Design and Analysis of Transmission Strategies
in Channel-Hopping Cognitive Radio Networks
Chi-Mao Lee, Jia-Shi Lin, Student Member, IEEE,
Kai-Ten Feng, Member, IEEE, and Chung-Ju Chang, Fellow, IEEE
Abstract—In recent years, channel-hopping-based medium access control protocols have been proposed to improve the capacity in a decentralized multichannel cognitive radio (CR) network without using extra control channels. Each CR user has to stochastically follow a default channel-hopping sequence in order to locate a channel and conduct its frame transmission. In this paper, theoretical analysis is conducted on the probability of channel availability and the average frame delay for primary users (PUs) by considering the impact caused by imperfect sensing of CR users and imperfect synchronization between the primary and CR networks. According to the proposed analytical model with realistic considerations, an optimal channel-hopping sequence (OCS) approach is designed for the CR users based on a dynamic programming technique. It is designed by exploiting the optimal load balance between channel availability and channel utilization within the delay constraints of PUs. By adopting the OCS approach, maximum aggregate throughput of CR users can be achieved while considering PU’s quality-of-service (QoS) requirements. Moreover, in addition to the paired CR networks, the logical partition problem that occurs in generalized CR networks will also be addressed. This problem can severely degrade the aggregate throughput due to the decreased probability of connectivity between CR users, especially in a CR network with heavy traffic. Therefore, both wake-up successive contention (WSC) and wake-up counter-reset successive contention (WCSC) algorithms are proposed to increase the number of negotiations by both exploring the blind spot of imperfect sensing and amending the contention mechanisms between CR users. Compared to conventional channel-hopping sequences, numerical results illustrate that the proposed approaches can effectively maximize aggregate throughput for CR users under the QoS requirements of PUs. Index Terms—Cognitive radio, queuing networks, channel-hopping sequence, dynamic programming.
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1
I
NTRODUCTIONT
HE increasing demand for spectrum resources has caused the so-called spectrum scarcity problem primar-ily because of the conventional approaches of static spectrum allocation. According to FCC regulations [1], a large portion of the priced frequency spectrum is under-utilized in most times and locations, which are known as spectrum holes. Consequently, cognitive radio (CR) for dynamic spectrum access (DSA) has been exploited for more efficient spectrum utilization over the licensed bands [2] such as the IEEE 802.22 [3], [4] standard. This is an emerging standard that allocates frequency spectrums for TV broad-cast services via a license-exempt basis. The CR user (CRU), i.e., unlicensed user, is capable of sensing channel conditions and can adapt internal parameters to access licensed channels while these channels are not being utilized by primary users (PUs), i.e., licensed users. In addition to the IEEE 802.22 standard which focuses on specifications for a centralized CR network, there are also a great number of studies interested in decentralized DSA in multichannel TDMA-based, i.e., time slotted-based, primary networks. The main focus is on designing a medium access control(MAC) protocol to effectively exploit channel availability under the overlay paradigm, considering that both PUs and CRUs cannot transmit data simultaneously [5].
These MAC protocols can be categorized into two different types of schemes according to their access strategies, including sensing-based and probability-based methods. In sensing-based schemes [6], [7], the CRUs have to sense part of the channels before deciding which channel to access. In general, this will lead to higher channel utilization and reduced complexity in the handshaking mechanism since the hidden multichannel problem [8] is alleviated. However, this method has been described as impractical [9], [10], [11] because each CRU must equip multiple transceivers to conduct spectrum sensing. It is also inefficient for a CRU to sense and switch among the entire frequency spectrums within a slot time in order to obtain the required spectrum map knowledge. On the other hand, with probability-based schemes, the CRUs have to decide which channel to sense according to certain statistical information from the PUs and subsequently transmit their data. This type of scheme is implemented to amend the problem arising with sensing-based protocols that each CRU is only required to possess a single transceiver for channel sensing. Therefore, it is important for the CRUs to accurately acquire the opportunities to access idle channels in an efficient manner.
In [12], an opportunistic spectrum access MAC protocol is proposed by utilizing a common control channel for the CRUs to both negotiate the channel reservation and to determine which channel to sense based on the stationary
. The authors are with the Department of Electrical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 30049, Taiwan, ROC. E-mail: [email protected], [email protected], {ktfeng, cjchang}@mail.nctu.edu.tw.
Manuscript received 24 Aug. 2010; revised 26 July 2011; accepted 25 Aug. 2011; published online 27 Sept. 2011.
For information on obtaining reprints of this article, please send e-mail to: [email protected], and reference IEEECS Log Number TMC-2010-08-0397. Digital Object Identifier no. 10.1109/TMC.2011.205.
idle probability of the PU in each channel. However, the usage of an additional common control channel is still controversial. The partially observable Markov decision process (POMDP) framework in [9] provides an optimal sensing strategy for a CRU to select and sense a channel that has the highest probability of maximizing the network throughput. However, the proposed framework is compu-tationally complex and is not suitable for networks with multiple CRUs. In [13], an optimal channel sensing policy for more practical CR networks is explored by considering imperfect global synchronization between the CR and primary networks. The Munkres algorithm with low computational complexity is adopted to solve the optimiza-tion problem in channel selecoptimiza-tion. However, the proposed scheme is appropriate for CR networks with only a single pair of CRUs to communicate with one another. On the other hand, channel-hopping based protocols are proposed in [8], [11], [14] where multiple pairs of CRUs switch among the licensed channels with their distinct default channel-hopping sequences. When a CR transmitter wants to communicate with its intended CR receiver, the CR transmitter changes its hopping schedule and follows the channel-hopping sequence of the intended receiver in order to conduct negotiation and transmit the data if the channel is not currently utilized by the PU. However, the channel-hopping sequences in these schemes are uniformly gener-ated in each channel, which is appropriate only for homogeneous primary channels. Within heterogeneous channels, there should exist more feasible channel-hopping sequences to explore channel availability for CRUs.
Furthermore, it is assumed in most sensing-based and probability-based protocols that the CRUs must be synchro-nized with the PUs and sense either the idle or busy state of PUs. However, these two assumptions are considered impractical in realistic circumstances for the following reasons: 1) there is no communication between the primary and the CR networks, which makes global synchronization difficult; and 2) perfect spectrum sensing requires excessive sensing time, which degrades channel utilization especially for shorter slot times. In this paper, based on channel-hopping schemes, we examine analytical models for both the probability of channel availability for the CRUs and the average frame delay of the PUs. It is noted that the CR networks with both the paired CRUs and arbitrary commu-nications between the CRUs, i.e., the generalized CR network, are considered for establishing the analytical models. The proposed models incorporate possible collision events due to imperfect synchronization and sensing under a primary network containing multiple channels. Each channel is modeled as a Geo/G/1 queuing. system. By exploiting this realistically coexisting system, an optimal channel-hopping sequence (OCS) based on dynamic pro-gramming (DP) is derived in order to achieve maximum aggregate throughput for the CRUs and the average frame delay of the PUs with quality-of-service (QoS) guaranteed. Based on the proposed OCS scheme, optimal load balance can be achieved between the probability of channel availability and channel utilization within the CR network by knowing the frame arrival probabilities of PUs.
Moreover, the logical partition problem as described in [15] will occur in generalized CR networks, where the CR transmitter cannot find its corresponding CR receiver if the receiver switches to another channel in order to serve as a transmitter to conduct data delivery for another receiver. In such a case, severe degradation in aggregate throughput can happen due to the decreased probability in connectivity between the CRUs, especially under heavy CR traffic. Therefore, two algorithms, i.e., the wake-up successive contention (WSC) and the wake-up counter-reset successive contention (WCSC) mechanisms, are proposed to enhance the aggregate throughput of CRUs in generalized CR networks. These two schemes focus on how to alleviate the logical partition problem by increasing the number of negotiations from a blind spot in imperfect sensing and revising the contention mechanisms between the CRUs. Numerical results are presented to illustrate the perfor-mance of the proposed approaches in comparison with conventional schemes. It is clear that the proposed algo-rithms can capture the rapidly varying opportunities of spectrum holes for CRUs.
Noted that a preliminary design of the OCS scheme for paired CR networks was first presented in our previous work in [16]. A more comprehensive design and perfor-mance comparison for generalized CR networks will be conducted in this paper. The rest of this paper is organized as follows: The system models for both paired and general-ized CR networks are presented in Section 2. Section 3 provides the throughput analysis in paired CR networks. Based on the analysis, the proposed OCS scheme is modeled and derived by dynamic programming. In Section 4, the proposed OCS algorithm associated with enhanced schemes are addressed under generalized CR networks. Section 5 illustrates performance evaluation for the proposed me-chanisms; while the conclusions are drawn in Section 6.
