Non-Saturated Throughput Analysis of IEEE 802.11-Based Cognitive Radio Networks

December 2012, 19(6): 6–13 www.sciencedirect.com/science/journal/10058885 http://jcupt.xsw.bupt.cn

The Journal of China Universities of Posts and Telecommunications

Non-saturated throughput analysis of IEEE 802.11-based cognitive radio networks

ZHAO Yuan1, JIN Shun-fu1 (�), TIAN Nai-shuo2

1. College of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China 2. College of Science, Yanshan University, Qinhuangdao 066004, China

Abstract

Technology of cognitive radio networks has emerged as an effective method to enhance the utilization of the radio spectrum where the primary users have priority to use the spectrum, and the secondary users try to exploit the spectrum unoccupied by the primary users. In this paper, considering the non-saturated condition, the performance analysis for the IEEE 802.11-based cognitive radio networks is presented with single-channel and multi-channel, respectively. For the single-channel case, an absorbing Markov chain model describing the system transitions is constructed, and one-step transition probability matrix of the Markov chain is given. By using the method of probability generating function, the non-saturated throughput of the secondary users is obtained. For the multi-channel case, taking into account the negotiation-based sensing policy, the mean number of unused channels perceived by the second users is given, and then the non-saturated aggregate throughput of the secondary users is derived. Finally, numerical examples are provided to show the influences of the non-saturated degree, the number of the secondary users and the channel utilization of the primary users on the performance measures for the non-saturated throughput with single-channel and the non-saturated aggregate throughput with multi-channel.

Keywords cognitive radio networks, IEEE 802.11, non-saturated throughput, absorbing Markov chain, probability generating function

1 Introduction �

Studies of wireless spectrum usage have shown that large portions of the allocated spectrum are highly underutilized, for example, only 6% in most of the time [1]. In order to improve the utilization of the spectrum, the Federal Communication Committee (FCC) has recently suggested a new policy for dynamically allocating the spectrum which is the basis of the cognitive radio networks [2]. In the cognitive radio networks, a licensed user is called a primary user (PU) and an unlicensed user is called a secondary user (SU). The SUs are allowed to opportunistically exploit the spectrum unoccupied by PUs. There have been numerous media access control (MAC) schemes for SUs to access the channels without interfering PUs. In this paper, we assume

Received date: 27-02-2012 Corresponding author: JIN Shun-fu, E-mail: [email protected] DOI: 10.1016/S1005-8885(11)60311-7

that SUs access to the channels by employing the IEEE 802.11 protocol.

IEEE 802.11b standard is widely deployed in campus, office and home setting, and the operating frequency of IEEE 802.11b is 2.4 GHz [3]. IEEE 802.11y was drafted in 2008, and it is deployed at the frequency of 3.65 GHz to 3.7 GHz in American [4]. In IEEE 802.11 protocol, the fundamental mechanism to access the channel is called distributed coordination function (DCF). There have been lots of researches on the analysis of IEEE 802.11 DCF performance [5–9]. Bianchi [5] proposed a two-dimensional Markov chain model to analyze the performance of IEEE 802.11 under saturated state and ideal channel condition. The classical formula of the normalized system throughput was obtained accordingly. Vardakas et al. [6] and Foh et al. [7] built different Markov chain models for IEEE 802.11 standards, the finite retry attempts and the freezing of back-off counter were considered respectively. Liaw et al. [8] extended the model

Issue 6 ZHAO Yuan, et al. / Non-saturated throughput analysis of IEEE 802.11-based cognitive radio networks 7

presented in Ref. [5] by considering non-saturated condition, and evaluated the throughput performance under limited load. Considering the impact of channel error and station retry limit, Prakash et al. [9] analyzed the non-saturated throughput by using the Markov chain method.

