Comparison of Mamdani and Sugeno Inference Systems for Dynamic Spectrum Allocation in Cognitive Radio Networks

Wireless Pers Commun (2013) 71:805–819DOI 10.1007/s11277-012-0845-6

Comparison of Mamdani and Sugeno Inference Systemsfor Dynamic Spectrum Allocation in Cognitive RadioNetworks

Mansi Subhedar · Gajanan Birajdar

Published online: 22 September 2012© Springer Science+Business Media, LLC. 2012

Abstract Dynamic spectrum access and cognitive radio are emerging technologies to uti-lize the scarce frequency spectrum in an efficient and opportunistic manner. Cognitive radio,built on software defined radio, is an intelligent radio technology that updates its operat-ing parameters to locate the unused spectrum segments. To assign these vacant bands tounlicensed users without causing harmful interference to licensed users, a novel approach isproposed in this article based on fuzzy logic. Two different fuzzy inference system models i.e.Mamdani and Sugeno systems are developed that compute spectrum access decision basedon the secondary user parameters such as signal strength, distance between the primary andsecondary user, spectrum utilization efficiency and degree of mobility. 81 fuzzy rules areused to obtain the output of proposed system stating the possibilities of allotment of whitespaces to secondary users.

Keywords Radio resource utilization · Cognitive radio · Rule based system · Fuzzy logic

1 Introduction to Cognitive Radio Network

Wireless technology is growing rapidly and the vision of pervasive wireless computing andcommunication offers the promise of many societal and individual benefits. While the devicessuch as cell phones, PDAs and laptops receive a lot of attention, the impact of wireless tech-nology is much broader. This explosion of wireless applications creates an ever increasingdemand for more radio spectrum. However, most easily usable spectrum bands have alreadybeen allocated, although many studies have shown that they are significantly underutilized.These considerations have motivated the search for breakthrough radio technologies that can

M. Subhedar (B)Pillai’s HOC College of Engineering and Technology, University of Mumbai, Mumbai, Indiae-mail: [email protected]

G. BirajdarSIES Graduate School of Technology, University of Mumbai, Mumbai, Indiae-mail: [email protected]

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806 M. Subhedar, G. Birajdar

Fig. 1 Spectrum concentration [1]

scale to meet future demands both in terms of spectrum efficiency and application perfor-mance. Figure 1 shows relatively low utilization of the licensed spectrum which is due toinefficient fixed frequency allocation rather than any physical shortage of spectrum.

The issue of spectrum underutilization has forced the regulatory bodies to find out amethod where secondary (unlicensed) systems are allowed to opportunistically utilize theunused primary (licensed) bands commonly referred to as white spaces. Same can be solvedin a better way using Cognitive Radio (CR) technology. Cognitive radio, built on a softwareradio platform, is a context aware intelligent radio, potentially capable of autonomous recon-figuration by learning from and adapting to the communication environment. While dynamicspectrum access is certainly an important application of cognitive radio, it represents a much

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Comparison of Mamdani and Sugeno Inference Systems 807

broader paradigm where many aspects of communication systems can be improved via cog-nition. They are fully programmable wireless devices which sense their environment anddynamically adapt their transmission waveforms, channel access method, spectrum usage,and networking protocols as and when needed for good network and application performance.

Cognitive radio includes four main functional blocks: spectrum sensing, spectrum manage-ment, spectrum sharing and spectrum mobility. Spectrum sensing aims to determine spectrumavailability and the presence of the licensed user. Spectrum management is to predict howlong the spectrum holes are likely to remain available for use to the unlicensed users. Spec-trum sharing is to distribute the spectrum holes fairly among the secondary users bearing inmind the usage cost. Spectrum mobility is to maintain seamless communication requirementsduring the transition to better spectrum [1–4].

A major challenge in cognitive radio is the detection of spectrum bands utilized by primaryuser (PU). If unused slots are identified, they can be allotted to secondary users (SU) providedSU need to quit the frequency band as quickly as possible when again needed by primaryuser in order to avoid interference. This technique is called as spectrum sensing. Spectrumsensing and estimation is the first step to implement cognitive radio system [5].

