# Reducing Spectrum Handoffs and Energy Switching Consumption of MADM-Based Decisions in Cognitive Radio Networks

Authors: Rafael Aguilar-Gonzalez; Marco Cardenas-Juarez; Ulises Pineda-Rico; Armando Arce; Matti Latva-aho; Enrique Stevens-Navarro
Journal: Mobile Information Systems
 (2016)

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## Abstract

In a cognitive radio network (CRN), the number of spectrum handoffs increases energy consumption of cognitive (or secondary) users due to the channel switching process. This might limit the operation of the CRN, especially in scenarios where secondary users terminals are battery-powered. Thus, reducing the number of times a cognitive user involved in a transmission switch to different spectrum holes is required to increase battery life-time. In this regard, available spectrum holes possess different attributes (e.g., bandwidth) that can be exploited to satisfy specific secondary users requirements (i.e., connection profile) for data transmission while saving energy. Here, three multiple attribute decision-making (MADM) algorithms for the spectrum decision functionality are evaluated using real spectrum measurements of TV bands. This is performed by proposing six decision parameters, which are extracted from the spectrum data to characterize its suitability. Then, these are used as inputs of the MADM algorithms to select the most suitable spectrum hole for a cognitive user. Thus, an enhanced MADM-based decision process is proposed to reduce the number of handoffs considering energy consumption due to channel switching (ECCS). Results quantify savings from 30% to 90% in ECCS and spectrum handoffs reductions from 47% to 90%.


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## Body

## 1. Introduction

Cognitive radio networks (CRNs) are envisioned to cope with the spectrum scarcity problem of future wireless networks [1, 2]. Moreover, recent trends have shown the need for developing novel energy-efficient cognitive functions and abilities to enable green CRNs [3, 4]. Among the main functions of a Cognitive Radio (CR) device, spectrum sensing and spectrum decision play key roles at supporting the envisioned opportunistic spectrum access. In such scenario, by performing the spectrum sensing function, an unlicensed user with a CR device or secondary user (SU) must sense first the surrounding radiofrequency (RF) environment to determine unused portions of the spectrum (i.e., spectrum holes) from licensed spectrum users or primary users (PUs). Then, through the spectrum decision function, the CR device should select the best spectrum hole for its opportunistic transmission either by itself or assisted by the network.Once a hole is selected, a spectrum handoff shall be executed. Hence, the RF front-end of the CR device requires several energy-consuming reconfiguration procedures to be able to transmit in the selected frequency. Indeed, this is known in the literature as the energy consumption due to channel switching (ECCS) [5]. Additionally, other problems may arise if the spectrum decision algorithm tends to select different spectrum holes very frequently; for example, the unwanted ping-pong effect may appear thus affecting SUs connection quality [6, 7]. Therefore, an adequate spectrum decision should take into account the intrinsic tradeoff among handoff execution and its related energy consumption.Selecting the best frequency band for a given transmission requires making preference decisions over the set of available alternatives of spectrum holes, which are indeed characterized by different attributes. Therefore, spectrum decision can be modeled as a multiple attribute decision-making (MADM) problem [8]. MADM algorithms have been previously utilized for network selection in the context of heterogeneous wireless networks [9–11]. Moreover, these algorithms have been also considered for the spectrum decision function in CRNs. Results on this matter have been presented in [12], where an Analytical Hierarchy Process (AHP) was utilized to select available frequency bands in CRNs. Furthermore, in earlier stages of this investigation [13, 14], we evaluated the performance of three MADM decision algorithms: Simple Additive Weighting (SAW), Technique for Order Preferences by Similarity to Ideal Solution (TOPSIS), and the Compromise Ranking Method VIKOR using real spectrum occupancy measurements in a practical scenario.In this paper, we propose an Enhanced MADM-based Spectrum Decision (EMSD) functionality for CRNs. In this regard, available spectrum holes possess different attributes (e.g., bandwidth size, occupancy, and central frequency) that can be taken into account for the spectrum decision. Also, the selected spectrum holes shall satisfy specific secondary users requirements (i.e., connection profile) for data transmission while trading off energy consumption. Here, the above-mentioned MADM algorithms for the spectrum decision functionality are evaluated using real spectrum usage information of TV bands. This is performed by considering six decision parameters, which are extracted from the spectrum data to characterize its suitability. Then, these are used as inputs of the MADM algorithms to select the most suitable spectrum hole for a cognitive user while reducing the number of spectrum handoffs considering ECCS.This paper is organized as follows. Section2 describes the system model as well as the six decision parameters considered. The MADM algorithms are presented in Section 3. Section 4 introduces the EMSD functionality. Results are shown and discussed in Section 5. Finally, Section 6 concludes this paper.


## 2. System Model for Spectrum Decision

Let us consider a wireless networking scenario consisting of a primary centralized network coexisting with a secondary centralized network implementing CR techniques in the same geographical area as shown in Figure1. Thus, SUs follow a network-assisted spectrum decision and hence a network-assisted spectrum handoff approach. The SUs execute power spectrum measurements periodically. The secondary base station (SBS) concentrates the two main data types generated by SUs: power spectrum measurements and connection profile. A set of prestored connection profiles are assumed and they can be selected by the SUs based on its connection QoS requirements. For example, for a data intensive connection requirement, a specific bandwidth-oriented connection profile is selected to match such requirements. Thus, the connection profile aims to match the connection requirements to the spectrum decision process. SUs and SBS are connected through a dedicated control channel. All the obtained information is sent back to the network, where it is processed in the proposed Enhanced MADM-based Spectrum Decision (EMSD) function and sent back to the SBS, which delivers the results to each SU spectrum decision. The system model proposed can be implemented by means of specific purposes equipment at the SBS or implemented in cutting-edge network technologies such as cloud cognitive networks [15–17].Figure 1
System model for the EMSD functionality.The spectrum decision process begins with the feeding of the EMSD function with corresponding spectrum measurements (i.e., samples of the spectrum power) and connection profile according to QoS requirements. Internally, the EMSD function computes six decision parameters to describe each spectrum hole available. Thus, the spectrum decision is formulated as a MADM problem with several alternatives (i.e., spectrum holes) and each one is described by a set of decision parameters (e.g., bandwidth size). Then, the MADM algorithms use this information and select the best spectrum hole. Finally, the decision is traded off for the energy consumption required to execute the spectrum handoff.


### 2.1. Decision Parameters

To start the spectrum decision process, the available spectrum holes have to be identified. Then, for each spectrum hole a set of parameters describing its features or characteristics have to be calculated. Thus, spectrum usage information is required to both identify the holes and calculate its features. Within the EMSD function, the information coming from spectrum usage is processed to characterize each spectrum hole. In a real system this process should be done according to PU activity and also based on SU connection requirements. Each time a connection requirement occurs, a spectrum decision should be executed to satisfy SU connection requirements. Once the connection is established in a specific spectrum hole, then periodic spectrum decisions have to be considered based on the availability of the current spectrum hole, connection requirements, and trading off energy consumption due to frequent spectrum handoffs (i.e., ping-pong effect). However, to increase the certainty of the exact moment for making a spectrum decision, sensing and statistical information need to be combined [18]. Finally, it is worth mentioning that the spectrum measurements can be affected by the presence of hidden nodes transmissions. To overcome this issue, a cooperative spectrum sensing approach has to be considered. For example, data fusion centers may be deployed in the SBSs to help overcome these scenarios as proposed in [19]. However, for the scope of this manuscript the cooperative spectrum sensing scenario is not considered.In this work, for each spectrum decision interval, a specific number of spectrum samples are obtained from spectrum measurements executed periodically in the SU terminal. This spectrum information is assigned into a matrix calledinterval decisionIDn, with n=1,…,N, and where N is the total number of consecutive spectrum decisions. The IDn matrix is expressed in (1). Thereby, every time a spectrum decision is made, the total number of spectrum samples analyzed during the decision interval is S, with s=1,…,S, and the total number of resolution points is P corresponding to the examined frequencies, with p=1,…,P. Here, it is important to mention the existence of the auxiliary vector fv that has the frequency value of each p resolution point and that is used as identifier. Thus, ids,p is any IDn element that has a sample of the spectral power in a frequency point:(1)IDn=ids,pS×P.It is worth mentioning that the spectrum sensing capabilities are in fact limited by the SU hardware capabilities which may vary from device to device. We assume that homogeneous CR devices are used in our scenario. This assumption may be valid for early deployments of CRNs. However, as these networks grow in deployments and in number of users, the homogeneity among CR devices will not be valid. Also, in case of missing frequency samples, the system may be delayed to obtain more samples or previous samples available may be used temporarily. In both cases, the accuracy of the spectrum sensing may be affected. Finally, once the available spectrum holes are found, for characterizing each one, six decision parameters are calculated with the information contained into each decision matrix intervalIDn. In the following sub-subsections, we describe how and why each of the decision parameters is calculated.


#### 2.1.1. Duty Cycle(dcn)

A fundamental parameter to establish the spectral occupation from spectrum measurements is theduty cycle (DC). The DC is the percentage of time in which a signal power is above a threshold. Through the method of the energy detector, it is possible to know the DC for each frequency band (i.e., channel). It requires the energy threshold γ, which must be carefully selected to avoid estimation errors in the state of a channel. In the present work, the m-dB criterion is used to set the decision threshold value [20]. Thus, we set the threshold value 10 dBm over the noise floor according to the methodology suggestions made in [20, 21] and by the International Telecommunications Union (ITU) in [22]. Note that a high value of DC means that the PU is using this frequency band most of the time, and a low value of DC means that the PU is absent for a long period of time. Each ids,p of IDn is passed through γ, where 0 or 1 values are assigned on a DCn matrix with same size as IDn, as explained by the following equation:(2)DCn=1,ifIDn≥γ,0,ifIDn<γ.Thereafter, theS rows of DCn are averaged. The result is stored in dcn, as shown in (3). The dcn variable has the average DC for each frequency point p with values between 0 and 1 for the decision n. Since a lower value of this parameter is the better, the DC represents a cost parameter.(3)dcn=1S∑s=1SDCn,0,1.