In cognitive radio networks, when the licensed channels allocated to PUs are not occupied, SUs will make opportunistic use of the channels. But the channel accesses from a large number of SUs without any restriction will cause great collisions among SUs and will degrade the system performance. For this case, in order to reduce the collisions of SUs efficiently, IEEE 802.11 DCF with binary back-off algorithm is applied in cognitive radio networks, and such cognitive radio networks are called IEEE 802.11-based cognitive radio networks. IEEE 802.11-based cognitive radio networks can be used in the scenario that a number of users who want to transmit data to the destination by making opportunistic use of the channels with IEEE 802.11 protocol. The operating frequency of IEEE 802.11-based cognitive radio networks is in fact the operating frequency of IEEE 802.11 protocol. The PUs and SUs in IEEE 802.11-based cognitive radio networks can be defined based on the network environment in practice. Considering the scenario that IEEE 802.11b and Bluetooth coexist in the 2.4 GHz Industrial, scientific and medical (ISM) frequency [10], the users of IEEE 802.11-based wireless local area network (WLAN) can be defined as PUs, and the users of Bluetooth can be defined as SUs.

Nowadays, the technology of cognitive radio networks has brought new challenges to IEEE 802.11 DCF. Recently, several researchers have focused on the performance analysis of IEEE 802.11-based cognitive radio networks. Su et al. [11] developed a Markov chain model and an M/GY/1 queue model to characterize the performance of a multi-channel MAC protocol under two types of channel sensing policies. They obtained the packet delay and throughput. Bae et al. [12] investigated the performance of distributed contention-based spectrum access in cognitive radio networks. They developed a Markov chain and obtained the stationary distribution by using censored Markov chain method. Hoang et al. [13] designed and analyzed a frame-based cognitive radio network. By incorporating spectrum sensing and false alarms, they obtained the saturated throughput. Zhai et al. [14] proposed a slot-based MAC protocol under multi-channel

environment and obtained the saturated throughput of the SUs. Bae et al. [15] proposed a slot-based MAC protocol employing a modified 802.11 DCF with single-channel. By using an absorbing Markov chain model, they obtained the saturated throughput of SUs.

As mentioned above, for simplifying the analysis, most of the available researches on IEEE 802.11-based cognitive radio networks were performed under the saturated condition. However, the buffer of the SUs may be empty in cognitive radio networks, so non-saturated condition is more valid when evaluating the system performance of cognitive radio networks. The main contribution of this paper is to model and evaluate the system performance of IEEE 802.11-based cognitive radio networks with super-slot boundary under non-saturated condition. Moreover, the absorbing Markov chain method is applied in non-saturated IEEE 802.11-based cognitive radio networks to obtain the throughput of SUs by considering both single-channel and multi-channel.

The rest of this paper is organized as follows: in Sect. 2, the working principle of the IEEE 802.11 DCF in cognitive radio networks is presented. In Sect. 3, considering the non-saturated condition, an absorbing Markov chain model is built and analyzed, and then the formula of the non-saturated throughput with single-channel is given. In Sect. 4, taking into account the working principle of the negotiation-based sensing policy, the mean number of unused channels perceived by SUs is given, and then the non-saturated aggregate throughput of SUs with multi-channel is obtained. In Sect. 5, numerical examples are given, and conclusions are drawn in Sect. 6.

2 The working principle of IEEE 802.11 DCF in cognitive radio networks

We consider cognitive radio networks with CN licensed channels, and suppose that there are N SUs in the system. SUs make opportunistic uses of the channels. To achieve synchronization between PUs and SUs in IEEE 802.11-based cognitive radio networks, we assume PUs can periodically transmit timing beacons to SUs, and SUs can exchange their own timing beacons each other. This is similar to that specified in IEEE 802.11-2007, Sect. 11.1 [3]. Moreover, we assume all the channels have the same channel utilization � with respect to the PUs. A PU operates on a super-slot basis. PUs can only arrive at the beginning instant of a super-slot, and depart at the end of a

8 The Journal of China Universities of Posts and Telecommunications 2012

super-slot. The packet transmission of a PU will occupy at least one super-slot. Each super-slot has a fixed length fT

in mini-seconds. One super-slot is divided into M slots, and each slot has a fixed length � in mini-seconds. SUs operate on a slot basis. The arrivals and departures of SUs can only occur at the boundary of a slot. We consider that each SU is equipped with a channel sensor which can sense one of the CN channels at one time. At the beginning instant of each super-slot, SUs will sense the channel to find out which channels at current super-slot are unoccupied by the PUs. The sensing policy will be introduced in later section. In order to simplify the analysis, we assume the channel sensing is perfect and the sensing duration is negligible.

