and categorization of co and adjacent channel interference is introduced, and determination of weighting coefficients is elaborated. We describe the phases of the proposed FA algorithms, saturation metric, and coloring label with the objective of interference minimization and throughput maximization and the transmit power control strategy in Section 5. In Section 6, considerations of the centralized and distributed implementation of the FA algorithms are discussed. In Section 7, generalization to the frequency and bandwidth spectrum assignment are proposed, as well as implementation consideration in practical CR systems. In Section 8, we present an evaluation of the proposed algorithms’ performance in the simulated environment of the PU and CR networks. Finally, we conclude the paper and outline the key results of this paper in Section 9.
2 Related work
Spectrum management is technical, procedural, and policy approach to the planning, coordination, and managing the use of the electromagnetic spectrum as a limited resource. The CR spectrum management functions have some specific capabilities, since the CR networks are focusing on the secondary access and spectrum sharing, while protecting the PUs and minimizing interference with the other SUs. An insightful overview of the spectrum management in the CR networks is presented in [7, 8]. The problem of the FA is commonly solved using different heuristic methods, the graph theory, game theory, or linear programming. In the FA modeled as a the graph coloring problem, the task is to color all the nodes of the graph with the minimum number of colors, in a way that no two adjacent nodes (nodes connected with an edge) have the same color [4–6]. A comprehensive analysis of the frequency assignment in the CR networks can be found in [9, 10].
Summary of FA problem solutions presented in related work
Ref.  Objective  Approach  Method 

[11]  Throughput/  Centralized single ch  Linear integer 
variance  optimization  
[12]  Power/total  Distributed / centralized  Graph theory 
throughput  
[13]  Fairness/throughput  Centralized multi ch  Graph theory 
[14]  Node connectivity/  Local  Heuristic 
interference  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 
So far, all the work done on the CR networks graph coloring FA employed simplistic binary cochannel interference model in order to assign frequencies and optimize utility function [10, 12–14, 16–19]. As we know, the interference control and management are of utmost importance for the spectrum sharing and efficient spectrum management in the CR systems. The CR FA algorithms have to deal with the mutual interference from cochannel or adjacent channel transmissions, which may cause significant performance degradation. Nevertheless, in the existing work, it was not possible to assess, quantify, or compare interference influence of the CR frequency selection on the neighboring SUs, nor to share spectrum between users when the interference exists, but it is bearable. Also, the adjacent channel interference was mainly neglected. To alleviate this deficiency, we propose a novel conflict graph model and algorithms with interference weighting and categorization, which enable interference sensitive frequency decisions, better interference control, and quantitative estimation of the individual components, as well as the calculation of the cumulative interference at the neighboring users. As a result, the proposed FA in the CR is performed with the interference sensitivity, achieving the efficient spectrum utilization, while enabling reliable transmissions.
3 The proposed FA framework

Spectrum sensing. A CR user can only utilize temporary unused parts of the spectrum. Therefore, CR should monitor the available spectrum bands, collect the information on the spectrum use, and identify possible spectrum holes and their characteristics.

Spectrum decision. Based on the spectrum availability information acquired through the spectrum sensing, policy guidelines, user requirements, and registry of the spectrum use, CR characterizes radio frequency spectrum possible for various models of the dynamic spectrum access. In the spectrum decision, CR or the centralized entity determines the carrier frequency, channel bandwidth, transmission power, modulation, coding, communication technology, together with other operational, and technical parameters used for the CR operation.

Dynamic spectrum access (DSA). The CR reconfigures its technical parameters in line with the selected operational technical parameters and operates in order to satisfy its primary goal of successful communication with a required QoS.

Learning. Since CR is operating in heterogeneous radio environment with different user characteristics, different requirements and many parameters determining its environment and performance, CR has to adapt to the constantly changing environment, observe performance of its operation, and has to adapt its spectrum decision function using reinforcement learning.
The process of assigning frequencies to the CR users as part of the spectrum decision step is of crucial importance for the CR network functioning and represents a focal point of the efficient radio spectrum use, distinguishing the CR from other wireless communications systems.
3.1 Problem formulation and system model

CR selfgoal: successfully transmit as much information as possible with required QoS

CR network goal:

