Optimal Transmission Strategy in a Practical Overlay Cognitive Radio System

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Optimal Transmission Strategy in aPractical Overlay Cognitive RadioSystem

babak abbasi bastami, Ebrahim SaberiniaDate Submitted: 30 April 2010Date Published: 14 May 2010

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1Optimal Transmission Strategy in a Practical

Overlay Cognitive Radio SystemBabak Abbasi Bastami, Ebrahim Saberinia

Department of Electrical and Computer Engineering

University of Nevada, Las Vegas

Abstract

In this paper, we consider a practical overlay cognitive radio system, where primary users have intervals

of silence in their access to the channel. The secondary user senses the channel status and switches either to a

transmission mode or to an idle period. We consider imperfect channel sensing by the secondary user. Furthermore,

to lower the complexity of the system and make it more practical, we assume no channel sensing by the secondary

user when it is in transmission mode. We analyze the system and derive analytical expressions for the interference

on the primary user and the overall data rate of the secondary user based on the system parameters. By the obtained

performance equations, we investigate the optimum values for the secondary user transmission and idle periods

which minimize the interference on the primary user and maximize the secondary user data rate. The results show

that in case of the secondary user imperfect channel sensing, providing the secondary user with a non-zero idle

duration, significantly improves the system performance. Finally, we validate our analysis by MATLAB simulation.

I. INTRODUCTION

The traditional scheme of allocating radio frequency bands for wireless services results in an inefficient

usage of the spectrum. To improve the utilization of the radio spectrum, a different allocation scheme has

been proposed using cognitive radio systems [1]. In such a system, the cognitive or secondary users sharethe licensed spectrum opportunistically with the primary users that hold the license. While these schemes

have the capability to increase the overall utilization of the spectrum, their implementation requires solving

several challenges. The main challenge is to control the amount of interference on the primary user (PU)caused by the secondary user (SU). Generally, two main approaches have been proposed to control theinterference on the PU. In the spectrum overlay scenario, the SU accesses the spectrum whenever it senses

that the PU is idle. The PU can transmit at any time and the cognitive user should have the ability to

monitor the channel status and decide whether to transmit or not. On the other hand, in the spectrumDownloaded from engine.lib.uwaterloo.ca on 20 July 2012 Page 1 of 19

2underlay technique, the secondary user can transmit at any time, but the power spectral density (PSD)of the transmitted signal should be low enough, preferably at noise level, for small interference on the

PU. However, even in the overlay scheme, channel sensing is used to increase the capacity of the SU.

Using channel information, a power control scheme can be designed for the SU such that it maximizes

its transmission capacity while keeping the interference on the PU below a threshold [2]. On the otherhand, a perfect overlay system may have zero interference. This requires the SU to have the capability to

detect the channel status without any error. Furthermore, it should have the ability to detect immediately

a PU transition from idle to active and suspend its own transmission. Designing such a system is very

complicated. In practical scenarios, we have to consider some possibility of sensing errors for the SU.

Furthermore, we can assume that the SU transmits its signal for a limited period of time without sensing

once it detects a free channel [3]. This means that there will be some interference on the PU. Performanceof overlay cognitive radio systems has been studied in different scenarios. In [4], the interference and thecapacity of the SU are analyzed assuming errorless sensing by the SU. The idle and the active durations

of the PU have been modeled as exponential random variables. Extension of [4] to a general distributionfor the idle and busy times of the PU is presented in [3]. In [5], an analysis has been done for the outagecapacity of the secondary user taking into account the possibility of sensing errors. However, the work in

[5] does not cover the amount of interference on the PU.In this paper, we study a practical overlay cognitive radio system that may have error in channel sensing.

