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Spectrum handoff in cognitive radio networks opportunistic and negotiated situations


This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings

Spectrum Handoff in C

ognitive Radio Networks: Opportunistic and Negotiated Situations
Yan Zhang
Simula Research Laboratory, Norway Email: yanzhang@ieee.org

Abstract—Spectrum handoff is an indispensable component in cognitive radio networks to provide resilient service for the secondary users. In this paper, we explore the spectrum handoff procedure and then propose four metrics to characterize both short-term and long-term spectrum handoff performance: link maintenance probability, the number of spectrum handoff, switching delay, and non-completion probability. In particular, the probability mass function (pmf) and the average number of spectrum handoff are developed. The tele-traf?c parameters are relaxed to follow a general distribution function, which will enable a wide applicability and theoretical signi?cance of the derived formulae. Both opportunistic and negotiated spectrum access strategies are investigated. Results show that these two mechanisms will generate signi?cantly different performance. Numerical examples are presented to demonstrate the performance trade-off and the interaction between the primary users and the secondary users. The impact of key parameters on spectrum handoff is also discussed. The techniques as well as the results are important for evaluating the primary and second users co-existence, and hence helpful for design and optimization of cognitive radio networks. Index Terms—Cognitive Radio, Spectrum Handoff, Switching Delay, Primary System, Primary User, Secondary User

I. I NTRODUCTION Spectrum is a scarce and precious resource in wireless communications. The scarcity challenge is largely caused by the current ?xed frequency assignment policy. This policy partitions the whole spectrum into a large number of different ranges. Each piece is exclusively speci?ed for a speci?c system. Recent measurement shows an undesirable situation that some wireless systems may only use the allocated spectrum to a very limited extent while others are heavily used [1] [2]. Motivated by this observation, Cognitive Radio (CR) has been proposed to effectively utilize the spectrum. CR refers to the potentiality that wireless systems are context-aware and capable of recon?guration based on the surrounding environments and their own properties [3] [4] [5] [6]. In the same frequency range, there are two co-existing systems: primary system and secondary system. Primary system refers to the licensed system with legacy spectrum. This system has the exclusive privilege to access the assigned spectrum. Secondary system refers to the unlicensed cognitive system and can only opportunistically access the spectrum holes which are not used by the primary system. We call the subscriber in the primary system as Primary User (PU) and the subscriber in the secondary system as Secondary User (SU). The SUs are able to dynamically access the licensed frequency bands without

any modi?cation to the primary system. Although the motivation of CR technology is simple, the design and implementation have a large number of challenges. Spectrum handoff is a major dif?culty and also an inherent capability to support reliable service. There are two phases in spectrum handoff: PU detection and link maintenance. On detecting a PU appearance, the SU has to vacate the frequency for the PU. After the channel release, the SU will perform the link maintenance to re-construct the communications in order to avoid service termination. During this procedure, the SU may search the spectral band and transfer its communications to another available spectrum, if available. This procedure is referred as spectrum handoff. Recently, there are few studies on the spectrum handoff issue. In the study [10], Guipponi et al. proposed a fuzzy-based spectrum handoff algorithm. In the work [7], Wang et al. studied the impact of spectrum handoff on the link maintenance when an SU vacates a channel due to PU appearance. In the study [9], Jo et al. reported the spectrum matching algorithms for SUs in order to reduce the spectrum handoff probability. It is observed that, in these studies, spectrum handoff performance has not been comprehensively proposed, developed, and discussed. In this paper, our contributions include three folds. These aspects also represent the major difference from the existed studies. Firstly, we proposed four performance metrics in order to completely characterize spectrum handoff: the number of spectrum handoff, link maintenance probability, switching delay, and non-completion probability. Secondly, the key teletraf?c parameters in both the primary system and the secondary system are generalized. This will enable a wide applicability and theoretical signi?cance of the derived formulae. The interaction between the primary user and the secondary user is presented and discussed. Thirdly, both opportunistic and negotiated situations (see Section II.A) on the PU and SU co-existence are considered. This investigation is motivated by the possibility that the spectrum handoff may be affected by different spectrum access strategies. Numerical examples are presented to exploit the interaction between the parameters and performance; and also the trade-off among the performance metrics. The remainder of the paper is organized as follows. Section II presents the system model. Section III and Section IV report the spectrum handoff performance in the opportunistic and negotiated situations, respectively. Section IV presents the illustrative numerical results. Section V concludes the work.