Minimizing the total network interference

Maximizing the network throughput


Requirements towards other users: not to cause excessive interference with the operating PUs, to keep the CR mutual interference under the reasonable limit and to efficiently share the radio frequency spectrum
The FA problem in the wireless communications can be modeled as a graphtheoretical problem by defining an undirected conflict graph describing the interference relations and assigning frequencies by coloring vertices. The graph coloring problem is known to be NPcomplete problem [21] and therefore computationally hard. Although any given solution of the NPcomplete problem can be verified in the polynomial time, there is no known efficient way to find the optimal solution. Also, the time required to solve the problem increases very quickly as the size of the problem grows. For example, 3.16 million years are needed to find a solution to the FA problem using brute force search approach for 20 terminals and 10 frequencies with 1 μs per solution [6]. Considering the basic characteristics of the FA in the CR already mentioned, and the computational complexity of finding an optimal solution, we are directing towards the use of the heuristic method for solving this problem. Although the heuristic algorithm leads to a suboptimal solution, it provides a reasonably good solution in the limited time, which works well in the practical applications of the assigning frequencies to the CR SUs.
Let us assume there are five available frequencies represented by numbers, which are opportunistically available to the CR operation. Since the PU and the CR networks share the same radio frequency band, the frequencies temporarily used by PUs cannot be utilized by the CR users if they are in the interference range, and therefore, those channels are blocked for corresponding CR link indicated by the corresponding blocked channels list. For the CR link, B channels {1,2} cannot be used due to the possible interference with the service area of the PU base station a, for the CR link C channels {3,4} are blocked, for the CR link F channels {1,2,4,5} are blocked, etc. The conflict edges represent the potential interference between the CR links with two edge weights per edge indicating cochannel and adjacent channel interference potential. In Fig. 2, the edge between the CR link A and CR link B has weights of 1 for cochannel and 0.1 for the adjacent channel, indicating very high interference potential between those links, and therefore, those links cannot use the same channel. The edge between the CR link C and CR link D has a conflict weight of 0.6/0.05 indicating a medium interference potential and the edge between CR link B and CR link F has a weight of 0.2/0 indicating a low cochannel interference and no adjacent channel interference. This indicates the possibility for sharing the channel. The existence of the conflict graph edges and the corresponding weights depends on the propagation channel characteristics and the antenna discrimination between the CR link pairs analyzed. For example, between the CR link A and CR link E, there is no edge because the terrain obstacle prevents possible interference path and corresponding links can use the same channel without danger of the mutual harmful interference. Practical implementation of constructing conflict graph and determining its weights is elaborated in Section 7.2.
Important notation and acronyms
Notation  Description 
G _{ c }=(V _{c},E _{co},E _{adj})  Conflict graph with vertices V _{c} and edges E _{co},E _{adj} 
F={1,..,M}  Set of M available frequencies 
B _{v}  List of blocked frequencies at CRv due to PU 
hard constraints  
W _{co}={wvi vjco}∈[0,1]  Set of cochannel continuous interference 
weight coefficients  
W _{adj}={wvi vjadj}∈[0,1]  Set of adjacent channel continuous 
interference weight coefficients  
N _{PU},N _{SU}  Number of primary and secondary users 
hPUiPUi ^{′} hPUiSUk ^{′}  Channel coefficients between PU Tx i ^{′}, SU Tx k ^{′}, 
and PU Rx i  
hSUlSUk ^{′} hSUlPUj ^{′}  Channel coefficients between SU Tx k ^{′}, PU Tx j ^{′}, 
and SU Rx l  
P _{Rx_SUl_D},P _{Rx_SUl_I}  Desired received signal strength and interfering 
received signal strength at the l t h SU  
\(P_{\text {Tx}\_\text {PU}m^{\prime }}, P_{\text {Tx}\_\text {SU}l^{\prime }}\phantom {\dot {i}\!}\)  Transmitting power at m ^{′}th PU and l ^{′}th SU 
S _{vi}  Saturation metrics label 
Col_{vi}  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 network 
interference FA algorithm  
CMaxSumCap  Centralized interference sensitive maximum 
throughput FA algorithm  
DminInt  Distributed minimum interference FA algorithm 
DMaxCap  Distributed interference sensitive maximum 
throughput FA algorithm 
3.2 Framework overview
The CR FA task is to assign the frequencies to the SUs when and where they request access to the spectrum, to assign new frequencies to the CR users when co or adjacent channel PU transmission occurs in the interference range, or when the quality of service reduces below the requested threshold. As a result of that, we are facing with the task of assigning frequencies in a partially colored graph. In that respect, the FA is a continuous process, as it is not possible to assign frequencies and optimize coloring to the entire CR network at the same moment. There is a need to constantly assign and reassign frequencies to active SUs. If the PU reactivates, new SU appears, or signal level drops due to dynamic characteristics of the radio channel, the FA process has to be reinitiated and channel allocation has to reconverge for the SUs influenced by these changes.
Based on the system model described in Section 3.1, we have developed a novel framework for assigning the frequencies in the CR environment. In the preparatory step, input data and the CR technical parameters are determined, including available frequencies, compatibility criteria, CR coverage area, and the interference potential. In the second step, the CR adjacency, interference levels, and weights are estimated, followed by communication and the conflict graph construction determining whether the CRs can share radio frequencies. In the CR FA step, an iterative process is performed consisting of labeling and ordering of the CRs, selecting the next transmitter to assign the frequency, and selecting the frequency maximizing network objective.

The local list of the blocked frequencies B _{v} associated with each conflict graph vertex representing frequencies which cannot be used by CR

Two layers of edges in conflict graph taking into consideration cochannel interference E _{co} and adjacent channel interference E _{adj}

Continuous interference weight coefficients w _{co} and w _{adj} associated to the conflict graph cochannel and adjacent channel edges incorporating quantification of possible interference between adjacent vertices corresponding to the interference “strength”