In this paper, at the beginning instant of each super-slot, all the SUs will sense the channels. If there is at least one channel sensed idle, the SUs with packets to be transmitted will contend to access the unoccupied channels according to the IEEE 802.11 DCF with binary back-off algorithm.

In the conventional IEEE 802.11 DCF, before a packet is to be transmitted, a back-off counter is uniformly chosen by this packet in the range [0, 1],iW � where

min2iiW W� is the size of back-off window after i

collisions, i is also called the back-off stage, and minW is the initial back-off window size. The unit of the back-off counter is a slot. The maximum back-off window size is

max min2 ,mW W� where m is an integer called the maximum back-off exponent. If the maximum back-off exponent is reached, the maximum back-off window size will be fixed. The back-off counter will decrease as long as the channel is sensed idle, freeze when either other transmissions or collisions are detected, and reactive when the channel is sensed idle again. When the back-off counter reaches to zero, the packets will be transmitted.

There are two kinds of mechanisms for packet transmission in DCF, namely, basic mechanism and request-to-send/clear-to-send (RTS/CTS) mechanism. We consider the former mechanism in this paper. This kind of mechanism is characterized as follows: when the sender station senses the channel idle for a distributed inter-frame space (DIFS), the packets in this sender station will be transmitted according to the back-off algorithm introduced before. If the destination receives the packet successfully, it will wait for a short inter-frame space (SIFS) interval and then transmit an acknowledgement (ACK) back to the sender station. Let ST � and CT � be the successful

transmission time and the collision lasting time of a packet in bits respectively. ST � is composed of the transmission time in bits of the PHY header, the MAC header, the DIFS, the SIFS, the ACK and a packet. CT � is composed of the transmission time in bits of the PHY header, the MAC header, the DIFS and a packet. When a fixed length of a packet is considered, we have S CT T� �� .

In cognitive radio networks, we have to take into account the impact of super-slot boundary. We focus on a single super-slot (called tagged super-slot) in steady state. When the back-off counter decreases, if the remaining time to the end of the tagged super-slot is not enough to transmit a packet completely, the back-off counter will be frozen until the end of the tagged super-slot. In the next super-slot unoccupied by PUs, the back-off process will be resumed again.

3 Non-saturated throughput analysis with single-channel

In this section, we deal with the non-saturated throughput of SUs with single-channel. An absorbing Markov chain model is built and analyzed, and then the formula of the non-saturated throughput with single-channel is given.

3.1 Notations

Under saturated condition, there are always packets in each SU to be transmitted. In practice, non-saturated condition is more valid. Under the non-saturated condition considered in this paper, the buffer of a SU may be empty. After a packet of a SU is transmitted successfully, the buffer of this SU is empty with probability 0 ,p non-empty with probability 01 ,p� where 0p represents the non-saturated degree of a SU. Consequently, the probability that there is no packet to be transmitted from any SU is given as follows:

0 0( )Np � (1) Obviously, 0 represents the non-saturated degree of

the channel with packets of SUs. Let ( )b t and ( )s t denote the stochastic process of

back-off counter and back-off stage for a SU (called tagged SU) respectively. When the buffer of the tagged SU is non-empty, we can model a two-dimensional process { ( ), ( )}s t b t with a discrete-time Markov chain, where embedded points consist of the instants in which back-off


counter is decrement. Applying the analysis result of the Markov chain given in Ref. [5], the probability that there is a packet of the tagged SU to be transmitted in a slot is obtained as follows:

� �min min

2(1 2 )(1 2 ) 1 1 (2 )m

pp W pW p

��

�� (2)

where p is the probability that there is a collision on condition that the tagged SU with a packet being transmitted on the channel. p is assumed to be constant and independent regardless of the retransmissions suffered.