978-1-4244-3435-0/09/$25.00 ?2009 IEEE

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings

II. S YSTEM M ODEL A. Opportunistic and Negotiated Situations We consider two scenarios: opportunistic and negotiated situations. In the opportunistic scenario, there is no centralized spectrum agency managing the spectral band. For an SU arrival, it can use a free channel if not all channels are busy. After the admission in the system, the SU sense its surroundings. Upon detecting a PU, the SU may vacate its channel to the PU and then perform the link maintenance. If the system has a free channel, the SU will switch to the new channel. Otherwise, the SU will wait for a period with maximum value Dth . In case there are no available channels during Dth , the link maintenance is failed and consequently the spectrum handoff. In the negotiated situation, there is a spectrum server centrally managing the whole spectrum. For an SU arrival, it can use a channel if the spectrum server has free channels. Upon a PU arrival, it will be always assigned a different channel from the one used by the SU. In case the spectrum server ?nds that all channels are occupied upon a PU arrival, the server will claim the SU to release its channel and re-assign the channel to the PU. The SU then performs the link maintenance. Similarly, the SU will wait for a period with maximum value Dth . If there is an available channel within Dth , the SU will switch to this channel and continue its service. Otherwise, the link maintenance is failed and hence the spectrum handoff. B. Primary System Let C denote the number of channels in the primary system. Let λ denote the average arrival rate of PU arrival Poisson process. Then, the PU inter-arrival time tpu follows an exponential distribution with the probability density function (pdf) ftpu = λe?λt . Let tcp denote the PU call holding time with the average 1/μcp , pdf ftcp (t), cumulative distribution function (CDF) Ftcp (t), and Laplace transform of pdf ft? (s). The cp residual PU call holding time tr terms the period from an incp termediate instant to the moment of the PU service completion. Referring to the Residual Life Theorem [11], we obtain the residual PU call holding time pdf ftr (t) = μcp [1 ? Ftcp (t)]. cp Let ρ denote the PU traf?c intensity, i.e. ρ = λ/μcp . We de?ne the system state as the number of occupied channels by PUs. Let i (0 ≤ i ≤ C) denote the system state. Let πi denote the steady state probability distribution. Referring to ErlangB formula, we have πi = ρi /i!
C i=0

C. Secondary User In either opportunistic or negotiated strategy, an SU connection can be accepted if there are unoccupied channels in the system. During the SU service, a PU may appear and reclaim this channel. In this case, the SU needs to perform spectrum handoff. Since the SU service might last for a time duration, the SU may experience a number of spectrum handoff. In each spectrum handoff, the link maintenance may be either successful or failed. In addition, during each spectrum handoff, there is a switching delay in transferring to a new channel. An unsuccessful link maintenance will lead to the SU connection termination. Hence, the spectrum handoff has both short-term and long-term performance. We propose the link maintenance probability and switching delay to demonstrate the shortterm behavior. The number of spectrum handoff and SU non-completion probability are proposed to exhibit long-term behavior. III. S PECTRUM H ANDOFF P ERFORMANCE : O PPORTUNISTIC S ITUATION A. Link Maintenance Probability Upon a PU appearance, there are three consequences on SU’s behavior: (1) the SU need not vacate its channel or perform spectrum handoff; (2) the SU vacates the channel and link maintenance is successful; and (3) the SU vacates the channel and link maintenance is failed. Let PV denote the probability that an SU vacates its channel. This probability is equal to the probability that a particular channel is reclaimed by a PU. Suppose that the system state is i upon a PU arrival. Under this condition, the probability that a particular channel is reclaimed by the PU is given by 1/(C ? i). Then, we have PV =
C?1 1 i=0 C?i πi

1 ? Pb

(3)

Here, the item (1 ? Pb ) shows the pre-requisite that there are free channels from the PU perspective owing to the SU in the system. Let PN V denote the probability that an SU need not vacate its channel. PN V =
C?1 i=0

1?