#### 2.1.2. Bandwidth(bwn)

One of the most important parameters to characterize spectrum holes is thebandwidth. Having a large value of bandwidth is preferable, since its size is related to the maximum data rate that can be attained by SU. Therefore, the bandwidth of a spectrum hole is considered a benefit parameter. Spectrum occupancy information can be utilized to determine the existence of spectrum holes. Here, using the information contained in dcn vector and the resolution points p, each spectrum hole is calculated. In this process, each element of dcn vector is rounded in two values (0 or 1) in order to determine empty or occupied frequencies.Algorithm1 and Figure 2 describe how the bwn vector is obtained. The beginning of a spectrum hole is considered when the l counting variable is odd or equal to 0 and dcn(p)<1. In that case, the value of the auxiliary vector fvn to which p is pointing out is stored in fi as can be seen in Figure 2. The spectrum hole ending appears when dcn(p)=0 and the next resolution point dcn(p+1)>0; in a similar way the fvn value where p is pointing out is stored in ff. Also, the size of this space is calculated by doing ff-fi; if it is larger than ϵ, it is saved in un, wherein r corresponds to all spectrum holes with r=1,…,R. For each r, there is a identifier that stores the value of central frequency of each spectrum hole.Algorithm 1:Bandwidth location.
Initializer=0,l=0 for  p=1→P  do if (lodd or l=0) and dcn(p)<1  then l=l+1 fi(l)=fvn(p) end if  (dcn(p)=0) and dcn(p+1)>0  then l=l+1 ff(l)=fvn(p) if  ff(l)-fi(l)>ϵ  then Initializer=r+1 un(r)=ff(l)-fi(l) end end endFigure 2
Example of how spectrum holes are found.In our work presented in [13], only 6 MHz, 7 MHz, and 8 MHz spectrum holes were considered. However, due to the presence of several spectrum holes smaller than 6 MHz (but larger than 5 MHz), spectrum holes of 5 MHz are also considered in this work, and so ϵ=5MHz. Contrary to IEEE 802.22 that does not consider spectrum holes smaller than 6 MHz, there are other wireless standards such as unlicensed LTE where this kind of empty spaces can be used [23, 24]. The four spectrum holes considered are the am elements of the set A=a1=5,a2=6,a3=7,a4=8. If there is an element of A equal to the spectrum hole size of un(r), it is directly assigned to bwn(k). In other cases, if the size of un(r) exceeds 8 MHz, it is randomly partitioned in the elements of A′. The A′ set includes random elements of A, as many as can be fitted in A′. The condition is that the sum of A′ elements should be less than or equal to un(r).Finally, the vector with the average bandwidth size of each spectrum hole in the decisionn is bwn, where the bwn length is k=1,…,K, where K is the number of spectrum holes per decision. It is important to mention that, similarly to p, the variable k has an auxiliary vector fkn where the central frequency values of each spectrum holes are stored. When un(r) is directly assigned to bwn(k), the mapping r to k is one to one, for the contrary case k will increase depending of the number of elements of A′. Hence, if all spectrum holes of un are among the spectrum holes considered, k=r. However, when spectrum holes of un are larger, then k>r. Thus, the size of this vector is not fixed, and hence it can change for each spectrum decision.


#### 2.1.3. Stability of Spectrum Holes(stn)

Spectrum holestability (stn) in time is a benefit parameter proposed in this work. A hole in the spectrum can appear to be always available, but that does not mean that it has the same size all the time. In fact, a spectrum hole can change in size affecting SU connection performance. Thus, this parameter measures how stable a spectrum hole is in time, and consequently the result provides the percentage of time that a spectrum hole is standing still.In order to know the spectrum holes for each rows of the DCn matrix, the vector ths is computed using the same procedures used for computing bwn. The result is stored in ths(g), where g=1,…,G with G being the temporal variable with the number of spectrum holes found in that row s. The temporal variable G has also an auxiliary vector fgs where the central frequency values of each spectrum holes of ths are stored. After that, the fkn vector with the central frequency of each element of the bwn vector is sought in the fgs vector corresponding to the ths(g) vector. The procedure follows the following restrictions: a spectrum hole has a variation, but it is considered the same if fgs∈fkn and if the difference between fkn(k) and the fgs(g) element is lower than V as is shown in (4) (the V variable is a threshold, and its value in this work is 1 MHz; the reason for this threshold value is explained in Section 5.1). In this case, the difference of change between fgs(g) and fkn(k) is calculated and the instability (i.e., variation in time of the spectrum hole) is posted to the ies(k) variable; in an opposite case, we assume that the spectrum hole has disappeared or has overly changed in size, and hence the instability is assumed and quantified as 1 also in ies(k), as can be seen in(4)iesk=fknk-fgsg,iffgsg∈fkn∧fknk-fgsg<V,1,iffgsg∉fkn.Theies vector with values between 0 and 1 is stored in the STn matrix with dimension S×K, as can be seen in(5)STns=ies,0,1.Finally, the rows of the matrix mentioned before are averaged, subtracted from 1, and multiplied by 100 to obtain the percentage of stabilitystn for the decision n, as can be seen in(6)stn=1-1S∑s=1SSTn∗100,0,100.


#### 2.1.4. Power Index(pin)

Thepower index is an important relation that should be considered in the spectrum decision process [13]. This relation indicates how a SU can be affected when a PU appears. A spectrum hole can be present for a long time, but if the PU requires using its frequency band, the PU can transmit suddenly and cause problems to the SU. This parameter quantifies how much a SU is affected by the phenomenon. For each frequency range that is considered a spectrum hole, (7) must be computed:(7)Pmaxk=maxs,p⁡IDn,∀bwnk,Pmink=mins,p⁡IDn,∀bwnk.After that, thepower indexpin(k) for the decision n is obtained by the division of Pmax⁡(k) by Pmin(k), as can be seen in (8). If Pmax⁡(k) is close to Pmin(k), pin(k) is near 1, and therefore the maximum power is low and the SU is not greatly affected by the PU presence. The pin(k) vector also can be near 1 when the minimum power is high; however, in that case the spectrum hole is occupied most of the time and it is not considered as a good candidate. This parameter is considered a benefit:(8)pink=Pmax⁡kPmink,0,1.


#### 2.1.5. Interference Temperature(itn)

A parameter that should be included in the selection of a spectrum hole is theinterference temperature (IT). The frequency spectrum is saturated, and most of the available spectrum holes are surrounded by occupied frequencies; in this way, users on those frequencies can generate interference. This interference may cause deficiencies in performance of SUs. Thereby, in the selection process, knowing the corresponding IT of the spectrum holes is important. The concept of IT was initially proposed in [25]. In [26], two challenges to implement the ideal IT model are mentioned: the first one is identifying licensed signals, and the second one is measuring IT in the presence of the PU. For the second challenge, the author pointed out that PU knowledge facilitates IT determination. Thereby, calculating the approximation of IT as shown in [26] is possible by means of the following equation:(9)itnk=Pfc-bwnk/2-τ+Pfc+bwnk/2+τ2Kbwnk,where P is the power in the central frequency fc in the selected bandwidth bwn(k), K is Boltzmann’s constant, and τ represents few kHz as guard band. The units of this parameter are Kelvin degrees and it is considered a cost parameter. In this parameter, a lower value of itn(k) is preferable in order to reduce interference and to obtain good communication performance. In (9), it has to be calculated for each spectrum hole in bwn(k), where the itn vector is obtained for each decision n. The range of IT changes according to the frequency measured and the size of the available spectrum holes.


#### 2.1.6. Selected Frequency(sfn)

The importance offrequency selection is based on the relation between the transmission frequency and the possible coverage zone of that transmission. Given an assigned value of power for performing a communication, here we assumed that the coverage zone for a lower frequency is expected to be larger than in a higher frequency. This means that choosing spectrum holes in lower frequency values is better than in upper frequency values. The communication process can be performed between farther points without increasing power transmission, which in turn may represent energy savings. However, it is worth mentioning that the considerations for this parameter may not be satisfactory for SUs near the SBSs and SUs at the edges of adjacent cells. To solve this issue, the interference has to be considered in the spectrum decision process and included as an additional decision parameter.The spectrum holes that appear inbwn receive a cost in the vector sfn. Equation (10) explains the distribution of penalty costs. The lowest possible frequency corresponds to the first spectrum hole k=1, which gets the lowest cost in sfn. The operation is repeated for each spectrum hole K with the same cost in sfn as the value of K; hence sfn is the same size as bwn and it is calculated for each decision n. This parameter is a cost; a lower cost or a lower frequency is preferable instead of a high frequency:(10)bwn1lowest  frequency;sfn1=1,⋮⋮⋮bwnKhighest  frequency;sfnK=K.


## 2.1. Decision Parameters

To start the spectrum decision process, the available spectrum holes have to be identified. Then, for each spectrum hole a set of parameters describing its features or characteristics have to be calculated. Thus, spectrum usage information is required to both identify the holes and calculate its features. Within the EMSD function, the information coming from spectrum usage is processed to characterize each spectrum hole. In a real system this process should be done according to PU activity and also based on SU connection requirements. Each time a connection requirement occurs, a spectrum decision should be executed to satisfy SU connection requirements. Once the connection is established in a specific spectrum hole, then periodic spectrum decisions have to be considered based on the availability of the current spectrum hole, connection requirements, and trading off energy consumption due to frequent spectrum handoffs (i.e., ping-pong effect). However, to increase the certainty of the exact moment for making a spectrum decision, sensing and statistical information need to be combined [18]. Finally, it is worth mentioning that the spectrum measurements can be affected by the presence of hidden nodes transmissions. To overcome this issue, a cooperative spectrum sensing approach has to be considered. For example, data fusion centers may be deployed in the SBSs to help overcome these scenarios as proposed in [19]. However, for the scope of this manuscript the cooperative spectrum sensing scenario is not considered.In this work, for each spectrum decision interval, a specific number of spectrum samples are obtained from spectrum measurements executed periodically in the SU terminal. This spectrum information is assigned into a matrix calledinterval decisionIDn, with n=1,…,N, and where N is the total number of consecutive spectrum decisions. The IDn matrix is expressed in (1). Thereby, every time a spectrum decision is made, the total number of spectrum samples analyzed during the decision interval is S, with s=1,…,S, and the total number of resolution points is P corresponding to the examined frequencies, with p=1,…,P. Here, it is important to mention the existence of the auxiliary vector fv that has the frequency value of each p resolution point and that is used as identifier. Thus, ids,p is any IDn element that has a sample of the spectral power in a frequency point:(1)IDn=ids,pS×P.It is worth mentioning that the spectrum sensing capabilities are in fact limited by the SU hardware capabilities which may vary from device to device. We assume that homogeneous CR devices are used in our scenario. This assumption may be valid for early deployments of CRNs. However, as these networks grow in deployments and in number of users, the homogeneity among CR devices will not be valid. Also, in case of missing frequency samples, the system may be delayed to obtain more samples or previous samples available may be used temporarily. In both cases, the accuracy of the spectrum sensing may be affected. Finally, once the available spectrum holes are found, for characterizing each one, six decision parameters are calculated with the information contained into each decision matrix intervalIDn. In the following sub-subsections, we describe how and why each of the decision parameters is calculated.


### 2.1.1. Duty Cycle(dcn)

A fundamental parameter to establish the spectral occupation from spectrum measurements is theduty cycle (DC). The DC is the percentage of time in which a signal power is above a threshold. Through the method of the energy detector, it is possible to know the DC for each frequency band (i.e., channel). It requires the energy threshold γ, which must be carefully selected to avoid estimation errors in the state of a channel. In the present work, the m-dB criterion is used to set the decision threshold value [20]. Thus, we set the threshold value 10 dBm over the noise floor according to the methodology suggestions made in [20, 21] and by the International Telecommunications Union (ITU) in [22]. Note that a high value of DC means that the PU is using this frequency band most of the time, and a low value of DC means that the PU is absent for a long period of time. Each ids,p of IDn is passed through γ, where 0 or 1 values are assigned on a DCn matrix with same size as IDn, as explained by the following equation:(2)DCn=1,ifIDn≥γ,0,ifIDn<γ.Thereafter, theS rows of DCn are averaged. The result is stored in dcn, as shown in (3). The dcn variable has the average DC for each frequency point p with values between 0 and 1 for the decision n. Since a lower value of this parameter is the better, the DC represents a cost parameter.(3)dcn=1S∑s=1SDCn,0,1.


