INT J COMPUT COMMUN, ISSN 1841-9836
9(1):85-92, February, 2014.

Spectrum Migration Approach Based on Pre-decision Aid and
Interval Mamdani Fuzzy Inference in Cognitive Radio Networks

Z. Wang, H. Wang, H. Lv, G. Feng

Zhendong Wang*, Huiqiang Wang,
Hongwu Lv, Guangsheng Feng
College of Computer Science and Technology
Harbin Engineering University, Harbin, China
*Corresponding author: wangzhendong@hrbeu.edu.cn

Abstract: This study intends to improve the QoS of SUs and CRNs performance.
A novel spectrum migration approach based on pre-decision aid and interval Mam-
dani fuzzy inference is presented. we first define spectrum migration factors as spec-
trum characteristic metrics for spectrum migration decision. In addition, we use pre-
decision aid to reduce system complexity and improve spectrum migration efficiency.
To shorten spectrum migration decision time and seek the optimal spectrum holes,
interval Mamdani fuzzy inference is put forward. Finally, simulation results show the
proposed approach can inhibit the upward trend of service retransmission probability
and average migration times effectively, and improve the effective utilization of CRNs
spectrum resource significantly.
Keywords: cognitive radio networks, spectrum migration, pre-decision aid, interval
Mamdani fuzzy inference

1 Introduction

Opportunistic spectrum access (OSA) technology due to help SUs utilize the idle spectrum,
effectively improve spectrum usage and system throughput for CRNs, and becomes a hotspot
that academia concerned [1]- [5]. However, existing OSA technologies mainly focus on improving
CRNs system throughput and spectrum resource utilization, the QoS requirement of SUs and the
effective utilization of CRNs spectrum resource are little considered, that maybe cause system
throughput and utilization of spectrum resource increase to a higher level, but the effective
utilization of spectrum resource is still maintained at a lower level [6]- [7].

In order to improve the QoS of SUs and the CRNs performance, this paper introduces the
concept of spectrum migration. Spectrum migration means SUs change their using spectrum dy-
namically for improving the success rate of SUs connections, it describes the whole process of SUs
service transmission. The occurrence of spectrum migration includes two cases: (1) PU arrives at
the spectrum that SU is using, (2) the quality of spectrum SUs using drops below the minimum
value that can maintain normal data transmission [8]- [10]. Under normal circumstance, the
probability of spectrum environment deterioration is lower, so we only consider SUs spectrum
migration when PU arrives. Actually, frequency spectrum migration operations can decrease
system performance and SUs QoS because of the operations is time-consuming. Therefore, the
objective of this paper we pursue are the longest occupation time to single spectrum hole, the
least spectrum migration times and the shortest spectrum migration decision time for SUs. In
this paper, we define spectrum migration factors as spectrum characteristic metrics for spectrum
migration decision, and use pre-decision aid to reduce system complexity and improved spectrum
migration efficiency. At last, we propose interval Mamdani fuzzy inference (IMFI) method based
on Mamdani fuzzy inference to shorten spectrum migration decision time and search for suitable
spectrum holes.

Copyright © 2006-2014 by CCC Publications



86 Z. Wang, H. Wang, H. Lv, G. Feng

2 Spectrum Migration Factors

2.1 Spectrum Occupation Probability

Spectrum occupation probability indicates the spectrum occupation degree for PUs and SUs.
For a SU, when the spectrum is being occupied by PUs or other SUs, it can not migrate to
the spectrum. Therefore, spectrum occupation includes spectrum occupation include PUs and
SUs. From this point, spectrum occupation probability is the occupation probability of sub-
spectrum divided, i.e., channel occupation probability. A higher spectrum occupation probability
can lead to higher migration blocking probability for SUs. Until now, there is no accurate
spectrum occupation model proposed, so we use statistical method to obtain spectrum occupation
probability by calculating spectrum occupation data in the past time.

Considering the ON-OFF average time of spectrum η are tα and tβ over a period of time t′ (
t′ = tα +tβ ) respectively, then spectrum occupation probability of spectrum η can be calculated
as SOP = t

α

tα+tβ
. When spectrum η undergoes k times state changes, the spectrum occupation

probability can be updated as

SOP =

k∑
i=1

tα,i

k∑
i=1

(tα,i + tβ,i)

(1)

Where tα,i and tβ,i indicate the ON-OFF time in the ith period on spectrum η respectively.