1 C?i

πi

1 ? Pb

(4)

ρi /i!

;0 ≤ i ≤ C

(1)

A PU is blocked when all channels are occupied by PUs. Hence, the PU call blocking probability, Pb , is given by P b = πC = ρC /C!
C i=0

Let qs denote the link maintenance probability. Link maintenance probability refers to the probability that link is successfully maintained when the SU vacates the channel. A link can be successfully maintained if there exists a free channel in the system after the SU vacates its original channel. If there is no available channel, the link can be still successfully maintained if there is a newly released channel within Dth . In case there is no available channel within Dth , the link maintenance is failed. The SU actual waiting time T is equal to the minimum of all PU call holding times. Upon the moment of SU channel vacation, there are C ? 1 ongoing PUs in service. Hence, T = min (tr , tr , · · · , tr cp,1 cp,2 cp,C?1 , tcp,C ) (5)

ρi /i!

(2)

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings

where tcp,j denote the call holding time of the PU using the j th (j = 1, 2, · · · , C) channel. The link maintenance probability is given by qs = PV [(1 ? Pb ) + Pb P r(T < Dth )] = PV [(1 ? Pb ) + Pb P r(min (tr , tr , · · · , tr cp,1 cp,2 cp,C?1 , tcp,C ) < Dth )] = PV {(1 ? Pb ) + Pb [1 ? = where α= P r(tr cp > Dth ) = 1 ? λ
Dth 0 C?1 1 i=0 C?i πi

Considering these two conditions leading to zero spectrum handoff, we have


P r(H = 0) = P r(tcs < tpu ) +
j=1

j P r(τj < tcs < τj+1 )PN V

(11) We ?rst compute the ?rst item in the right-side of (11). P r(tcs < tpu ) =
∞ 0 ∞ x

(P r(tr cp

> Dth ))

C?1

P r(tcp > Dth )]} (6)

ftcs (x)

ftpu (y)dydx

= ft? (λ) cs (12)

(1 ? Pb ) + Pb (1 ? αC?1 β) 1 ? Pb

Before computing the second item, we develop an identity which will be used frequently in the following. P r(τj < tcs < τj+1 )


[1 ? Ftcp (x)]dx

(7)

= = = =

0

ftcs (t)P r(τj < t < τj+1 )dt ftcs (t) ftcs (t)
t



β = P r(tcp > Dth ) = 1 ?

Dth 0

ftcp (x)dx

(8)

0



Let qf denote the probability that the SU vacates its channel and the spectrum handoff is failed. qf = PV (Pb P r(T > Dth )) =
C?1 1 i=0 C?i πi

(?λ)j ?(j) ftcs (λ) j!

0

λ t e j!

0 j j ?λt

fτj (x) dt

∞ t?x

ftpu (y)dydxdt

Pb αC?1 β

1 ? Pb

(9)

where ftcs (λ) denotes the derivative of jth order. We continue the second item in the right-side of (11).
∞ j P r(τj < tcs < τj+1 )PN V j=1

?(j)

B. The Number of Spectrum Handoff Let H denote the number of spectrum handoff for an SU from its beginning of service to the end of the service. The SU connection can be either successfully completed or forcedly terminated due to failed link maintenance. In this section, we will develop the probability mass function of the discrete random variable H. Let tcs denote the SU call holding time with the average 1/μcs , pdf ftcs (t), CDF Ftcs (t), and Laplace Transform of pdf ft? (s). Let F tcs (t) denote the cs complementary cumulative distribution function (CCDF), i.e. F tcs (t) = 1 ? Ftcs (t). Let tpu,j denote the PU inter-arrival time between (j ? 1)th and j th PU with the generic form tpu . Here, the ?rst PU refers to the immediate next PU after SU k admission in the system. Denote τk = j=1 tpu,j . For Poisson PU arrival process, τk follows Erlang distribution with pdf fτk (t) = λ(λt)k?1 ?λt e (k ? 1)! (10)

