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Performance of MADM Algorithms with Real Spectrum Measurements for Spectrum Decision in Cognitive Radio Networks Rafael Aguilar-Gonzalez, Marco Cardenas-Juarez, Ulises Pineda-Rico and Enrique Stevens-Navarro Facultad de Ciencias, Universidad Aut´onoma de San Luis Potos´ı (UASLP), Av. Salvador Nava Mtz. s/n, Zona Universitaria, 78290, San Luis Potos´ı, SLP, M´exico. e-mail: {raguilar, estevens}@fc.uaslp.mx

Abstract— Spectrum decision is an important functionality of a cognitive radio terminal, which allows the selection of the appropriate frequency band from the available underutilized spectrum. Spectrum decision conducts itself in accordance to the communication requirements of the secondary (or cognitive) users in the forthcoming Cognitive Radio Networks (CRNs). Selecting the best spectrum for a given transmission involves making preference decisions over the set of available alternatives of frequency bands, which are indeed characterized by different attributes. Therefore, spectrum decision can be modeled as a multiple attribute decision making (MADM) problem. In this paper, we evaluate the performance of MADM decision algorithms such as Simple Additive Weighting (SAW), Technique for Order Preferences by Similarity to Ideal Solution (TOPSIS) and the Compromise Ranking Method VIKOR for spectrum decision. The study, however, is conducted using real spectrum occupancy measurements to evaluate the performance of the aforementioned algorithms in a practical scenario. Some important attributes of underutilized spectrum are proposed for consideration in the decisions. Results show that SAW algorithm performs well for the preferred spectrum attributes in the selected scenarios, while offering a good performance also in other parameters.

I. I NTRODUCTION It is expected that Cognitive Radio Networks (CRNs) will co-exist with current wireless networks with fixed allocation of spectrum and offering services only to their users (i.e., the primary users). In the background, users of the CRNs (i.e., the secondary users) will be using the unused space in the spectrum. However, to fully operate as expected, CRNs require supporting a set of challenging spectrum management functionalities [1]: spectrum sensing, spectrum sharing, spectrum decision, and spectrum mobility. The last two functionalities are the less explored and still they execute two key mobility processes in CRNs such as the selection of the best free channel to use and the prevention of collision of transmissions among primary and secondary users, respectively. There are proposals in the literature to perform the decision making functionality, as the case of [2] and [3], where frameworks for decision spectrum with different control steps and algorithms are presented. In such studies, decisions are taken based on the demand of Quality of Service (QoS) of each primary user and based on various services offered. However,

there are also several additional decision parameters that can be considered in the spectrum decision process. In fact, this problem becomes a decision of multiple options (e.g., frequency bands) and each one described by multiple parameters (e.g., bandwidth, quality, etc.) which can be formulated as a Multiple Attribute Decision Making (MADM) problem. MADM algorithms to solve decision problems have been used in a wide range of engineering areas [4]. Such algorithms have been proposed for mobility management to deal with the decision process of the vertical handoff of users in heterogeneous wireless networks [5], [6], [7]. Although the use of MADM techniques for spectrum decision in CRNs is explored in [8], we consider that in order to deal with a more accurate spectrum decision it is required to use realistic models of the real occupancy of the spectrum. In order to test and validate the implementation of CRNs, several spectrum occupancy measurements campaigns have been conducted worldwide for the past few years [9], [10]. The aim of measurement campaigns is to obtain accurate models of the real behaviour of the spectrum occupancy that can be used on the design and development of CRNs. In [11], we conducted the first spectrum measurement campaign in our country which shown that the average spectrum occupancy in the place where the study was executed is around 12.5%. Such values, clearly demonstrate the potential of CRNs since there are plenty of unused spectrum that can be accessed dynamically and opportunistically for communication services. In this paper, we present the performance of three MADM algorithms for spectrum decision in CRNs. The MADM algorithms: Simple Additive Weighting (SAW) [12], Technique for Order Preference by Similarity to Ideal Solution Algorithm (TOPSIS) [12], and the Compromise Ranking Method VIKOR [13] are tested with data that have been collected from the measurement campaign previously reported in [11]. In some publications the data from measurement campaigns are used in the statistical modeling of the environments, however, this work aims at assessing the behaviour of these MADM algorithms in a real environment. The rest of the paper is organized as follows. In Section II the MADM algorithms are presented. In Section III details re-