### 2.1.2. Bandwidth(bwn)

One of the most important parameters to characterize spectrum holes is thebandwidth. Having a large value of bandwidth is preferable, since its size is related to the maximum data rate that can be attained by SU. Therefore, the bandwidth of a spectrum hole is considered a benefit parameter. Spectrum occupancy information can be utilized to determine the existence of spectrum holes. Here, using the information contained in dcn vector and the resolution points p, each spectrum hole is calculated. In this process, each element of dcn vector is rounded in two values (0 or 1) in order to determine empty or occupied frequencies.Algorithm1 and Figure 2 describe how the bwn vector is obtained. The beginning of a spectrum hole is considered when the l counting variable is odd or equal to 0 and dcn(p)<1. In that case, the value of the auxiliary vector fvn to which p is pointing out is stored in fi as can be seen in Figure 2. The spectrum hole ending appears when dcn(p)=0 and the next resolution point dcn(p+1)>0; in a similar way the fvn value where p is pointing out is stored in ff. Also, the size of this space is calculated by doing ff-fi; if it is larger than ϵ, it is saved in un, wherein r corresponds to all spectrum holes with r=1,…,R. For each r, there is a identifier that stores the value of central frequency of each spectrum hole.Algorithm 1:Bandwidth location.
Initializer=0,l=0 for  p=1→P  do if (lodd or l=0) and dcn(p)<1  then l=l+1 fi(l)=fvn(p) end if  (dcn(p)=0) and dcn(p+1)>0  then l=l+1 ff(l)=fvn(p) if  ff(l)-fi(l)>ϵ  then Initializer=r+1 un(r)=ff(l)-fi(l) end end endFigure 2
Example of how spectrum holes are found.In our work presented in [13], only 6 MHz, 7 MHz, and 8 MHz spectrum holes were considered. However, due to the presence of several spectrum holes smaller than 6 MHz (but larger than 5 MHz), spectrum holes of 5 MHz are also considered in this work, and so ϵ=5MHz. Contrary to IEEE 802.22 that does not consider spectrum holes smaller than 6 MHz, there are other wireless standards such as unlicensed LTE where this kind of empty spaces can be used [23, 24]. The four spectrum holes considered are the am elements of the set A=a1=5,a2=6,a3=7,a4=8. If there is an element of A equal to the spectrum hole size of un(r), it is directly assigned to bwn(k). In other cases, if the size of un(r) exceeds 8 MHz, it is randomly partitioned in the elements of A′. The A′ set includes random elements of A, as many as can be fitted in A′. The condition is that the sum of A′ elements should be less than or equal to un(r).Finally, the vector with the average bandwidth size of each spectrum hole in the decisionn is bwn, where the bwn length is k=1,…,K, where K is the number of spectrum holes per decision. It is important to mention that, similarly to p, the variable k has an auxiliary vector fkn where the central frequency values of each spectrum holes are stored. When un(r) is directly assigned to bwn(k), the mapping r to k is one to one, for the contrary case k will increase depending of the number of elements of A′. Hence, if all spectrum holes of un are among the spectrum holes considered, k=r. However, when spectrum holes of un are larger, then k>r. Thus, the size of this vector is not fixed, and hence it can change for each spectrum decision.


### 2.1.3. Stability of Spectrum Holes(stn)

Spectrum holestability (stn) in time is a benefit parameter proposed in this work. A hole in the spectrum can appear to be always available, but that does not mean that it has the same size all the time. In fact, a spectrum hole can change in size affecting SU connection performance. Thus, this parameter measures how stable a spectrum hole is in time, and consequently the result provides the percentage of time that a spectrum hole is standing still.In order to know the spectrum holes for each rows of the DCn matrix, the vector ths is computed using the same procedures used for computing bwn. The result is stored in ths(g), where g=1,…,G with G being the temporal variable with the number of spectrum holes found in that row s. The temporal variable G has also an auxiliary vector fgs where the central frequency values of each spectrum holes of ths are stored. After that, the fkn vector with the central frequency of each element of the bwn vector is sought in the fgs vector corresponding to the ths(g) vector. The procedure follows the following restrictions: a spectrum hole has a variation, but it is considered the same if fgs∈fkn and if the difference between fkn(k) and the fgs(g) element is lower than V as is shown in (4) (the V variable is a threshold, and its value in this work is 1 MHz; the reason for this threshold value is explained in Section 5.1). In this case, the difference of change between fgs(g) and fkn(k) is calculated and the instability (i.e., variation in time of the spectrum hole) is posted to the ies(k) variable; in an opposite case, we assume that the spectrum hole has disappeared or has overly changed in size, and hence the instability is assumed and quantified as 1 also in ies(k), as can be seen in(4)iesk=fknk-fgsg,iffgsg∈fkn∧fknk-fgsg<V,1,iffgsg∉fkn.Theies vector with values between 0 and 1 is stored in the STn matrix with dimension S×K, as can be seen in(5)STns=ies,0,1.Finally, the rows of the matrix mentioned before are averaged, subtracted from 1, and multiplied by 100 to obtain the percentage of stabilitystn for the decision n, as can be seen in(6)stn=1-1S∑s=1SSTn∗100,0,100.


### 2.1.4. Power Index(pin)

Thepower index is an important relation that should be considered in the spectrum decision process [13]. This relation indicates how a SU can be affected when a PU appears. A spectrum hole can be present for a long time, but if the PU requires using its frequency band, the PU can transmit suddenly and cause problems to the SU. This parameter quantifies how much a SU is affected by the phenomenon. For each frequency range that is considered a spectrum hole, (7) must be computed:(7)Pmaxk=maxs,p⁡IDn,∀bwnk,Pmink=mins,p⁡IDn,∀bwnk.After that, thepower indexpin(k) for the decision n is obtained by the division of Pmax⁡(k) by Pmin(k), as can be seen in (8). If Pmax⁡(k) is close to Pmin(k), pin(k) is near 1, and therefore the maximum power is low and the SU is not greatly affected by the PU presence. The pin(k) vector also can be near 1 when the minimum power is high; however, in that case the spectrum hole is occupied most of the time and it is not considered as a good candidate. This parameter is considered a benefit:(8)pink=Pmax⁡kPmink,0,1.


### 2.1.5. Interference Temperature(itn)

A parameter that should be included in the selection of a spectrum hole is theinterference temperature (IT). The frequency spectrum is saturated, and most of the available spectrum holes are surrounded by occupied frequencies; in this way, users on those frequencies can generate interference. This interference may cause deficiencies in performance of SUs. Thereby, in the selection process, knowing the corresponding IT of the spectrum holes is important. The concept of IT was initially proposed in [25]. In [26], two challenges to implement the ideal IT model are mentioned: the first one is identifying licensed signals, and the second one is measuring IT in the presence of the PU. For the second challenge, the author pointed out that PU knowledge facilitates IT determination. Thereby, calculating the approximation of IT as shown in [26] is possible by means of the following equation:(9)itnk=Pfc-bwnk/2-τ+Pfc+bwnk/2+τ2Kbwnk,where P is the power in the central frequency fc in the selected bandwidth bwn(k), K is Boltzmann’s constant, and τ represents few kHz as guard band. The units of this parameter are Kelvin degrees and it is considered a cost parameter. In this parameter, a lower value of itn(k) is preferable in order to reduce interference and to obtain good communication performance. In (9), it has to be calculated for each spectrum hole in bwn(k), where the itn vector is obtained for each decision n. The range of IT changes according to the frequency measured and the size of the available spectrum holes.


### 2.1.6. Selected Frequency(sfn)

The importance offrequency selection is based on the relation between the transmission frequency and the possible coverage zone of that transmission. Given an assigned value of power for performing a communication, here we assumed that the coverage zone for a lower frequency is expected to be larger than in a higher frequency. This means that choosing spectrum holes in lower frequency values is better than in upper frequency values. The communication process can be performed between farther points without increasing power transmission, which in turn may represent energy savings. However, it is worth mentioning that the considerations for this parameter may not be satisfactory for SUs near the SBSs and SUs at the edges of adjacent cells. To solve this issue, the interference has to be considered in the spectrum decision process and included as an additional decision parameter.The spectrum holes that appear inbwn receive a cost in the vector sfn. Equation (10) explains the distribution of penalty costs. The lowest possible frequency corresponds to the first spectrum hole k=1, which gets the lowest cost in sfn. The operation is repeated for each spectrum hole K with the same cost in sfn as the value of K; hence sfn is the same size as bwn and it is calculated for each decision n. This parameter is a cost; a lower cost or a lower frequency is preferable instead of a high frequency:(10)bwn1lowest  frequency;sfn1=1,⋮⋮⋮bwnKhighest  frequency;sfnK=K.


## 2.1.1. Duty Cycle(dcn)

A fundamental parameter to establish the spectral occupation from spectrum measurements is theduty cycle (DC). The DC is the percentage of time in which a signal power is above a threshold. Through the method of the energy detector, it is possible to know the DC for each frequency band (i.e., channel). It requires the energy threshold γ, which must be carefully selected to avoid estimation errors in the state of a channel. In the present work, the m-dB criterion is used to set the decision threshold value [20]. Thus, we set the threshold value 10 dBm over the noise floor according to the methodology suggestions made in [20, 21] and by the International Telecommunications Union (ITU) in [22]. Note that a high value of DC means that the PU is using this frequency band most of the time, and a low value of DC means that the PU is absent for a long period of time. Each ids,p of IDn is passed through γ, where 0 or 1 values are assigned on a DCn matrix with same size as IDn, as explained by the following equation:(2)DCn=1,ifIDn≥γ,0,ifIDn<γ.Thereafter, theS rows of DCn are averaged. The result is stored in dcn, as shown in (3). The dcn variable has the average DC for each frequency point p with values between 0 and 1 for the decision n. Since a lower value of this parameter is the better, the DC represents a cost parameter.(3)dcn=1S∑s=1SDCn,0,1.


## 2.1.2. Bandwidth(bwn)

One of the most important parameters to characterize spectrum holes is thebandwidth. Having a large value of bandwidth is preferable, since its size is related to the maximum data rate that can be attained by SU. Therefore, the bandwidth of a spectrum hole is considered a benefit parameter. Spectrum occupancy information can be utilized to determine the existence of spectrum holes. Here, using the information contained in dcn vector and the resolution points p, each spectrum hole is calculated. In this process, each element of dcn vector is rounded in two values (0 or 1) in order to determine empty or occupied frequencies.Algorithm1 and Figure 2 describe how the bwn vector is obtained. The beginning of a spectrum hole is considered when the l counting variable is odd or equal to 0 and dcn(p)<1. In that case, the value of the auxiliary vector fvn to which p is pointing out is stored in fi as can be seen in Figure 2. The spectrum hole ending appears when dcn(p)=0 and the next resolution point dcn(p+1)>0; in a similar way the fvn value where p is pointing out is stored in ff. Also, the size of this space is calculated by doing ff-fi; if it is larger than ϵ, it is saved in un, wherein r corresponds to all spectrum holes with r=1,…,R. For each r, there is a identifier that stores the value of central frequency of each spectrum hole.Algorithm 1:Bandwidth location.
Initializer=0,l=0 for  p=1→P  do if (lodd or l=0) and dcn(p)<1  then l=l+1 fi(l)=fvn(p) end if  (dcn(p)=0) and dcn(p+1)>0  then l=l+1 ff(l)=fvn(p) if  ff(l)-fi(l)>ϵ  then Initializer=r+1 un(r)=ff(l)-fi(l) end end endFigure 2
Example of how spectrum holes are found.In our work presented in [13], only 6 MHz, 7 MHz, and 8 MHz spectrum holes were considered. However, due to the presence of several spectrum holes smaller than 6 MHz (but larger than 5 MHz), spectrum holes of 5 MHz are also considered in this work, and so ϵ=5MHz. Contrary to IEEE 802.22 that does not consider spectrum holes smaller than 6 MHz, there are other wireless standards such as unlicensed LTE where this kind of empty spaces can be used [23, 24]. The four spectrum holes considered are the am elements of the set A=a1=5,a2=6,a3=7,a4=8. If there is an element of A equal to the spectrum hole size of un(r), it is directly assigned to bwn(k). In other cases, if the size of un(r) exceeds 8 MHz, it is randomly partitioned in the elements of A′. The A′ set includes random elements of A, as many as can be fitted in A′. The condition is that the sum of A′ elements should be less than or equal to un(r).Finally, the vector with the average bandwidth size of each spectrum hole in the decisionn is bwn, where the bwn length is k=1,…,K, where K is the number of spectrum holes per decision. It is important to mention that, similarly to p, the variable k has an auxiliary vector fkn where the central frequency values of each spectrum holes are stored. When un(r) is directly assigned to bwn(k), the mapping r to k is one to one, for the contrary case k will increase depending of the number of elements of A′. Hence, if all spectrum holes of un are among the spectrum holes considered, k=r. However, when spectrum holes of un are larger, then k>r. Thus, the size of this vector is not fixed, and hence it can change for each spectrum decision.