2
S
YSTEMM
ODELSIn order to discuss the channel-hopping protocol for multiple CRUs, a simplified CR network with CRUs communicating in pairs will first be discussed. On the other hand, generalized network with CRUs arbitrarily communicating with each other will be addressed there-after. This section will describe the system models including the network architecture, traffic model, and sensing model for the proposed OCS scheme. Section 2.1 explains those models under paired CR network; while those for general-ized CR networks are addressed in Section 2.2.
2.1 System Models for Paired CR Network 2.1.1 Network Architecture and Traffic Model
The schematic diagram for coexistence of both the primary and CR networks is illustrated in Fig. 1. Noted that centralized downlink communication is considered for primary network while the CRUs in CR network commu-nicate with each other based on distributed manner. The timing diagram of multichannel operations for these two networks is shown in Fig. 2. Both the primary and CR networks are slotted systems with the same slot duration Ts,
dotted vertical lines in Fig. 2. Since there is no communica-tion between the PUs and CRUs, imperfect synchronizacommunica-tion is considered where the time difference between these two networks can be observed at each starting epoch. For example, as shown in Fig. 2, the asynchronous time difference is obtained as t ¼ t2 t1 where the PU in
channel 2 starts transmitting the data at time t1and a CRU
transmits its frame at t2. Furthermore, the primary network
has M channels with identical bandwidth, and each channel is independently occupied by a PU with Bernoulli arrival process [17], [18] with the probability iof one frame arrival
and the probability 1 iof no frame arrival at the starting
epochs for i ¼ 1; 2; . . . ; M. Note that infinite queue capacity is assumed for each channel, where the frame duration is equal to a slot length as shown in Fig. 2.
Moreover, the proposed OCS scheme is designed based on PU’s long term statistics. The assumption of known PU’s traffic model is considered feasible since there are different organizations and companies concentrate on the establish-ment of traffic models in order to provide reasonable simulation assumptions for system performance compar-isons. For example, two FTP traffic models have been constructed in the 3GPP [19] for performance evaluation of long term evolution (LTE) standard. Therefore, it is reason-able to assume that PU’s traffic is known to CRUs. Moreover, there also exists a great amount of research studies for CR networks that adopt the same assumption of known PU’s traffic pattern, e.g., [6], [7], [8], [9], [11], [12], [17]. The service length of each PU can be determined given that the PU will retransmit data until success, and the derivation will be presented in Section 3.1.
The single-hop CR network contains Np pairs of CRUs
(CRPs) where each pair is consisted of two CRUs including a transmitter and a receiver. Since centralized downlink communication is adopted for primary network, it is reasonable to consider single-hop scenario that all CRPs in CR network are communicating based on distributed manner. Furthermore, multihop transmissions within a CRP, i.e., with the existence of intermediate relaying nodes,
is not considered in this paper due to its difficulties on both implementation and analysis. Moreover, saturation traffic is considered for data transmission of CRPs within the network. The reason is that the worst case that affects PU’s QoS requirement can therefore be examined with saturation traffic from CRPs. Meanwhile, it can be utilized to observe the maximum transmission capacity that is allowed for each CRP in the network.
It is also considered that data communication only happens within a CRP and all CRPs are affected by the same set of PUs. As mentioned at the beginning of this section, centralized downlink communication is adopted for primary network. Therefore, every CRU will be impacted by the same set of PUs since all PU’s data transmissions are originated from a centralized base station. Based on the channel-hopping protocol as in [11], each CRP has to follow a default channel-hopping sequence generated by a pseudo random generator with the same discrete probability distribution P, which is defined as P ¼ ½p1; . . . ; pM; pvir
with pi denoting the channel-hopping probability for
i¼ 1; 2; . . . ; M. The distribution P is utilized to stochasti-cally determine which channel to hop to, and to carry out sensing and contending for data transmission in a reason-ably fair manner. In other words, the design of P corresponds to the design of a channel-hopping sequence. The frame structure of CRPs including sensing, contending, and data transmission phases is illustrated in Fig. 2. Moreover, the virtual channel that accounts for the relinquishment in transmissions of certain CRPs is repre-sented as pvir¼ 1 PMi¼1pi.
2.1.2 Sensing Model
In realistic situation, sensing decisions of CRPs is considered imperfect. In order to represent the effects from imperfect sensing, two probabilities are considered as follows: 1) the detection probability pd for detecting the PU when the PU
does exist, and 2) the probability of false alarm pfa for
detecting the PU while the PU does not exist. The relation-ship between pd and pfa has been studied in [20] for an
energy detector, which can be obtained for each CRP as
Fig. 1. Network scenarios for the coexistence of both the primary and the CR networks.
Fig. 2. Timing diagram for the coexistence of both the primary and the CR networks.
pfa¼ Q ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2þ 1 p Q1ðpdÞ þ ffiffiffiffiffiffiffi fs p ; ð1Þ where is the sensing time, is PU’s signal-to-noise ratio (SNR) acquired at the CRP’s receiver, and fs denotes the
channel sampling rate of the CRP. The QðÞ function represents the complementary distribution function of a standard Gaussian variable. Noted that detection probabil-ity pd is also called the sensing threshold which can be
adjusted by CRP, and pfa is an increasing function of pd
under fixed values of , , and fs. Moreover, it is reasonable
to assume that the detection probabilities as well as false alarm probabilities of all CRPs are independent under realistic environment. The reason is that incorrect decisions, i.e., false alarm and misdetection, are in general background noises, which is considered feasible to be assumed as i.i.d. background noise for each CRP. On the other hand, the detection probabilities pdof all CRPs are conditional on all
CRPs with the same SNR value, which is employed to let all CRPs have the same sensing behavior.
According to (1), it can be found that significant amount of sensing time is required for achieving perfect sensing, i.e., to exactly sense the state of PU to be either busy (pd¼ 1)
or idle (pfa¼ 0). The required time for perfect sensing is
considered much larger than the slot duration Ts¼ 10 ms as
specified in IEEE 802.22 standard [3], [21] owing to the limitation in hardware and sensing algorithms. Therefore, perfect sensing is considered impractical and will severely degrade channel utilization. Furthermore, by assuming all CRPs with the same sensing threshold pd, the equivalent
detection probability can be written as pn
d given that n out of
Np CRPs hopping to a specific channel. The reason is that
PU’s data will not be collided by CR transmitters only if all the CR transmitters can correctly detect the signals from PU. Note that n CRPs indicate that there are n transmitters and nreceivers in paired CR networks. The effective false alarm probability pn
fa for n out of Np CRPs hopping to a channel
can also be computed in the similar manner. Hence, the average detection probability PD;i for CRPs hopping to
channel i all with correct detection and the average false alarm probability PF ;i for CRPs hopping to channel i all
with false alarm can be, respectively, written as PD;i¼ XNp n¼0 HNp;n;ip n d¼ ½1 pið1 pdÞNp; ð2aÞ PF ;i¼ XNp n¼0 HNp;n;ip n fa¼ ½1 pið1 pfaÞNp; ð2bÞ
where HNp;n;i represents the probability of n out of the Np
CRPs hopping to channel i with probability pi as
HNp;n;i¼
Np
n
pnið1 piÞNpn: ð3Þ
Note that the detection probability PD;i and false alarm
probability PF ;i in (2a) and (2b) are defined to be average
values considering that the number of CRPs hopping to a channel can range from 0 to Np. In fact, detection
probabilities in all channels are correlated, so are false alarm probabilities. However, all PD;i and PF ;i8i are
approximated to be independent in (2) in order to reduce
derivation complexity such that the design of channel-hopping sequence can be implemented. Based on the probabilities PD;i and PF ;i as derived in (2a) and (2b), the
probability of channel availability, average frame delay of PUs, and aggregate throughput in paired CR network will be obtained in the next section.