garding the measurements data and the description of decision parameters used in this study are presented. In Section IV the results are discussed. Finally, Section V concludes the paper. II. MADM A LGORITHMS MADM is a branch of the field of Multi-Criteria Decision Making (MCDM) [4]. The characteristics of a MADM problem are: alternatives to select, multiple attributes describing the alternatives in different units, and a set of weights representing the relative importance of each attribute. For notation, let M be the set of alternatives and N be the set of attributes. Thus, the decision matrix of the MAMD problem is shown in (1) where the columns are the attributes and rows indicate the alternatives, xij is the rating of the ith alternative in the j th attribute. The importance P is represented by the weights N in w, the sum of w with j=1 wj = 1. The weights are assigned according to the user’s preference toward each attribute. Finally, it is important to note that in a benefit attribute, the larger the value is the better, while in a cost attribute; the lower value is the better.   x11 x12 . . . x1|N |  x21 x22 . . . x2|N |    (1)  . .. .. .. ..   . . . . x|M|1

x|M|2

. . . x|M||N |

In the following subsection, we briefly present the MADM algorithms that were implemented for this study. A. SAW

SAW, also called the weighted sum method, was developed in [12]. This method is expressed in (2), where wj is the importance weight of the j th attribute. Each attribute rij is multiplied by wj to obtain the score of each candidate alternative. The normalization rij of each rating xij is described as follows: if rij is a benefit parameter, it is normalized as + rij = xij /x+ j where xj = maxi∈M xij . On the other hand, if it is a cost parameter, it is normalized as rij = x− j /xij , where x− = min x . i∈M ij j X A∗SAW = arg max wj rij . (2) i∈M

j∈N

B. TOPSIS TOPSIS method was developed in [12]. This method chooses the alternative with the shortest Euclidian distance to the ideal alternative and with the largest Euclidian distance to the negative-ideal alternative. The ideal alternative is the one with the best values in each attribute while the negative-ideal is the one with the worst values. To compute the alternatives ranking-list, TOPSIS requires the following steps: Step 1: Construct the normalized decision matrix, which allows comparison across the attributes as: xij . (3) rij = qP m 2 i=1 xij

Step 2: Construct the weighted normalized decision matrix as vij = wj ∗ rij .

Step 3: Determine ideal and negative-ideal alternatives by: A+ = {(max vij |j ∈ J), (min vij |j ∈ J ′ )},

(4)

A− = {(min vij |j ∈ J), (max vij |j ∈ J ′ )},

(5)

i∈M

i∈M

and i∈M

i∈M

where J is the set of benefit parameters, and J ′ is the set of cost parameters. Step 4: Calculate the separation measure between the alternatives and the positive and negative ideal alternatives by: sX sX + + 2 − si = (vij − vj ) , si = (vij − vj− )2 . (6) j∈N

j∈N

Step 5: Calculate the relative closeness to the ideal alternative. s− (7) c∗i = + i − . (si + si ) A set of alternatives can now be preference ranked according to the descending order of c∗i . Then the selected alternative A∗T OP is: A∗T OP = arg max c∗i . (8) i∈M

C. VIKOR The compromise ranking method, also called by VIKOR, is a MADM method that was developed in [13]. This method chooses a feasible alternative which is closer to the ideal alternative and compromised (weighted) among the rest of the alternatives. For VIKOR method the following steps are required: Step 1:For each parameter j = 1, 2, 3, ..., N , determine the best and the worst values given by: Fj+ = {(max xij |j ∈ Nb ), (min xij |j ∈ Nc )}, i∈M

i∈M

(9)

and Fj− = {(min xij |j ∈ Nb ), (max xij |j ∈ Nc )}, i∈M

i∈M

(10)

where Nb ⊂ N is the set of benefit parameters, and Nc ⊂ N is the set of cost parameters. Step 2:Compute the values of Si and Ri for i = 1, 2, 3, ..., M given by: Si =

X

wj

j∈N

and

"

Ri = max wj j∈N

(Fj+ − xij ) (Fj+ − Fj− ) (Fj+ − xij ) (Fj+ − Fj− )

,

#

(11)

,

(12)

where wj is the importance weight of parameter j. Step 3:Compute the values of Qi for i = 1, 2, 3, ..., M given by:     Si − S + Ri − R+ Qi = γ + (1 − γ) , (13) S− − S+ R− − R+

where S + = min Si , i∈M

+

R = min Ri , i∈M

S − = max Si , i∈M

−

R = max Ri , i∈M

(14)

consider: duty cycle (dck ), economic cost (eck ), and selected frequency (fsk ).