## 2.1.3. Stability of Spectrum Holes(stn)

Spectrum holestability (stn) in time is a benefit parameter proposed in this work. A hole in the spectrum can appear to be always available, but that does not mean that it has the same size all the time. In fact, a spectrum hole can change in size affecting SU connection performance. Thus, this parameter measures how stable a spectrum hole is in time, and consequently the result provides the percentage of time that a spectrum hole is standing still.In order to know the spectrum holes for each rows of the DCn matrix, the vector ths is computed using the same procedures used for computing bwn. The result is stored in ths(g), where g=1,…,G with G being the temporal variable with the number of spectrum holes found in that row s. The temporal variable G has also an auxiliary vector fgs where the central frequency values of each spectrum holes of ths are stored. After that, the fkn vector with the central frequency of each element of the bwn vector is sought in the fgs vector corresponding to the ths(g) vector. The procedure follows the following restrictions: a spectrum hole has a variation, but it is considered the same if fgs∈fkn and if the difference between fkn(k) and the fgs(g) element is lower than V as is shown in (4) (the V variable is a threshold, and its value in this work is 1 MHz; the reason for this threshold value is explained in Section 5.1). In this case, the difference of change between fgs(g) and fkn(k) is calculated and the instability (i.e., variation in time of the spectrum hole) is posted to the ies(k) variable; in an opposite case, we assume that the spectrum hole has disappeared or has overly changed in size, and hence the instability is assumed and quantified as 1 also in ies(k), as can be seen in(4)iesk=fknk-fgsg,iffgsg∈fkn∧fknk-fgsg<V,1,iffgsg∉fkn.Theies vector with values between 0 and 1 is stored in the STn matrix with dimension S×K, as can be seen in(5)STns=ies,0,1.Finally, the rows of the matrix mentioned before are averaged, subtracted from 1, and multiplied by 100 to obtain the percentage of stabilitystn for the decision n, as can be seen in(6)stn=1-1S∑s=1SSTn∗100,0,100.


## 2.1.4. Power Index(pin)

Thepower index is an important relation that should be considered in the spectrum decision process [13]. This relation indicates how a SU can be affected when a PU appears. A spectrum hole can be present for a long time, but if the PU requires using its frequency band, the PU can transmit suddenly and cause problems to the SU. This parameter quantifies how much a SU is affected by the phenomenon. For each frequency range that is considered a spectrum hole, (7) must be computed:(7)Pmaxk=maxs,p⁡IDn,∀bwnk,Pmink=mins,p⁡IDn,∀bwnk.After that, thepower indexpin(k) for the decision n is obtained by the division of Pmax⁡(k) by Pmin(k), as can be seen in (8). If Pmax⁡(k) is close to Pmin(k), pin(k) is near 1, and therefore the maximum power is low and the SU is not greatly affected by the PU presence. The pin(k) vector also can be near 1 when the minimum power is high; however, in that case the spectrum hole is occupied most of the time and it is not considered as a good candidate. This parameter is considered a benefit:(8)pink=Pmax⁡kPmink,0,1.


## 2.1.5. Interference Temperature(itn)

A parameter that should be included in the selection of a spectrum hole is theinterference temperature (IT). The frequency spectrum is saturated, and most of the available spectrum holes are surrounded by occupied frequencies; in this way, users on those frequencies can generate interference. This interference may cause deficiencies in performance of SUs. Thereby, in the selection process, knowing the corresponding IT of the spectrum holes is important. The concept of IT was initially proposed in [25]. In [26], two challenges to implement the ideal IT model are mentioned: the first one is identifying licensed signals, and the second one is measuring IT in the presence of the PU. For the second challenge, the author pointed out that PU knowledge facilitates IT determination. Thereby, calculating the approximation of IT as shown in [26] is possible by means of the following equation:(9)itnk=Pfc-bwnk/2-τ+Pfc+bwnk/2+τ2Kbwnk,where P is the power in the central frequency fc in the selected bandwidth bwn(k), K is Boltzmann’s constant, and τ represents few kHz as guard band. The units of this parameter are Kelvin degrees and it is considered a cost parameter. In this parameter, a lower value of itn(k) is preferable in order to reduce interference and to obtain good communication performance. In (9), it has to be calculated for each spectrum hole in bwn(k), where the itn vector is obtained for each decision n. The range of IT changes according to the frequency measured and the size of the available spectrum holes.


## 2.1.6. Selected Frequency(sfn)

The importance offrequency selection is based on the relation between the transmission frequency and the possible coverage zone of that transmission. Given an assigned value of power for performing a communication, here we assumed that the coverage zone for a lower frequency is expected to be larger than in a higher frequency. This means that choosing spectrum holes in lower frequency values is better than in upper frequency values. The communication process can be performed between farther points without increasing power transmission, which in turn may represent energy savings. However, it is worth mentioning that the considerations for this parameter may not be satisfactory for SUs near the SBSs and SUs at the edges of adjacent cells. To solve this issue, the interference has to be considered in the spectrum decision process and included as an additional decision parameter.The spectrum holes that appear inbwn receive a cost in the vector sfn. Equation (10) explains the distribution of penalty costs. The lowest possible frequency corresponds to the first spectrum hole k=1, which gets the lowest cost in sfn. The operation is repeated for each spectrum hole K with the same cost in sfn as the value of K; hence sfn is the same size as bwn and it is calculated for each decision n. This parameter is a cost; a lower cost or a lower frequency is preferable instead of a high frequency:(10)bwn1lowest  frequency;sfn1=1,⋮⋮⋮bwnKhighest  frequency;sfnK=K.


## 3. MADM-Based Spectrum Decision

Multiple attribute decision-making (MADM) methods deal with decision problems where a selection has to be made over several available alternatives that are characterized each by multiple and usually conflicting attributes [4]. MADM is a branch of the field multiple criteria decision-making (MCDM). There are MADM-based decision problems in a diverse range of engineering disciplines, but they all share the following common characteristics: alternatives to select, multiple attributes describing the alternatives in different measurement units, and a set of weights representing the relative importance among attributes. In the following, the spectrum decision problem in CRNs is formulated as a MADM-based decision and the MADM methods considered in this work are presented.


### 3.1. Decision Matrix(DMn)

First, according to the previous section, the available spectrum holes and their corresponding parameters are arranged as follows to form the decision matrixDMn for each decision n as can be seen in(11)DMn=bw11st12pi13dc14it15sf1J⋮⋮⋮⋮⋮⋮bwK1stK2piK3dcK4itK5sfKJ,where the first three columns correspond to benefit decision parameters,bandwidthbw,stabilityst, andpower indexpi, while the next three columns correspond to cost decision parameters,duty cycledc,interference temperatureit, andselected frequencysf. Thus, in this paper J=6 always in (11). On the other hand, the K rows correspond to the K available spectrum holes at decision n, and thus K may vary from decision to decision based on the occupancy of the spectrum. Note that in (3) dc was in terms of p; however, for the DMn matrix dc is resized with the corresponding duty cycle of the spectrum holes found.It is important to mention that although the spectrum decision MADM-based formulation presented in this work considers only decision parameters extracted from the spectrum measurements (i.e., physical layer level), other types of parameters may be considered. For example, parameters describing the network-level performance of the network may be considered such as packet delay and jitter, security level, and access cots. In fact, network-level parameters must be considered for spectrum decision in scenarios with several coexisting CRNs. Nevertheless, such scenario can be also considered with the presented MADM-based approach by extending the number of columns to the decision matrixDMn.


### 3.2. Connection Profiles

As mentioned before, a set of connection profiles are assumed to be prestored in the SU terminal. Once the decision matrixDMn is defined, it is required to assign the different level of importance or relevance of each decision parameter. This level of importance is established in the connection profile which is defined by the set of the corresponding six importance weights. The sum of those weights has to satisfy the constraint ∑j=1J‍wj=1 where wj corresponds to the importance weight of parameter j with J=6. From the six decision parameters defined in Section 2.1 and considered in the proposed spectrum decision formulation, the bandwidth size of the spectrum hole bw is the one with major impact in the connection requirements since it is directly related to the maximum achievable data rate among the SU terminal and the SBS. Thus, here such parameter will be assumed to be the one ensuring the connection requirements. However, in order to have a more accurate connection profile, network-level parameters should be considered as discussed before.TheDMn matrix and the set of importance weights wj are the input information to the MADM algorithms. The MADM algorithms first calculate a score for each alternative based on their specific procedures, and then the alternative with the best value score is selected. Usually, the alternatives are listed in ranking, and thus the first place in the ranking list is the selected option. Hence, the final result of each MADM algorithm is the selection of a row (i.e., a spectrum hole) from DMn. To make the notation easier, for each decision n, this row is given byselected spectrum holehsn. It includes the six decision parameters, as can be seen in(12)hsn=bwstipdcitsf.In the following subsections, the MADM algorithms implemented in this work are presented.


### 3.3. Simple Additive Weighting (SAW)

This algorithm was introduced for decision process in wireless networking in [27]; SAW is also called the weighted sum method. The variable atkj corresponds to the normalization of each decision parameter and dmkj is an element of the DMn matrix. This method performs homogenization; each atkj parameter is multiplied by wj to obtain the score of each candidate alternative. The normalization of atkj is described as follows: if atkj is a benefit parameter, it is normalized as can be seen in (13), where dmj+=maxk⁡dmkj. On the other hand, if atkj is a cost parameter, it is normalized as it is shown in (14), where dmj-=mink⁡dmkj:(13)atkj=dmkjdmj+,(14)atkj=dmj-dmkj.The alternative selected by this method is (15), where wj is the importance weight of jth parameter:(15)hsSAW∗=arg⁡maxk⁡∑j=1Jwjatkj.


### 3.4. Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)

TOPSIS is another MADM method, which was also used in wireless networking in [27]. This algorithm calculates the alternative with the shortest Euclidian distance being the ideal alternative and the alternative with the largest Euclidian distance to the negative-ideal solution, using the information contained in wj and dmij. TOPSIS performs the following steps in order to compute the alternatives ranking list.Step 1.
Construct the normalized decision matrix, which allows comparison across the attributes as(16)atkj=dmkj∑k=1Kdmkj2.Step 2.
Construct the weighted normalized decision matrix asvkj=wj∗atKj.Step 3.
Determine ideal alternative with (17) and negative-ideal alternatives with (18) as follows:(17)Al+=maxk⁡vkj∣j∈BC,mink⁡vkj∣j∈BC′,(18)Al-=mink⁡vkj∣j∈BC,maxk⁡vkj∣j∈BC′,where BC is the set of benefit parameters and BC′ is the set of cost parameters.Step 4.
Calculate the distance between the ideal positive alternatives with (19) and the negative-ideal alternatives with (20) as follows:(19)sk+=∑j=1Jvkj-vj+2,(20)sk-=∑j=1Jvkj-vj-2.Step 5.
Calculate the relative closeness to the ideal alternative:(21)ck∗=sk-sk++sk-.Equation (22) corresponds to the final step of this algorithm, where the best spectrum hole according to the SU’s connection requirements is hsTOP∗:(22)hsTOP∗=arg⁡maxk⁡ck∗.