2.2 System Models for Generalized CR Networks 2.2.1 Network Architecture and Traffic Model
The CR network with CRUs in pairs for communication has been addressed in the previous section. However, the CRUs are not always transmitting in pairs since they may have data to be delivered to different CRUs in the network. In generic scenarios, the CRUs can be classified into either the transmitting group when they have data to deliver or the nontransmitting group if they have no data to transmit. The traffic of each CRU is considered to be Bernoulli arrival with the probability CR of one frame arrival and the
probability 1 CR of no frame arrival at the starting
epochs as in [22]. Note that it is not feasible to consider saturation traffic for CRUs in generalized networks since there will be no CR receiver to accept data from those CRUs in the transmitting group. Furthermore, no queue capacity is considered for each CRU and every CRU has equal probability in transmission with other CRUs. 2.2.2 Sensing Model
As was presented in Section 2.1.2 for paired CR networks, the problem resulting from imperfect sensing will also be addressed in generalized CR networks. The average detection probability PD;i and average false alarm
prob-ability PF ;ifor CRUs as stated in (2a) and (2b), respectively,
will be recomputed under generalized CR networks, which are denoted as ~PD;i and ~PF ;i. The main feature of
general-ized CR networks is that there is comparably smaller probability for the transmitter and its corresponding receiver to have the same hopping sequences under either large number of channels or large number of CRUs. Consider that all CRUs are with the same sensing threshold pd, ~PD;i represents the average detection probability for
CRUs in the transmitting group hopping to channel i all with correct detection; while ~PF ;i denotes the average false
alarm probability for CRUs in the transmitting group hopping to channel i all with false alarm. Therefore, ~PD;i
and ~PF ;ican be, respectively, obtained as
~ PD;i¼ XNu n¼0 Xn y¼0 Nu n nCRð1 CRÞNun n y pyið1 piÞny pyd ¼X Nu n¼0 Xn y¼0 Hn;y;iTNu;np y d ¼ ½1 CRþ CRð1 piþ pipdÞNu; ð4Þ ~ PF ;i¼ XNu n¼0 Xn y¼0 Hn;y;iTNu;np y fa ¼ ½1 CRþ CRð1 piþ pipfaÞNu; ð5Þ
where Nudenotes the total number of CRUs in the network.
The parameter Hn;y;iis defined similar to (3) indicating the
probability of y out of n CRUs hopping to channel i with probability pi. Note that both ~PD;i and ~PF ;i8i are also
approximated to be independent. Moreover, TNu;n
repre-sents the probability of n out of Nu CRUs possess data for
delivery with transmitting probability CR as
TNu;n¼
Nu
n
nCRð1 CRÞNun: ð6Þ
Note that both ~PD;iand ~PF ;iare defined to be average values
considering that the number of CRUs hopping to a channel can range from 0 to Nu, and each CRU possesses with the
transmitting probability CR for data delivery.
3
P
ROPOSEDO
PTIMALC
HANNEL-H
OPPINGS
EQUENCEA
PPROACH UNDERP
AIREDCR
N
ETWORKSIn this section, the proposed OCS scheme will be derived under paired CR networks. The probability of channel availability for CRPs and the PU’s average frame delay will first be computed in Section 3.1, which result in the derivation of CRPs’ aggregate throughput in Section 3.2. The formulation of proposed OCS approach and its corresponding DP scheme will be addressed in Sections 3.3 and 3.4, respectively.
3.1 Probability of Channel Availability for CRPs and PU’s Average Frame Delay
In this section, the impacts caused by imperfect synchroni-zation and sensing of CRPs are analyzed for the probability of channel availability and average frame delay of primary queuing network. The primary network in each channel is a Geo/G/1 discrete-time queuing system with retransmitting capability if its frames are collided by CRPs. Noted that the arrivals and departures, i.e., the service completions, of primary network should occur at the starting epochs simultaneously. However, this type of system is considered intractable for analyzing the average system size. In order to ensure the analysis to be tractable, the arrival first (AF) scheme [23] is introduced as the scheduling policy for the queue. In other words, the frame arrivals take precedence over departures at the starting epochs, e.g., at time t3 in
channel 2 as shown in Fig. 2. It has been proven in [23] that the distribution of system size observed at the departure points by adopting the AF scheme will be identical to that of the original Geo/G/1 system. Therefore, the probability of channel availability for CRPs and the average frame delay of PU can be analyzed based on the derivation of system size distribution [24], [25] at the departure points.
Considering channel i for i ¼ 1; 2; . . . ; M, let Xm;i be
defined as the discrete random variables (RVs) of the number of PU’s frames waiting for transmission observed at the mth departure point. S1;i and S2;i are denoted as the
RVs of service time (or delay) of one PU’s frame under the condition that Xm;i¼ 0 and Xm;i> 0, respectively. Note that
both S1;i and S2;i are independent of m. A1;i and A2;i are
defined as the RVs of the number of PU’s frames who arrive
during the service time S1;i and S2;i, respectively. The
relationship between Xm;i, A1;i, and A2;ican be obtained as
Xmþ1;i¼ AX1;i Xm;i¼ 0; m;iþ A2;i 1 Xm;i 1:
ð7Þ Consequently, the probability mass function (PMF) ar;k;i¼
P rðAr;i¼ kÞ for the number of arrival frames Ar;iwith r ¼ 1
and 2 can be obtained as ar;k;i¼
X1 l¼k
P rðSr;i¼ lÞP rðAr;i¼ kjSr;i¼ lÞ
¼X 1 l¼k l k P rðSr;i¼ lÞkið1 iÞlk: ð8Þ
Fig. 2 depicts the relationship between S1;i and CRPs’
sensing results by considering the cases of S1;i¼ 1, 2, and 3.
For channel i, let E1j1;i, E0j1;i, E1j0;i, and E0j0;i be,
respectively, denoted as the sensing results of detection for PU, misdetection for PU, false alarm, and correct rejection. Hence, it can be intuitively observed that PrðE1j1;iÞ ¼ PD;i, PrðE0j1;iÞ ¼ 1 PD;i, PrðE1j0;iÞ ¼ PF ;i, and
PrðE0j0;iÞ ¼ 1 PF ;i. Noted that S1;i also indicates the
service time under the condition that there does not exist PU’s frame in the previous slot according to PU’s clock. Therefore, it can be observed that the sensing result made by CRPs in the previous slot becomes either E1j0;i or E0j0;i,
instead of either E1j1;i or E0j1;i. As in Fig. 2, it can be seen
that the successful frame transmitted by the PU requires two CRPs’ successive E1j1;i except for S1;i¼ 1.
Conse-quently, both the two cases S1;i¼ 1 and S1;i> 1should be
considered in the analysis. Moreover, the first sensing probability of either PF ;i or 1 PF ;i condition on S1;i> 1
needs to be studied since the second sensing result should be E0j1;iif the first sensing result is E1j0;i. Noted that S1;i¼ 1
represents the first sensing result as E1j0;i and the second
sensing result to be E1j1;i. Furthermore, the SNR of CRPs is
considered higher than that of PUs owing to the shorter communication range in CR networks. The carrier sensing before the contention phase cannot detect the existence of PU due to the different natures of spectrum sensing in the detector [26]. Let c1;iðzÞ and qiðzÞ be, respectively, defined as
the z-transform of the PMF of S1;i and the PMF of
transmitting until the existence of two successive E1j1;i.