2.2 Link Maintenance Probability

Link maintenance probability mainly reflects the link support degree for SUs data transmis-
sion. It indicates the capacity of continuous data transmission for SUs on a specific licensed
spectrum. From Sect. 1 we know only PUs arrival can force SUs vacate the using spectrums
and makes link maintenance fail. From this point, link maintenance probability is the same for
licensed spectrum and its channels. When a PU arrives, there are three consequences for SUs:
(1) SU needs to vacate its using spectrum and migrate to other spectrum to continue its data
transmission. (2) SU vacates its using spectrum and waits for PU to leave, then SU continues
its data transmission through the original spectrum. (3) SU vacates its using spectrum and link
maintenance is failed.

Let Pv denote the probability that an SU vacates its using spectrum, we have link maintenance
probability as follows

LMR = Pv[(1−rb) + rbPr(ψt < τt)] (2)

Where rb denotes PU call blocking probability, and it is given by

rb = (ρ
M
/
M!)

/
(

M∑
i=1

ρi
/
i!) (3)

Where ρ denotes the PU traffic intensity.

2.3 Spectrum Migration Degree

Spectrum migration degree reflects the pros and cons of the spectrum holes on each licensed
spectrum for SUs directly. Before defuzzification operations, it is denoted as a specific level, and



Spectrum Migration Approach Based on Pre-decision Aid and Interval Mamdani Fuzzy
Inference in Cognitive Radio Networks 87

after defuzzification operations, it denotes as a specific value. We consider that the spectrum
with higher spectrum migration degree, the more suitable for SUs spectrum migration.

Spectrum migration degree can be obtained by SOP and LMP using fuzzy inference, it is
expressed as

SMD = Inf(SOP,LMP) (4)

3 Spectrum Migration Approach Based on Pre-decision Aid and
IMFI

3.1 Spectrum Migration Pre-decision Aid

In order to avoid all the SUs enter into fuzzy decision module and reduce CRNs complexity,
we propose spectrum migration pre-decision aid method. It can be described as follows

1) When SU arrives at the spectrum for the first time, i.e., A = Af , where A denotes the
arrival of SU, and Af denotes the arrival of SU for the first time. When there are more than
one spectrum hole, SU needs to enter into fuzzy decision. If there is only one spectrum hole, SU
migrates to it directly, and if all spectrums are occupied, spectrum migration operations will be
blocked. The process is shown as Figure 1 (a).

Figure 1: Process of Spectrum Migration Pre-decision Aid

2) When SU arrives and A ̸= Af , if there are more than one spectrum hole, SU enters into
fuzzy decision module. If there is only one spectrum hole, SU migrates to it directly. If there is
no idle spectrum and the occupied duration is more than τt , i.e., ψt + ζt > τt , SU connection
will be interrupted, the data has been transmitted will be considered as ineffective. Then, A will
be reset to Af , and the retransmission operation will start for this SU. Otherwise, SU judges
whether the idle spectrum is current spectrum, if it is indeed the current spectrum, then SU
does not need to migration. Otherwise, SU selects spectrum migration manner according to the
number of idle spectrums. This process is described as Figure 1 (b).

3.2 Spectrum Migration Method Based on IMFI

A. Spectrum Migration Factors Fuzzification



88 Z. Wang, H. Wang, H. Lv, G. Feng

In fuzzification process, the more the number of fuzzy sets, the lower the probability of
entering into the 2nd decision, then, the spectrum migration decision time can be saved much.
However, the number of fuzzy rules is polynomial growth with the growth of the number of
fuzzy sets, when SUs enter into the 2nd decision, excessive fuzzy rules will cause longer inference
time, which may make SU on the effective use time of spectrum holes shorten, and the system
throughput reduced. When ψt + ζt > τt happens, it even leads to SU data retransmission.
Simultaneously, rare fuzzy sets have fewer fuzzy rules, but they cause the probability of entering
into the 2nd decision increase, also extend the fuzzy inference time. In this subsection, we
consider SOP and LMP as input fuzzy parameters, and SMD as output fuzzy parameter. Then,
we establish the membership functions for SOP, LMP and SMD as Figure 2. In Figure 2, the
universes of all the fuzzy variables are set to [0, 1]. For every licensed spectrum, SOP and LMP
have five fuzzy sets, that denote as VL, L, M, H, VH, mean “Very Low”, “Low”, “Medium”, “High”
and “Very High” respectively. The fuzzification operations are same for SOP and LMP, they are
shown as Figure 2 (a). Fuzzy variable SMD also has five fuzzy sets, and they denote as VS, S,
M, B, VB, that mean “Very Small”, “Small”, “Medium”, “Big” and “Very Big” respectively, they
are shown as Figure 2 (b).