### 3.5. VIKOR

The VIKOR compromise ranking method was proposed for wireless networks in [28]. This method selects an alternative close to the ideal among the rest of the alternatives. This algorithm carries out the following steps.Step 1.
For each parameterj=1,2,3,…,J, determine the best value (23) and the worst value (24) given by(23)Fj+=maxk⁡dmkj∣j∈Jb,mink⁡dmkj∣j∈Jc,(24)Fj-=mink⁡dmkj∣j∈Jb,maxk⁡dmkj∣j∈Jc,where Jb⊂BC is the set of benefit parameters and Jc⊂BC′ is the set of cost parameters.Step 2.
Compute the values ofSk (25) and Rk (26) with k=1,2,3,…,K:(25)Sk=∑j=1JwjFj+-dmkjFj+-Fj-,(26)Rk=maxj⁡wjFj+-dmkjFj+-Fj-,where wj is the importance weight of parameter j.Step 3.
Compute the values ofQk with (27) for k=1,2,3,…,K, where γ is the weight of the strategy with 0≤γ≤1:(27)Qk=γSk-S+S--S++1-γRk-R+R--R+,where(28)S+=mink⁡Sk,S-=maxk⁡Sk,R+=mink⁡Rk,R-=maxk⁡RK.Step 4.
Given the values ofQ for all k∈K, rank the candidate networks in an increasing order.Equation (29) expresses the final step of this algorithm in the hsVIK∗ vector, where Qk∗ is the best solution for satisfying the SU’s connection requirements.(29)hsVIK∗=arg⁡mink⁡Qk∗.


## 3.1. Decision Matrix(DMn)

First, according to the previous section, the available spectrum holes and their corresponding parameters are arranged as follows to form the decision matrixDMn for each decision n as can be seen in(11)DMn=bw11st12pi13dc14it15sf1J⋮⋮⋮⋮⋮⋮bwK1stK2piK3dcK4itK5sfKJ,where the first three columns correspond to benefit decision parameters,bandwidthbw,stabilityst, andpower indexpi, while the next three columns correspond to cost decision parameters,duty cycledc,interference temperatureit, andselected frequencysf. Thus, in this paper J=6 always in (11). On the other hand, the K rows correspond to the K available spectrum holes at decision n, and thus K may vary from decision to decision based on the occupancy of the spectrum. Note that in (3) dc was in terms of p; however, for the DMn matrix dc is resized with the corresponding duty cycle of the spectrum holes found.It is important to mention that although the spectrum decision MADM-based formulation presented in this work considers only decision parameters extracted from the spectrum measurements (i.e., physical layer level), other types of parameters may be considered. For example, parameters describing the network-level performance of the network may be considered such as packet delay and jitter, security level, and access cots. In fact, network-level parameters must be considered for spectrum decision in scenarios with several coexisting CRNs. Nevertheless, such scenario can be also considered with the presented MADM-based approach by extending the number of columns to the decision matrixDMn.


## 3.2. Connection Profiles

As mentioned before, a set of connection profiles are assumed to be prestored in the SU terminal. Once the decision matrixDMn is defined, it is required to assign the different level of importance or relevance of each decision parameter. This level of importance is established in the connection profile which is defined by the set of the corresponding six importance weights. The sum of those weights has to satisfy the constraint ∑j=1J‍wj=1 where wj corresponds to the importance weight of parameter j with J=6. From the six decision parameters defined in Section 2.1 and considered in the proposed spectrum decision formulation, the bandwidth size of the spectrum hole bw is the one with major impact in the connection requirements since it is directly related to the maximum achievable data rate among the SU terminal and the SBS. Thus, here such parameter will be assumed to be the one ensuring the connection requirements. However, in order to have a more accurate connection profile, network-level parameters should be considered as discussed before.TheDMn matrix and the set of importance weights wj are the input information to the MADM algorithms. The MADM algorithms first calculate a score for each alternative based on their specific procedures, and then the alternative with the best value score is selected. Usually, the alternatives are listed in ranking, and thus the first place in the ranking list is the selected option. Hence, the final result of each MADM algorithm is the selection of a row (i.e., a spectrum hole) from DMn. To make the notation easier, for each decision n, this row is given byselected spectrum holehsn. It includes the six decision parameters, as can be seen in(12)hsn=bwstipdcitsf.In the following subsections, the MADM algorithms implemented in this work are presented.


## 3.3. Simple Additive Weighting (SAW)

This algorithm was introduced for decision process in wireless networking in [27]; SAW is also called the weighted sum method. The variable atkj corresponds to the normalization of each decision parameter and dmkj is an element of the DMn matrix. This method performs homogenization; each atkj parameter is multiplied by wj to obtain the score of each candidate alternative. The normalization of atkj is described as follows: if atkj is a benefit parameter, it is normalized as can be seen in (13), where dmj+=maxk⁡dmkj. On the other hand, if atkj is a cost parameter, it is normalized as it is shown in (14), where dmj-=mink⁡dmkj:(13)atkj=dmkjdmj+,(14)atkj=dmj-dmkj.The alternative selected by this method is (15), where wj is the importance weight of jth parameter:(15)hsSAW∗=arg⁡maxk⁡∑j=1Jwjatkj.


## 3.4. Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)

TOPSIS is another MADM method, which was also used in wireless networking in [27]. This algorithm calculates the alternative with the shortest Euclidian distance being the ideal alternative and the alternative with the largest Euclidian distance to the negative-ideal solution, using the information contained in wj and dmij. TOPSIS performs the following steps in order to compute the alternatives ranking list.Step 1.
Construct the normalized decision matrix, which allows comparison across the attributes as(16)atkj=dmkj∑k=1Kdmkj2.Step 2.
Construct the weighted normalized decision matrix asvkj=wj∗atKj.Step 3.
Determine ideal alternative with (17) and negative-ideal alternatives with (18) as follows:(17)Al+=maxk⁡vkj∣j∈BC,mink⁡vkj∣j∈BC′,(18)Al-=mink⁡vkj∣j∈BC,maxk⁡vkj∣j∈BC′,where BC is the set of benefit parameters and BC′ is the set of cost parameters.Step 4.
Calculate the distance between the ideal positive alternatives with (19) and the negative-ideal alternatives with (20) as follows:(19)sk+=∑j=1Jvkj-vj+2,(20)sk-=∑j=1Jvkj-vj-2.Step 5.
Calculate the relative closeness to the ideal alternative:(21)ck∗=sk-sk++sk-.Equation (22) corresponds to the final step of this algorithm, where the best spectrum hole according to the SU’s connection requirements is hsTOP∗:(22)hsTOP∗=arg⁡maxk⁡ck∗.


## 3.5. VIKOR

The VIKOR compromise ranking method was proposed for wireless networks in [28]. This method selects an alternative close to the ideal among the rest of the alternatives. This algorithm carries out the following steps.Step 1.
For each parameterj=1,2,3,…,J, determine the best value (23) and the worst value (24) given by(23)Fj+=maxk⁡dmkj∣j∈Jb,mink⁡dmkj∣j∈Jc,(24)Fj-=mink⁡dmkj∣j∈Jb,maxk⁡dmkj∣j∈Jc,where Jb⊂BC is the set of benefit parameters and Jc⊂BC′ is the set of cost parameters.Step 2.
Compute the values ofSk (25) and Rk (26) with k=1,2,3,…,K:(25)Sk=∑j=1JwjFj+-dmkjFj+-Fj-,(26)Rk=maxj⁡wjFj+-dmkjFj+-Fj-,where wj is the importance weight of parameter j.Step 3.
Compute the values ofQk with (27) for k=1,2,3,…,K, where γ is the weight of the strategy with 0≤γ≤1:(27)Qk=γSk-S+S--S++1-γRk-R+R--R+,where(28)S+=mink⁡Sk,S-=maxk⁡Sk,R+=mink⁡Rk,R-=maxk⁡RK.Step 4.
Given the values ofQ for all k∈K, rank the candidate networks in an increasing order.Equation (29) expresses the final step of this algorithm in the hsVIK∗ vector, where Qk∗ is the best solution for satisfying the SU’s connection requirements.(29)hsVIK∗=arg⁡mink⁡Qk∗.


## 4. Comparison Function of the EMSD

This section presents the Comparison Function of the EMSD that performs the tradeoff among handoff execution and its related energy consumption. Basically, the result of this function depends on the selected spectrum hole characteristics in the time beforehsn-1, the selected spectrum hole in the current time hsn, and ECCS. This function compares and decides the best spectrum hole that satisfies SU’s connection requirements, while trading off energy consumption. In order to set units in the same range and compare the results, normalization is required [8].


### 4.1. Energy Consumption due to Channel Switching(Ecsn)

An important issue in wireless communication technologies is energy consumption, which can be reduced through less complex algorithms, among several solutions [3, 4]. In CRNs, however, additional issues related to energy consumption should be considered since CR devices necessitates additional tasks. In [5], an energy consumption model is presented where the authors consider energy consumption due to transmission (Etx), circuits (Ec), channel switching (Ecs), and idling (Ed). This paper is focused on calculating the Ecs, given that this parameter is related to the execution of spectrum handoffs due to energy consumed by the RF front-end in the reconfiguration process to use a new transmission frequency. According to [5, 29–31], Ecs can be obtained by the power dissipation for switching Pc and channel switching latency Tc. To adapt Tc to our notation, it is calculated as follows:(30)Tc=tcsfhsn-1-fhsn,where tcs is the time delay for switching multiplied by the difference of the central frequency of the previously selected spectrum hole fhsn-1 minus the central frequency of the new selected spectrum hole fhsn, as shown in(31)Ecsn=PcsTcs=Pcstcsfhsn-1-fhsn.