(λt)j e?λt j dtPN V j! j=1 0 ? ? ∞ ∞ (λtPN V )j ? = ftcs (t)e?λt ? dt j! 0 j=1 = ftcs (t) = = ftcs (t)e?λt eλtPN V ? 1 0 ft? (λ(1 ? PN V )) ? ft? (λ) cs cs






dt (13)

Substituting (12) (13) into (11), we obtain P r(H = 0) = ft? (λ(1 ? PN V )) cs (14)

1) Zero Spectrum Handoff: For an accepted SU, there are two situations leading to zero spectrum handoff. If the SU can complete its service before a PU appears, the SU will not experience any spectrum handoff. This shows that the SU call holding time is smaller than the PU inter-arrival time. On the other hand, from the starting moment of SU service to the SU service completion, there are several PU arrivals. However, these PUs use different channels from the one used by the SU. In this case, the SU is not necessary to vacate the channel or perform spectrum handoff.

2) k (k ≥ 1) Spectrum Handoff: During the SU call holding time tcs , there are k spectrum handoff. We consider two conditions, i.e. the successfully completed SU connection and terminated SU connection due to failed spectrum handoff. Let SUCCk and TERMk denote the successful and terminated events, respectively. Then, the probability for k spectrum handoff is expressed by P r(H = k) = P r(SUCCk ) + P r(TERMk ) (15)

The successfully situation includes the following possibilities. During the SU service, there are k + j (k ≥ 1, j ≥ 0) PU arrivals. Among these PU arrivals, k PU requests the same channel used by the SU and the other j PU arrivals

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requests different channels. Hence, the SU has to perform k number of spectrum handoff and all these spectrum handoff are successful. Considering all possibilities on the variable j, we obtain the probability for the event SUCCk . P r(SUCCk )


=
j=0 ∞

P r(τk+j < tcs < τk+j+1 )


k+j j k PN V q s j

(?λqs )k ?(k) ftcs (λ(1 ? PN V )) k! k?1 λqf ?(k?1) (?λqs ) F tcs (λ(1 ? PN V )) (18) + (k ? 1)! C. Average Spectrum Handoff In practice, we may have interest in the statistical moments on the number of spectrum handoff H, especially the expectation. Following the de?nition of expectation, we have P r(H = k) =


(k + j)! j k (λt)k+j e?λt dt PN V qs = ftcs (t) (k + j)! j!k! 0 j=0 ? ? ∞ ∞ (λt)j j ? (λt)k e?λt ? k P dtqs = ftcs (t) k! j! N V 0 j=0 =
∞ 0

E(H) =
k=0 ∞

kP r(H = k)


=
k=0

kP r(SUCCk ) +
k=0

kP r(TERMk )

(19)

tk ftcs (t)e?λ(1?PN V )t dt
k

λk k q k! s (16)

where E(·) represents the expectation of a non-negative random variable.


(?λqs ) ?(k) ftcs (λ(1 ? PN V )) = k!

kP r(SUCCk ) =
k=1

∞ 0

ftcs (t)e?λ(1?PN V )t
∞ 0

∞ k=1

(λqs t)k dt (k ? 1)!

The terminated situation includes the following possibilities. During the SU service, there are k + j (k ≥ 1, j ≥ 0) PU arrivals. Among these PU arrivals, k PU requests the channel used by the SU and the rest j PU arrivals requests a different channel. Hence, the SU has to perform k number of spectrum handoff operations. The 1st , 2nd · · · , (k ? 1)st spectrum handoff are successful and the k th spectrum handoff is failed. Considering all possibilities on the variable j, we obtain the probability P r(TERMk )


= λqs

tftcs (t)e?λqf t dt (20)

= ?λqs ftcs (λqf )


?(1)

kP r(TERMk )
k=1

=λ =λ

∞ 0 ∞ 0

F tcs (t)e?λ(1?PN V )t F tcs (t)e
? ?λ(1?PN V )t ?(1)

∞ k=1

k(λqs t)k?1 dtqf (k ? 1)!