�

p1
0

1

0 1.0

VS S M B VB

0.25 0.75
(b)
0.5

0

1

0 1.0

M

0.25 0.75

(a)

0.5

VL L H VH

Figure 2: Membership Function of Fuzzy Variables

B. IMFI Method
In fuzzy decision phase, decision time has a big impact on spectrum migration performance.

Traditional Mamdani fuzzy inference method calculates each fuzzy rule by max-min mode, makes
it compute-intensive, and fuzzy inference time is long. For two-input single-output and 7-divisions
fuzzy controller, the inference time accounts for 60% to 80% of the total fuzzy inference time,
and the proportion will increase with the increase of the number of rules.

Definition 1. Let the universe of fuzzy variable π is U , its membership function is F(x) . If
there is an interval X = [a,b] ⊂ U , and its membership function is f(x) , f(x) ∈ F(x) , i.e.,
f(π) = F(π) . Then, we define interval [a,b] as an inference interval for π .

Definition 2. Inference interval [a,b] is an effective inference interval if and only if f(x) ̸= 0 for
any x ∈ [a,b] . Conversely, [a,b] is defined to be ineffective inference interval.

Definition 3. Inference intervals X1,X2,X3, ...,Xh are defined to complete inference interval if
and only if X1 ∪X2 ∪X3 ∪ ...∪Xh = U .

Theorem 1. Fuzzy relationship on the universe is equal to fuzzy relationship on complete
inference interval.

Proof: Assuming A1,A2, ...,An are complete inference intervals on universe U . According to
definition 3, we have A1 ∪A2 ∪ ...∪An = U . Assuming the membership functions of A1, ...,An
are µA1(x), ...,µAn(x) respectively, and the membership function of U is µ(x) , then, we have
µA1(x) ∈ µ(x) , i.e., µA1(a1) = µ(a1) for any a1 ∈ A1 according to definition 1. Similarly, we
have µA2(a2) = µ(a2) , . . . , µAn(an) = µ(an) for a2 ∈ A2, an ∈ An on the intervals A2, ...,An .
It completes the proof.



Spectrum Migration Approach Based on Pre-decision Aid and Interval Mamdani Fuzzy
Inference in Cognitive Radio Networks 89

From Theorem 1, we can simplify MFI to IMFI.
In order to apply IMFI method to spectrum migration, we formulate spectrum migration

fuzzy rules as Table Table 1. Furthermore, according to Figure 2 (a), we make interval Mam-
dani fuzzy inference decision table as Table 2. For ease of comprehension, we provide detailed
information on Table Table 1 and Table Table 2. In Table 3.2, we give an example to explain the
expression of fuzzy rules. The three shaded tables with “M”, “VL” and “S” stand for the fuzzy
rule of “If SOP is M and LMP is VL, then SMD is S”. For Table Table 2, I1 , I2 , I3 , I4 denote
effective inference intervals for [0, 0.25], [0.25, 0.5], [0.5, 0.75], [0.75, 1.0] respectively, and 1, 2,
3, 4, 5 stand for VL, L, M, H, VH respectively. It can be seen that I = I1∪ I2∪ I3∪ I4 = [0, 1],
so I is a complete inference interval for the universe. To explain the meaning of Table Table 2,
we also use the shaded tables as an example. If the value of SOP located at the effective infer-
ence interval I3 , and the value of LMP located at the effective inference interval I2 , I3 and I2
denote the effective inference intervals [0.5, 0.75] and [0.25, 0.5], i.e., if 0.5 ≤ V alueSOP ≤ 0.75,
0.25 ≤ V alueLMP ≤ 0.5, then, we use fuzzy inference rules (3,4/2,3). The number on the left of
backslash is fuzzy sets of SOP, and number on the right of backslash is fuzzy sets of LMP, they
correspond to the following four fuzzy rules

If SOP is M and LMP is L, then SMD is S, If SOP is M and LMP is M, then SMD is M
If SOP is H and LMP is L, then SMD is S, If SOP is H and LMP is M, then SMD is S
If we do not use interval Mamdani fuzzy inference, there will be twenty five fuzzy rules used

under the same case. Due to the limited space, we will not list the fuzzy rules. For the same
inference results, interval Mamdani fuzzy inference can save more than three-quarters of the time
compared with Mamdani fuzzy inference under our condition.