The categorization of the interference weights reducing communication overhead
Since the CR user has to protect and not cause the interference to the licensed PUs, each CR keeps its own list of blocked frequencies and the FA algorithm avoids selecting the channels causing harmful interference to the PUs which are temporarily operating in the close vicinity of the observed CR. As the PUs frequency usage is constantly changing, the list of the blocked channels at the CR is dynamically updated using the spectrum sensing, the geolocation database or some other method of the spectrum awareness. In the proposed approach, the FA is interference sensitive, as the edges have associated cochannel and adjacent channel weights determining the level of the interference between the vertices. In this paper, we are proposing the algorithms which can be categorized under the sequential graph coloring class of algorithms with a saturation degree dynamic vertex ordering. This class of algorithms was first introduced by Brélaz [22] as saturation largest first algorithm known under the name Degree of saturation algorithm (DSATUR). In DSATUR algorithm, the vertices are ordered by a decreasing order of saturation, where the saturation degree is determined as a number of different colors to which a vertex is adjacent. In [13], colorsensitive graph coloring is used where dynamic vertex ordering is determined using labeling based on channel capacity divided by vertex degree and selecting most valuable SU to assign frequencies first (CR link contributing the most to the network throughput).
In our approach, we are also using labeling and dynamic SUs ordering to determine the prioritization of assigning frequencies to the CR users, but with the different saturation metric and network objectives compared to the existing literature on graph coloring FA. We are selecting the most difficult SUs to assign frequencies first using a specially designed CR saturation metric. Proposed novel CR saturation metric is determined as a level of freedom in selecting the frequency for the SU, taking into consideration channel limitations due to local PUs transmissions and a level of interference from adjacent assigned SUs as a combination of hard and soft frequency assignment constraints. The saturation metric is calculated using the interference weight coefficients. In this paper, we are proposing two different FA problem solutions with objective functions determined as minimal total network interference and as maximal throughput with the interference susceptibility.
Taking into account the CR network topology, we are considering centralized FA where centralized resource manager optimizes frequency use on the network or cluster level, and distributed FA where the selection of the frequencies is performed on a level of CR and its neighboring nodes. More detailed algorithm description and the mathematical formulation of the saturation metrics and objective functions are provided in Sections 5 and 6.
4 Interference modeling and characterization
4.1 Interference model
where \(\phantom {\dot {i}\!}X_{\text {PU}i^{\prime }}\) is the signal from PU transmitter i ^{′}, \(X_{\text {SU}l^{\prime }}\phantom {\dot {i}\!}\) is the signal from SU transmitter l ^{′}, hPUiPUi ^{′} denotes the channel coefficient between PU transmitter i ^{′} and PU receiver i, hPUiSUk ^{′} is the channel coefficient between SU transmitter k ^{′} and PU receiver i, hSUlSUl ^{′} is the channel coefficient between SU transmitter l ^{′} and SU receiver l, hSUlPUj ^{′} is the channel coefficient between PU transmitter j ^{′} and SU receiver l, N _{PU} is the number of PUs, and N _{SU} is the number of SUs, as illustrated in the Fig. 3. Z _{PUi } and Z _{SUl } represent additive white Gaussian noise at the PU receiver i and SU receiver l with the variances \(\sigma _{\text {PU}i}^{2}\) and \(\sigma _{\text {SU}l}^{2}\).
where \(\phantom {\dot {i}\!}P_{\text {Tx}\_{\text {PU}}m^{\prime }}\), \(\phantom {\dot {i}\!}P_{\text {Tx}\_{\text {SU}}l^{\prime }}\), and \(\phantom {\dot {i}\!}P_{\text {Tx}\_{\text {SU}}k^{\prime }}\) are PU and SU transmitting powers, and \(\left {h}^{\text {SU}l^{\prime }}_{\text {SU}l} \right ^{2}\phantom {\dot {i}\!}\) and \(\left  {h}^{\text {PU}m^{\prime }}_{\text {SU}l} \right ^{2}\phantom {\dot {i}\!}\) are the wanted and interfering channel gain coefficients. Received interfering power \(\phantom {\dot {i}\!}P_{\text {Rx}\_{\text {SU}}l\_I}\) takes into account the interference received from PUs, interference from other SUs on cochannel, and adjacent channel operating in the interference range of the corresponding SU and the noise. All those interferences add up to the cumulative interference, which reduces quality and reliability of the SU link. Similarly, we can calculate the desired received signal, and interfering received signal at the PU, which is omitted for brevity.
where F(x)=P(hSUlSUk ^{′}^{2}>x) is the complementary cumulative distribution function of SU channel gain hSUlSUk ^{′}^{2}, ε is an error probability of the secondary transmissions, and SINR is the desired signaltointerferenceplusnoise ratio at the SU receiver. If the SU channel gain is below minimal threshold level x, no useful data transmission can be obtained between the SU transmitter and receiver. In Eq. (5), the theoretical relation between SU throughput and an ergodic channel capacity for the fading channel is shown. In the numerical simulation in Section 8, we assume that SU system utilizes Mary quadrature amplitude modulation (MQAM) and we use the approximation (19) for SU throughput. Additionally, in the simulation, we have set up the upper limit of the achievable individual SU throughput in order to avoid unfair spectrum usage between the SUs.
4.2 Weighting coefficients characterization
where w _{co} and w _{adj} are co and adjacent channel interference edge weights, p _{co} and p _{adj} are co and adjacent channel penalties, and w _{ i } is the nominal edge weight.
Co and adjacent channel interference edge weights are the network penalties for violation of the soft FA constraints in the neighboring vertex, resulting in the deterioration of the objective function used for the optimization of the FA process. The channel penalties p _{co} and p _{adj} represent the portion of the CR transmitter power which is absorbed by the CR receiver on the same or adjacent channel. Generally, channel penalty is calculated as the reduction of the interference power caused by the filter shape of the transmitter spectrum density mask and the receiver selectivity mask or it can be measured. As we are analyzing network with a predefined set of frequencies and aligned channel bandwidths, in network simulation in Section 8, we assume that the channel penalties are predefined and have the constant values. The nominal edge weight w _{ i } corresponds to the channel coefficient including propagation loss, antenna gain, and discrimination between the SU Tx and SU Rx under the consideration.
We propose to classify level of the potential interference in four main categories (harmful—high interference; disturbing—mediumhigh interference; annoying—mediumlow interference; permissible—low interference) and assign the corresponding conflict edge weight coefficients w _{ i }∈{0;0.4;0.7;1}. To classify the potential interference in the appropriate category, a value of the potential interference between the SU Tx and Rx is compared with the cumulative probability density function of the average received interference power between the SUs. The cumulative probability density function (cdf) is empirically determined from the previous spectrum sensing measurements in the frequency band under consideration. On the basis of this comparison, it is identified to which category out of four this potential interference belongs and the characteristic value of the nominal edge weight factor is assigned for the identified interference category. Proposed values for the categorization of the nominal edge weights are calculated by evaluating the cdf of the average received interference power between the SUs. Interference cdf is divided into four nonoverlapping areas and a median cumulative probability value for each area is calculated. Channel weights representing each category are calculated as the ceiling round up (rounded off to the higher value) for the edge weight coefficients (0.4;0.7;1) and as floor round up for edge weight coefficient (0). Specific weights for four different categories of the interference are chosen in such way that the possible harmful interference between SUs is emphasized. We have tested proposed algorithms with the variation of the values of discrete interference weights, and the results show similar behavior as the algorithms with a small variation of the nominal network weight coefficients representing four categories.
This novel interference categorization allows the introduction of the susceptibility of the FA protocol to the level of the interference, taking into account the probabilistic nature of the received signal as described above, as well as possible interference estimation errors.
5 Interference sensitive FA algorithms
The proposed FA in the CR networks is based on the efficient heuristic based algorithms that can run reasonably fast and provide a good quality solution. In this paper, nonuniform traffic on the different communication links and frequencies, weighted interference model, and nonorthogonal channels are considered based on the CR networks specifics.
5.1 Algorithm description

Phase 1. FA preparation:

Establish the list of the blocked channels at all SUs.

Determine the SU transmitting power for each available channel at all SUs.

Calculate the SU throughput for each available channel at all SUs.

Establish a conflict graph edges and determine the interference weights for cochannel and adjacent channel transmissions.

Interference categorization.


Phase 2. Selecting the next SU to assign frequency:

Label the nonassigned SUs using specific CR FA saturation metric.

Dynamically order the SUs with decreasing saturation score.

Select the SU with the highest saturation metric to assign frequency as the next SU to process.


Phase 3. Assigning frequency to the selected SU:

Calculate objective function for each available frequency at the selected SU.

Select and assign frequency maximizing objective function at the selected SU.


Phase 4. CR FA performance evaluation and conflict graph update:

Calculate interference, throughput, and throughput variance for all SUs.

Determine the overall network performance and update conflict graph.