According to (2a) and (2b), c1;iðzÞ can be written as
c1;iðzÞ ¼ PF ;i½PD;izþ ð1 PD;iÞqiðzÞz þ ð1 PF ;iÞqiðzÞ; ð9Þ
and qiðzÞ is derived by recursive method as
qiðzÞ ¼ fiðzÞ½PD;izþ ð1 PD;iÞqiðzÞz;
which can further be reorganized as qiðzÞ ¼
PD;ifiðzÞz
1 ð1 PD;iÞfiðzÞz
; ð10Þ where fiðzÞ represents the z-transform of geometric
dis-tribution with parameter PD;i as
fiðzÞ ¼
PD;iz
1 ð1 PD;iÞ z
Furthermore, S2;idenotes the service time for a new frame,
i.e., not a retransmitted frame, that is served right after the previous frame. It indicates that the sensing result of CRPs in the last slot must be E1j1;i such that the previous frame
can leave the queue. The z-transform of the PMF of S2;ican
be derived similar to S1;i as
c2;iðzÞ ¼ PD;izþ ð1 PD;iÞqiðzÞz; ð12Þ
where qiðzÞ is obtained from (10). Let hr;iðzÞ be defined as
the z-transform of ar;k;i in (8) for r ¼ 1 and 2, the following
relationship between hr;iðzÞ and cr;iðzÞ can be obtained:
hr;iðzÞ ¼ X1 k¼0 ar;k;izk¼ X1 l¼0 P rðSr;i¼ lÞð1 iþ izÞl ¼ cr;ið1 iþ izÞ: ð13Þ
Moreover, let j;i be defined as the steady state probability
of Xm;i¼ j, i.e., with m ! 1. The value of j;icorresponds
to the steady state system size observed at the departure points, which can be acquired as
j;i¼ 0;ia1;j;iþ
Xjþ1 k¼1
k;ia2;jkþ1;i: ð14Þ
Based on (13), the z-transform of j;i, denoted as giðzÞ, can
be derived as
giðzÞ ¼
0;i½h1;iðzÞz h2;iðzÞ
z h2;iðzÞ
: ð15Þ Therefore, according to the boundary conditions gið1Þ ¼ 1,
h1;ið1Þ ¼ 1, and h2;ið1Þ ¼ 1, the probability of channel
availability for CRPs in the ith channel can be obtained by using the L’Hopital’s rule as
0;i¼
1 h0 2;iðzÞ
h0
1;iðzÞz þ h1;iðzÞ h02;iðzÞ
z¼1 ; ð16Þ where h0
r;idenotes the derivative of hr;ifor r ¼ 1 and 2. The
average frame delay of PU in the ith channel can be derived by adopting the Little’s Theorem as
DiðpiÞ ¼ LiðpiÞ=i; ð17Þ
where the average system size for the ith channel LiðpiÞ is
acquired by taking the derivative of (15) at z ¼ 1 using the L’Hopital’s rule as
LiðpiÞ ¼
X1 j¼0
jj;i¼ g0iðzÞjz¼1: ð18Þ
Noted that the probability of channel availability for CRPs 0;i in (16) will be utilized in the computation of system
throughput in next section. The average frame delay of the PU DiðpiÞ in (17) will be adopted as a major constraint of
proposed optimization problem in Section 3.3. 3.2 Aggregate Throughput of CRPs
Based on the analysis in primary network under certain channel-hopping sequence of CRPs, the aggregate through-put of CRPs can be obtained according to CRP’s frame structure as shown in Fig. 2. With the CRPs transmitting in
a single-hop wireless network, there are n out of Np CRPs
hopping to the ith channel with the probability HNp;n;i as
defined in (3). Due to imperfect sensing, there is probability of out of n CRPs with correct sensing while channel i is idle as Fn;¼ n ð1 pfaÞpnfa : ð19Þ
After sensing the channel availability, the contention-based scheme as defined in IEEE 802.11 distributed coordination function (DCF) mode [27] will be adopted, which consists of two-way handshakes including data transmission and acknowledgement. The CRPs who sense the channel idle will have the privilege to contend for data transmission. Each CRP transmitter will wait for a randomly chosen backoff value in the interval of ½0; W 1 before data delivery, where W denotes a fixed window size. The CRPs can transmit data only if their backoff values count down to zero, and they will stop the backoff process if data transmission from other CRP has been observed while listening. Noted that exponential backoff and request-to-send/clear-to-send (RTS/CTS) exchanges are not adopted in this approach since small frame size of CRP is considered. The reason of using smaller CRP’s frame size is due to the requirements for frequent channel sensing in order to serve for highly time-varying CR traffic. Moreover, the slot size Tsis in general selected with small values [3],
[28] according to the underlying CR specifications. Conse-quently, it is reasonable to allow only a single frame transmission in each time slot. Therefore, the average successful transmission time C with no intercollision
between CRPs can be obtained as C¼ W XW ¼1 ½Ts ð 1Þ 1 W 1 ; ð20Þ where denotes the minislot for carrier sensing. The term ð1 =W Þ1in (20) denotes the probability for success-ful data transmission in the th minislot. ½Ts ð 1Þ
indicates the corresponding data transmission time, where ð 1Þ represents the waiting time for random backoff. Based on (3), (16), (19), and (20), the throughput of CRPs in the ith channel iðpiÞ can be acquired as
iðpiÞ ¼ 1 Ts 0;ið1 iÞ XNp n¼1 Xn ¼1 HNp;n;iFn;C; ð21Þ
where the unit of throughput is in time slots. The throughput of CRPs in the ith channel iðpiÞ in (21) scaled
with normalization factor 1=Ts is composed by the
prob-ability of channel availprob-ability 0;iin (16) and the probability
of ð1 iÞ that no PU is conducting data transmission while
a CRP is successfully transmitting. Moreover, the term PNp
n¼1
Pn
¼1HNp;n;iFn;C in (21) denotes average
through-put of the ith channel on condition that CRPs are with correct channel sensing. As a result, the aggregate through-put for all M channels with probability distribution P can be obtained as
ðPÞ ¼X M i¼1 iðpiÞ ¼ 1 Ts XM i¼1 0;ið1 iÞ Nppið1 pfaÞ W X W ¼1 ½Ts ð 1Þ 1 pið1 pfaÞ W Np1 : ð22Þ In the next section, the aggregate throughput ðPÞ derived in (22) will be utilized as the optimization criterion for proposed OCS scheme.
3.3 Proposed OCS Approach
In previous section, throughput analysis is conducted under realistic circumstances with the coexistence of PUs and CRPs. In this section, an approach for obtaining OCS will be developed in order to maximize aggregate throughput of CRPs in (22) under the QoS constraints of PUs. The optimization problem for OCS can be formulated as
P¼ arg max P ðPÞ s:t: Dmin DiðpiÞ Dc;i; 0 pi 1; XM i¼1 pi 1; for i ¼ 1; 2; . . . ; M; ð23Þ where P¼ ½p
1; . . . ; pM; pvir represents the corresponding
OCS with p
i denoting the optimal channel-hopping
prob-ability. The average frame delay of PU in the ith channel DiðpiÞ is obtained from (17). The parameter Dc;i indicates
the delay constraint for QoS requirement of PU in channel i, and Dmin corresponds to a slot size if there is no collision
within PU’s transmissions. In other words, the emphasis of this paper is to obtain OCS within NpCRPs for optimal load
balance considering PU’s QoS requirements.
Intuitively, the optimization problem in (23) can be viewed as a sequential optimal decision problem from channel 1 to M. However, due to nonlinear relationship between throughput at the ith channel iðpiÞ in (21) and the
probability pi for i ¼ 1 to M, each decision on hopping
probability pi cannot be independently determined since
the throughput will be influenced by the rest of undecided channels. In other words, it is not possible to directly allocate 100 percent hopping probability into a channel with the lowest frame arrival probability since potential throughput may exist in the remaining channels that are unassigned with hopping probabilities. In order to resolve this problem, the DP-based approach in [29] is utilized for obtaining the OCS as will be shown in next section. 3.4 Dynamic Programming Formulation for
Proposed OCS Approach
In this section, the optimization problem in (23) for multiple channel operations can be formulated into a DP problem based on [29]. A reward function ið iÞ for channel i denotes
the maximum throughput summed from channel i to channel M with channel available probability i, which
indicates the probability to be allocated from channel i to M. Moreover, an instant reward function is defined to be iðpiÞ as in (21) plus the constraint pc;i on channel-hopping
probability pi. Noted that the constraint pc;iis a replacement
of delay constraint Dc;isince the average frame delay DiðpiÞ
in (17) is a strictly increasing function, i.e., one-to-one mapping, of channel-hopping probability pi. The DP
recursive form for proposed OCS scheme can therefore be written as
ið iÞ ¼ max 0piminfpc;i; ig
f iðpiÞ þ iþ1ð i piÞg; ð24Þ
where 1¼ 1 and iþ1¼ i pi. The maximum aggregate
throughput in OCS can be obtained as
ðPÞ ¼ 1ð 1Þ; ð25Þ
where P from the OCS approach is the combination of channel-hopping probabilities acquired by the DP recursion in each channel. The allowable channel-hopping probability pi for each channel is quantized from 0 to 1 with
quantization level p. The selection of p is determined
based on the quantization level in power as depicted in [30], which will relate to the accuracy of proposed OCS approach. First of all, the original problem can be partitioned into 1
4pþ 1 subproblems by assigning p1¼ 0;
p1¼ 4p; p1¼ 24p; . . . ; p1¼ 1, and the remaining
corre-sponding unassigned probabilities becomes 1; 1 4p;
1 24p; . . . ; 0. For example, the first subproblem of (24)
can be written as
1ð 1¼ 1Þ ¼ maxf 1ðp1¼ 0Þ þ 2ð 1 ðp1¼ 0ÞÞ;
1ðp1¼ 4pÞ þ 2ð 1 ðp1¼ 4pÞÞ; . . . ;
1ðp1¼ 1Þ þ 2ð 1 ðp1¼ 1ÞÞg:
Similarly, the remaining subproblems 2to M can also be
acquired by recursively breaking them into smaller sub-problems until the probability pM is assigned. After these
1
4pþ 1 subproblems are solved, the solution for original
optimization problem in (24) can therefore be acquired. As indicated in [31], linear complexity of OðM ð1=pÞ2Þ that is
proportional to the number of channels M can be obtained by adopting the DP formulation in (24) and (25) for proposed OCS approach. After offline solving the OCS for different numbers of CRPs, the proposed OCS scheme can consequently be recorded into a lookup table in order to acquire the optimal channel-hopping probability for N CRPs in real-time implementation. As a result, under the same p, the DP scheme for proposed OCS approach will
be computationally efficient in finding the optimal hopping probability compared to the brute force scheme with exponential complexity of Oðð1=pÞMÞ. Therefore, the
computation time for executing DP can be considered a small and negligible overhead for CRPs to acquire updated channel-hopping sequence.