### 4.2. Comparison Function Description

In the system model presented in Figure1, multiple spectrum decisions are performed continuously; the proposed Comparison Function is executed after the preliminary decision of the MADM algorithms but before the final decision returned to the SU via SBS. The preliminary selection offered by MADM algorithms in CRNs presents an issue. In our work in [13], we demonstrated how these algorithms satisfy SUs connection profiles and provide the best spectrum hole selections. However, the MADM algorithms do not take into account additional expenses that a SU can have in order to reach the suggestion made for them, showing that they need to be improved for CRNs. For example, let us suppose that a SU is occupying a spectrum hole hsn-1; after a certain time the next spectrum decision has to be executed. In the moment of the decision, there is a spectrum hole hsn similar to hsn-1 but with a minor improvement (e.g., in bandwidth) than the actual one occupied by the SU; however, this spectrum hole is located in a very distant frequency band. The MADM algorithms are going to recommend to SU hsn no matter what the necessary resources to reach it are. Therefore, the SU will waste a considerable amount of ECCS Ecs in comparison with the marginal improvement of switching to hsn. In this stage, to enhance the MADM algorithms performance, a balance between Ecs and spectrum holes characteristics is required.The Comparison Function of EMSD is an adapter to improve the MADM algorithms performance in CRNs. Thus, the Comparison Function set the equivalence between the parameters of the spectrum holes and the energy consumed by switching among frequencies. However, spectrum holes parameters andEcs are in different units; nevertheless they can be compared after a normalization process [8]. Here, it is important to emphasize that the Comparison Function is dependent of the MADM algorithms and works as a complement. Also, it is important to point out that if hsn-1 is no longer available, the Comparison Function is not used and only the decision of MADM algorithms is taken into account. The whole process is carried out under certain restrictions that are explained below.This Comparison Function starts forn>1. The selected spectrum hole in a previous time hsn-1, the selected spectrum hole in the present time hsn, and the average spectrum holes in the current time DMn are necessary. The algorithm has two restrictions. The first one is hsn≠hsn-1; that is, the selected spectrum holes must be different, whereas an opposite case means the selection has no changes and the comparison is not necessary. The second one is hsn-1∈DMn; that is, the selected spectrum hole in the previous time hsn-1 should be included in DMn in the present time, and this is why if hsn-1 is not present in the current time, it has disappeared, which means that it is not possible to perform the comparison and the best selection is hsn.The Comparison Function calculates two important values. The first calculation corresponds to theEcsn′, as can be seen in (32). Here, the unit-based normalization was implemented. The max⁡(Ecs) and the min⁡(Ecs) values depend on the frequency range and spectrum holes size considered:(32)Ecsn′=Ecsn-min⁡Ecsmax⁡Ecs-min⁡Ecs,0,1.Also, the Comparison Function computes the changes among parameters of the selected spectrum holes. Every selected spectrum hole has six decision parameters, as shown in (12). The algorithm measures the distance between the parameters of hsn and the parameters of hsn-1. Thus, every element of hsn is subtracted from every element of hsn-1; the subtraction is made between parameters of the same kind. After that, each parameter subtraction uses the absolute value and it is normalized following the max-min method [8, 32]. This procedure is done in order to get a proportion of all decision parameters, which define the properties of each spectrum hole. For example, for a benefit parameter such as bw, the normalization process is made according to(33)bw′=bwhsn-bwhsn-1max⁡bw-min⁡bw,0,1.On the other hand, for a cost parameter such asdc, the process is made according to(34)dc′=max⁡dc-min⁡dcdchsn-dchsn-1,0,1.Thereby, the resultant vector with the proportion of all parametersrn is conformed as shown in(35)rn=bw′st′pi′dc′it′sf′.In order to quantifyrn in a scalar number that can be compared with Ecsn′, the values of rn are summed. Finally the result is normalized again in rn′ as can be seen in(36)rn′=1J∑j=1Jrnj,0,1.After that, asEcsn and rn are under the same range, it is possible to compare them. The algorithm looks for the minimum value between rn′ and Ecsn′. The result is assigned to dn as(37)dn=min⁡Ecsn′,rn′.Afterwards, the final selected spectrum holefhn for the decision n is obtained with (38). If dn is equal to Ecsn′, which means that the ECCS does not involve excessive cost and the benefits offered by the new selected spectrum hole hsn are better than the current one, hence the device should take hsn. The contrary case points out that it is better to keep the previously selected spectrum hole hsn-1, because the benefits of hsn are lower than the Ecsn:(38)fhn=hsn,ifdn=Ecsn′;hsn-1,ifdn=rn′.Thus,fhn is the result of this Comparison Function, which can be integrated to any MADM algorithm.


### 4.3. EMSD Summary

In this section, we explain an example of how our EMSD proposal works. Figure3 summarizes all the parts included in this proposal. As noted above, the proposal runs after the first decision (n=2). In the ID2 matrix, the spectrum measurements between spectrum decisions n=1 and n=2 are considered. All six decision parameters presented in the previous section are extracted form that matrix. These parameters comprise the decision DM2 matrix, which is stored and at the same time sent to the MADM algorithms. For this example, we consider a SU with a bandwidth-oriented connection profile. Thus,w has the highest weight in the bandwidth parameter. MADM algorithms select the best spectrum hole according to the connection profile and the spectrum holes in DM2. The selected spectrum hole hs2 is compared with the previous one hs1, which was stored in the history holes repository. The Comparison Function evaluates whether it is suitable to change to hs2 or remain in hs1, taking into account each spectrum hole characteristic and the ECCS. Finally, according to its connection profile, the final selected spectrum hole fsn is delivered to the SU to continue or not with the execution of the spectrum handoff.Figure 3
Summary of the EMSD, a spectrum decision proposal for an SU bandwidth-oriented connection profile.


## 4.1. Energy Consumption due to Channel Switching(Ecsn)

An important issue in wireless communication technologies is energy consumption, which can be reduced through less complex algorithms, among several solutions [3, 4]. In CRNs, however, additional issues related to energy consumption should be considered since CR devices necessitates additional tasks. In [5], an energy consumption model is presented where the authors consider energy consumption due to transmission (Etx), circuits (Ec), channel switching (Ecs), and idling (Ed). This paper is focused on calculating the Ecs, given that this parameter is related to the execution of spectrum handoffs due to energy consumed by the RF front-end in the reconfiguration process to use a new transmission frequency. According to [5, 29–31], Ecs can be obtained by the power dissipation for switching Pc and channel switching latency Tc. To adapt Tc to our notation, it is calculated as follows:(30)Tc=tcsfhsn-1-fhsn,where tcs is the time delay for switching multiplied by the difference of the central frequency of the previously selected spectrum hole fhsn-1 minus the central frequency of the new selected spectrum hole fhsn, as shown in(31)Ecsn=PcsTcs=Pcstcsfhsn-1-fhsn.


## 4.2. Comparison Function Description

In the system model presented in Figure1, multiple spectrum decisions are performed continuously; the proposed Comparison Function is executed after the preliminary decision of the MADM algorithms but before the final decision returned to the SU via SBS. The preliminary selection offered by MADM algorithms in CRNs presents an issue. In our work in [13], we demonstrated how these algorithms satisfy SUs connection profiles and provide the best spectrum hole selections. However, the MADM algorithms do not take into account additional expenses that a SU can have in order to reach the suggestion made for them, showing that they need to be improved for CRNs. For example, let us suppose that a SU is occupying a spectrum hole hsn-1; after a certain time the next spectrum decision has to be executed. In the moment of the decision, there is a spectrum hole hsn similar to hsn-1 but with a minor improvement (e.g., in bandwidth) than the actual one occupied by the SU; however, this spectrum hole is located in a very distant frequency band. The MADM algorithms are going to recommend to SU hsn no matter what the necessary resources to reach it are. Therefore, the SU will waste a considerable amount of ECCS Ecs in comparison with the marginal improvement of switching to hsn. In this stage, to enhance the MADM algorithms performance, a balance between Ecs and spectrum holes characteristics is required.The Comparison Function of EMSD is an adapter to improve the MADM algorithms performance in CRNs. Thus, the Comparison Function set the equivalence between the parameters of the spectrum holes and the energy consumed by switching among frequencies. However, spectrum holes parameters andEcs are in different units; nevertheless they can be compared after a normalization process [8]. Here, it is important to emphasize that the Comparison Function is dependent of the MADM algorithms and works as a complement. Also, it is important to point out that if hsn-1 is no longer available, the Comparison Function is not used and only the decision of MADM algorithms is taken into account. The whole process is carried out under certain restrictions that are explained below.This Comparison Function starts forn>1. The selected spectrum hole in a previous time hsn-1, the selected spectrum hole in the present time hsn, and the average spectrum holes in the current time DMn are necessary. The algorithm has two restrictions. The first one is hsn≠hsn-1; that is, the selected spectrum holes must be different, whereas an opposite case means the selection has no changes and the comparison is not necessary. The second one is hsn-1∈DMn; that is, the selected spectrum hole in the previous time hsn-1 should be included in DMn in the present time, and this is why if hsn-1 is not present in the current time, it has disappeared, which means that it is not possible to perform the comparison and the best selection is hsn.The Comparison Function calculates two important values. The first calculation corresponds to theEcsn′, as can be seen in (32). Here, the unit-based normalization was implemented. The max⁡(Ecs) and the min⁡(Ecs) values depend on the frequency range and spectrum holes size considered:(32)Ecsn′=Ecsn-min⁡Ecsmax⁡Ecs-min⁡Ecs,0,1.Also, the Comparison Function computes the changes among parameters of the selected spectrum holes. Every selected spectrum hole has six decision parameters, as shown in (12). The algorithm measures the distance between the parameters of hsn and the parameters of hsn-1. Thus, every element of hsn is subtracted from every element of hsn-1; the subtraction is made between parameters of the same kind. After that, each parameter subtraction uses the absolute value and it is normalized following the max-min method [8, 32]. This procedure is done in order to get a proportion of all decision parameters, which define the properties of each spectrum hole. For example, for a benefit parameter such as bw, the normalization process is made according to(33)bw′=bwhsn-bwhsn-1max⁡bw-min⁡bw,0,1.On the other hand, for a cost parameter such asdc, the process is made according to(34)dc′=max⁡dc-min⁡dcdchsn-dchsn-1,0,1.Thereby, the resultant vector with the proportion of all parametersrn is conformed as shown in(35)rn=bw′st′pi′dc′it′sf′.In order to quantifyrn in a scalar number that can be compared with Ecsn′, the values of rn are summed. Finally the result is normalized again in rn′ as can be seen in(36)rn′=1J∑j=1Jrnj,0,1.After that, asEcsn and rn are under the same range, it is possible to compare them. The algorithm looks for the minimum value between rn′ and Ecsn′. The result is assigned to dn as(37)dn=min⁡Ecsn′,rn′.Afterwards, the final selected spectrum holefhn for the decision n is obtained with (38). If dn is equal to Ecsn′, which means that the ECCS does not involve excessive cost and the benefits offered by the new selected spectrum hole hsn are better than the current one, hence the device should take hsn. The contrary case points out that it is better to keep the previously selected spectrum hole hsn-1, because the benefits of hsn are lower than the Ecsn:(38)fhn=hsn,ifdn=Ecsn′;hsn-1,ifdn=rn′.Thus,fhn is the result of this Comparison Function, which can be integrated to any MADM algorithm.


## 4.3. EMSD Summary

In this section, we explain an example of how our EMSD proposal works. Figure3 summarizes all the parts included in this proposal. As noted above, the proposal runs after the first decision (n=2). In the ID2 matrix, the spectrum measurements between spectrum decisions n=1 and n=2 are considered. All six decision parameters presented in the previous section are extracted form that matrix. These parameters comprise the decision DM2 matrix, which is stored and at the same time sent to the MADM algorithms. For this example, we consider a SU with a bandwidth-oriented connection profile. Thus,w has the highest weight in the bandwidth parameter. MADM algorithms select the best spectrum hole according to the connection profile and the spectrum holes in DM2. The selected spectrum hole hs2 is compared with the previous one hs1, which was stored in the history holes repository. The Comparison Function evaluates whether it is suitable to change to hs2 or remain in hs1, taking into account each spectrum hole characteristic and the ECCS. Finally, according to its connection profile, the final selected spectrum hole fsn is delivered to the SU to continue or not with the execution of the spectrum handoff.Figure 3
Summary of the EMSD, a spectrum decision proposal for an SU bandwidth-oriented connection profile.