In this paper, a novel approach is proposed so as to make proper choice of allotmentof spectrum band to access the network. A knowledge representation frame work based onfuzzy logic which enables the implementation of a cognition process which is both cross-layer and network-aware approach, is developed. Subsequently, Mamdani and Sugeno FISnetwork access schemes are developed to have a comparative analysis of chances of spectrumallocation to secondary users.

The rest of this paper is organized as follows. In Sect. 2, spectrum access schemes andbasics of fuzzy logic for cognitive radios are reviewed. Fuzzy inference system is illustratedin Sect. 3. In Sect. 4, the simulation results are discussed and Sect. 5 concludes the paper.

2 Spectrum Access Scheme and Fuzzy Logic for Cognitive Radio Networks

Opportunistic spectrum access has been enabled by cognitive radio. Unlike conventionalradios, CRs have the capability to sense their surroundings and actively adapt their operationalmode to maximize the quality of service for secondary users while minimizing interferenceto primary users. Hence, CRs must carry out spectrum sensing to identify white spaces orspectrum holes which are bands of frequencies assigned to primary users, but at a particulartime and specific geographic location, are not being utilized by those [6]. Some methods onspectrum sensing have been proposed in [7,8], and [9] such as Cooperative, Non cooperativeand Interference based spectrum sensing. Once spectrum holes are identified, CRs oppor-tunistically utilize these spectrum holes for communication without causing interference toprimary users. If only single secondary user in a particular location and at a specific time cansense the available spectrum band, that secondary user can use the band after the primaryuser finishes its communication session. However, if more than one SU demand for the sameband then priority should be given based on spectrum access decision technique developedin this paper.

In cognitive radio, the decision making for resource management is based on knowledgeof the operational environment. Information on the current spectrum usage will be criticalfor the successful deployment of cognitive radio networks. Research on fuzzy logic basedcognitive radio has emerged in recent years at rapid rate [10–18]. Fuzzy logic is used toselect the most suitable secondary user to whom permission can be granted to access theunused spectrum band [14]. The rule based decision scheme takes in to account various

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secondary user parameters such as spectrum efficiency, user mobility and distance betweenPU and SU. In [15], a fuzzy logic power control scheme is proposed to allow SU to transmitsimultaneously with the primary user operating in the same band.

The fuzzy approach discussed in this paper deals with additional parameters such as spec-trum utilization efficiency and sensing power. The combination of all these parameters helpsto choose the appropriate secondary user which may use the spectrum band without creatingany interference to primary user. The decision rules based on these parameters result in 81 Ifthen Else statements.

3 Fuzzy Inference System

The fuzzy rule based approach introduced by Zadeh [19] is common element of expert systemwith an increasing rate of interest and widely used over the past few years due to its applica-tions in many of the control and prediction systems. It is a qualitative modelling scheme inwhich the system behaviour is described using natural language and is widely used due to itsability in representing the vagueness, imprecise information or missing input information.A fuzzy set can be defined mathematically by assigning each possible individual in the uni-verse of discourse a value, representing its grade of membership in the fuzzy set. This gradecorresponds to the degree to which that individual is similar to or compatible with the conceptrepresented by the fuzzy set. Fuzzy set theory differs from traditional set theory in that partialmembership is allowed i.e. an element can belong to a set only up to a certain degree. Thisdegree of membership is commonly referred to as the membership value and is representedas,

µA(x) ∈ [0, 1] (1)

where 0 and 1 corresponds to full non-membership and full membership value respectivelyand symbol µA (x) is the degree of membership of element x in fuzzy set A. The processof formulating the mapping from a given input to an output using fuzzy logic is called thefuzzy inference system (FIS). Fuzzy inference systems have been successfully applied infields such as expert systems, data classification, automatic control, decision analysis andcomputer vision. Figure 2 shows the functional block diagram of a fuzzy inference systemused in the proposed approach.As shown in figure, crisp input is converted to fuzzy input by using process of fuzzification.When an input is applied to a FIS, the inference engine computes the output set correspond-ing to each rule. The defuzzifier then computes a crisp output from the number of fuzzyIF–THEN rules. A fuzzy system with two inputs x1 and x2 (antecedents) and a single outputy (consequent) is described by a collection of r linguistic IF-THEN rules in Mamdani formas [20],