4
P
ROPOSEDO
PTIMALC
HANNEL-H
OPPINGS
EQUENCEA
PPROACH UNDERG
ENERALIZEDCR N
ETWORKSWhen CRUs are in the transmitting group, they have to follow the channel-hopping sequence of their correspond-ing receivers to conduct channel negotiations and data transmission. On the other hand, for those CRUs in the nontransmitting group, they only need to follow their own channel-hopping sequence to hop between channels.
However, there is a severe problem that arises in general-ized CR networks called logic partition problem as stated in [15]. The CR transmitter cannot find its corresponding CR receiver since the receiver may also be in the transmitting group, which can severely degrade the CR network throughput. This type of situations frequently occur under CR network with heavy traffic. In order to address the logic partition problem, the OCS approach for generalized CR network will be presented and the associated analysis of aggregate throughput will be provided in Section 4.1.
Furthermore, in paired CR networks, the events of fail transmission for CRPs are composed of intercollision among the CRPs and collision between PUs and CRPs. However, with the admission control and utilization of comparably larger contention window size in CR network, the probability of intercollision among CRPs can be considered insignificant. Therefore, it is unnecessary for all CRPs to contend successively by adopting the DCF mode in IEEE 802.11 standard. As described in Section 3.2, the two-way handshake process is utilized that the CRP who sense the channel idle can start the contention process and will terminate the backoff counter while observing the other CRP’s transmissions. However, this type of simple negotia-tion will not be sufficient for generalized CR networks. The aggregate throughput for CR network will be severely degraded if the CR transmitter does not hop to the same channel as its corresponding CR receiver, especially in the network with heavy CR traffic. In order to further alleviate this problem for throughput enhancement, both the WSC and the WCSC algorithms are proposed to be combined with the OCS approach in Sections 4.2 and 4.3.
4.1 Aggregate Throughput and Proposed OCS Approach
Based on ~PD;i in (4) and ~PF ;i in (5), the probability of
channel availability for CRUs and the average frame delay for PUs in generalized CR network can also be derived similar to the analysis as presented in Section 3.1, which are, respectively, denoted as ~0;i and ~DiðpiÞ for the ith channel.
The aggregate throughput for generalized CR network can therefore be computed in this section. Unlike the situations in paired CR networks, it is required to first obtain the rendezvous probability pv;iin generalized CR network which
refers to the probability for a CR transmitter to find its intended CR receivers in the same channel i. It indicates that a CR transmitter can have the chance to communicate with its corresponding CR receiver. Under the assumption of equal probability for CR transmitters in choosing the receivers, the rendezvous probability pv;iat channel i can be
obtained as pv;i¼ Nu n Nu 1 þ yi 1 Nu 1 ; ð26Þ with the total number of CRUs Nu> 1. The parameter n
denotes the number of CRUs in the transmitting group, and yirepresents the number of CRUs in the transmitting group
that hop to the same channel i. The first term in (26) indicates the probability that the corresponding CR receiver of a CR transmitter exists in the nontransmitting group. On
the other hand, the second term in (26) represents the probability that the corresponding CR receiver of a CR transmitter is in the transmitting group but hops to the same channel i as the CR transmitter. Noted that yi¼ 1
indicates that only a single CR transmitter hops to the ith channel. Similar to the derivation in Section 3.2, the throughput for channel i can be obtained by combining ~0;i
and pv;iin (26) as ~ iðpiÞ ¼ 1 Ts ~ 0;ið1 iÞ XNu n¼1 Xn y¼1 Xy ¼1
pv;iHn;y;iTNu;nFy;C; ð27Þ
for Nu> 1, where Hn;y;i, Fy;, and Care obtained from (3),
(19), and (20), respectively. Consequently, the aggregate throughput for generalized CR networks with the prob-ability distribution P can be acquired as
~ ðPÞ ¼X M i¼1 ~ iðpiÞ ¼ 1 Ts XM i¼1 ~ 0;ið1 iÞ NupiCRð1 pfaÞ W X W ¼1 1þ piCR CR piCRð1 pfaÞ W ½Ts ð 1Þ CR 1 pið1 pfaÞ W þ 1 CR Nu2 ; ð28Þ for Nu> 1. Intuitively, ~ ðPÞ ¼ 0 for Nu¼ 1. Similar to the
derivations as stated in Section 3.3, the optimization problem to obtain the OCS ~Pfor generalized CR networks can be formulated similar to (23). Moreover, the DP formulation for OCS approach as described in Section 3.4 can also be applied for generalized CR networks.
4.2 Enhancement with Wake-Up Successive Contention Algorithm
In order to provide higher efficiency for generalized CR networks, the WSC scheme is proposed to increase the transmission opportunity for the contention mechanism. First of all, the four-way handshake RTS/CTS/DATA/ ACK as stated in [27] is used for communication between a CR transmitter and a CR receiver. In the original OCS approach, each CRU will only contend the channel once if its backoff counter reaches zero. In the WSC scheme, on the other hand, the CRUs will successively contend the channel until the end of contention phase if other CRUs’ failed transmission has been observed. Noted that failed trans-mission of a CRU is indicated by the time duration of a single RTS frame plus a short interframe space (SIFS), which represents that a corresponding CR receiver either cannot correctly receive the RTS frame or the receiver hops to the other channel.
Furthermore, due to the probability of false alarm caused by imperfect sensing, some CRUs will mistakenly think there exists a PU in the channel while the PU is not actively transmitting data in the channel. The CRUs will remain in the silent state without conducting channel contention and negotiation processes with their corresponding CR recei-vers. There will exist comparably less CRUs in a channel
that are actively contending the channel which conse-quently decreases the transmission opportunities between CRUs. Therefore, as shown in Fig. 3, the wake-up mechanism in proposed WSC scheme is designed to increase the number of CRUs in the contention phase by allowing all CRUs who were blocked from accessing the channel into the contention phase while listening to the failed transmission of the other CRUs. Moreover, those wake-up CRUs will select their own backoff counter C within the range of ½0; W 1. Noted that the CR transmitter that failed in its transmission will not succes-sively join the afterwards contention process. In summary, the WSC algorithm is formed by the combination of four-way handshake, successive contention, and wake-up mechanism.
4.3 Enhancement with Wake-Up Counter-Reset Successive Contention Algorithm
The proposed WCSC scheme is designed based on the WSC algorithm by modifying the wake-up mechanism in each CRU. The design target of WCSC algorithm is to increase the number of negotiations between CRUs which conse-quently results in higher probability of successful transmis-sions. As in the WCSC scheme shown in Fig. 4, each time after the wake-up for channel contention, the CRU will reset its own backoff counter C by randomly choosing a value in the range of ½Wp; W 1. The parameter Wp¼
dtp=e represents the number of minislot for the
corre-sponding time interval tp that a CRU has encountered
within the contention period. It can be observed that there can be more CRUs that possess the opportunity for channel contention compared to that in the WSC scheme which
utilizes fixed interval of backoff window in ½0; W 1. Noted that there is no guarantee for the proposed WCSC algorithm to outperform the WSC scheme. The reason is that there can be more collision happened with the existence of larger number of CRUs in a channel compared to the WSC scheme.
Moreover, these two enhancement schemes will not affect PU’s average frame delay with reasons explained as follows: The major design concept of both schemes is that CRUs will successively contend the channel if other CRUs’ failed transmission has been observed. Considering the case with the existence of PU in a channel, there can exist a CRU that misdetects the existence of PU and transmits its own data in a channel. Consequently, data from both PU and CRU will collide with each other and fail in transmission. According to the design of proposed schemes, other CRUs that listen to the occurrence of failed transmission will start to enter a channel and contend for data transmission in this frame duration. However, the PU’s average frame delay will not be affected by the successive contention scheme since the PU’s data have already been collided by the previous CRU that causes failed transmission. On the other hand, considering the case without the existence of PU in a channel, it is intuitive that no matter how many CRUs entering the channel will not affect the PU transmission behaviors, specifically on the average frame delay. Note that negotiations between CRUs are not required in order to recognize failed transmission since a CR transmitter can identify either the successful or failed transmission via listening to the existence of CTS
Fig. 3. Flow diagram of proposed WSC algorithm.
packet delivered by a CR receiver. Therefore, the proposed two enhanced schemes will not increase PU’s average frame delay. This observation will further be validated in the performance evaluation section.