(1 + λqs t)eλqs t dtqf

=
j=0 ∞

P r(tcs
∞ 0 ∞

k+j?1 j k?1 > τk+j ) P N V qs qf j k+j?1 j k?1 P N V qs qf j

= λqf F tcs (λqf ) ? λqs F tcs (λqf ) =
? (qs + qf )(1 ? ftcs (λqf )) ?(1) + λqs ftcs (λqf ) qf

(21)

=
j=0 ∞

fτk+j (t)F tcs (t)dt
k+j?1 ?λt

λ(λt) e (k + j ? 1)! j k?1 P q F tcs(t)dt qf (k + j ? 1)! j!(k ? 1)! N V s j=0 0 ? ? ∞ ∞ λk tk?1 ?λt (λtPN V )j ? k?1 e F tcs (t) ? dtqs qf = (k ? 1)! j! 0 j=0 =
∞ λk k?1 = tk?1 F tcs (t)e?λ(1?PN V )t dtqs qf (k ? 1)! 0 (?λqs )k?1 λqf ?(k?1) = F tcs (λ(1 ? PN V )) (k ? 1)!

Substituting (20) (21) into (19), we can obtain the theorem for the average number of spectrum handoff. Theorem 2: In cognitive radio networks, the average number of SU spectrum handoff is given by E(H) =
? (qs + qf )(1 ? ftcs (λqf )) qf

(17)

Substituting (16) (17) into (15), we can obtain the probability for k spectrum handoff. As a consequence, we obtain the following theorem for the number of spectrum handoff. Theorem 1: In cognitive radio networks, the probability mass function of the number of spectrum handoff H is given by P r(H = 0) = ft? (λ(1 ? PN V )) cs

D. Switching Delay For real-time multimedia services, such as video and audio, the latency is very signi?cant for its quality evaluation. For a successfully completed SU service, it may experience a number of spectrum handoff. During each spectrum handoff, if there is an available channel for the SU, the SU can transfer to the new channel instantly without delay. Otherwise, the SU has to wait for a period before it can capture a free channel. We de?ne this waiting time as switching delay, d. Then, the delay d is equal to T if T is shorter than the threshold Dth , the SU vacates its channel, and also all the channels are busy upon operating the link maintenance. d = T; if T < Dth (22)

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings

provided that SU vacates and all channels are occupied. The average value of d is hence given by E(d) = Pb PV
Dth 0

tfT (t)dt

Dth 0

fT (t)dt

(23)

where α and β are given by (7) and (8), respectively. Substituting the results above into Theorem 1, Theorem 2, (24) and (25), we can obtain the number of spectrum handoff, average spectrum handoff, switching delay, and non-completion probability in negotiated situation. V. N UMERICAL R ESULTS In this section, our major objectives are to demonstrate the characteristics of the performance metrics and their different behaviors in the opportunistic and negotiated situations. The interaction between the performance and key parameters will be also explored. In addition, we will report the trade-off among the spectrum access strategies, the number of spectrum handoff, and the non-completion probability. If not speci?ed, the following parameters are chosen: C = 12, 1/μcp = 180.0sec and Dth = 18.0sec. Without speci?cation, the PU and SU call holding times follow 2-stage Erlang distribution.
0.9 0.8 opportunistic Link maintenance probability qs 0.7 0.6 Opportunistic (D =18.0)
th

To further simplify, we need to derive the pdf of T . However, it is known that there is no closed-form expression for the pdf of the random variable T for the generally distributed PU call holding time. Here, we employ an alternative approach by using phase-type (PH) distribution for the PU call holding time [12]. We denote the PH representation of the PU call holding time as PH(λ, R) with pdf ftcp (t) = λeRt (?R1R ) where λ1R + ηr+1 = 1 and R1R + R0 = 0. The residual PU call holding time also follows the PH distribution with the representation PH(γ, R) and γ = (ηR?1 1R )?1 ηR?1 . The random variable T = min (tr , tr , · · · , tcp,C ) follows the cp,1 cp,2 PH distribution with the representation (θ, U ). θ = γ ? · · · ? γ ?λ;
C?1