The initial SU transmitting power for each available channel at SUs is determined in a way that SU does not cause harmful interference to the closest PU using this channel and that the minimal required SINR at the SU user is achieved. In the following phases, the SU calculated transmitting power per channel is updated using power control ratio parameter. The details of the power control mechanism are described in Section 5.3, while establishing the list of blocked channels, calculation of the conflict graph edge weights, and its categorization are performed as described in Section 4.2.
Summary of proposed FA algorithms
Objective  

Implementation  Minimal interference  Maximal throughput 
Centralized  CminSumInt  CMaxSumCap 
Distributed  DminInt  DMaxCap 
5.2 Saturation metric labeling and coloring
where B _{vi} are blocked frequencies, which cannot be used at the SU vi, E _{co vi vj}, and E _{adj vi vk} are co and adjacent channel edges indicating the interference between the SUs, wvi vjco and wvi vkadj are the conflict edge weights determining the interference potential of the adjacent SUs, x _{vj} and x _{vk} are variables indicating that the adjacent SUs have the frequency assigned. All the vertices are sorted in the decreasing order of the saturation label. The vertex with the largest label is selected for coloring. Saturation metrics score is changing in each iteration step due to the continuous process of the assigning frequencies to the SUs, and therefore, the order of the SUs also dynamically changes. In the assignment phase, the selected SU is colored with a color which contributes the most to the system utility function. Here, we investigate the different algorithms with the objective of the minimal interference and maximal throughput.
5.2.1 Minimum cumulative network interference FA
where α and β are co and adjacent channel cumulative interference at the adjacent vertices. In coloring, the algorithm is selecting the frequency which contributes the least to the cumulative network interference. Having the interference represented by edge weights, the individual interference contributions can be quantified and the level of total network interference can be controlled.
5.2.2 Interference sensitive maximum throughput FA
where C _{ f vi} is the SU throughput at frequency f. The SU throughput is calculated using Eq. (5), and its value can be between 0 and the maximum available throughput per SU. This value is set to 16 Mbit/s in the numerical simulation in Section 8. The coloring is done with the preference given to the frequencies having the highest throughput, while having the minimal influence to the rest of the SU network.
5.3 Transmit power control
The proposed transmit power control strategy is based on the balancing of the SU transmit power level between minimal required to satisfy QoS requirements and maximal permissible level in order to avoid interference with the PUs. In order to minimize the interference to the other concurrent SUs, it is recommended to maintain the transmission power level at a minimum, while ensuring an adequate signal quality at the receiving end. Minimum required transmit power is determined by adjusting the power level until the targeted SINR at the SU receiver is satisfied. Maximum acceptable transmit power is established by considering the permissible interference at the PUs.
A possible implementation of the proposed adaptive transmit power control strategy using fuzzy logic power controller is described in [23].
6 Centralized and distributed algorithm
6.1 Centralized FA algorithm
In each iteration, the centralized algorithm calculates the saturation metrics of all unassigned vertices. In order to detect the most difficult vertex to process first, the vertices are sorted and vertex with the largest saturation metrics is selected. For the selected SU, coloring is performed with the frequency which maximizes the objective function. In CminSumInt algorithm, the frequency is selected on the basis of the minimal interference caused to the adjacent vertices. In CMaxSumCap algorithm, the selected frequency maximizes the comprehensive metric that integrates both interference and throughput. The centralized solution requires an additional communication overhead to collect and distribute information between the vertices. In that respect, the common communication channel and protocol are necessary. Also, the centralized solution is sensitive to the potential failures of the central entity, which can result in the discontinuities of the FA in the CR networks. In the cluster topology, the CR network is subdivided in a number of geographically distinguished clusters. Each cluster uses a different resource manager and an independent algorithm determining the next SU to assign frequency using the saturation metric label and frequency assignment maximizing the network objective.
In order to determine the complexity of the algorithm, it is essential to determine the number of iterations needed for the algorithm to terminate. The number of iterations in the centralized algorithm is bounded by O(N _{SU}), where N _{SU} is the number of the secondary users requesting access to the CR network. Since the single vertex coloring can be completed in O(M) where M is the number of available frequencies, the overall complexity of the proposed centralized algorithm is O(N _{SU} M).
6.2 Distributed FA algorithm
The algorithm initializes and the SU requesting frequency access calculates its own saturation metrics label. Vertex saturation label and set of blocked frequencies are communicated to other adjacent nonassigned vertices requesting access to the same frequency band. In order to avoid transmission collision, contention window for the transmission backoff time is calculated as a random value in the interval [0,window], where the window is calculated as 1/S _{vi}. On the basis of the exchanged information on the local vertex saturation metric, ordering of the vertex coloring is determined. Vertex with a local maximum saturation score is selected first to color, and then it selects a frequency with the maximum contribution to the objective function. Selected frequency is then communicated to the adjacent vertices and the list of assigned frequencies is updated. Subsequently, new saturation labeling is performed and the next vertex to color is determined.
Each iteration of the single vertex coloring can be completed in O(M) where M is the number of the available frequencies. The number of the iterations in the distributed algorithm is bounded by O(Δ), where Δ is a maximum degree of a vertex in the conflict graph. The overall complexity of the proposed distributed algorithm is O(Δ M). The complexity of the distributed algorithm is N _{ SU }/Δ times smaller compared to the centralized algorithm, indicating that the distributed algorithm is simpler and converges faster.
7 Generalizations and implementation
7.1 Central frequency and bandwidth CR spectrum assignment
In the proposed FA, we assume fixed set of the channels with predetermined bandwidth and channel separation. In general, the problem of the FA in the CR networks should include not only the identification of the central frequency but also the optimal bandwidth to be used according to the service requirements of the SUs. Generally, spectrum holes can be of the various bandwidth and frequency separation, and CR devices by definition should be able to use these spectrum opportunities. The question of the assigning spectrum fragments of the different sizes is still an open area in research of the CR FA [10]. In this section, we present the generalization of the proposed model of the FA in order to relax input assumptions of the fixed channel division, to an implementation considering bandwidth and central frequency decision. This generalization is quite useful in the practical deployments of the CR systems.
where \(C_{\text {SUr\_i}}\) and \(C_{\text {SUr\_j}}\) are the requested throughputs of SU i and SU j and B _{free} is the available idle spectrum in the frequency band considered and not currently used by PUs.
where ack_{SUi } is the binary acceptance variable, C _{SUa } is the achievable SU throughput, c _{SINR} is the normalized channel throughput of the SU with observed SINR and C _{SUs_i } is the minimal sustainable throughput. Achievable SU throughput of the SU is calculated using Eq. (5) or by approximation Eq. (19) in case of MQAM.
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 band which can barely satisfy the bandwidth requirements B _{ SUi } of the SU in consideration relating to all unassigned SUs. In MSA algorithm, the SUs are sorted by the bandwidth requirements and the idle spectrum is sorted by the available bandwidth of the spectrum regions. For the bandwidth reservation, the MSA algorithm firstly chooses the SU with the highest bandwidth requirements and try to assign the spectrum region with the least available bandwidth. The reservation continues in the decreasing order of SU’s bandwidth requirements and ascending order of the available spectrum regions, until all users are assigned or there is no available spectrum.
where S _{SUTx} is the Tx signal’s power distribution across the frequency spectrum, S _{SURx} is the SU receiver filter frequency response, f is the frequency, f _{ l } and f _{ h } are lower and higher limits of the frequency band in consideration, and Δ f=f _{Tx0}−f _{Rx0} is the spectrum gap between the SU Tx and Rx center frequency. If Δ f=0, both Tx and Rx are operating at the same central frequency and we are coming to the special case of cochannel penalty.
7.2 Implementation considerations
The CR networks utilizing algorithms with the objective of the minimal total network interference (CminSumInt, DminInt) are more suitable for the user scenarios where there exists a large number of SUs and scarcity of the available frequencies, requiring reliable but not very data demanding communications. The realworld applications of CR networks with this objective function could be the wireless sensor networks, the radiometers in the smart grid networks, the medical body area network devices for monitoring, diagnosing or treating of the patients, the utility companies’ telemetry networks, location services in the search and rescue applications, different machine to machine communications, backup system for the emergency networks, and the military communications in the hostile interference environment. The CR networks using algorithms with the objective of the maximal throughput with the interference susceptibility (CMaxSumCap, DMaxCap) are more appropriate for the capacity oriented applications encompassing different scenarios including internet connectivity, cellular networks, and TV white space applications. The realworld applications could be the cellular networks data offload, realizing femtocells in the cellular networks, the best effort wireless hotspots, the local internet connectivity, the internet of things applications, the public protection and disaster relief networks realizing communication between the emergency respondents and the public safety agencies, and the wireless cameras video transfer.
The FA in the CR is an eventbased functionality and continuously reiterated process. In a given moment in time, frequencies for only part of the active SUs have to be assigned. When the PU appears, all active SUs in the interference range have to move to the new spectrum bands [11]. This event triggers reinitiation of the FA process for multiple 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 deteriorates due to dynamic channel conditions, the SU wants to switch to a better frequency. In those cases, the process of 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 ID and test message on the common communication channel, while all other SUs are temporarily monitoring the channel and receiving. The test message and default transmission parameters of the SU are known to all of the SUs in the same geographic area. By monitoring the received signal strength, each of the SUs can determine its adjacent SU transceivers and categorize the interference potential with the corresponding interference category (harmful, disturbing, annoying, permissible). Accordingly, each SU can construct a local conflict network graph with edges corresponding to all of the received SUs transmissions and associated weighting coefficient proportionate to the received signal strength. In the centralized implementation, these network weights are then communicated to the central spectrum management entity, which constructs the network graph and assigns frequencies. The implementation of the protocol determining network conflict graph and corresponding weights is easy to implement and it can be coded by only 2 bits. Since determining of the conflict graph edges and corresponding weights adds additional communication overhead to the CR communication, it is rational to construct the conflict graph and perform weight determining protocol only when needed. In the case of the stationary SU, the weight determining protocol should be performed at the time of the establishing the network or when some change in the network configuration or propagation parameters occurs, while in the case of moving SUs, the weight determining protocol should be performed more often. This could be determined by a network policy and triggered when the CR terminals determine the increased probability level of dropped or severely disturbed transmissions.
8 Numerical results and discussion
8.1 Simulation setup
Simulation parameters
Parameter  Value 