The performance of proposed WSC and WCSC schemes will be incorporated with the original OCS approach, i.e., denoted as OCS-WSC and OCS-WCSC schemes, respec-tively, and will be evaluated in the performance evaluation section under generalized CR networks. Noted that the major purpose for both the proposed WSC and OCS-WCSC schemes is to increase the probability for the CR transmitter to find its corresponding CR receiver in generalized CR networks. Both enhancement can also be adopted for paired CR networks. However, it is intuitive to recognize that the overhead resulting from the four-way handshake can degrade the throughput performance for paired CR networks. It is considered sufficient to utilize the original OCS scheme for paired CR networks. On the other hand, in a network with both paired and nonpaired CRUs, the OCS-WSC and OCS-WCSC algorithms should be adopted which will treat each CRP as two individual CRUs. The negotiation between CRUs by adopting the four-way handshake and successive contention will be applied to all CRUs in order to effectively enhance the transmission probability and system throughput.
5
P
ERFORMANCEE
VALUATIONIn this section, theoretical analysis for proposed OCS approach will be validated via simulations under both paired and generalized CR networks. The performance of proposed OCS, OCS-WSC, and OCS-WCSC schemes will be evaluated and compared to the other conventional channel-hopping sequences. Moreover, for finding the suboptimal solution of OCS, the discussion on quantization level p in
the DP formulation will also be provided. Simulation parameters for both primary and CR networks are, respectively, listed in Table 1. Noted that the parameters
are adopted from the IEEE 802.22 standard in [3], [4] for CR network operating on TV bands; while those for the contention process are acquired from the IEEE 802.11 standard.
5.1 Determination of Quantization Level in DP Formulation
As described in Section 3.4, it is required to determine the quantization level p for DP formulation to obtain the
suboptimal solution of OCS approach. Considering various values of quantized level p, Figs. 5a and 5b show the
comparison for aggregate throughput of CRUs and average frame delay of PU, respectively, with respect to different numbers of CRUs. The number of channels is equal to M ¼ 4 where the PU’s arrival rate for each channel is i¼
0:1; 0:1; 0:3; 0:3 for i ¼ 1; 2; 3; 4. Two cases of arrival rates for CRUs are considered as CR¼ 0:4 and 0.8. The analytical
results are obtained for aggregated throughput ~ ðPÞ and aggregate frame delay from Section 4.1 under generalized CR networks with sensing threshold pd¼ 0:93. The
aggre-gate frame delay is the summation of average frame delay in each channel, i.e., ~D¼PMi¼1D~iðpiÞ, which can be utilized as
a measurement for the QoS requirement in primary system. Noted that the aggregate throughput ~ ðPÞ is normalized with slot duration Tsfor performance comparison.
It can be observed from both Figs. 5a and 5b that consistent suboptimal solution for OCS approach can be achieved with the selection of smaller value of quantization level p. However, the granularity of quantization level p
will be constrained by considering the hardware limitations and the computational complexity in DP approach. There-fore, according to Figs. 5a and 5b, the quantization level p
for searching the OCS is set as 0.001, which is accurate enough to obtain the proposed OCS in the simulation settings with reasonable number of CRUs and channels. In the following sections, p¼ 0:001 will be adopted for
performance validation and comparison.
TABLE 1 Simulation Parameters
5.2 Performance Validation and Comparison under Paired CR Networks
5.2.1 Characterization of Channel-Hopping Probability for a Single Channel
In this section, the channel-hopping probability will be characterized for the single channel case under paired CR networks. Figs. 6a and 6b illustrate the throughput performance of CRPs and the average frame delay of PU under different values of hopping probability pi,
respec-tively. There are total of Np¼ 14 CRPs with sensing
thresholds pd¼ 0:93 and 0.95 under PU’s arrival rate
i ¼ 0:05, 0.2, and 0.4. Noted that the detection probability
pd is in general prescribed by primary network in order to
regulate the delay constraint for satisfying PU’s QoS requirements [22], [26]. However, Pdcan still be determined
by CRUs themselves based on the control of channel-hopping sequences. In other words, the QoS requirement in primary network can be achieved by adopting admission control for CRUs. As shown in Fig. 6a, the throughput performance will first increase with pi due to the
augmen-ted number of CRPs hopping to the channel which
effectively increase the channel utilization. However, the throughput of CRPs decreases with larger pi values owing
to insufficient channel availability. Comparing the two values of pd, the case with pd¼ 0:95 will result in enhanced
throughput under larger value of pi since there exists
additional CRPs to utilize the channels. On the other hand, with smaller value of pi, the detection probability pd¼ 0:93
will incur smaller pfa which can allow CRPs to quickly
discover the idle slots and consequently increase the channel utilization.
Fig. 6b shows that the average frame delay is an increasing function of pi which can become significantly
large with increased value of pi, i.e., the primary queue can
go unstable especially for large PU’s arrival probability i
and small sensing threshold pd. It can be explained that
larger pi corresponds to more CRPs hopping into the ith
channel based on HNp;n;iin (3). The transmitted frames from
those CRPs will produce more collisions with the PU’s frame which makes the increased time in retransmission and therein larger average frame delay in primary network. Moreover, with smaller detection probability pd, more
collisions from CRPs to PU will be observed. With larger
Fig. 6. Performance of CRPs for a single channel with pd¼ 0:93 (dashed line) and pd¼ 0:95 (solid line) under PU’s arrival rate i¼ 0:05, 0.2, and 0.4
denoted by, 4, and ut curves, respectively.
Fig. 5. Determination of quantization level pwith pd¼ 0:93 and number of channels M ¼ 4 (each channel with PU’s arrival rate i¼ 0:1; 0:1; 0:3; 0:3
value of i, it is intuitive that long waiting time in the queue
will further increase the average frame delay of PU. 5.2.2 Performance Validation and Comparison
Two conventional channel-hopping sequences are simu-lated for comparison purpose as follows: 1) uniform channel-hopping sequence (UCS) with channel-hopping probability pi¼ 1=M for i ¼ 1; 2; . . . ; M; and 2) proportional
channel-hopping sequence (PCS) with channel-hopping probability proportioning to the complement of i= , where
represents the service rate. The PCS scheme is designed according to the situation that smaller frame arrival probability is assumed to result in larger channel avail-ability, which can be written as
pi¼ 1i PM i¼1 1i ; i ¼ 1; 2; . . . ; M: ð29Þ Noted that the service rate is selected as ¼ 1 frame/slot which is the stationary idle probability under no collision between the CR and primary network. For validation purpose, it can be seen from both Figs. 7a and 7b that the simulation results can match with the analytical results for all the three approaches. Fig. 7a shows that the proposed OCS can provide higher aggregate throughput compared to the other channel-hopping sequences since it can exactly exploit the potential throughput in multiple channels. It is noticed that the aggregate throughput in OCS will saturate after exceeding a certain number of CRPs where the number of CRPs is large enough to utilize each channel with optimal throughput. With excessive CRPs in the network, the OCS approach will assign those additional CRPs into the virtual channel in order to reduce packet collision with PU.
On the other hand, as shown in Fig. 7b, the aggregate frame delay of primary network can be limited by adopting the proposed OCS approach; while that for the other two conventional schemes become significantly large. Even though the delay constraints is not taken into consideration, the OCS approach can still confine the aggregate frame delay to be less than 16 slots under different numbers of CRPs. In order to provide tighter QoS requirement for PUs, the cases with delay constraint Dc;i¼ 2 for i ¼ 1; 2; 3; 4 are
also shown in both Figs. 7a and 7b. With Dc;i¼ 2, the
aggregate frame delay of PUs can be effectively constrained along with lowered aggregated throughput of CRPs. More-over, considering different sensing thresholds pd with the
same Dc;i¼ 2, large pd will provide enhanced aggregate
throughput than small pd case if there exists larger amount
of CRPs to exploit the channel availability. On the other hand, under smaller number of CRPs, the OCS scheme with pd¼ 0:93 case results in higher aggregate throughput
compared to that with pd¼ 0:97. The reason is that the
case with pd¼ 0:93 will incur smaller pfawhich can provide
CRP to quickly discover the idle slots and consequently increases channel utilization.