## 5. Results

This section presents a performance comparison among the MADM algorithms (SAW, TOPSIS, and VIKOR) standalone and the same MADM algorithms when utilizing the Comparison Function of our EMSD proposal. Also, as a reference a random spectrum hole selection is included in the results. To evaluate the performance, the algorithms are executed over real spectrum holes from a spectrum occupancy measurements campaign described below. To achieve high accuracy results, this spectrum decision process is simulated by means of a 1000-round Montecarlo method using MATLAB. The tables and plots correspond to the average values of the selected spectrum holes. Also, the results are quantified in terms of number of spectrum handoffs and ECCS per each algorithm. In this paper, two connection profiles are considered. The first one issimilar weights-oriented profile; it occurs when a SU does not have a specific preference for any parameter in the spectrum hole. The second connection profile is thebandwidth-oriented profile, when a SU has a preference on getting a spectrum hole with the largest value of bandwidth.


### 5.1. Spectrum Occupancy Measurements on TV Bands

Realistic results can be obtained with information coming from real data. In [14], the spectrum opportunities for CRNs below 1 GHz were shown. In this work, data from a spectrum occupancy campaign are included. We focused the spectrum measurements on frequencies with low DC in TV frequency bands. The proposed methodology for this campaign includes three observation points, which were set to detect the spectrum usage surrounding a specific zone within the city. This study considered the frequencies from 170 MHz to 220 MHz, 525 MHz to 575 MHz, and 625 MHz to 675 MHz in the Mexican city of San Luis Potosí. Similar equipment used in [14] was used to obtain the spectrum usage information. The results showed a low presence of PUs with an average DC of 20%. Spectrum measurements were taken in each observation point around 24 hrs for each frequency range in a week day. For each observation point, the spectrum samples were averaged according to each frequency range. Thus, for each frequency range an average of 80 000 spectrum usage samples were obtained; these samples were used for each Montecarlo round. In order to process this information, N=80 spectrum decisions were made. The samples of each spectrum decision were assigned into the matrix IDn. Thus, a spectrum decision was conducted each 1.25% of the total spectrum time analyzed, where S=1000 samples and the number of resolution points of the frequencies examined is P=1500. Given that, the spectrum measurements come from TV frequency bands, and we considered the technical details from the IEEE 802.22 standard [33]. This guideline points out that there is an effective signal bandwidth of 5.5 MHz for a 6 MHz TV channel. Thus, the remaining 0.5 MHz is twice the size of the value of V mentioned in Section 2.1.3, and the value of τ presented in Section 2.1.5 is once that remaining value. For the ECCS presented in Section 4.2, we have assigned the values taken in [5]: Pcs = 1000 mW and tcs = 0.1 ms/MHz, and thus Ecs is given in Joules.


### 5.2. Similar Weights-Oriented Connection Profile

In this case, the SU connection requirements do not have a preference over any of the decision parameters; the vector of importance weightsw receives equal values. Thus, this connection profile requires an available spectrum hole with affordable characteristics in all parameters. The average values of the six parameters corresponding to the selected spectrum holes appear in Table 1. Note that all the selected spectrum holes have an average bandwidth size of approximately 6 MHz. However, by combining MADM algorithms and the Comparison Function, now spectrum holes in lower frequencies are selected. This might represent a larger coverage zone and energy savings for the SU. For example, by using VIKOR combined with the function, the SU obtains on average spectrum holes with 0.7 MHz less bandwidth compared by VIKOR alone. On the contrary, in this same example, the average of the selected spectrum holes exhibits the lowest selected frequency in 252 MHz and also the stability increases 27% compared to VIKOR alone. The random selection obtains average values in all the parameters, except for the lowest stability with 51%.Table 1
Average selected spectrum holes for a similar weights-oriented connection profile.
Algorithm b w s t p i dc i t s f SAW 6.2 66.8 0.98 6.74∗10-5 3.59 ∗ 1 0 4 509.9 SAW + Comparison Function 5.8 77.1 0.97 3.73∗10-4 1.66 ∗ 1 0 5 406.7 TOPSIS 6.2 76.1 0.97 2.86∗10-4 2.67 ∗ 1 0 4 587.2 TOPSIS + Comparison Function 6.1 71.6 0.97 2.66∗10-4 2.73 ∗ 1 0 4 581.2 VIKOR 6.1 60.4 0.98 6.15∗10-4 1.18 ∗ 1 0 5 463.6 VIKOR + Comparison Function 5.4 87.9 0.97 0.001 3.52 ∗ 1 0 5 252.5 Random 6.1 50.9 0.97 0.009 2.06 ∗ 1 0 5 449.5Figure4(a) shows a significant reduction in the number of spectrum handoffs when the Comparison Function is used. For the considered cases, the number of spectrum handoffs successfully avoided is approximately from 20 to 60. It can be seen that MADM algorithms (alone) reduce between 5 and 30 the number of spectrum handoffs when compared to the random selection. Moreover, the combination MADM algorithms with Comparison Function obtain between 50 and 60 less spectrum handoffs compared to the random case. As expected, this reduction is directly related to a decrement in the amount of ECCS as shown in Figure 4(b). The ECCS saved by using the Comparison Function for SAW and TOPSIS is approximately of 4 Joules. Nevertheless, combining VIKOR plus the Comparison Function saves on average about 15 Joules. However, the combination of MADM algorithms with Comparison Function saves between 18 and 19 Joules compared to the random selection. Thus, the inconvenient ping-pong effect due to frequent spectrum handoffs is avoided and the energy saved at the SUs battery is available for other tasks.Figure 4
Average performance of MADM algorithms, MADM algorithms combined with Comparison Function of the EMSD and a random case for a similar weights-oriented connection profile.
(a)
Number of spectrum handoffs (b)
Energy consumption due to channel switching


### 5.3. Bandwidth-Oriented Connection Profile

For this case, the SU connection requirements demand a large amount of bandwidth. Thus, the bandwidth parameter has the highest weight, with a 1 : 5 proportion with respect to the other decision parameters. The decision algorithms look for the spectrum hole with the largest bandwidth and give less importance to the other parameters. But still the MADM algorithms have to consider the six parameters in the spectrum decision. Table2 shows the average values of the selected spectrum holes for this connection profile. In this table, the number of selected spectrum holes increased the bandwidth size with respect to the previous connection profile. Note that VIKOR and the combination of VIKOR with Comparison Function select on average the largest values of bandwidth. Also the combination of VIKOR plus Comparison Function achieves on average the lowest selected frequency with 292.9 MHz. On the other hand, SAW and TOPSIS (both alone) present similar results in bandwidth size, power index, and interference temperature. However, when SAW and TOPSIS include the Comparison Function, they present a reduction of 0.3 MHz in the average bandwidth size. Nevertheless, the stability increases 2–6% more in both algorithms while for SAW plus the Comparison Function a reduction of the selected frequency to 448.8 MHz is attained as well. Finally, the random selection as expected achieves similar values to the previous user profile.Table 2
Average selected spectrum holes for a bandwidth-oriented connection profile.
Algorithm b w s t p i d c i t s f SAW 6.6 63.5 0.98 5.53∗10-4 2.91 ∗ 1 0 4 529.2 SAW + Comparison Function 6.2 69.1 0.97 0.003 1.58 ∗ 1 0 5 448.8 TOPSIS 6.6 67.1 0.98 3.46∗10-4 2.49 ∗ 1 0 4 584.8 TOPSIS + Comparison Function 6.3 68.5 0.98 3.45∗10-4 3.59 ∗ 1 0 4 573.4 VIKOR 6.8 35.8 0.97 0.022 3.11 ∗ 1 0 5 427.7 VIKOR + Comparison Function 6.8 25.4 0.97 0.039 5.61 ∗ 1 0 5 292.9 Random 6.1 50.7 0.97 0.009 2.05 ∗ 1 0 5 449.9Figure5(a) shows an increment of 8–10 more spectrum handoffs only for SAW and TOPSIS compared to the similar weights-oriented profile. However, for this connection profile the number of spectrum handoffs avoided is approximately from 20 to 55. The combination of MADM algorithms plus the Comparison Function compared to the random selection avoids between 45 and 55 spectrum handoffs. MADM algorithms (alone) obtain between 8 to 21 spectrum handoffs less than random case. Similarly to the previous results, an augmentation in the number of spectrum handoffs generates an increment in the amount of ECCS as shown in Figure 5(b). The energy saved by the Comparison Function follows the trend of the last connection profile, 2–15 Joules. An important amount of ECCS is saved by the MADM plus the Comparison Function compared to the random selection. The first algorithm consumes between 2 and 3 Joules, while the random case consumes 20 Joules. Therefore, it is clearly shown that the use of the Comparison Function always reduces more than half of the energy consumed in all cases.Figure 5
Average performance of MADM algorithms, MADM algorithms combined with Comparison Function of the EMSD and a random case for a bandwidth-oriented connection profile.
(a)
Number of spectrum handoffs (b)
Energy consumption due to channel switchingFigure6 shows the average value of bandwidth as well as the selected frequency of the selected spectrum holes during the spectrum decision process of the 80 successive decisions by SAW and SAW combined with the Comparison Function for a bandwidth-oriented connection profile. From this figure, it is easy to see how the EMSD proposal avoids an important number of spectrum handoffs. Note also in the same figure that SAW combined with the Comparison Function tends to select spectrum holes in lower values of frequencies. On the other hand, both options select spectrum holes with similar bandwidth sizes. However, the SU which includes the Comparison Function can save an important amount of energy.Figure 6
Frequency distribution and bandwidth size of the selected spectrum holes by SAW and SAW combined with Comparison Function of the EMSD for 80 decisions.In both Tables1 and 2, a small reduction of the average bandwidth with the three MADM algorithms is shown when the Comparison Function from our EMSD proposal is used. In order to show this issue and to appreciate the possible QoS impact that a SU’s connection can experience, Figure 7 presents the data rate and energy consumption for SAW (alone) and SAW combined with the Comparison Function for a bandwidth-oriented connection profile. According to [34], the standard IEEE 802.22 considers a data rate between 0.5 and 5 bits/sec/Hz. The data rate is directly proportional to the size of the bandwidth. Thus, in Figure 7 an estimated average data rate of 3 bits/sec/Hz is considered. Also, this figure shows the energy consumption per decision by both algorithm options. In most of the decisions, the data rate is almost the same for SAW and SAW plus the Comparison Function. However, in several decisions SAW with the Comparison Function shows a data rate reduction between 5% and 10%. Nevertheless, the energy consumed by the Comparison Function in all the spectrum decision is considerably lower compared with SAW (alone), and the percentage of energy consumed is of at least 50% less per decision. For the scenario in Figure 7, the spectrum holes selected by SAW combined with the Comparison Function achieve almost the same data rate. Nonetheless, the energy consumed by the Comparison Function makes it widely recommendable.Figure 7
Data rate and energy consumed by SAW and SAW combined with Comparison Function of the EMSD for 80 decisions.Finally, Figure8 shows the percentage of the total ECCS saved with the MADM algorithms combined with the Comparison Function in our EMSD proposal. Connection profiles bandwidth and similar weights save from 60% to 90% of the ECCS. Also, results of VIKOR have improved for both connection profiles by using the Comparison Function. For the three MADM algorithms considered, it is shown that by following our EMSD proposal their performance can be satisfactory while trading off energy consumption. The proposed EMSD is able to reduce the number of spectrum handoffs considering the ECCS, which significantly improves the overall spectrum decision process in the forthcoming CRNs.Figure 8
Energy saved by using the MADM algorithms combined with Comparison Function of the EMSD regarding MADM algorithms for two different connection profiles.