If x1 is Ak1 and x2 is Ak

2 THEN yk is Bk (2)

where Ak1 and Ak

2 are the fuzzy sets representing the kth antecedent pairs and Bk is the fuzzyset representing the kth consequent. For a set of conjunctive rules, the aggregated output forthe ‘r’ rules is given by,

µy (y) = min[µ2

y (y) ,µ2y (y) . . . .µr

y (y)]

for ye Y (3)

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(Fuzzy Output)

Sensing Power

Velocity

Spectrum Efficiency

Distance

Fuzzifier

(Crisp Input)

Inference Defuzzifier

Rule

Base

(Crisp Output)

Spectrum Access

Decision

(Fuzzy Input)

Fig. 2 Functional block diagram of a fuzzy inference system (FIS)

The weighted average method is the most frequently used technique for defuzzificationbut usually restricted to symmetrical output membership function and is given by,

z∗ =∑

µc (z) · z∑µc (z)

(4)

where∑

denotes the algebraic sum and z is the centroid of each symmetric membershipfunction.Fuzzy inference system is used to obtain the spectrum access decision in cognitive radionetworks. The proposed FIS consists of four inputs and one output membership function.The secondary user with maximum spectrum utilization efficiency, farthest distance to theprimary user, moving with low velocity and having low or high sensing power is given maxi-mum spectrum access. Based on the knowledge of the linguistic variables, 81 IF THEN ELSEfuzzy rules are used to take the decision for opportunistic spectrum access. At a particulartime and place, the secondary user with maximum possibility of decision will be allowed touse vacant band.The various membership functions used to describe input and output parameters are describedbelow.

3.1 Membership Functions

The parameters which mainly contribute to working style of cognitive radio are chosen tobe the input parameters. The output will be the decision i.e. the chances of granting theaccess to utilize the white spaces. The five parameters used in the FIS model along with theirmembership functions are discussed below:

(a) Sensing Power: In order to fully exploit the potential of opportunistic spectrum access,transmit power control scheme which enables cognitive user to achieve its required trans-mission rate and quality while minimizing interference to the primary user and otherconcurrent secondary users can be employed [21]. Transmit power control scheme isbased on sensing power

(PRx−Sensing

)parameter measured at the secondary user trans-

mitter which in turn determines transmit power interference constraint(PT x_SU_Sensing).Figure 3 shows membership function used for sensing power. Gaussian membershipfunctions are chosen due to low rise time and less fluctuations. The linguistic descriptorused to represent the sensing power is divided into three levels: low, moderate and high.

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Fig. 3 Sensing power membership function

Fig. 4 Velocity membership function

(b) Velocity: The SU velocity is also one of the input parameters which play an importantrole as more the velocity more will be the chance for a mobile node to change the positionresulting in Doppler Effect. Figure 4 shows membership function used for velocity. Thelinguistic descriptor used to represent the velocity is divided into three levels: low, mod-erate and high. Mobility can reduce capability of detecting signal from the primary users.If the secondary user is not capable of detecting the primary signal, it will incorrectlydetermine that the spectrum is unused thereby leading to potential interference to adja-cent users i.e. the signal transmitted by the secondary user will interfere with the signalthat the primary user is trying to decode. Hence SU with low velocity is given maximumspectrum access.

(c) Spectrum efficiency: The spectrum utilization efficiency is defined as ratio between thespectrum band requirements for the secondary user to the total available spectrum. SU

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Fig. 5 Spectrum efficiency membership function

Fig. 6 Distance membership function

with highest spectrum efficiency will be given maximum access to the spectrum. Figure 5shows membership function used for spectrum efficiency.

