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

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.Thismight 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%.


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 decisionmaking (MADM) problem [8].MADM algorithms have been previously utilized for network selection in the context of heterogeneous wireless networks [9][10][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 abovementioned 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.Section 2 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.

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 Figure 1.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][16][17].
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.

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 called interval decision ID  , with  = 1, . . ., , and where  is the total number of consecutive spectrum decisions.The ID  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 , with  = 1, . . ., , and the total number of resolution points is  corresponding to the examined frequencies, with  = 1, . . ., .Here, it is important to mention the existence of the auxiliary vector fk that has the frequency value of each  resolution point and that is used as identifier.Thus, id , is any ID  element that has a sample of the spectral power in a frequency point: 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 interval ID  .In the following subsubsections, we describe how and why each of the decision parameters is calculated.

Duty Cycle (dc 𝑛 ).
A fundamental parameter to establish the spectral occupation from spectrum measurements is the duty 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 , 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 id , of ID  is passed through , where 0 or 1 values are assigned on a DC  matrix with same size as ID  , as explained by the following equation: Thereafter, the  rows of DC  are averaged.The result is stored in dc  , as shown in (3).The dc  variable has the average DC for each frequency point  with values between 0 and 1 for the decision .Since a lower value of this parameter is the better, the DC represents a cost parameter.
2.1.2.Bandwidth (bw  ).One of the most important parameters to characterize spectrum holes is the bandwidth.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 dc  vector and the resolution points , each spectrum hole is calculated.In this process, each element of dc  vector is rounded in two values (0 or 1) in order to determine empty or occupied frequencies.Algorithm 1 and Figure 2 describe how the bw  vector is obtained.The beginning of a spectrum hole is considered when the  counting variable is odd or equal to 0 and dc  () < 1.In that case, the value of the auxiliary vector fk  to which  is pointing out is stored in   as can be seen in Figure 2. The spectrum hole ending appears when dc  () = 0 and the next resolution point dc  ( + 1) > 0; in a similar way the fk  value where  is pointing out is stored in   .Also, the size of this space is calculated by doing   −   ; if it is larger than , it is saved in   , wherein  corresponds to all spectrum holes with  = 1, . . ., .For each , there is a identifier that stores the value of central frequency of each spectrum hole.
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  Initialize  = 0,  = 0 for  = 1 →  do if ( odd or  = 0) and dc  () < 1 then considered in this work, and so  = 5 MHz.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   elements of the set  = { 1 = 5,  2 = 6,  3 = 7,  4 = 8}.If there is an element of  equal to the spectrum hole size of u  (), it is directly assigned to bw  ().In other cases, if the size of u  () exceeds 8 MHz, it is randomly partitioned in the elements of   .The   set includes random elements of , as many as can be fitted in   .The condition is that the sum of   elements should be less than or equal to u  ().
Finally, the vector with the average bandwidth size of each spectrum hole in the decision  is bw  , where the bw  length is  = 1, . . ., , where  is the number of spectrum holes per decision.It is important to mention that, similarly to , the variable  has an auxiliary vector fk  where the central frequency values of each spectrum holes are stored.When u  () is directly assigned to bw  (), the mapping  to  is one to one, for the contrary case  will increase depending of the number of elements of   .Hence, if all spectrum holes of u  are among the spectrum holes considered,  = .However, when spectrum holes of u  are larger, then  > .Thus, the size of this vector is not fixed, and hence it can change for each spectrum decision.