## 5.1. Spectrum Occupancy Measurements on TV Bands

Realistic results can be obtained with information coming from real data. In [14], the spectrum opportunities for CRNs below 1 GHz were shown. In this work, data from a spectrum occupancy campaign are included. We focused the spectrum measurements on frequencies with low DC in TV frequency bands. The proposed methodology for this campaign includes three observation points, which were set to detect the spectrum usage surrounding a specific zone within the city. This study considered the frequencies from 170 MHz to 220 MHz, 525 MHz to 575 MHz, and 625 MHz to 675 MHz in the Mexican city of San Luis Potosí. Similar equipment used in [14] was used to obtain the spectrum usage information. The results showed a low presence of PUs with an average DC of 20%. Spectrum measurements were taken in each observation point around 24 hrs for each frequency range in a week day. For each observation point, the spectrum samples were averaged according to each frequency range. Thus, for each frequency range an average of 80 000 spectrum usage samples were obtained; these samples were used for each Montecarlo round. In order to process this information, N=80 spectrum decisions were made. The samples of each spectrum decision were assigned into the matrix IDn. Thus, a spectrum decision was conducted each 1.25% of the total spectrum time analyzed, where S=1000 samples and the number of resolution points of the frequencies examined is P=1500. Given that, the spectrum measurements come from TV frequency bands, and we considered the technical details from the IEEE 802.22 standard [33]. This guideline points out that there is an effective signal bandwidth of 5.5 MHz for a 6 MHz TV channel. Thus, the remaining 0.5 MHz is twice the size of the value of V mentioned in Section 2.1.3, and the value of τ presented in Section 2.1.5 is once that remaining value. For the ECCS presented in Section 4.2, we have assigned the values taken in [5]: Pcs = 1000 mW and tcs = 0.1 ms/MHz, and thus Ecs is given in Joules.


## 5.2. Similar Weights-Oriented Connection Profile

In this case, the SU connection requirements do not have a preference over any of the decision parameters; the vector of importance weightsw receives equal values. Thus, this connection profile requires an available spectrum hole with affordable characteristics in all parameters. The average values of the six parameters corresponding to the selected spectrum holes appear in Table 1. Note that all the selected spectrum holes have an average bandwidth size of approximately 6 MHz. However, by combining MADM algorithms and the Comparison Function, now spectrum holes in lower frequencies are selected. This might represent a larger coverage zone and energy savings for the SU. For example, by using VIKOR combined with the function, the SU obtains on average spectrum holes with 0.7 MHz less bandwidth compared by VIKOR alone. On the contrary, in this same example, the average of the selected spectrum holes exhibits the lowest selected frequency in 252 MHz and also the stability increases 27% compared to VIKOR alone. The random selection obtains average values in all the parameters, except for the lowest stability with 51%.Table 1
Average selected spectrum holes for a similar weights-oriented connection profile.
Algorithm b w s t p i dc i t s f SAW 6.2 66.8 0.98 6.74∗10-5 3.59 ∗ 1 0 4 509.9 SAW + Comparison Function 5.8 77.1 0.97 3.73∗10-4 1.66 ∗ 1 0 5 406.7 TOPSIS 6.2 76.1 0.97 2.86∗10-4 2.67 ∗ 1 0 4 587.2 TOPSIS + Comparison Function 6.1 71.6 0.97 2.66∗10-4 2.73 ∗ 1 0 4 581.2 VIKOR 6.1 60.4 0.98 6.15∗10-4 1.18 ∗ 1 0 5 463.6 VIKOR + Comparison Function 5.4 87.9 0.97 0.001 3.52 ∗ 1 0 5 252.5 Random 6.1 50.9 0.97 0.009 2.06 ∗ 1 0 5 449.5Figure4(a) shows a significant reduction in the number of spectrum handoffs when the Comparison Function is used. For the considered cases, the number of spectrum handoffs successfully avoided is approximately from 20 to 60. It can be seen that MADM algorithms (alone) reduce between 5 and 30 the number of spectrum handoffs when compared to the random selection. Moreover, the combination MADM algorithms with Comparison Function obtain between 50 and 60 less spectrum handoffs compared to the random case. As expected, this reduction is directly related to a decrement in the amount of ECCS as shown in Figure 4(b). The ECCS saved by using the Comparison Function for SAW and TOPSIS is approximately of 4 Joules. Nevertheless, combining VIKOR plus the Comparison Function saves on average about 15 Joules. However, the combination of MADM algorithms with Comparison Function saves between 18 and 19 Joules compared to the random selection. Thus, the inconvenient ping-pong effect due to frequent spectrum handoffs is avoided and the energy saved at the SUs battery is available for other tasks.Figure 4
Average performance of MADM algorithms, MADM algorithms combined with Comparison Function of the EMSD and a random case for a similar weights-oriented connection profile.
(a)
Number of spectrum handoffs (b)
Energy consumption due to channel switching


## 5.3. Bandwidth-Oriented Connection Profile

For this case, the SU connection requirements demand a large amount of bandwidth. Thus, the bandwidth parameter has the highest weight, with a 1 : 5 proportion with respect to the other decision parameters. The decision algorithms look for the spectrum hole with the largest bandwidth and give less importance to the other parameters. But still the MADM algorithms have to consider the six parameters in the spectrum decision. Table2 shows the average values of the selected spectrum holes for this connection profile. In this table, the number of selected spectrum holes increased the bandwidth size with respect to the previous connection profile. Note that VIKOR and the combination of VIKOR with Comparison Function select on average the largest values of bandwidth. Also the combination of VIKOR plus Comparison Function achieves on average the lowest selected frequency with 292.9 MHz. On the other hand, SAW and TOPSIS (both alone) present similar results in bandwidth size, power index, and interference temperature. However, when SAW and TOPSIS include the Comparison Function, they present a reduction of 0.3 MHz in the average bandwidth size. Nevertheless, the stability increases 2–6% more in both algorithms while for SAW plus the Comparison Function a reduction of the selected frequency to 448.8 MHz is attained as well. Finally, the random selection as expected achieves similar values to the previous user profile.Table 2
Average selected spectrum holes for a bandwidth-oriented connection profile.
Algorithm b w s t p i d c i t s f SAW 6.6 63.5 0.98 5.53∗10-4 2.91 ∗ 1 0 4 529.2 SAW + Comparison Function 6.2 69.1 0.97 0.003 1.58 ∗ 1 0 5 448.8 TOPSIS 6.6 67.1 0.98 3.46∗10-4 2.49 ∗ 1 0 4 584.8 TOPSIS + Comparison Function 6.3 68.5 0.98 3.45∗10-4 3.59 ∗ 1 0 4 573.4 VIKOR 6.8 35.8 0.97 0.022 3.11 ∗ 1 0 5 427.7 VIKOR + Comparison Function 6.8 25.4 0.97 0.039 5.61 ∗ 1 0 5 292.9 Random 6.1 50.7 0.97 0.009 2.05 ∗ 1 0 5 449.9Figure5(a) shows an increment of 8–10 more spectrum handoffs only for SAW and TOPSIS compared to the similar weights-oriented profile. However, for this connection profile the number of spectrum handoffs avoided is approximately from 20 to 55. The combination of MADM algorithms plus the Comparison Function compared to the random selection avoids between 45 and 55 spectrum handoffs. MADM algorithms (alone) obtain between 8 to 21 spectrum handoffs less than random case. Similarly to the previous results, an augmentation in the number of spectrum handoffs generates an increment in the amount of ECCS as shown in Figure 5(b). The energy saved by the Comparison Function follows the trend of the last connection profile, 2–15 Joules. An important amount of ECCS is saved by the MADM plus the Comparison Function compared to the random selection. The first algorithm consumes between 2 and 3 Joules, while the random case consumes 20 Joules. Therefore, it is clearly shown that the use of the Comparison Function always reduces more than half of the energy consumed in all cases.Figure 5
Average performance of MADM algorithms, MADM algorithms combined with Comparison Function of the EMSD and a random case for a bandwidth-oriented connection profile.
(a)
Number of spectrum handoffs (b)
Energy consumption due to channel switchingFigure6 shows the average value of bandwidth as well as the selected frequency of the selected spectrum holes during the spectrum decision process of the 80 successive decisions by SAW and SAW combined with the Comparison Function for a bandwidth-oriented connection profile. From this figure, it is easy to see how the EMSD proposal avoids an important number of spectrum handoffs. Note also in the same figure that SAW combined with the Comparison Function tends to select spectrum holes in lower values of frequencies. On the other hand, both options select spectrum holes with similar bandwidth sizes. However, the SU which includes the Comparison Function can save an important amount of energy.Figure 6
Frequency distribution and bandwidth size of the selected spectrum holes by SAW and SAW combined with Comparison Function of the EMSD for 80 decisions.In both Tables1 and 2, a small reduction of the average bandwidth with the three MADM algorithms is shown when the Comparison Function from our EMSD proposal is used. In order to show this issue and to appreciate the possible QoS impact that a SU’s connection can experience, Figure 7 presents the data rate and energy consumption for SAW (alone) and SAW combined with the Comparison Function for a bandwidth-oriented connection profile. According to [34], the standard IEEE 802.22 considers a data rate between 0.5 and 5 bits/sec/Hz. The data rate is directly proportional to the size of the bandwidth. Thus, in Figure 7 an estimated average data rate of 3 bits/sec/Hz is considered. Also, this figure shows the energy consumption per decision by both algorithm options. In most of the decisions, the data rate is almost the same for SAW and SAW plus the Comparison Function. However, in several decisions SAW with the Comparison Function shows a data rate reduction between 5% and 10%. Nevertheless, the energy consumed by the Comparison Function in all the spectrum decision is considerably lower compared with SAW (alone), and the percentage of energy consumed is of at least 50% less per decision. For the scenario in Figure 7, the spectrum holes selected by SAW combined with the Comparison Function achieve almost the same data rate. Nonetheless, the energy consumed by the Comparison Function makes it widely recommendable.Figure 7
Data rate and energy consumed by SAW and SAW combined with Comparison Function of the EMSD for 80 decisions.Finally, Figure8 shows the percentage of the total ECCS saved with the MADM algorithms combined with the Comparison Function in our EMSD proposal. Connection profiles bandwidth and similar weights save from 60% to 90% of the ECCS. Also, results of VIKOR have improved for both connection profiles by using the Comparison Function. For the three MADM algorithms considered, it is shown that by following our EMSD proposal their performance can be satisfactory while trading off energy consumption. The proposed EMSD is able to reduce the number of spectrum handoffs considering the ECCS, which significantly improves the overall spectrum decision process in the forthcoming CRNs.Figure 8
Energy saved by using the MADM algorithms combined with Comparison Function of the EMSD regarding MADM algorithms for two different connection profiles.


## 6. Conclusions

The aim of this investigation was to reduce the energy switching consumption due to handoffs in CRNs by studying the performance of MADM algorithms in the context of spectrum decision using real spectrum measurements. Thus, an enhanced MADM-based decision functionality was proposed by taking as inputs the spectrum information of the SUs surrounding environment and its connection requirements. Hence, six decision parameters were considered to characterize each available spectrum hole. Then, these were extracted from real power spectrum measurements and used as inputs of the new MADM-based spectrum decision. It was shown that the proposed spectrum decision algorithm can reduce the number of handoffs by trading off the ECCS. Results quantified savings from 30% to 90% in ECCS and reduced number of spectrum handoffs from 47% to 90% in TV bands using two different connection profiles.



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*Source: 6157904-2016-11-28.xml*