The conditional probability p is then given as follows: 1

11 0 0

01 (1 ) (1 )

Nv N v v vN

vp C p p

��

��

� � � �� (3)

where (0 1)v v N � is the remaining number of SUs with packets to be transmitted except the tagged SU.

Eqs. (2) and (3) constitute a nonlinear system. Therefore, a unique solution of 0p can be given.

Let IP denote the probability that there is no packet of SUs being transmitted in a slot under the condition that there are (1 )i i N SUs contending on the channel. Note that each packet of a SU is transmitted in a slot with probability , not transmitted with probability 1 ,� IP is then given as follows:

I 0 01

(1 ) (1 )N

i N i i iN

iP C p p �

�

� � �� (4)

Let SP denote the probability that there is a successful transmission in a slot under the condition that there are

(1 )i i N SUs contending on the channel. When there is one and only one packet is being transmitted, this packet will be transmitted successfully. So SP is given as follows:

1S 0 0

1(1 ) (1 )

Ni N i i iN

iP C p p i � �

�

� � �� (5)

Let CP denote the probability that there is a collision in a slot under the condition that there are (1 )i i N SUscontending on the channel. CP is given as follows:

� �C 0 0 I S1

(1 ) 1N

i N i iN

iP C p p P P�

�

� � � � ��

10 0

1

(1 ) 1 (1 ) (1 )N

i N i i i iN

iC p p i � �

�

�� (6)

Combining Eqs. (1), (4)–(6), we have I S C 0 1P P P � � � � (7)

3.2 Absorbing markov chain model

Note that there are M slots in a super-slot, we order

these slots as 1, 2,..., ,M where the slot M is an absorbing state, and other slots are transient states. The transient states will reach to the absorbing state after some step transitions. Let (1 )n nY Y M be the slot number after n-step transitions. Each super-slot starts from slot 1 and ends at slot ,M so 0 1Y � with probability 1. Therefore, we can construct an absorbing Markov chain model with one absorbing state and 1M � transient states to describe the state transitions of the IEEE 802.11 DCF in cognitive radio networks. Let { : 0,1, 2,..., 1}nY n M� � denote this Markov chain.

Let ST be the successful transmission time of a packet in slots, and CT be the collision lasting time of a packet in slots. The embedded points of this discrete time absorbing Markov chain are defined under two cases:

1) When there is at least one SU with packets to be transmitted, the embedded points are defined as the slots that back-off counter is decremented and the last embedded point in the current super-slot is identified with the first embedded point in the next super-slot unoccupied by PUs. For example, given that the system is in slot

S(1 1)k k M T� � currently, after one-step transition, the next slot reached is slot 1k � with probability I ,P slot Sk T� with probability S ,P and slot Ck T� with probability C.P

2) When there is no SU with packets to be transmitted, the embedded points are defined as the slots that at least one SU’s buffer becomes non-empty from empty, and the last embedded point of current super-slot is also identified with the first embedded point in the next super-slot unoccupied by PUs. For example, given that the system is in slot S(1 1)k k M T� � currently, after one-step transition, the next slot reached is slot 1k � withprobability 0 0(1 ), � slot ( )k i i M k� � � with probability 0 0(1 ),i � and slot M with probability

0 .M k � The one-step transition probability matrix of the discrete

time Markov chain { : 0,1, 2,..., 1}nY n M� � is given as follows:

0

1 �

� � �� 0R R

Q (8)

where R is a matrix of size ( 1) ( 1),M M� � � 0 is a row vector of zero with dimension 1,M � 0R is a column vector with dimension 1.M �

Obviously, 0 ,= �R I RI where I is a column vector


of one with dimension 1.M � Let ijR (1 1i M � and 1 1)j M � be the

element of ,R ijR is given as follows: 1) For ,i j 0ijR � 2) For S1 i M T� and 1 1,j M �

0 0 I

0 0 C C

0 0 S S

0 0

(1 ) ; 1

(1 ) ;

(1 ) ;

(1 ); otherwise

j i

j i

ij j i

j i

P j iP j i T

RP j i T

�

�

�

�

� � � � ��

� � � ��

� ��

3) For S 1 2M T i M� � � and 1 1,j M �

0 0(1 )j iijR �� 4) For 1i M� � and 1 1,j M � 0ijR �

Let 01iR be the element of 0,R 1 1.i M � 0

1iR is given as follows:

1) For S1 1,i M T� � 01 0

M iiR ��

2) For S ,i M T� � 01 0

M ii SR P ��

3) For S 1 2,M T i M� � � 01 0 0(1 )M i

iR �� 4) For 1,i M� � 0

1 1iR � Let D be the number of steps required to reach to the

absorbing state M from state 1. According to the back-off algorithm in the IEEE 802.11-based cognitive radio networks proposed in Sect. 2, D follows a phase-type (PH) distribution represented by ( , )� R , where � is the initial distribution. In our model, (1,0,...,0).� � The probability distribution of D is given as follows:

1 0{ } n-P D n �� R R (9) where 1 1.n M �

By introducing a dummy variable z into R and 0 ,R we can obtain the matrix ( )zR and matrix 0 ( )zR respectively.

For 1 1i M � and 1 1,j M � the elements of ( )zR are given as follows: 1) For ,i j 0ijR � 2) For S1 i M T� and 1 1,j M �

0 0 I

0 0 C C

0 0 S S

0 0

(1 ) ; 1

(1 ) ;

(1 ) ;

(1 ); otherwise

j i

j i

ij j i

j i

P j iP j i T

RP z j i T

�

�

�

�

� � � � ��

� � � ��

� ��

3) For S 1 2M T i M� � � and 1 1,j M � ijR �

0 0(1 )j i � � 4) For 1i M� � and 1 1,j M � 0ijR �

For 1 1i M � , the elements of 0 ( )zR are given as follows:

1) For S1 1,i M T� � 01 0

M iiR ��

2) For S ,i M T� � 01 0 S

M iiR P z ��

3) For S 1 2,M T i M� � � 01 0 0(1 )M i

iR �� 4) For 1,i M� � 0

1 1iR � We define 1 0( ) [ ( )] ( ),n

nr z z z� �� R R 1 1,n M � ( )nr z can be expressed as follows:

0( ) ( ) l

nl n

r z h l z� � (10)

where the coefficient ( )h l indicates the conditional probability that there are l successful transmissions during a transition duration, given that the system reach to the state M after n-step transitions.

3.3 Non-saturated throughput

Let TSN be the number of successful transmissions during the tagged super-slot, TSN be the mean value of

TS.N Obviously, the probability generating function

TS ( )N z of TSN is given as follows: 1

TS TS0 1

( ) { } ( )M

un

u nN z P N u z r z

� �

� �

� � �� (11)

Differentiating Eq. (11) with respect to z at 1,z � we can give the average value TSN of TSN as follows:

1

TS1 1

d ( )d

M

nn z

N r zz

�

� �

� � (12)

The throughput singleS of SUs with single-channel is

defined as the ratio of mean length in bits for transmitting packets successfully to the one super-slot length in bits. Under the non-saturated condition, singleS is given as

follows: TS

singlef

PNS

CT� (13)

where C is the channel bit rate, P is the mean length of a packet in bits, and fT is the length of a super-slot in

mini-seconds.

4 Non-saturated aggregate throughput analysis with multi-channel

In this section, we deal with the non-saturated aggregate throughput of SUs with multi-channel. By using the results obtained in Sect. 3 and considering the working principle of the negotiation-based sensing policy (NSP), the formula


of the non-saturated aggregate throughput with multi-channel is given.