Stability of Spectrum Holes (st 𝑛
). Spectrum hole stability (st  ) 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 row  of the DC  matrix, the vector th  is computed using the same procedures used for computing bw  .The result is stored in th  (), where  = 1, . . .,  with  being the temporal variable with the number of spectrum holes found in that row .The temporal variable  has also an auxiliary vector fg  where the central frequency values of each spectrum holes of th  are stored.After that, the fk  vector with the central frequency of each element of the bw  vector is sought in the fg  vector corresponding to the th  () vector.The procedure follows the following restrictions: a spectrum hole has a variation, but it is considered the same if fg  ∈ fk  and if the difference between fk  () and the fg  () 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 fg  () and fk  () is calculated and the instability (i.e., variation in time of the spectrum hole) is posted to the ie  () 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 ie  (), as can be seen in Mobile Information Systems 5 The ie  vector with values between 0 and 1 is stored in the ST  matrix with dimension  × , as can be seen in Finally, the rows of the matrix mentioned before are averaged, subtracted from 1, and multiplied by 100 to obtain the percentage of stability st  for the decision , as can be seen in 2.1.4.Power Index (pi  ).The power 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: After that, the power index pi  () for the decision  is obtained by the division of  max () by  min (), as can be seen in ( 8).If  max () is close to  min (), pi  () is near 1, and therefore the maximum power is low and the SU is not greatly affected by the PU presence.The pi  () 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: 2.1.5.Interference Temperature (it  ).A parameter that should be included in the selection of a spectrum hole is the interference 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: where  is the power in the central frequency   in the selected bandwidth bw  (), K is Boltzmann's constant, and  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 it  () 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 bw  (), where the it  vector is obtained for each decision .The range of IT changes according to the frequency measured and the size of the available spectrum holes.
2.1.6.Selected Frequency (sf  ).The importance of frequency 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 in bw  receive a cost in the vector sf  .Equation (10) explains the distribution of penalty costs.The lowest possible frequency corresponds to the first spectrum hole  = 1, which gets the lowest cost in sf  .The operation is repeated for each spectrum hole  with the same cost in sf  as the value of ; hence sf  is the same size as bw  and it is calculated for each decision .This parameter is a cost; a lower cost or a lower frequency is preferable instead of a high frequency:

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.
Mobile Information Systems

Decision Matrix (DM 𝑛
).First, according to the previous section, the available spectrum holes and their corresponding parameters are arranged as follows to form the decision matrix DM  for each decision  as can be seen in where the first three columns correspond to benefit decision parameters, bandwidth bw, stability st, and power index pi, while the next three columns correspond to cost decision parameters, duty cycle dc, interference temperature it, and selected frequency sf.Thus, in this paper  = 6 always in (11).
On the other hand, the  rows correspond to the  available spectrum holes at decision , and thus  may vary from decision to decision based on the occupancy of the spectrum.Note that in (3) dc was in terms of ; however, for the DM  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 matrix DM  .

Connection Profiles.
As mentioned before, a set of connection profiles are assumed to be prestored in the SU terminal.Once the decision matrix DM  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 ∑  =1   = 1 where   corresponds to the importance weight of parameter  with  = 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.
The DM  matrix and the set of importance weights   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 DM  .To make the notation easier, for each decision , this row is given by selected spectrum hole hs  .It includes the six decision parameters, as can be seen in In the following subsections, the MADM algorithms implemented in this work are presented.

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 at  corresponds to the normalization of each decision parameter and dm  is an element of the DM  matrix.This method performs homogenization; each at  parameter is multiplied by   to obtain the score of each candidate alternative.The normalization of at  is described as follows: if at  is a benefit parameter, it is normalized as can be seen in (13), where dm +  = max  dm  .On the other hand, if at  is a cost parameter, it is normalized as it is shown in (14), where dm −  = min  dm  : The alternative selected by this method is (15), where   is the importance weight of th parameter:

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   and dm  .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 Step 2. Construct the weighted normalized decision matrix as V  =   * at  .
Step 3. Determine ideal alternative with (17) and negativeideal alternatives with (18) as follows: 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: Step 5. Calculate the relative closeness to the ideal alternative: Equation ( 22) corresponds to the final step of this algorithm, where the best spectrum hole according to the SU's connection requirements is hs * TOP : 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 parameter  = 1, 2, 3, . . ., , determine the best value (23) and the worst value (24) given by where   ⊂ BC is the set of benefit parameters and   ⊂ BC  is the set of cost parameters.
Step 3. Compute the values of   with (27) for  = 1, 2, 3, . . ., , where  is the weight of the strategy with 0 ≤  ≤ 1: where Step 4. Given the values of  for all  ∈ , rank the candidate networks in an increasing order.
Equation ( 29) expresses the final step of this algorithm in the hs * VIK vector, where  *  is the best solution for satisfying the SU's connection requirements.

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 before hs −1 , the selected spectrum hole in the current time hs  , 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].