(15)

C. Bandwidth (bwk )

and parameter γ with 0 ≤ γ ≤ 1 is the weight of the strategy. Step 4:Given the values for the Q, R and S for all i ∈ M , rank the candidate alternatives in an increasing order. This provides a set of three different ranking lists. The selected alternative A∗V IK is: A∗V IK = arg min Q∗i . i∈M

(16)

III. S PECTRUM M EASUREMENTS AND D ECISION PARAMETERS A. Spectrum measurements campaign Spectrum measurements campaigns have been carried out around the world to explore the real occupancy of the spectrum and to seize the opportunities for developing CRNs. In [11], we conducted a spectrum measurement campaign in an urban district of a mid-size city in Mexico to show the spectral activity inside the frequency range from 30 to 910 MHz. The measurements showed average spectrum occupancy of 12.5% in that range and also showed an even lower occupancy in the frequency bands allocated for TV services. To execute the measurements, the frequency range was divided in ranges of 40 MHz each, each range of 40 MHz was sampled 40 times with 321 dots of resolution. Since the measurements were conducted with a directional antenna, same number of samples was taken in the four cardinal points. This process was made for a morning, noon, and evening of a normal day of the week. Finally, since each frequency sample point has 120 data of information, the data is post-processed offline in MATLAB. Due to space limitation, for further details, please refer to [11]. Recently, the tendency is to work with real data obtained from measurement campaigns and then use this information to generate a model of the spectrum utilization [14]. In this work, all data used as parameters for spectrum decision are obtained from our spectrum occupancy measurements as described in the following subsections. B. MADM for spectrum decision To model the spectrum decision problem of a CR-enabled mobile terminal in CRNs, let define the alternatives k as the spectrum holes available (i.e., empty spaces) for opportunistic access and the attributes as the decision parameters calculated from the measurement campaign. To form the decision matrix in (1) of the MADM problem, we require defining the parameters that will be taken into account in the spectrum decision. Thus, a set of descriptors of each portion of the spectrum specifying the performance and constraints have to be cleverly defined since such information may account for the potential consequences of selecting a particular spectrum hole [15]. To this end, we propose the following decision parameters, as benefit parameters, we consider: bandwidth (bwk ), data rate (drk ), and power index (pik ), while for cost parameters, we

Different measurements campaigns have shown that spectrum is indeed poorly utilized. Bandwidth is a fundamental parameter that is necessary to know for the spectrum decision. According to the IEEE 802.22 standard, empty spaces to be used in cognitive radio are expected to be of 6, 7, and 8 MHz [16]. For this reason, although in our spectrum occupancy measurements there are holes in the spectrum greater than 8 MHz, we partitioned the empty spaces with only these bandwidth sizes. This process is described as follows. If in the empty space it is possible to accommodate two bandwidth spaces of 6 MHz or 7 MHz or 8 MHz, it is done. Otherwise, if space is for more than two empty spaces of any size, the empty space is randomly partitioned in 6 MHz or 7 MHz or 8 MHz spaces. This information is stored in the vector bwk , in which the size depends of the empty space and in indexed by k. D. Data Rate (drk ) The data rate is directly proportional to the size of the bandwidth, but it also depends of more factors (e.g., signal-to-noise ratio, radio channel, etc.). In [16], the spectral efficiencies for the standard IEEE 802.22 are in the range of 0.5 to 5 bit/sec/Hz with an estimated average of 3 bits/sec/Hz. Based on such vales, the estimated average data rate in the decision matrix appear with 18 Mbps for 6 MHz, 21 Mbps for 7 MHz and 24 Mbps for 8 MHz and it is shown in (??). The data rate is a benefit parameter and it is stored in the vector drk . E. Power Index (pik ) This parameter is obtained through the data from the measurement campaign. The power index show the relation between the maximum power and the minimum power of a primary user in a frequency channel selected. This parameter is important since it gives an idea of how high is the power of the signal of the primary user when it appears compared when it is absent. This relation of powers indicates how high can be affected a cognitive radio transmission if a primary user appear. In the decision matrix, this is a benefit parameter, because a higher opportunity index is better and express that there is a low signal of primary users. The power index can be calculated as: Pmink pik = , (17) Pmaxk where Pmink is the minimum measured power, Pmaxk is the maximum measured power in the frequency selected and k refers to the bandwidth space selected. F. Duty Cycle (dck ) One of the most important parameter that can be obtained by the measurements campaign is the duty cycle (DC). The DC is the percentage of time that a signal is above a threshold. Using an energy detector is possible to know the DC, all the