(d) Distance between PU and SU: The distance between the primary and secondary userhas been considered to be the determining parameter because the secondary user at along distance with respect to PU should be given priority to access spectrum. Figure 6shows membership function used for distance. The linguistic descriptor used to representthe distance between PU and SU is shown in terms of three levels: near, medium and far.Spectrum access decision: The spectrum access decision i.e. the possibility that thesecondary user is allowed to access the spectrum is divided into five levels which arevery low, low, medium, high and very high. Trapezoidal membership functions (MFs)are used to represent this parameter to represent very low and very high and triangle MFsto represent low, medium and high. These MFs are as shown in Fig. 7.

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Fig. 7 Decision membership function

Table 1 Sugeno FIS constantoutput

Very high 1.0

High 0.75

Moderate 0.5

Low 0.25

Very low 0

Since Sugeno FIS uses weighted average for the output, the output is divided into five lev-els and labelled corresponding to Mamdani’s five output membership functions. The fiveconstant membership functions along with their values are given in Table 1.

3.2 FIS Types

There are two different types of FIS: Mamdani which is the most commonly seen methodintroduced by Mamdani and Assilian [22] and Sugeno or Takagi–Sugeno–Kang (TSK)method, introduced by Sugeno [23]. The main difference between these methods lies inthe consequent of fuzzy rules and thus their aggregation and defuzzification procedures.Mamdani fuzzy systems use fuzzy sets as rule consequent where as TSK fuzzy systemsemploy linear functions of input variables. Figure 8 shows FIS models developed here withall the input parameters discussed above.The advantages of using Mamdani FIS are: [24]

• Intuitive and interpretable nature of the rule base. For this reason, Mamdani FIS is widelyused in particular for decision support application.

• Easy formalization and interpretability.• Expressive power.• Can be used for both MISO and MIMO systems.

The advantages of using Sugeno FIS are:

• Computational efficiency and accuracy.

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Fig. 8 Proposed FIS model a Sugeno FIS b Mamdani FIS

• Better processing time since the weighted average replaces the time consuming defuzzifi-cation process.

• Rule consequents can have as many parameters per rule as input values allowing moredegrees of freedom and more flexibility in the design.

• Adequate for functional analysis because of the continuous structure of output function.

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4 Result and Discussion

Predefined rule base consisting of 81 IF THEN ELSE statements is used for both types ofFIS models. For e.g. IF sensing power is low and velocity is low and spectrum utilizationefficiency of the secondary user is low and distance is near THEN the possibility that thissecondary user will be allowed to access the available spectrum is low. A decision value closeto 1 is considered for granting spectrum access to the secondary user. All the simulations areperformed using Matlab 9.1.The simulation results are shown in Figs. 9, 10, 11, 12, 13, 14 for Mamdani and Sugeno FIS.To verify the significance of every parameter in spectrum access decision, we have derivedthe surface plots for each of the input parameter with respect to decision which clearly indi-cates their influence on the output.It is evident from the results in Fig. 9 that the probability of allocation of spectrum band tothe secondary user increases if the sensing power is either low or high and the velocity islow. Figure 10 suggests that the possibility of getting access to spectrum is more when theSU is located away from PU. In similar ways, Fig. 11 shows the relation between velocityand spectrum efficiency for decision process. As the SU is moving with low velocity andhigh spectrum efficiency then available spectrum can be assigned to the SU. Figure 12 shows

Fig. 9 Spectrum access decision surface with fixed spectrum efficiency and distance

Fig. 10 Spectrum access decision surface with fixed spectrum efficiency and velocity

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Fig. 11 Spectrum access decision surface with fixed sensing power and distance

Fig. 12 Spectrum access decision surface with fixed velocity and distance

Fig. 13 Spectrum access decision surface with fixed velocity and sensing power

that the probability of assigning spectrum to the secondary user increases if the spectrumefficiency is high and sensing power is either low or high. Figures 13 and 14 depicts thatdecision is mainly based on distance between PU and SU.