For the case of multi-channel, at the beginning instant of each super-slot, we assume that the SUs apply the NSP depicted in Ref. [11] to sense the channels and to identify which channels are unused by PUs. In the NSP, the basic idea is that each SU can select one channel to sense, and all the SUs exchange beacons each other. This is to say that the SUs know which channels are already perceived by their neighboring SUs and select different one to sense. If the number of the SUs is larger than or equal to the number of the channels, all the unused channels can be perceived by SUs according to the NPS. For simplifying the analysis, we assume all the channels have the same channel utilization � for PUs. Let NSPL be the number of the unused channels perceived by the SUs. By referring to Ref. [11], the probability distribution of NSPL can be given as follows:

C C

NSPC

(1 ) ; and 0

{ }(1 ) ; and 0

0; otherwise

CC N

N

NN N N

P L NN N N

� �

� �

� � ��

��

�

�

�

�� !

" #�� !�

" #��

(14) Let NSPL be the mean number of unused channels

perceived by SUs according to the NSP, NSPL can be obtained by

C

NSP NSP0

{ }N

L P L�

� ��

� �� (15)

Before the transmissions, all the SUs will sense the channels according to the NSP. By using the channel-bonding technology depicted in Ref. [16], the SUs can send multiple data packets during every super-slot. In practice, the SU which is the winner in contending for the channels will transmit packets over all the unused channels. With Eq. (15), we can obtain the mean non-saturated aggregate throughput multiS for SUs with multi-channel as follows:

multi NSP singleS L S� (16)

5 Numeral examples

In this section, by using the analysis results presented in Sects. 3 and 4, we give the numerical examples for the system model under the non-saturated condition.

By Ref. [15], the system parameters of our model are summarized as follows: channel bit rate is 2 Mbit/s,

50 �s,� � SIFS is 60 bits, DIFS is 100 bits, MAC header is 272 bits, PHY header is 128 bits, ACK is 240 bits, P =700 bits. Moreover, the maximum back-off exponent m is set to 4, and the number M of slots in a super-slot is set to 30.

Fig. 1 depicts the non-saturated throughput singleS with single-channel changes vs. the non-saturated degree 0p for different number N of SUs.

Fig. 1 Non-saturated throughput singleS vs. non-saturated

degree 0p with initial back-off window size min 32W �

From Fig. 1, we can observe that, for the same number N of SUs, the non-saturated throughput singleS will increase a bit

firstly and then decrease sharply as the non-saturated degree 0p increases. The reason is that when the non-saturated degree

is not large enough, there will be a greater number of packets to be transmitted, which will lead to more collisions to interfere with the transmission. The larger the non-saturated degree is, the less the collisions among the SUs are, the greater the non-saturated throughput will be. When the non-saturated degree increases to a certain value, the larger the non-saturated degree is, the fewer the number of packets to be transmitted are, and the smaller the non-saturated throughput will be. Specially, when the non-saturated degree 0 0,p � we can get the throughput under the saturated condition; when the non-saturated degree 0 1,p � the non-saturated throughput is 0, it is because there is no SU with packets to be transmitted.

On the other hand, we can also conclude that, for the same non-saturated degree 0 ,p when the non-saturated degree

0p is smaller, the non-saturated throughput singleS will increase as the number N of SUs decreases. This is because when the non-saturated degree is smaller, there will be a greater number of packets to be transmitted, which will lead to more collisions. The larger the number of SUs is, the more


the collisions among the SUs are, and then the smaller the non-saturated throughput will be. When the non-saturated degree is larger than a certain value, the non-saturated throughput will increase as the number of SUs increases. The reason is that when the non-saturated degree is larger, there will be a smaller number of packets to be transmitted, and the interference to the transmission will decrease. The larger the number of SUs is, the more the packets to be transmitted are, and then the greater the non-saturated throughput will be.

Fig. 2 plots the non-saturated throughput singleS with

single-channel changes vs. the number N of SUs for different non-saturated degree 0.p

Fig. 2 Non-saturated throughput singleS vs. number N of SUs

with initial back-off window size min 32W �

From Fig. 2, it can be found that, for the same non-saturated degree 0 ,p the change trend of the non-saturated throughput singleS experiences two stages.