Furthermore, as shown in Fig. 7a, the aggregate throughput of PCS algorithm is higher than that of UCS scheme under lower number of CRPs. The reason is that more CRPs are allocated by the PCS method into channels with lower arrival probabilities compared to the UCS scheme. On the other hand, with larger number of CRPs, the aggregate throughput will degrade quickly by adopting the PCS scheme owing to additional packet collisions between CRPs. Moreover, as in Fig. 7b, the UCS scheme will result in the largest aggregate frame delay compared to the other algorithms. The primary network will quickly go unstable due to excessive allocation of CRPs into the channels with larger arrival probabilities. As a result, the merits of adopting OCS approach under paired CR net-works can be observed.
5.3 Performance Validation and Comparison under Generalized CR Networks
5.3.1 Performance Validation of Proposed OCS Approach
Figs. 8a and 8b show performance validation between the simulation and analytical results by adopting proposed OCS scheme under generalized CR networks. Considering different arrival rates CRof CRUs, the sensing threshold is
selected as pd¼ 0:93 and the number of channels is M ¼ 4
with PU’s arrival rate at each channel as i¼ 0:1; 0:1; 0:3; 0:3
for i ¼ 1 to 4. As in Fig. 8a, the aggregate throughput increases with the number of CRUs and decreases at higher number of CRUs due to insufficient channel availability.
Fig. 7. Performance validation and comparison under pd¼ 0:93 and number of channels M ¼ 4 with PU’s arrival rate at each channel as
Lowered aggregate throughput is observed at high CR traffic, e.g., at CR¼ 1, due to the decreased rendezvous
probability pv;i. The CR transmitters do not have much
chance to meet with their corresponding CR receivers since those receivers may also conduct data transmission in other channels.
Moreover, as shown in Fig. 8b, the aggregate frame delay in primary network will increase with the augmenta-tion of CR traffic. It can be observed that the peak value of aggregate frame delay will be reached at a larger number of CRUs than that of the aggregate throughput. For instance, under CR¼ 0:8, the maximum delay occurs at the number
of CRUs ¼ 38; while the maximum throughput happens at the number of CRUs ¼ 15. The concept of proposed OCS scheme is to consider the tradeoff between the rendezvous probability and the channel availability. In other words, the major target is to compromise the rendezvous probability for resolving the logical partition problem, i.e., by increasing the number of CRUs in a channel, and the channel availability by decreasing the number of CRUs in a channel. Between the number of CRUs equal to 15 and 38, the OCS approach will continue to increase the number of CRUs in a channel in order to augment the rendezvous probability. It indicates that the effect of rendezvous probability will dominate the channel availability, which results in the increased PU’s aggregate frame delay. On the other hand, at higher number of CRUs, e.g., the number of CRUs > 38, the channel availability becomes more impor-tant than the rendezvous probability which makes the proposed OCS scheme decrease the number CRUs in a channel. The aggregate frame delay can consequently be decremented as shown in Fig. 8b.
Furthermore, with higher arrival rate CR¼ 1 from
CRUs, the PU’s aggregate frame delay will not be decreased after reaching the maximum value compared to the cases with lower CR. The reason is mainly due to the excessive
CR traffic in the channels. Even though the OCS scheme decreases the number of CRUs in a channel, it is still difficult to increase channel availability which makes PU’s aggregate frame delay remain at the same level. It can also be observed from both figures that the analytical results can match with the simulation results in most cases, where the
slight discrepancies are resulted from the approximation of binomial distribution adopted in (4), (5), and (28). The larger variation from the approximation occurs under the situations with higher number of CRUs and low rendezvous probability, e.g., as shown in Fig. 8b under CR¼ 1 with the
number of CRUs > 30.
5.3.2 Performance Comparison
Figs. 9 and 10 show the performance comparison between the proposed OCS approach and the conventional UCS and PCS schemes under the generalized CR networks, where three cases of CRUs’ arrival rates CR¼ 0:1, 0.4, and 0.7 are
illustrated. Compared to the conventional schemes, it is observed from both figures that the proposed OCS algorithm can provide higher aggregate throughput of CRUs with lowered PU’s aggregate frame delay. As shown in Fig. 9 under light CR traffic with CR¼ 0:1, the proposed
OCS scheme increases the rendezvous probability that effectively allocates the CR transmitters into more feasible channels in order to provide higher channel utilization. With larger CRUs’ arrival rate, i.e., CR¼ 0:4, higher
Fig. 9. Performance comparison: aggregate throughput versus number of CRUs with pd¼ 0:93 and number of channels M ¼ 4 with PU’s arrival
rate at each channel as i¼ 0:1; 0:1; 0:3; 0:3 for i ¼ 1; 2; 3; 4.
Fig. 8. Performance validation of OCS scheme under pd¼ 0:93 and number of channels M ¼ 4 with PU’s arrival rate at each channel as
aggregate throughput is obtained by adopting these three approaches since higher channel utilization can be achieved with feasible amount of CR traffic in the network, e.g., the aggregate throughput of OCS approach can reach around 0.79 slots under the number of CRUs equal to 40. Furthermore, as CRreaches 0.7, the proposed OCS scheme
can still outperform the other two methods even though the aggregate throughput is reduced in all three schemes owing to the decrement of rendezvous probability pv;i. On the other
hand, as illustrated in Fig. 10, the proposed OCS approach can provide lowered PU’s aggregate frame delay compared to the other two schemes. Especially under high CRUs’ arrival rate with CR¼ 0:7, the OCS scheme can limit the
PU’s maximum frame delay by reaching to a saturated value of 20 time slots.
5.3.3 Enhancement with WSC and WCSC Mechanisms Figs. 11 and 12 show the comparison between the proposed OCS, OCS-WSC, and OCS-WCSC approaches in general-ized CR network under different detection probabilities pd
and contention window sizes W , i.e., pd¼ 0:93 and W ¼ 64
for Fig. 11 and pd¼ 0:96 and W ¼ 16 for Fig. 12. As shown
in the left plots of both Figs. 11 and 12, the proposed OCS-WSC and OCS-WCSC mechanisms can always outperform the original OCS approach in aggregate throughput especially in heavy CR traffic owing to the increased rendezvous probability between CRUs. The benefit of OCS-WSC and OCS-WCSC schemes can also be revealed in the right plots of both figures that they will not incur additional PU’s aggregate frame delay with the enhancement of aggregate throughput.
With the counter-reset mechanism, it is intuitive that the OCS-WCSC scheme can provide more opportunities in the channel negotiation process compared to the OCS-WSC approach as illustrated in Fig. 11. However, with higher pd
and smaller contention window W as in Fig. 12, higher collision probability between CRUs will be induced by adopting the OCS-WCSC scheme since more CRUs will be allocated to the channels for increasing channel utilization.
Consequently, the aggregate throughput from OCS-WCSC scheme will be comparably smaller than that from the WSC mechanism. It can be observed that both the OCS-WSC and OCS-WCSC schemes will outperform the original OCS approach under generalized CR network. The feasible circumstance for adopting either the WSC or OCS-WCSC approach will depend on the system parameters, especially the detection probability pd and the contention
window size W . As a result, the proposed OCS-WSC and OCS-WCSC schemes can be implemented by constructing offline look-up table based on the key system parameters,
Fig. 11. Performance comparison between proposed algorithms: (left plot) aggregate throughput of CRUs versus number of CRUs, (right plot) aggregate frame delay of PUs versus number of CRUs. Parameters for simulations: pd¼ 0:93, W ¼ 64, and number of channels M ¼ 4 with
PU’s arrival rate i¼ 0:1; 0:1; 0:3; 0:3 for i ¼ 1; 2; 3; 4. The OCS,
OCS-WSC, and OCS-WCSC schemes are denoted by4, , and ut curves, respectively, with CR¼ 1 (dashed line) and CR¼ 0:6 (solid line).
Fig. 12. Performance comparison between proposed algorithms: (left plot) aggregate throughput of CRUs versus number of CRUs, (right plot) aggregate frame delay of PUs versus number of CRUs. Parameters for simulations: pd¼ 0:96, W ¼ 16, and number of channels M ¼ 4 with
PU’s arrival rate i¼ 0:1; 0:1; 0:3; 0:3 for i ¼ 1; 2; 3; 4. The OCS,
OCS-WSC, and OCS-WCSC schemes are denoted by4, , and ut curves, respectively, with CR¼ 1 (dashed line) and CR¼ 0:6 (solid line).
Fig. 10. Performance comparison: aggregate frame delay versus number of CRUs with pd¼ 0:93 and number of channels M ¼ 4 with
including the number of CRUs Nu, the CR traffic CR, the
probability of detection pd, and the contention window size
W. Afterwards, the table look-up process can be executed for realtime implementation. The benefits of proposed approaches can therefore be observed.