Area under test  30 km × 30 km 
Number of PUs (N _{PU})  15–40 
Number of SUs (N _{SU})  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 MQAM  M = [4, 16, 32, 64] 
Maximal SU throughput (64 QAM)  16 Mbit/s 
PU network model. In the simulation, we considered the network of the PU base stations, each of them operating on one channel, which has to be protected by all SUs in the corresponding interference range. We have randomly placed a number of PUs in a given area. For simplicity, we assumed that the PUs have a constant Tx power of 43 dBm and omnidirectional antenna radiation pattern. Each one of the PUs is defined as an information source, which can be in two distinctive states: an active state in which PU constantly generates information packets and requests for data transmission or in a passive state in which PU is not active as an information source. The PU entity is modeled as a two state Markov birthdeath process with birth rate α and death rate β. Since each user arrival is independent, transition follows the Poisson arrival process.
where \({d}^{\text {SU}i}_{\text {SU}j}\) is the distance between SUi and SUj, d _{ST} is the SU transmission range, d _{SI} is the SU interference range, p _{co} is the cochannel penalty set to 1, p _{adj} is the adjacent channel penalty set to 0.1. Interference is classified in four categories as described in Section 4.2.

Average throughput per SU (Mbit/s): the ratio of the cumulative CR network throughput over the number of active SUs

Average interference per SU: the ratio of the cumulative interference of all interference sources over the number of active SUs