U = R ⊕ ··· ⊕ R
C

where ? and ⊕ represents the kronecker product and the kronecker sum, respectively. Substituting the PH representation of T into (23), we obtain the switching delay θ(Dth I + U )(I ? e )1U (24) U Dth )1 θ(I ? e U E. SU Non-Completion Probability SU non-completion probability refers to the probability that the SU can not complete its service. This shows the impact of spectrum handoff on SU long-term consequence. Let Pnc denote the SU non-completion probability. An SU is completed if all the spectrum handoff are successful or there are no spectrum handoff. E(d) = Pb PV
∞ ?1 U Dth

0.5 0.4 0.3 0.2 0.1 0 0 0.05 0.1 0.15 0.2 λ negotiated

Negotiated (D =18.0)
th

Opportunistic (D =36.0)
th

Negotiated (Dth=36.0)

0.25

0.3

0.35

0.4

Fig. 1.

Link maintenance probability in terms of PU arrival rate

1 ? Pnc =
k=0

P r(τk < tcs < τk+1 )(PN V + qs )k

= ft? (λqf ) cs Hence, the SU non-completion probability Pnc is given by Pnc = 1 ? ft? (λqf ) cs (25) IV. S PECTRUM H ANDOFF P ERFORMANCE : N EGOTIATED S ITUATION In the negotiated situation, there is a spectrum server centrally managing the available whole spectrum. Owing to different spectrum access strategy, the link maintenance probability should be different from that in the opportunistic situation. Upon a PU arrival, the SU has to vacate its channel only when the system stage is C ? 1. After the SU evacuates its channel, it can tolerate maximum duration Dth before its termination. Hence, we developed the following probabilities PV PN V qs qf = πC?1 = 1 ? πC?1 = PV P r(T < Dth ) = πC?1 (1 ? αC?1 β) = PV P r(T > Dth ) = πC?1 αC?1 β

Fig. 1 shows the link maintenance probability in terms of PU arrival rate in the opportunistic and negotiated situations. It is clear that, in either situation, longer threshold Dth leads to higher link maintenance probability, which is intuitively understandable. This will eventually result in higher probability to perform successful spectrum handoff. The comparison indicates that the opportunistic scheme is always more effective than the negotiated scheme. This can be explained as follows. In the negotiated spectrum access, the SU has to vacate its channel and performs spectrum handoff only when all channels are busy. For the opportunistic spectrum access, the SU may perform spectrum handoff when the system still has free channels. Hence, the chance in capturing a free channel in the negotiated situation should be always lower the one in the opportunistic situation. A fundamental requirement of the PU and SU co-existence is that the secondary system operates transparently for the primary system. Hence, it is necessary to investigate the effect of SU dynamics on the spectrum handoff performance. In the following, we ?x the PU arrival rate as λ = 0.04, if unspeci?ed. Fig. 2 shows the probability mass function of spectrum handoff in terms of λ/μcs in the opportunistic and negotiated situations. The big gap between the two

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings

1 0.9 0.8 0.7 Pr(H=0)

Opportunistic Negotiated

1 0.9 0.8 0.7 Pr(H=1) Pr(H=2) 0.6 0.5 0.4 0.3 0.2 0.1
Opportunistic Negotiated

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 20 λ/μcs 40 0 0 20 λ/μcs 40
Opportunistic Negotiated

0.6 0.5 0.4 0.3 0.2 0.1 0 0 20 λ/μcs 40

0 0

Fig. 2.

Probability mass function of spectrum handoff in terms of λ/μcs

mechanism, the opportunistic access is able to achieve higher SU service completion but more spectrum handoff operations. The observed trade-off behavior should be very instructive in designing effective spectrum access approaches. A major motivation in this paper is the tele-traf?c parameters generalization. Hence, it is necessary to demonstrate the effect of different tele-traf?c parameter distributions. Fig. 4 shows the impact of different PU and SU call holding times on the non-completion probability. For the sake of illustration, we choose exponential, hyper-exponential and 4-stage Erlang distribution functions with the same average value. There is clear gap in using different distributions for call holding time. This veri?es our motivation in generalizing tele-traf?c parameters to derive formulae for the proposed metrics. VI. C ONCLUSIONS Spectrum handoff is an inherent operation in cognitive radio networks to support resilient and continuous communications. In this paper, the spectrum handoff procedure is characterized. Its short-term performance and long-term behavior are thoroughly investigated with respect to four metrics: link maintenance probability, the number of spectrum handoff, switching delay, and non-completion probability. Results show that the opportunistic and negotiated spectrum access strategies can lead to signi?cantly different performance. The techniques as well as the results are very helpful for optimizing cognitive radio networks. R EFERENCES