information about how the threshold was selected and how was obtained the DC is in [11]. If the DC is high means that the primary user is using this bandwidth for much time, a DC low means that the primary user is absent a large amount of time. The spaces with a low DC are good and suitable for cognitive radio access. In the decision matrix, the DC is a cost parameter and is expressed like dck . G. Economic Costs (eck ) The cost is an important decision parameter on the selection of an empty space in CRNs. The cost of an available space may directly affect the behaviour of a cognitive radio user. Now days, there is not a specific regulation for the cost for an empty space. However, it is reasonably that the prices will depend on the size of the space (i.e., bandwidth). In this work, a different weight is assigned to each one of the different bandwidth sizes, the highest cost is for the bandwidth of 8 MHz and the lowest is for the bandwidth of 6 MHz, as shown in (18). In the decision matrix, this parameter appears as eck and it is a cost parameter, since for a user is always better in a communication process to obtain the lowest price.  if bwk == 8,  High cost; M edium cost; if bwk == 7, eck = (18)  Low cost; if bwk == 6.

H. Selected Frequency (fsk ) The frequency selected for transmission represents also an important parameter for the spectrum decision. The frequency ranges assigned for TV in several countries (including Mexico) are: 54-72 MHz, 76-88 MHz, 174-216 MHz and 470-698 MHz. It is important to note that if an available spectrum hole is selected in a low frequency it requires less transmission power for a specific coverage compared to a transmission in a high frequency. If we consider that is better to save power for transmission in a mobile device, thus is better decision to select a low frequency. For this reason, in the frequency selected vector fsk in (19), the low frequencies with empty spaces are assigned with low cost; while the high frequencies have more cost. The frequencies were ordered from low to high frequency.  F irst f requency selected; cost = 1,     Second f requency selected; cost = 2,   T hird f requency selected; cost = 3, (19) fsk =  ..    .   k f requency selected; cost = k. I. Decision Matrix All the parameters described before form the decision matrix DM in (20). The first three columns are benefit parameters while the next three are cost parameters. The matrix DM is the input to all the MADM algorithms explained in section II.   bw1 dr1 pi1 dc1 ec1 fs1  bw2 dr2 pi2 dc2 ec2 fs2    DM =  . (20) .. .. .. .. ..  .  .. . . . . .  bwk

drk

pik

dck

eck

fsk

IV. R ESULTS We study via simulations the performance of the proposed MADM algorithms for spectrum decision in CRNs. We, however, use real spectrum usage information obtained from spectrum occupancy measurements carried out in previous studies of this investigation. For comparison purposes, we present simulation results obtained from three different weighting parameter scenarios. Thus, the vector of preferences, w, is modified to evaluate the performance of the MADM algorithms under equally weighted parameters, bandwidth weighting parameter, and economic cost weighting parameter. The total number of decisions is set to 15. A. Equally weighted parameters Figure 1 shows the performance of TOPSIS, SAW, and VIKOR algorithms for spectrum decision in CRNs, considering that all the attributes of w are equally significant for secondary users’ transmissions. For a given decision, the frequency band is selected from the available spectrum, which is indeed a real scenario. The results are summarized in Table I, where a comparison of the attributes for each algorithm is presented. For simplicity, better results of the benefit (high) and cost (low) parameters are highlighted in bold case letters to indicate which one is preferred accordingly. Here, it can be seen that the SAW algorithm showed a good performance in terms of power index, duty cycle, and economic cost, whereas TOPSIS exhibited a good performance in terms of duty cycle and economic cost only and VIKOR algorithm outperformed SAW and TOPSIS in terms of the selected frequency. TABLE I: Performance comparison of MADM algorithms with equally-weighted parameters. Algorithm TOPSIS SAW VIKOR

Bandwidth Size Low (6MHz) Low (6MHz) Medium (7MHz)