SU throughput fairness: Jain’s fairness index as a measure of the throughput distribution of all of the active SUs in the CR network
where n is the number of the SU and x _{ i } is the quantity of resources (i.e., throughput in our case) allocated to each user i. The value of JFI varies from 1/n representing poor fairness to 1 representing excellent fairness. Typically, systems with JFI larger than 0.5 are considered to provide a good 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 investigation. As a benchmark algorithm, we use the centralized and distributed version of Collaborative Max Sum Reward (CSUM) algorithm presented in [13], with a difference of assigning only one frequency per CR. As the performance of graph coloring depends on the conflict graph topology, we test algorithms on a large number of different networks for each setup of the input parameters, in order to have network neutral performance results. Each deployment of the PUs and SUs produces different network topology and a different corresponding conflict graph. All simulations are repeated 500 times with the selected set of input parameters. In each iteration, the new set of PUs and CR TxRx pairs are generated, frequencies are assigned to the PUs, transmit power and throughput are calculated for all SUs, communication and conflict graph is constructed with corresponding interference weighting and categorization. After that, the process of assigning frequencies to all SUs is performed with the proposed algorithms and the experimental performance of the algorithms is compared to the benchmark algorithms. The results are averaged to reduce the influence of the network topology or simulations variance on the network performance and presented results.
8.2 Overall FA algorithms results
The CR network using centralized interference minimizing algorithm (CminSumInt) for assigning frequencies results in the lowest interference with the other concurrent users but also results in a lower individual throughput reward comparing to other algorithms. Throughput maximization algorithm (CMaxSumCap), on the other hand, outperforms all other analyzed algorithms taking into account the achieved SU throughput but causes more interference with the other users compared to a minimum interference algorithm. Figure 7 also shows tradeoff of the average interference level and the average throughput for the proposed algorithms. Using cumulative CR network interference minimization as the objective for FA also results a downturn in the lower level of average throughput compared to the algorithm using throughput maximization as the objective. For example, for the 90 % of the SUs in the network utilizing CminSumInt algorithm, the average interference level is below 0.4, while the average throughput is higher than 8 Mbit/s. On the other side, for the 90 % of the SUs in the network using CMaxCap algorithm, the average interference is below 0.7, and the average throughput is higher than 10.2 Mbit/s. The cumulative distribution functions in Fig. 7 show that labeling and coloring rules have been appropriately selected to achieve the minimal interference and maximal throughput objective. In the analyzed case, the network using CSUM algorithm have 2.5–3.5 times larger average level of interference per user compared to the network using CminsumInt algorithm. Introducing the interference sensibility in the proposed FA algorithms with cochannel and adjacent channel interference modeling, edge weights coefficients, and interference categorization significantly contribute to the algorithm efficiency related to interference reduction compared to benchmark CSUM algorithm, which employs binary interference model.
8.3 Centralized FA algorithms performance
Figure 9 shows the average throughput per SU, the average interference per SU, and the throughput fairness depending on the number of the frequencies, for the network with 25 active PUs, 40 SUs, and other simulation parameters according to Table 4. It can be seen that the average throughput per SU steadily increases with the increase of a number of the available frequencies. CMaxSumCap algorithm reaches maximum throughput per SU, which is set at 16 Mbit/s with a frequency pool of 23 channels. In order to achieve an average throughput of 13 Mbit/s per SU, a network with CMaxSumCap algorithm uses 16 frequencies, with CSUM algorithm uses 18 frequencies and with CminSumInt uses 22 frequencies which is 35 % more than the best performing algorithm. The average interference per SU is decreasing with a larger number of the available frequencies, since the same number of SUs is distributed in a larger frequency pool, resulting in a lower number of SUs per frequency and therefore lower mutual interference. If the average mutual interference per SU is limited to 0.1, the CR network with 40 SUs and CminSumInt algorithm can operate with 16 frequencies. The network with CMaxSumCap algorithm needs more than 18 frequencies and network with CSUM algorithm needs at least 23 frequencies. If the number of frequencies is set to 20, it can be observed that the average interference is below 0.05 for CMaxSumCap and CminSumInt algorithms, while it is 0.22 for CSUM algorithm (i.e., 4.5 times larger). This clearly shows the benefits of the interference weighting and categorization on the network performance. A comparison of throughput fairness shows that the algorithms have Jain’s fairness index larger than 0.8, meaning that algorithms provide a good fairness of network resources. As the number of available frequencies increases, fairness also increases. From Fig. 9, we conclude that the SU networks using CMaxSumCap and CSUM algorithms have excellent fairness. The network using CminsumInt algorithms has a higher discrepancy in the SU throughput, but nevertheless, it is still satisfactory.
Figure 10 shows the average throughput per SU, the average interference per SU and the throughput fairness depending on the number of SUs in the CR network with 25 active PUs, and the available pool of 15 frequencies. The average throughput decreases, and the interference increases with an increasing number of secondary users in the CR network. Intuitively, when we set the CR network area and available frequencies, while the number of SUs increases, there are more conflicts between SUs, since the distance between the interfering SUs is decreasing. Consequently, there is a smaller choice of the available frequencies, frequencies are more saturated, the SINR per SU is decreasing, and an average throughput per user decreases. If an average interference per SU is set to 0.2, the CR network with 15 frequencies using CSUM algorithm can accommodate 22 SUs, the network using CMaxSumCap algorithm can accommodate 33 SUs, and the network using CminSumInt algorithm can accommodate 42 SUs. Therefore, the results show that network using CMaxSumCap can accommodate almost two times more users than the network using CSUM algorithm. The CR network with 30 SUs using CminSumInt algorithm has a very low average interference of 0.03, comparing to 0.14 for the network using CMaxSumCap algorithm and 0.37 for the network using CSUM algorithm (i.e., 12 times larger). Due to its greedy nature, fairness of all three algorithms in Fig. 10 is decreasing with increasing number of the SUs accessing the network. CMaxSumCap results in Jain’s fairness index above 0.9 in whole tuning range, while in networks using CminSumInt algorithm fairness is worse due to larger differences in SU’s throughput. Generally, we can conclude that among the studied algorithms, the centralized minimum cumulative network interference algorithm CminSumInt causes the lowest interference levels in all investigated scenarios and most efficiently uses the radio frequency spectrum. The CR networks using CminSumInt algorithm have a low harmful interference footprint, and therefore, they