During the first stage when the number N of SUs is smaller, the non-saturated throughput singleS will increase sharply

with the increase of the number N of SUs. It is because when the number of SUs is not large enough, as the number of SUs increases, the packets to be transmitted will increase, then the non-saturated throughput singleS will increase. During the

second stage when the number N of SUs is greater, the non-saturated throughput will decrease smoothly with the increase of the number N of SUs. Note that a greater number of SUs will induce more collisions among SUs, when the number of SUs increases to a certain value, the greater the number of the SUs is, the more the collisions among the SUs are, the less the number of packets transmitted successfully, so the non-saturated throughput will decrease.

On the other hand, we can also observe that, for the same number N of SUs, when the number N of SUs is smaller than a certain value, the larger the non-saturated degree 0p is, the smaller the non-saturated throughput singleS will be. The

reason is that when the number of SUs is smaller, a larger

non-saturated degree can result in fewer packets to be transmitted. This will lead to a smaller non-saturated throughput. When the number of SUs increases to a value large enough, the larger the non-saturated degree is, the greater the non-saturated throughput singleS will be. The

reason is that when the number of SUs is large enough, there will be a greater number of packets to be transmitted, which will induce more collisions. The larger the non-saturated degree is, the less the collisions among the SUs are, so the greater the non-saturated throughput will be.

Moreover, the case of 0 0p � in Fig. 2 means a saturated condition. We can conclude that, when a saturated condition is considered, the throughput will be over estimated when the number of SUs is smaller. On the contrary, the throughput will be lower evaluated when the number of SUs is greater.

Fig. 3 depicts the aggregate throughput multiS with multi-channel changes versus the number N of SUs for different channel utilization � of PUs in which the number

CN of the channels is set to 10.

Fig. 3 Aggregate throughput multiS vs. number N of SUs with non-saturated degree 0 0.2p �

From Fig. 3, we can observe that, for the same channel utilization � of PUs, the change trend of the aggregate throughput multiS experiences two stages. During the first stage when the number N of SUs is smaller than the number

CN of the channels, the aggregate throughput multiS will increase sharply with the increase of the number N of SUs. It is because when the number of SUs is smaller than the number of the channels, according to NSP, as the number of SUs increases, the number of the unused channels perceived by SUs will increase, then the aggregate throughput will increase. During the second stage when the number N of SUs is greater than or equal to the number CN of the channels, the aggregate throughput multiS will decrease smoothly with the increase of the number N of SUs. The reason is that when the number of SUs is greater than or equal to the number of the channels, according to NSP, the numbers of the unused channels


perceived by SUs will be the same. Note that a greater number of SUs means more collisions among SUs, which will result in the decrease of the aggregate throughput.

On the other hand, we can also conclude that, for the same number N of SUs, the larger the channel utilization � of PUs is, the smaller the aggregate throughput multiS will be. The reason is that the larger the channel utilization of PUs is, the less the number of unused channels can be perceived by SUs is, then the smaller the aggregate throughput will be.

6 Conclusions

As an effective method for solving the issues of spectrum shortage, the technology of cognitive radio networks has been widely studied. Concerning the synchronous relationship of primary users and secondary users in cognitive radio networks, the working principle of a super-slot based IEEE 802.11 DCF in cognitive radio networks was described in this paper. Considering the non-saturated condition, an absorbing Markov chain model was constructed to represent the system transition from transient state to absorbing state. The non-saturated throughput with single-channel and the non-saturated aggregate throughput with multi-channel were derived, respectively. Finally, with numerical examples, the influences of the non-saturated degree, the number of secondary users and the channel utilization of PUs on the non-saturated throughput with single-channel and the non-saturated aggregate throughput with multi-channel were investigated.