The primary user switches between idle and busy states according to a Markov model. The secondary user

based on its channel sensing outcome, goes through an idle period or transmits a package with a constant

data length. The duration of the SU transmission time after an idle channel sensing and the duration of

the SU idle time after a busy channel sensing are the two important design parameters in this system. We

derive the analytical expressions of the interference on the primary user and the data rate of the secondary

user and validate our analysis by the simulation results. We apply our analysis to find the optimal values

of the SU transmission and idle periods that maximize the SU data rate while keeping the interference

on the PU below a threshold or minimize the interference on the PU in order to achieve a desired SU

data rate . In [6], we have studied the similar system where the secondary user didnt have any idle time.The system has been based on a keep sensing scheme in which the SU keeps sensing the channel until

it detects an unoccupied channel and starts data transmission. The addition of the SU idle period results

in saving the energy and avoiding the possible interference on the PU that might occur due to another

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3sensing. However, this idle duration decreases the data rate transmission of the cognitive user. Therefore,

it seems that if we consider the interference on the PU and the bit rate of the SU as our only criteria, the

SU idle period would be unnecessary. This would be true whenever the channel sensing is errorless. It

can be easily verified that providing an idle SU period for an errorless channel sensing does not have any

effect on the interference amount on the PU and just degrades the data rate of the SU. However we showthat, in case of imperfect channel sensing with specified values of probabilities of errors, introducing an

idle time decreases the interference on the PU and therefore, the problem of the optimal SU idle length

should be investigated. We obtain the optimal length of the SU idle period in order to achieve the best

system performance . The paper is organized as follows: in section 2, we introduce the system model.

The analysis of the interference on the primary user and the data rate of the secondary user are discussed

in sections 3 and 4. In section 5, we provide the simulation results and compare them with the derived

analytical results. The effects of the SU parameters on the system performance metrics are investigated

in section 6. The optimization problems of the SU idle and transmission periods are discussed in section

7. Section 8 concludes the paper.

II. SYSTEM MODEL

We consider a wireless communication system where primary users can be inactive for some portion

of time. The busy and idle periods of the primary channel are modeled with two random variables 1

and 2 respectively. The idle period, 1, is assumed to have exponential distribution. The length of the

transmitted packet of the PU is usually considered as a random variable with a long tail distribution.

Hence, exponential distribution would be a good choice for the busy period, 2, as well. The markov

model of the primary user is shown in Figure 1. The exponential distribution functions for 1 and 2 ,

f(i), i = 1, 2, can be written as:

f(i) = i exp(ii), (1)

Fig. 1. The markov model of the primary user.


4Fig. 2. The secondary user markov model.

where, 1 = 1TOFF and 2 =1

TONand TOFF and TON are respectively the average PU idle and active

durations. The secondary user senses the spectrum. If the SU senses a busy channel, it will go thorough

an idle period with duration of Tidle. During this time, the SU neither senses the spectrum nor transmits

any signal. On the other hand, if the SU detects an unoccupied channel, it transmits a packet for duration

of T . During the transmission time, the SU does not perform any sensing. To be more general in our

analysis, we do not assume perfect sensing. The probability of incorrect sensing by the SU when the PU

is idle is assumed to be Pfa (probability of false alarm) and the probability of the incorrect sensing whenthe PU is busy is assumed to be Pm (probability of miss detection). Lets denote the sensing durationof the SU with Ts . We assume that the value of Ts is small comparing to TOFF, TON, Tidle and T . In

fact, we have two types of intervals in the time line of the SU. The first type of the interval is a sensing

interval that follows with an idle duration.The length of this interval is Ts + Tidle. The second type of

the interval is a sensing which results in a SU packet transmission. The duration of this type of interval

is Ts + T .The SU markov model is shown in Figure 2. Based on the aforementioned system model, the

values of the transition probabilities in this figure are P11 = Pfa,P12 = 1 Pfa whenever the primary

channel is unused and are P11 = 1 Pm,P12 = Pm whenever the primary channel is busy. Evidently, for

the two other transition probabilities, we have P22 = 1 P11 and P21 = 1 P12.

The values of the transmission time, T , and the SU idle duration Tidle are the main system design

parameters. They affect two important system performance metrics. The first performance metric is the

amount of interference on the PU from the SU. Since the SU does not perform any sensing during its

transmission period, it is probable that the PU starts transmitting within the transmission time of the SU.

More interference can happen if an erroneous sensing takes place within the PU busy time. Apparently,

increasing the SU idle duration decreases the interference on the primary user. The second performance

metric which is affected by T and Tidle is the bit rate of the SU. The longer the SU transmits once it

detects an idle channel, the higher its achievable data rate is. Also, choosing smaller SU idle duration,


5leads to a higher data rate. The PU alternates between idle and busy periods, but the secondary user time

line has a different behavior. After each sensing interval of the SU, we may have a transmission interval or

an idle interval based on the output of the sensing information. On the other hand, after any transmission

or idle interval we definitely have a sensing interval. Our analysis of the system is based on the alignment

of the time line of the SU compared to the time line of the primary user. Figure 3 shows the typical time

lines of the primary and secondary users. In the following sections, we evaluate the system performance

equations based on this system model.