Energy Consumption due to Channel Switching (𝐸 cs 𝑛 ).
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 ( tx ), circuits (  ), channel switching ( cs ), and idling (  ).This paper is focused on calculating the  cs , 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.
To adapt   to our notation, it is calculated as follows: where  cs is the time delay for switching multiplied by the difference of the central frequency of the previously selected  1, 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 hs −1 ; after a certain time the next spectrum decision has to be executed.In the moment of the decision, there is a spectrum hole hs  similar to hs −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 hs  no matter what the necessary resources to reach it are.Therefore, the SU will waste a considerable amount of ECCS  cs in comparison with the marginal improvement of switching to hs  .In this stage, to enhance the MADM algorithms performance, a balance between  cs 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 and  cs 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 hs −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 for  > 1.The selected spectrum hole in a previous time hs −1 , the selected spectrum hole in the present time hs  , and the average spectrum holes in the current time DM  are necessary.The algorithm has two restrictions.The first one is hs  ̸ = hs −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 hs −1 ∈ DM  ; that is, the selected spectrum hole in the previous time hs −1 should be included in DM  in the present time, and this is why if hs −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 hs  .
The Comparison Function calculates two important values.The first calculation corresponds to the   cs  , as can be seen in (32).Here, the unit-based normalization was implemented.The max( cs ) and the min( cs ) values depend on the frequency range and spectrum holes size considered: 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 hs  and the parameters of hs −1 .Thus, every element of hs  is subtracted from every element of hs −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 On the other hand, for a cost parameter such as dc, the process is made according to Thereby, the resultant vector with the proportion of all parameters r  is conformed as shown in In order to quantify r  in a scalar number that can be compared with   cs  , the values of r  are summed.Finally the result is normalized again in    as can be seen in After that, as  cs  and   are under the same range, it is possible to compare them.The algorithm looks for the minimum value between    and   cs  .The result is assigned to   as Afterwards, the final selected spectrum hole fh  for the decision  is obtained with (38).If   is equal to   cs  , which means that the ECCS does not involve excessive cost and the benefits offered by the new selected spectrum hole hs  are better than the current one, hence the device should take hs  .The contrary case points out that it is better to keep the previously selected spectrum hole hs −1 , because the benefits of hs  are lower than the  cs  : Thus, fh  is the result of this Comparison Function, which can be integrated to any MADM algorithm.

EMSD Summary.
In this section, we explain an example of how our EMSD proposal works.Figure 3 summarizes all the parts included in this proposal.As noted above, the proposal runs after the first decision ( = 2).In the ID 2 matrix, the spectrum measurements between spectrum decisions  = 1 and  = 2 are considered.All six decision parameters presented in the previous section are extracted form that matrix.These parameters comprise the decision DM 2 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 DM 2 .The selected spectrum hole hs 2 is compared with the previous one hs 1 , which was stored in the history holes repository.The Comparison Function evaluates whether it is suitable to change to hs 2 or remain in hs 1 , taking into account each spectrum hole characteristic and the ECCS.Finally, according to its connection profile, the final selected spectrum hole fs  is delivered to the SU to continue or not with the execution of the spectrum handoff.

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 is similar 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 the bandwidth-oriented profile, when a SU has a preference on getting a spectrum hole with the largest value of bandwidth.

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  [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,  = 80 spectrum decisions were made.The samples of each spectrum decision were assigned into the matrix ID  .Thus, a spectrum decision was conducted each 1.25% of the total spectrum time analyzed, where  = 1000 samples and the number of resolution points of the frequencies examined is  = 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  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]:  cs = 1000 mW and  cs = 0.1 ms/MHz, and thus  cs is given in Joules.

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 weights w 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%. Figure 4(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.

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.Table 2 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.Figure 5(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 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 6 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   In both Tables 1 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.Finally, Figure 8 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.

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.

Figure 1 :
Figure 1: System model for the EMSD functionality.

Figure 2 :
Figure 2: Example of how spectrum holes are found.

Figure 3 :
Figure 3: Summary of the EMSD, a decision proposal for an SU bandwidth-oriented connection profile.
to channel switching (J) (b) Energy consumption due to channel switching

Figure 4 :
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.
(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.
Comparison Function TOPSIS + Comparison Function VIKOR + Comparison Function (b) Energy consumption due to channel switching

Figure 5 : 8 F
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.

Figure 6 :
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.

Figure 7 :
Figure 7: Data rate and energy consumed by SAW and SAW combined with Comparison Function of the EMSD for 80 decisions.

Figure 8 :
Figure 8: Energy saved by using the MADM algorithms combined with Comparison Function of the EMSD regarding MADM algorithms for two different connection profiles.
bw 11 st 12 pi 13 dc 14 it 15 sf 1 1 st 2 pi 3 dc 4 it 5 sf bw) , Mobile Information Systems spectrum hole  hs −1 minus the central frequency of the new selected spectrum hole  hs  , as shown in  cs  =  cs  cs =  cs ( cs       hs −1 −  hs       ) .

Table 1 :
Average selected spectrum holes for a similar weights-oriented connection profile.

Table 2 :
Average selected spectrum holes for a bandwidth-oriented connection profile.