This paper extends the performance analysis of the contention-based cognitive radio networks under saturated condition to non-saturated condition. The model building and performance evaluation in this paper provide a theoretical basis for the optimal design of the system parameters in IEEE 802.11-based cognitive radio networks. The research in this paper has also potential applications in the improvement of channel access strategy for cognitive radio networks.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (71101124, 11201408), the Natural Science Foundation of Heibei Province (2012203093).

References

1. Marinho J, Monteiro E. Cognitive radio: survey on communication protocols, spectrum decision issues, and future research directions. Wireless Networks, 2012, 18(2): 147�164

2. Garhwal A, Bhattacharya P P. A survey on dynamic spectrum access techniques for cognitive radio. International Journal of Next-Generation Networks, 2011, 3(4): 15�32

3. IEEE 802.11�2007. IEEE standard for information technology� Telecommunications and information exchange between systems�Local and metropolitan area networks�Specific requirements, Part 11: Wireless LAN medium access control (MAC) and physical layer (PHY) specifications. 2007

4. IEEE 802.11y�2008. IEEE standard for information technology� Telecommunications and information exchange between systems�Local and metropolitan area networks�Specific requirements, Part 11: Wireless LAN medium access control (MAC) and physical layer (PHY) specifications, amendment 3: 3650-3700 MHz operation in USA. 2008

5. Bianchi G. Performance analysis of the IEEE 802.11 distributed coordination function. IEEE Journal on Selected Areas in Communications, 2000, 18(3): 535�547

6. Vardakas J S, Sidiropoulos M K, Logothetis M D. Performance behaviour of IEEE 802.11 distributed coordination function. IET Circuits, Devices and Systems, 2008, 2(1): 50�59

7. Foh C H, Tantra J W. Comments on IEEE 802.11 saturation throughput analysis with freezing of backoff counters. IEEE Communications Letters, 2005, 9(2): 130�132

8. Liaw Y S, Dadej A, Jayasuriya A. Performance analysis of IEEE 802.11 DCF under limited load. Proceedings of the 11th Asia-Pacific Conference on Communications (APCC’05): Oct 3�5, 2005, Perth, Australia. Piscataway, NJ, USA: IEEE , 2005: 759�763

9. Prakash G, Thangaraj P. Non-saturated throughput analysis of IEEE 802.11 distributed coordination function. European Journal of Scientific Research, 2011, 51(2): 157�167

10. Geirhofer S, Tong L, Sadler B M. Cognitive medium access: constraining interference based on experimental models. IEEE Journal on Selected Areas in Communications, 2008, 26(1): 95�105

11. Su H, Zhang X. Cross-layer based opportunistic MAC protocols for QoS provisionings over cognitive radio wireless networks. IEEE Journal on Selected Areas in Communications, 2008, 26(1): 118�129

12. Bae Y H, Alfa A S, Choi B D. Analysis of a contention-based opportunistic spectrum access under general channel activity model. Performance Evaluation, 2011, 68(3): 271�289

13. Hoang A T, Wong D T C, Liang Y C. Design and analysis for an 802.11-based cognitive radio network. Proceedings of the Wireless Communications and Networking Conference (WCNC’09), Apr 5�8, 2009, Budapest, Hungary. New York, NY,USA: IEEE, 2009: 6p

14. Zhai L B, Liu K M, Liu Y N, et al. A slot-based MAC protocol in cognitive radio wireless networks. Proceedings of the 4th International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM’08), Oct 12�14, 2008, Dalian, China. Piscataway, NJ, USA: IEEE, 2008: 4p

15. Bae Y H, Alfa A S, Choi B D. Performance analysis of modified IEEE 802.11-based cognitive radio networks. IEEE Communications Letters, 2010, 14(10): 975�977

16. Cordeiro C, Challapali K, Birru D. IEEE 802.22: an introduction to the first wireless standard based on cognitive radios. Journal of Communications, 2006, 1(1): 38�47

(Editor: ZHANG Ying)

Non-Saturated Throughput Analysis of IEEE 802.11-Based Cognitive Radio Networks

Documents

Transcript of Non-Saturated Throughput Analysis of IEEE 802.11-Based Cognitive Radio Networks