III. INTERFERENCE ANALYSIS OF THE PRIMARY USER

The interference on the PU is proportional to the overlapping time in which both PU and SU are

simultaneously transmitting. In other words we have

Ip = K1Tov, (2)

where, Ip is the expected value of the interference and Tov is the expected value of the overlapping time.

Constant K1denotes the interference per unit of the overlapping time and depends on the power spectral

density of the SU transmitted signal and the distance between the primary receiver and the secondary

transmitter.

We categorize the collision between the SU and PU busy times into two types. The first type occurs

whenever the PU in in the idle interval and then starts transmission while the SU is still in transmission

period. In this case, the SU senses the unoccupied channel correctly, but the transmission time extends

to the busy period of the PU. Figure 4(a) shows an example of this scenario of collision. On the otherhand, as shown in Figures 4(b) and 4(c), the second type collision, is a result of wrong sensing of theSU when the channel is being used by the PU. In the following subsections, we derive the corresponding

equations of these two scenarios.

A. Type I collision

This type of collision occurs whenever we have a correct sensing at the idle time of the PU and when

a duration less than T is remaining from that idle time. If the random idle period of the PU, 1, is

less than the the SU transmission time T , (1 < T ), any correct sensing fits in this scenario and we

dont have interference if all the sensing outcomes in 1 are wrong. Otherwise, if (1 > T ), we have no


6interference on the PU if we end up with a wrong sensing. In the Appendix, the probability of having this

type of interference has been calculated as P1 and P2 for two different cases of T > Tidle and T < Tidle

respectively.

Suppose with the interference occurrence probability calculated, we have an overlapping period of type

I. Hence, a last correct sensing occurs at a time tls where 0 1 tls T . Let ls = 1 tls. Using

the memoryless property of the exponential distribution, the probability density function of ls would be1

TOFFexp(

lsTOFF

)

1exp( TTOFF

). The perfect sensing at the time tls causes an overlapping time between the PU and the

SU transmission periods. This overlapping time (ov1) can be simply written as follows

ov1 =

T ls T ls 22 T ls > 2 . (3)

Since Ts is very small compared to T , we ignored its effect on (3). Using equations (16) and (17) derivedin the Appendix as P1 and P2 , the average value of the overlapping duration would be [7]

Tov1 = E(ov1)P1 Tidle T

= TONTOFF exp(T/TOFF) TON exp(T/TON) + (TON TOFF)

(TON TOFF)(1 exp(T/TOFF))(1

T0

P

[

1

Tidle

]+1

fa

1TOFF

exp(

1

TOFF)

1 exp( TTOFF

)d

1),

(4)

whenever T Tidle and would be

Tov1 = E(ov1)P2 0 T < Tidle

= TONTOFF exp(T/TOFF) TON exp(T/TON) + (TON TOFF)

(TON TOFF)(1 exp(T/TOFF))(

Tidle0

(1 Pfa)

[

2

T

]+1 1

TOFFexp(

2

TOFF)

1 exp( TidleTOFF

)d

2),

(5)

whenever T < Tidle. Therefore, in overall, the overlapping time duration of type I, can be obtained by

equations (4) and (5), depending on the value of the SU transmission length respect to its idle period. Forvery low probabilities of false alarm, P1 0 and P2 1, thus, this type of the overlapping time would

not be much dependent on Tidle. For perfect sensing scenario Tov1 = E(ov1) for all T [6], [7].


7B. Type II collision

The second type of collision may occur in the busy period of the PU. A portion of the SU idle or

transmission time would be extended to the busy period of the PU. Since the length of the SU idle time is

small compared to TON, for slightly low false alarm probabilities, we can ignore the corresponding portion

of the SU idle time. The average portion of the SU transmission time extended to the busy period of the

PU is the average type I overlapping time (Tov1) obtained in the previous subsection. Hence, the totalaverage duration within which type II of interference may occur is TONTov1. During the busy period of

the PU, a combination of the SU sensing and idle intervals (Ts+Tidle)occurs with the probability (1Pm)and a combination of a sensing interval with the transmission length (Ts +T ) occurs with the probabilityPm. In the total average time TON Tov1, the number of the occurrence of the SU transmission would be

approximatelyPm(TON Tov1)

(1 Pm)(Tidle + Ts) + Pm(T + Ts).