C. Spectrum Migration Decision
According to interval Mamdani fuzzy inference, we can get three kinds of inference results:

1) Some of the licensed spectrums have the same SMD levels, but there only one spectrum has
the highest SMD level. 2) Some of the licensed spectrums have the same SMD levels, and there
are more than one spectrum has the highest SMD level. 3) The SMD level for each spectrum is
different. For 1) and 3), the system selects the spectrum with the highest SMD level to migration,
we call it the 1st migration decision. For the case of 2), the system should take defuzzification
operations and selects the spectrum with the maximum SMD value to migration, we call it the
2nd migration decision. Spectrum migration decision can be expressed as



90 Z. Wang, H. Wang, H. Lv, G. Feng

Ch∗ = arg max ΘSMD(Ch)
∀Ch

(5)

4 Numerical and Simulation Results

We simulate and evaluate the performance of spectrum migration approach proposed in this
paper. Meanwhile, we use the existing approaches that are RANDOM [6], MFI and GREEDY [7]
to comparison. The following assumptions are adopted in the simulation. The CRN in which
SUs coexist with PUs in a 5km × 5km area. The number of licensed spectrums in the area is
5, and each spectrum is divided to 5 channels. All the spectrums are independent identically
distributed. We set the total bandwidth of licensed spectrum is 5 MHz. So, the bandwidth of
each secondary channel is 0.2 MHz. This assumption is reasonable since that one voice channel
is only 0.2 MHz in GSM cellular network. The signal to interference plus noise ratio (SINR)
is set to 3dB. The average arrival rate of SUs is assumed to be 1.0, the retransmission waiting
threshold is set to be 1.0s. Simulation data is recorded for 10000 times to avoid the contingency
of the results.

Figure 3: Average Migration Times Figure 4: Service Retransmission Probability of
SU at τt =1.0s

Figure 3 and Figure 4 show the average migration times of SU single service transmission
and SU service retransmission probability at τt =1.0s respectively. It is obviously that IMFI
algorithm has the least average migration times. Compared with RANDOM, the average migra-
tion times of IMFI reduce by about 65%, and also reduce nearly half compared with the MFI.
Under the premise of service size fixed, average migration times are related to spectrum holes
during time, migration waiting threshold and spectrum migration decision time. Compared with
RANDOM and GREEDY, the advantage of IMFI reflects the accuracy and timeliness for the
optimal spectrum selection. MFI has the same inference results with IMFI, so the advantage
of IMFI reflects the timeliness of spectrum migration decision. When τt =1.0s, the tendency of
service retransmission probability is close to average migration times for the four algorithms, that
indicates there exists a positive relationship between SU service retransmission probability and
average migration times. When λ =1.0, service retransmission probability only reaches to 20%
using IMFI, that is much lower than GREEDY and MFI, which confirms superior performance
on the optimal spectrum selection and spectrum migration decision once again.

In Figure 5, we can see that the average throughput of CRNs all decrease with the increase
of arrival rate of PUs. This is because the increase of λ makes the spectrum holes duration



Spectrum Migration Approach Based on Pre-decision Aid and Interval Mamdani Fuzzy
Inference in Cognitive Radio Networks 91

shorten, and cause the use of spectrum holes tend to be difficult. Compared with RANDOM,
the tendencies of GREEDY and MFI decrease obviously, the main reason is the two intelligent
algorithms consume an inordinate amount of time for spectrum migration decision. Because of
using spectrum migration pre-decision aid, and IMFI method, spectrum migration decision time
with IMFI algorithm is shortened greatly. Compared with RANDOM, the average throughput
of CRNs increases slightly.

Figure 5: Average Throughput of CRNs Figure 6: Effective Utilization of CRNs Spec-
trum Resource of SU

Figure 6 shows the effective utilization of CRNs spectrum resource. When λ is small, the
four algorithms are closer to this parameter and the effective utilization for each is higher. With
the increase of λ , service retransmission with RANDOM, GREEDY and MFI increases quickly,
makes invalid data rapid upward, and cause the effective utilization of CRNs spectrum resource
decline rapidly. IMFI can inhibit the service retransmission probability upward effectively, espe-
cially in the condition that the arrival rate of PUs is higher, the advantage is more obvious. When
λ =1.0, the effective utilization of CRNs spectrum resource using IMFI still reaches to 70%, that
makes more efficient use of spectrum sources, and improve system performance effectively.

5 Conclusions

The objective of this paper is to improve the QoS of SUs and CRNs performance. In view of
the problems that existing methods exist, we put forward a spectrum migration approach based
on pre-decision aid and interval Mamdani fuzzy inference in CRNs. Through the establishment
and analysis of the spectrum migration model, we define spectrum migration factors (SOP,
LMP and SMD) as spectrum characteristic metrics for spectrum migration decision. Moreover,
pre-decision is put forward to reduce system complexity and improve migration efficiency. For
shorten spectrum migration decision time and seek the optimal spectrum holes, we propose an
interval Mamdani fuzzy inference method based on Mamdani fuzzy inference, which can reduce
inference time significantly. At last, simulation results show the effectiveness of our approach
compared with other existing algorithms.

Acknowledgments

This work was supported by the Fundamental Research Fund for the Central Universities
(HEUCFZ1213), and Doctoral Fund of Ministry of Education of China (20122304130002).



92 Z. Wang, H. Wang, H. Lv, G. Feng

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