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Fig. 14 Spectrum access decision surface with fixed Spectrum efficiency and sensing power

Fig. 15 Input parameter versus decision when all inputs are set at low, medium and high. a Sensing powerversus decision. b Spectrum efficiency versus decision. c Velocity versus decision. d Distance versus decision

Now, to demonstrate the effect of individual input parameters on the output function Fig. 15a–d are evaluated. It shows the relationship between input parameters and the decision processin Mamdani FIS e.g. figure a exhibits the effect of sensing power on the decision processwhen velocity, spectrum efficiency and distance between PU and SU are low, medium and

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Table 2 Mamdani and SugenoFIS correlation for various results

Input variable Correlationbetween Mamdaniand Sugeno FIS

Sensing power 0.9822

Velocity 0.9646

Spectrum efficiency 0.9833

Distance between PU and SU 0.9689

high. Similar results can be obtained using Sugeno FIS.To compare Mamdani and Sugeno FIS, correlation coefficient is computed for each of thefour cases. The strength of the linear association between two variables is quantified by thecorrelation coefficient which is obtained using the following relation:

r = 1

n − 1

∑(x − x

Sx

) (y − y

Sy

)(5)

where x and y are two separate series (here they are the Mamdani FIS result and the SugenoFIS result), bar value is the average of the series, S is the standard deviation, and n indicatesthe number of elements in the series.

The Table 2 indicates high correlation between both FISs for all four inputs justifyingtheir reliability for evaluating spectrum access decision.Mamdani FIS results are closer to expected values. For example, when sensing power andvelocity are set to low, where as spectrum efficiency and distance are set to high, MamdaniFIS generates 78.4674 as spectrum access decision while Sugeno FIS results in 72.8021.The SU with low (or high) sensing power, low velocity, high spectrum efficiency and largerdistance between PU and SU have maximum chances to access spectrum.Checking the boundaries of the system for minimum and maximum input, we find that whenall input values are set to one, Mamdani FIS results in the spectrum access decision as 30.8150and Sugeno FIS results in 26.9549. On the other hand, when the inputs are at their maximumvalue, the spectrum access decision is 81.5472 for Mamdani FIS and it is 84.1853 for SugenoFIS. At the boundary, Sugeno FIS establishes to be more accurate than its Mamdani FIScounterpart.

5 Conclusion

A novel approach is proposed using the fuzzy logic for the opportunistic spectrum accessin cognitive radio networks. The secondary user is selected based on four descriptors i.e.sensing power, spectrum utilization efficiency, velocity and distance to the primary user.Spectrum access decision is simulated to validate our approach. Results in terms of spectrumaccess decision are compared for Mamdani and Sugeno FIS. Sugeno FIS model demon-strates higher accuracy at the boundaries and more dynamic values as compared to Mamdanimodel. Mamdani FIS, on the other hand displays consistency for optimum values of con-sidered parameters. Both models show high correlation value and thus reflect fairly reliableresults and can be utilized to come up with a crisp decision value.

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Author Biographies

Mansi Subhedar is working as Assistant Professor in the departmentof Electronics & Telecommunication Engineering at Pillai’s HOC Col-lege of Engineering & Technology, Raigad, India. She obtained B.E.(Elect. & Telecom) from Dr. B. A. M. University, Aurangabad, Maha-rashtra and M.E. (Electronics) from Mumbai University. She has beenin teaching for the past 5 years. She is life member of ISTE. She hasattended several workshops and conferences. She has published andpresented papers in various conferences and journals. Her research areaincludes next generation networks and signal processing.

Gajanan Birajdar received B.E. (Electronics) degree from Dr. B.A.M.University, Aurangabad in 1996. M. Tech. in Electronics and Tele-communication from Dr. B.A. Technological University, Maharashtra,India in 2004. He has more than 14 years of experience in teaching andindustry. He is currently working as Assistant Professor in Electron-ics and Telecommunication Engineering at S.I.E.S. Graduate School ofTechnology, Navi Mumbai. He is life member of IETE and ISTE. Hisarea of interests are Signal and image processing and soft computing.

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Comparison of Mamdani and Sugeno Inference Systems for Dynamic Spectrum Allocation in Cognitive Radio Networks