cause low interference pollution of the radio spectrum environment. Having minimized the level of harmful interference to the SUs and limited interference to the primary network, the largest number of the SUs can be accommodated in the available radio spectrum space. Therefore, networks using CminSumInt algorithm provide the most efficient use of the radio spectrum among the studied algorithms. On the other hand, minimizing interference leads to the greater differences of the throughput between the SUs as the JFI score is lesser compared to the other studied algorithms. Centralized interference sensitive maximum throughput frequency assignment algorithm CMaxSumCap has the highest CR network throughput and excellent fairness among the studied algorithms. Considering that, the CR network using CMaxSumCap algorithm makes the best selfuse of the available radio frequency spectrum without causing excessive interference to the PU network. Since the CMaxSumCap algorithm is selecting the frequency with high throughput, causing minimum interference in the selection phase, it is very efficient in frequency usage. CMaxSumCap algorithm causes more interference than CminSumInt algorithm, but it is a wellbalanced algorithm, since it distributes throughput more fairly between the users. Both proposed algorithms show significant reduction of the average interference compared to the benchmark binary interference algorithm CSUM. CMaxSumCap algorithm performs better than the benchmark algorithm in throughput value, average interference, and throughput fairness due to the introduction of a cochannel and an adjacent channel interference gradation with edge weights and new saturation metric for dynamic sorting of vertices in the process of frequency assignment.
8.4 Distributed FA algorithms performance
In this section, we evaluate the performance of the distributed FA algorithms in the CR networks, as presented in Figs. 11 and 12. Comparing the distributed algorithms to their centralized counterparts as a benchmark, distributed algorithms are inferior because they perform a local optimization only, with the cooperation among the neighboring SUs, while the centralized algorithms tend to objectivize the whole CR network under their control, resulting in an overall better results. However, distributed algorithms are much faster as shown in Fig. 8, more robust and simpler to implement.
Figure 11 shows an average throughput per SU depending on the number of SUs, the number of frequencies, and the number of PUs for centralized and distributed algorithms. In the distributed algorithms, the average throughput per SU decreases with the increase of the number of PUs or SUs, similarly to centralized algorithms. Also, an average throughput per SU increases with a larger number of available frequencies, due to a lower frequency congestion. An average SU throughput in the network of 30 SUs and with 15 frequencies is 14 Mbit/s for distributed CSUM algorithm (DCSUM), 14.48 Mbit/s for DMaxCap algorithm, and 15 Mbit/s for CMaxSumCap algorithm. In the environment with 25 active PUs and CR network with 50 SUs, 18 frequencies (17.84) is needed for CMaxSumCap algorithm, 20 frequencies (19.31) for DMaxCap algorithm, and 21 frequencies (20.95) for DCSUM algorithm, in case of setting 14 Mbit/s for the average throughput. In the CR network with 40 SUs and 19 frequencies assigned to 25 PUs, an average throughput for the CR network using DCSUM algorithm is 13.1 Mbit/s, for the CR network using DMaxCap is 13.8 Mbit/s and for the CR network using CMaxSumCap is 14.5 Mbit/s. Comparing an average network throughput per SU, we can conclude that the distributed algorithm achieves 5 % lower average throughput per user compared to a centralized version of the algorithm with the advantage of a faster algorithm convergence and reduced network complexity and communications overhead. The throughput difference between centralized and distributed algorithms is not large, but if we sum over a large number of SUs, the total CR network throughput of the network with distributed frequency assignment is lower than the CR network with the centralized frequency assignment algorithm.
Figure 12 shows an average interference per SU depending on the number of SUs, the number of frequencies, and the number of PUs for centralized and distributed algorithms. Having primary network of 25 PUs using 15 frequencies, CR network utilizing DCSUM algorithm can operate 23 SUs with an average interference 0.1, CR network utilizing DminInt algorithm can handle 40 SUs, and the CR network utilizing CminSumInt algorithm can operate 47 SUs. The CR network with 50 SUs using a distributed frequency assignment algorithm needs two to three frequencies more than the CR network using a centralized algorithm, which roughly corresponds to 15 % but significantly less than the SU network using DCSUM algorithm. Increasing the number of PUs in the analyzed area deteriorates the performance of the CR network because the number of available frequencies is reduced due to the fact that SUs cannot operate on the same frequencies as PUs in the interfering area.
From the presented analysis, we can conclude that the distributed algorithms are less efficient in frequency assignment compared to their centralized counterparts. On the other hand, the distributed algorithms are simpler and easier to implement, since they do not require an extensive cooperation and communication between the SUs. Taking into account analyzed and presented distributed frequency assignment algorithms, we can conclude that the distributed minimum interference algorithm DminInt causes the lowest interference levels and most efficiently uses the radio frequency spectrum in all investigated distributed scenarios. Considering a throughput performance, distributed interference sensitive maximum throughput frequency assignment algorithm DMaxCap has the highest CR network throughput and the lowest SUs throughput imbalance among the studied distributed algorithms.
9 Conclusions
In this paper, we have formulated and addressed the FA problem in the CR networks. The FA ensures that the appropriate frequency is selected to satisfy the requirements of the SUs, while enabling an efficient usage of the radio frequency spectrum. The FA is a crucial function that limits the interference between the CR devices and PUs operating in a heterogeneous and dynamic radio environment. We have treated the FA problem as a graph coloring problem, while introducing the CR specificity. We have introduced the interference susceptibility with a twolayered conflict graph determining the interference potential using co and adjacent channel edge weights. The protection of the PUs is realized with a local dynamically changing list of blocked channels in the PUs interference range. We have proposed the interference characterization with four categories as an extension to a continuous interference model. As a generalization of our model, we proposed frequency and bandwidth selection instead of channel selection in the FA decision process. We have presented centralized and distributed sequential algorithms that can assign channels to the SU communication links in the CR network with the objective of minimizing network interference (CminSumInt, DminInt) and maximizing network throughput (CMaxSumCap, DMaxCap). The algorithms use dynamic vertex ordering with CR specific novel saturation metrics, which takes into account the frequency limitations due to the PUs activities and interference potential of the already assigned neighboring SUs determining the degree of freedom in selecting the frequency. We showed the effectiveness of our algorithms in the reducing interference and improving the SU network throughput using the network simulation and performance evaluation.