6
C
ONCLUSIONIn this paper, a multichannel primary network with the existence of CR users is considered under imperfect spectrum sensing and synchronization. Analytical models are developed for both the probability of channel avail-ability of CR users and the average frame delay of PUs under paired and generalized CR networks. Based on the analysis, an approach for obtaining the optimal channel-hopping sequence is designed based on the dynamic programming technique. The proposed OCS approach can both achieve maximum aggregate throughput of CR users and ensure feasible average frame delay of PUs under their QoS requirements. Moreover, the wake-up successive contention and the wake-up counter-reset successive con-tention algorithms are proposed in order to alleviate the logic partition problem occurs in generalized CR network. By exploring a blind spot in the imperfect sensing and amending the conventional contention mechanisms, the proposed schemes can enhance the original OCS approach with increased number of channel negotiations between CR users. Both the analytical and simulation results show that the proposed OCS, OCS-WSC, and OCS-WCSC approaches can effectively enhance the aggregate throughput of CR users with satisfactory aggregate frame delay of PUs.
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CKNOWLEDGMENTSThis work was in part funded by the Aiming for the Top University and Elite Research Center Development Plan, NSC 99-2628-E-009-005, NSC 98-2221-E-009-065, the Med-iaTek research center at National Chiao Tung University, and the Telecommunication Laboratories at Chunghwa Telecom Co. Ltd, Taiwan.
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EFERENCES[1] Fed. Comm. Commission, “Spectrum Policy Task Force Report, FCC 02-155,” Nov. 2002.
[2] S. Haykin, “Cognitive Radio: Brain-Empowered Wireless Com-munications,” IEEE J. Selected Areas in Comm., vol. 23, no. 2, pp. 201-220, Feb. 2005.
[3] C.R. Stevenson, G. Chouinard, Z. Lei, W. Hu, S.J. Shellhammer, and W. Caldwell, “IEEE 802.22: The First Cognitive Radio Wireless Regional Area Network Standard,” IEEE Comm. Maga-zine, vol. 47, no. 1, pp. 130-138, Jan. 2009.
[4] IEEE 802.22 Wireless RAN, Std., Functional Requirements for the 802.22 WRAN Standard, IEEE 802.22- 05/0007r46, IEEE, Oct. 2005. [5] I.F. Akyildiz, W.Y. Lee, M.C. Vuran, and S. Mohanty, “Next Generation/Dynamic Spectrum Access/Cognitive Radio Wireless Networks: A Survey,” Computer Networks, vol. 50, pp. 2127-2159, Sept. 2006.
[6] S. Srinivasa and S.A. Jafar, “How Much Spectrum Sharing Is Optimal in Cognitive Radio Networks?” IEEE Trans. Wireless Comm., vol. 7, no. 10, pp. 4010-4018, Oct. 2008.
[7] A.C.-C. Hsu, D.S.L. Wei, and C.-C.J. Kuo, “A Cognitive MAC Protocol Using Statistical Channel Allocation for Wireless Ad-Hoc Networks,” Proc. IEEE Wireless Comm. and Networking Conf. (NWCNC), pp. 105-110, Mar. 2007.
[8] A.L. Yau, P. Komisarczuk, and P.D. Teal, “On Multi-Channel MAC Protocols in Cognitive Radio Networks,” Proc. Australasian Telecomm. Networks and Applications Conf. (ATNAC), pp. 300-305, Dec. 2008.
[9] Q. Zhao, L. Tong, A. Swami, and Y. Chen, “Decentralized Cognitive MAC for Opportunistic Spectrum Access in Ad Hoc Networks: A POMDP Framework,” IEEE J. Selected Areas in Comm., vol. 25, no. 3, pp. 589-600, Apr. 2007.
[10] J. Jia, Q. Zhang, and X. Shen, “HC-MAC: A Hardware-Constrained Cognitive MAC for Efficient Spectrum Manage-ment,” IEEE J. Selected Areas in Comm., vol. 26, no. 1, pp. 106-117, Jan. 2008.
[11] H. Su and X. Zhang, “Channel-Hopping Based Single Transceiver MAC for Cognitive Radio Networks,” Proc. 42nd Ann. Conf. Information Sciences and Systems (CISS), pp. 197-202, Mar. 2008. [12] L. Le and E. Hossain, “OSA: A MAC Protocol for Opportunistic
Spectrum Access in Cognitive Radio Networks,” Proc. IEEE Wireless Comm. and Networking Conf. (WCNC), pp. 1426-1430, Apr. 2008.
[13] J. Cai and A.S. Alfa, “Optimal Channel Sensing in Wireless Communication Networks with Cognitive Radio,” Proc. IEEE Int’l Conf. Comm. (ICC), pp. 1-5, June 2009.
[14] C. Xin and X. Cao, “A Cognitive Radio Network Architecture without Control Channel,” Proc. IEEE GlobeCom, pp. 1-6, Dec. 2009.
[15] P. Bahl, R. Chandra, and J. Dunagan, “SSCH: Slotted Seeded Channel Hopping for Capacity Improvement in IEEE 802.11 Ad-Hoc Wireless Networks,” Proc. ACM MobiCom, pp. 216-230, 2004.
[16] C.-M. Lee, J.-S. Lin, Y.-P. Hsu, and K.-T. Feng, “Design and Analysis of Optimal Channel-Hopping Sequence for Cognitive Radio Networks,” Proc. IEEE Wireless Comm. and Networking Conf. (WCNC), pp. 1-6, Apr. 2010.
[17] J. Gambini, O. Simeone, Y. Bar-Ness, U. Spagnolini, and T. Yu, “Packet-Wise Vertical Handover for Unlicensed Multi-Standard Spectrum Access with Cognitive Radios,” IEEE Trans. Wireless Comm., vol. 7, no. 12, pp. 5172-5176, Dec. 2008.
[18] I. Suliman and J. Lehtomaki, “Optimizing Detection Parameters for Time-Slotted Cognitive Radios,” Proc. IEEE Vehicular Technol-ogy Conf. (VTC), pp. 1-4, Apr. 2009.
[19] “3GPP TR36.814 v9.0.0 Release 9,” technical report, Mar. 2010. [20] Y.-C. Liang, Y. Zeng, E.C.Y. Peh, and A.T. Hoang,
“Sensing-Throughput Tradeoff for Cognitive Radio Networks,” IEEE Trans. Wireless Comm., vol. 7, no. 4, pp. 1326-1337, Apr. 2008.
[21] A. Ghasemi and E.S. Sousa, “Spectrum Sensing in Cognitive Radio Networks: Requirements, Challenges and Design Trade-Offs,” IEEE Comm. Mag., vol. 46, no. 4, pp. 32-39, Apr. 2008.
[22] S. Zheng, Y.-C. Liang, P.Y. Kam, and A.T. Hoang, “Cross-Layered Design of Spectrum Sensing and MAC for Opportunistic Spectrum Access,” Proc. IEEE Wireless Comm. and Networking Conf. (WCNC), pp. 1-6, Apr. 2009.
[23] A. Gravey and G. Hebuterne, “Simultaneity in Discrete-Time Single Server Queues with Bernoulli Inputs,” Performance Evalua-tion, vol. 14, pp. 123-131, Jan. 1992.
[24] T. Meisling, “Discrete-Time Queuing Theory,” Operations Research, vol. 6, pp. 96-105, Jan. 1958.
[25] D. Gross and C.M. Harris, Fundamentals of Queuing Theory, fourth ed. Wiley, 2008.
[26] A.T. Hoang, D.T.C. Wong, and Y.-C. Liang, “Design and Analysis for an 802.11-Based Cognitive Radio Network,” Proc. IEEE Wireless Comm. and Networking Conf. (WCNC), pp. 1-6, Apr. 2009. [27] IEEE Std 802.11b-1999 (R2003): Part 11: Wireless LAN Medium
Access Control (MAC) and Physical Layer (PHY) specifications: Higher-Speed Physical Layer Extension in the 2.4 GHz Band, IEEE, 2003.
[28] A.V. Adamis, K.N. Maliatsos, and P. Constantinou, “Methods for Reducing Interference Caused to Licensed Systems by Overlay-CSMA/CA Cognitive Radios,” Proc. Third Int’l Conf. Cognitive Radio Oriented Wireless Networks and Comm. (CROWNCOM), pp. 1-6, May 2008.
[29] D. Bertsekas, Dynamic Programming and Optimal Control, third ed. Athena Scientific, 2005.
[30] L. Gao and S. Cui, “Power and Rate Control for Delay-Constrained Cognitive Radios via Dynamic Programming,” IEEE Trans. Vehicular Technology, vol. 58, no. 9, pp. 4819-4827, Nov. 2009. [31] T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Steinyd,