Data Rate 18 Mbps 18 Mbps 21 Mbps

Power Index Medium High Low

Duty Cycle Low Low High

Economic Cost Low Low High

Selected Frequency High Medium Low

B. Bandwidth-based decision. In this case, we consider the fact that, for some applications spectrum bandwidth is the most important parameter from the secondary user’s perspective. Therefore, we assign a heavier weight to the bandwidth parameter. Thus, the algorithm that selects the largest bandwidths is considered the best choice for the secondary transmission. Figure 2 shows the performance of TOPSIS, SAW, and VIKOR algorithms for spectrum decision in CRNs, considering that cognitive users make decisions based in the bandwidth of the practical spectrum opportunity. We summarize the results in Table II, where a comparison of the attributes for each algorithm is presented. For bandwidthbased decisions, it can be seen that the SAW algorithm exhibited a good performance in terms of bandwidth, data rate, power index, and duty cycle. TOPSIS algorithm performed similarly to SAW, except for the power index parameter, which is medium for this case. On the contrary, VIKOR algorithm reaches only a medium performance in terms of bandwidth, data rate, economic cost, and selected frequency parameters.

(a)

(a)

(b)

(b)

(c) (c)

Fig. 1: Performance of (a) TOPSIS, (b) SAW, and (c) VIKOR with equally weighted parameters for spectrum decision. TABLE II: Performance comparison of MADM algorithms with bandwidth-based decisions. Algorithm TOPSIS SAW VIKOR

Bandwidth Size High (8MHz) High (8MHz) Medium (7MHz)

Data Rate 24 Mbps 24 Mbps 21 Mbps

Power Index Medium High Low

Duty Cycle Low Low High

Economic Cost High High Medium

Selected Frequency High Medium Medium

C. Economic cost-based decision. In this case, we consider the fact that some cognitive users might require to access the cheapest service for economic reasons. Therefore, a heavier weight is assigned to economic cost attribute of the available spectrum bands. Thus, the algorithms selecting the lowest economic cost are considered the best choice for the opportunistic transmission of secondary users. Figure 3 shows the performance of TOPSIS, SAW, and VIKOR considering that cognitive users make decisions based in the economic cost. A summary of the results is presented in Table III, which shows a comparison of the attributes for each MADM algorithm. In this case, it can be seen that TOPSIS,

Fig. 2: Performance of (a) TOPSIS, (b) SAW, and (c) VIKOR for bandwidth-based spectrum decision.

SAW, and VIKOR algorithms attain the expected performance in terms of economic cost. Interestingly, the SAW and TOPSIS algorithms also exhibit a similar performance in terms of power index and duty cycle. However, in terms of selected frequency, SAW shows a medium performance, which is better than the high grade of TOPSIS since selected frequency is a cost parameter. On the contrary, VIKOR algorithm performs well also in the selected frequency parameter. TABLE III: Performance comparison of MADM algorithms with economic cost-based decisions. Algorithm TOPSIS SAW VIKOR

Bandwidth Size Low (6MHz) Low (6MHz) Low (6MHz)

Data Rate 18 Mbps 18 Mbps 18 Mbps

Power Index High High Low

Duty Cycle Low Low High

Economic Cost Low Low Low

Selected Frequency High Medium Low

Finally, after the evaluating the three different weighting scenarios it is important to highlight the fact that as shown in Figures 1 to 3, SAW algorithm tend to select spectrum holes that are closer in frequency compared to TOPSIS and

ACKNOWLEDGMENT This work was supported by the Program for the Improvement of the Teachers Faculty (PROMEP), the FAI-UASLP Research Grant C13-FAI-03-43.43, and the Mexican National Council for Science and Technology (CONACYT). R EFERENCES

(a)

(b)

(c)

Fig. 3: Performance of (a) TOPSIS, (b) SAW, and (c) VIKOR for economic cost-based spectrum decision.

VIKOR. This behaviour has a direct impact in the delay and complexity of executing every spectrum decision in the CRenabled mobile terminal. V. C ONCLUSIONS The spectrum decision functionality of a cognitive radio terminal was modeled as an MADM problem. We used real spectrum usage information to study the performance of TOPSIS, SAW, and VIKOR algorithms for spectrum decision in CRNs. We proposed important attributes of the available spectrum to make a decision according to the MADM algorithms. For the given spectrum data, the SAW algorithm exhibited a better performance not only when the spectrum attributes are considered to be equally significant for secondary users, but also when the bandwidth and economic cost is considered the most important spectrum parameter to make a decision. Further research to assess the performance of the algorithms is needed taking into account other parameters that were not considered in this study, such as delay and number of handoffs.

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