CminSumInt algorithm minimizes the influence of the SU to the other PUs and SUs, resulting in 70 % average reduction of the interference compared to the benchmark CSUM algorithm. CMaxSumCap maximizes the SU network throughput resulting in 15 % increase of the average throughput per SU. CMaxSumCap is a wellbalanced algorithm with a good performance in all three performance indicators: throughput, fairness, and interference. The CR networks using the FA algorithms with the interference weighting and categorization can accommodate almost twice as much CR users compared to the networks using algorithms with only binary interference model. Distributed algorithms DminInt and DMaxCap carrying out local optimization provide benefits comparable to a centralized approach. The distributed algorithms reduce the computation complexity and have the faster algorithm convergence and linear increase with the number of SUs. It is shown that the centralized algorithms are more suitable for smaller CR networks, or networks with longer lasting spectrum opportunities, while distributed algorithms are more suitable for the bigger SU networks and more dynamic spectrum environment.
We can conclude that the proposed interference weighting and categorization is beneficial to the CR network performance, since it is possible to quantify the individual interference components and aggregate interference. This approach results in a significantly reduced mutual influence between terminals (2.5–12 times less then with binary interference model) and more efficient spectrum usage. Based on the proposed interference metric, the resource manager can make more knowledgeable and more frequency efficient decisions. The downturn of the interference minimum algorithms is in lower fairness of the throughput. This problem is not present in the maximum capacity algorithms. In future work, the proposed framework can be extended to add a selection of appropriate frequency band and type of the CR spectrum access for multiband CR operation in heterogeneous environment and to investigate implementation of the fuzzy logic membership function for the interference categorization.
Declarations
Acknowledgements
The authors would like to thank Dr. Hongjian Sun, the associate editor coordinating the review of this paper and approving it for publication. The authors would also like to express sincere appreciation to the anonymous reviewers and Dr. Ninoslav Majurec from NASAJPL for their valuable comments which helped in significantly improving this manuscript.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
 J Mitola, GQ Maguire Jr, Cognitive radio: making software radios more personal. Pers. Commun. IEEE. 6(4), 13–18 (1999).View ArticleGoogle Scholar
 J Mitola, Cognitive Radio—An Integrated Agent Architecture for Software Defined Radio. PhD dissertation, Royal Institute of Technology (KTH) (2000).Google Scholar
 S Haykin, Cognitive radio: brainempowered wireless communications. Sel. Areas Commun. IEEE J. 23(2), 201–220 (2005).View ArticleGoogle Scholar
 R Murphey, in Encyclopedia of Optimization. vol. 1, 2nd ed., ed. by CA Floudas, PM Pardalos. Frequency assignment problem (Springer Science & Business MediaNew York, 2008), pp. 1097–1101. ISBN: 9780387747606.Google Scholar
 KI Aardal, SP Van Hoesel, AM Koster, C Mannino, A Sassano, Models and solution techniques for frequency assignment problems. Ann. Oper. Res. 153(1), 79–129 (2007).View ArticleMathSciNetMATHGoogle Scholar
 R Beutler, Frequency assignment and network planning for digital terrestrial broadcasting systems (Springer Science & Business Media, New York, 2004). ISBN: 9781402078729.Google Scholar
 IF Akyildiz, WY Lee, MC Vuran, S Mohanty, A survey on spectrum management in cognitive radio networks. Commun. Magazine, IEEE. 46(4), 40–48 (2008).View ArticleGoogle Scholar
 G Salami, O Durowoju, A Attar, O Holland, R Tafazolli, H Aghvami, A comparison between the centralized and distributed approaches for spectrum management. Commun. Surv. Tutorials, IEEE. 13(2), 274–290 (2011).View ArticleGoogle Scholar
 R Zhang, YC Liang, S Cui, Dynamic resource allocation in cognitive radio networks. Signal Proc. Mag. IEEE. 27(3), 102–114 (2010).View ArticleMathSciNetGoogle Scholar
 EZ Tragos, S Zeadally, AG Fragkiadakis, VA Siris, Spectrum assignment in cognitive radio networks: a comprehensive survey. Commun. Surv. Tutorials, IEEE. 15(3), 1108–1135 (2013).View ArticleGoogle Scholar
 WY Lee, IF Akyldiz, A spectrum decision framework for cognitive radio networks. Mobile Comput. IEEE Trans. 10(2), 161–174 (2011).View ArticleGoogle Scholar
 AT Hoang, YC Liang, MH Islam, Power control and channel allocation in cognitive radio networks with primary users’ cooperation. Mobile Comput. IEEE Trans. 9(3), 348–360 (2010).View ArticleGoogle Scholar
 C Peng, H Zheng, BY Zhao, Utilization and fairness in spectrum assignment for opportunistic spectrum access. Mobile Netw. Appl. 11(4), 555–576 (2006).View ArticleGoogle Scholar
 J Wu, Y Dai, Y Zhao, Effective channel assignments in cognitive radio networks. Comput. Commun. 36(4), 411–420 (2013).View ArticleGoogle Scholar
 H Xu, B Li, Resource allocation with flexible channel cooperation in cognitive radio networks. Mobile Comput. IEEE Trans. 12(5), 957–970 (2013).View ArticleGoogle Scholar
 M Vishram, LC Tong, C Syin, in Region 10 Symposium, 2014 IEEE. List multicoloring based fair channel allocation policy for self coexistence in cognitive radio networks with QoS provisioning (IEEEKuala Lumpur, 2014), pp. 99–104. ISBN: 9781479920280. doi:http://dx.doi.org/10.1109/TENCONSpring.2014.6863005.Google Scholar
 S Anand, S Sengupta, R Chandramouli, MAximum SPECTrum packing: a distributed opportunistic channel acquisition mechanism in dynamic spectrum access networks. IET commun. 6(8), 872–882 (2012).View ArticleMathSciNetMATHGoogle Scholar
 P Hu, J Ye, F Zhang, S Deng, C Wang, W Wang, in Vehicular Technology Conference (VTC Fall), 2012 IEEE. Downlink resource management based on crosscognition and graph coloring in cognitive radio femtocell networks (IEEEQuebec City, 2012), pp. 1–5. ISBN: 9781467318808. doi:http://dx.doi.org/10.1109/VTCFall.2012.6399054.Google Scholar
 AP Subramanian, H Gupta, SR Das, J Cao, Minimum interference channel assignment in multiradio wireless mesh networks. Mobile Comput. IEEE Trans. 7(12), 1459–1473 (2008).View ArticleGoogle Scholar
 N Nie, C Comaniciu, P Agrawal, in Wireless Communications. A game theoretic approach to interference management in cognitive networks (Springer Science & Business MediaNew York, 2007), pp. 199–219. ISBN: 9780387372693. doi:http://dx.doi.org/10.1007/9780387489452_9.View ArticleGoogle Scholar
 RM Karp, in Complexity of computer computations. vol. 1, 1st ed, ed. by RE Miller, JW Thatcher. Reducibility among combinatorial problems (Plenum PressNew York, 1972), pp. 85–103.View ArticleGoogle Scholar
 D Brélaz, New methods to color the vertices of a graph. Commun. ACM. 22(4), 251–256 (1979).View ArticleMATHGoogle Scholar
 Z Tabakovic, S Grgic, M Grgic, in Systems, Signals and Image Processing, 2009. IWSSIP 2009. 16th international conference on. Fuzzy logic power control in cognitive radio (IEEEChalkida, 2009), pp. 1–5. ISBN: 9781424445301. doi:http://dx.doi.org/10.1109/IWSSIP.2009.5367794.View ArticleGoogle Scholar
 F Huang, W Wang, H Luo, G Yu, Z Zhang, in Vehicular technology conference (VTC 2010Spring), 2010 IEEE 71st. Predictionbased spectrum aggregation with hardware limitation in cognitive radio networks (IEEETaipei, 2010), pp. 1–5. ISBN:9781424425181. doi:http://dx.doi.org/10.1109/VETECS.2010.5494044.Google Scholar
 ST Chung, AJ Goldsmith, Degrees of freedom in adaptive modulation: a unified view. Commun. IEEE Trans. 49(9), 1561–1571 (2001).View ArticleMATHGoogle Scholar
 R Jain, DM Chiu, WR Hawe, A quantitative measure of fairness and discrimination for resource allocation in shared computer system (Digital Equipment Corporation, Hudson, 1984).Google Scholar