10 9 8 7 6 E(H) P 5 4 3 2 1 0 0 20 λ/μ 40
nc

0.45 Opportunistic Negotiated 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0 20 λ/μ 40 Opportunistic Negotiated

cs

cs

Fig. 3.

Average spectrum handoff and non-completion probability

mechanisms shows the close relevance between the spectrum handoff and a speci?c spectrum access strategy. This observation alternatively validates our motivation that the spectrum handoff should be developed, discussed, and evaluated by differentiating spectrum access mechanisms. Fig. 3 shows the trade-off between the average spectrum handoff and non-completion probability in the opportunistic and negotiated situations. Comparing with the negotiated

0.1 Exponential t 0.09 0.08 0.07 0.06 Pnc 0.05 0.04 0.03 0.02 0.01 0 0 5 10 15 20 λ/μ 25 30 35 40
cp

and t

cs

HyperExponential t 4?stage Erlang t
cp

cp

and t
cs

cs

and t

cs

[1] M. A. McHenry and D. McCloskeyk, ”Spectrum occupancy measurements: Chicago, Illinois, November 16-18, 2005,” Shared Spectrum Company Report, 2005. [2] T. Erpek, M. Lofquist and K. Patton, ”Spectrum occupancy measurements: Loring Commerce Centre, Limestone, Maine, September 18-20, 2007,” Shared Spectrum Company Report, 2007. [3] J. Mitola III, ”Cognitive radio for ?exible mobile multimedia communications”, the 6th International Workshop On Mobile Multimedia Communications, November 1999 [4] I. F. Akyildiz, W.-Y. Lee, M. C. Vuran, and S. Mohantly, ”Next generation/ dynamic spectrum access/cognitivw radio wireless network: a survey,” Elsevier Computer Networks, vol.50, pp.2127-2159, Sept.2006. [5] S. Haykin, ”Cognitive radio: brain-empowered wireless communications”, IEEE J. Sel. Areas Commun., vol. 23, no.2, pp.201-220, Feb.2005. [6] Q. Zhao and B.M. Sadler ”A Survey of Dynamic Spectrum Access” IEEE Signal Processing Magazine, vol. 24, no. 3, pp. 79-89, May, 2007 [7] L.-C. Wang and A. Chen, ”On the performance of spectrum handoff for link maintenance in cognitive radio”, the 3rd International Symposium on Wireless Pervasive Computing (ISWPC 2008), May 2008. [8] D. Willkomm, J. Gross, A. Wolisz, ”Reliable link maintenance in cognitive radio systems”, IEEE New Frontiers in Dynamic Spectrum Access Networks (DySPAN) 2005, pp. 371-378, Nov. 2005. [9] O. Jo and D.-H. Cho, ”Ef?cient Spectrum Matching Based on Spectrum Characteristics in Cognitive Radio System”, IEEE Wireless Telecomunications Symposium (WTS 2008), April 2008. [10] L. Giupponi and A. Perez-Neira, ”Fuzzy-based Spectrum Handoff in Cognitive Radio Networks”, the 3rd International Conference on Cognitive Radio Oriented Wireless Networks and Communications (CROWNCOM 2008), May, 2008, Singapore. [11] L.Kleinrock, Queueing Systems. New York, NY: John Wiley and Sons, 1975. [12] M. F. Neuts, Structured Stochastic Matrices of M/G/1 Type and Their Applications, New York: Marcel Dekker, 1989.

Fig. 4. Non-completion probability with different call holding time distribution functions (opportunistic situation)


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