Hence, the average value of the second type of collision, which is the average portion of the time occupied

by the SU transmission period, would be

Tov2 = TPm(TON Tov1)

(1 Pm)(Tidle + Ts) + Pm(T + Ts). (6)

Using equations (4),(5) and (6), the total average of the overlapping time would be obtained as

Tov = Tov1 + Tov2. (7)

IV. DATA RATE ANALYSIS OF THE SECONDARY USER

The data rate of the SU is proportional to the amount of time that the SU transmits without overlapping

with the PU. The data rate, Cs, of the SU is

Cs = K2Tnov, (8)

where Tnov is the expected value of the non-overlapping time. Constant K2 denotes the data rate per

unit of the non-overlapping time and depends on factors such as modulation type and symbol duration

of the secondary user. The non-overlapping time occurs in the idle period of the PU. Like what we did

for evaluating the overlapping time, we have to compute the non-overlapping time for two scenarios. The

first scenario as shown in Figure 4(c), happens whenever the PU switches to its idle mode and the SUDownloaded from engine.lib.uwaterloo.ca on 20 July 2012 Page 7 of 19

8is still transmitting because of a bad sensing result when the PU was busy. For low probabilities of miss

detection, the probability of having an incorrect sensing in the last T seconds of the PU busy period,

which causes this type of non-overlapping time, would be very small. Actually, with the same argument

we have made in the Appendix to obtain (16) and (17), the probability of the occurrence of this eventwould be

P

1 = 1

T0

(1 Pm)

[

1

Tidle

]+1 1

TONexp(

1

TON)

1 exp( TTON

)d

1, (9)

whenever T Tidle and would be

P

2 =

Tidle0

P

[

2

T

]+1

m

1TON

exp(

2

TON)

1 exp( TidleTON

)d

2, (10)

whenever T < Tidle. Both of the equations (9) and (10) have very small values for a low probability ofmiss detection. Therefore, with an accurate approximation, the non-overlapping time value causing from

a miss detection of a busy channel, would be near zero. The values of (9) and (10) also show that forlow miss detection probabilities, it is high probable that the SU idle period occurs within the switching

instant of the PU from busy status to idle status. Suppose a correct sensing occurs somewhere in the last

Tidle seconds of the PU busy period. Let

3 denote the time in which this correct sensing happens before

the ending of the PU busy period. The distribution of 3 is1

TONexp(

3

TON)

1exp(TidleTON

)for 0 3 Tidle. A portion of

the SU idle period occupies some time within the idle duration of the PU. We denote the average value

of this portion of time by . It can be easily verified that

= E(Tidle

3)(1 P

i ), (11)

where, the value of P i (i is either 1 or 2)is determined by (9) or (10). Recall that we assumed that thevalue of Tidle is smaller than TOFF or TON. Hence, we didnt consider the case in which Tidle

3 may

occupy the whole TOFF. Manipulating E(Tidle

3), (11) can be derived as

= (Tidle TON + Tidleexp(Tidle/TON)

1 exp(Tidle/TON))(1 P

i ). (12)

For a low probability of miss detection Pi = 0 and we have

= Tidle TON + Tidleexp(Tidle/TON)

1 exp(Tidle/TON), (13)


9which is independent of T .

During the idle period of the PU, a combination of the SU sensing and idle intervals (Ts + Tidle)occurswith the probability (Pfa) and a combination of a sensing interval with the transmission length (Ts + T )occurs with the probability 1 Pfa. Therefore, the mean value of the non-overlapping time which is the

average of the time occupied by the SU transmission time during TOFF, can be approximately obtained

as

Tnov = T(1 Pfa)(TOFF )

Pfa(Tidle + Ts) + (1 Pfa)(T + Ts). (14)

From 14, it can be verified that the maximum value of the non-overlapping time is TOFF, which shows

that the longer the idle period of the SU is, the smaller the maximum achievable data rate of the SU is.

V. SIMULATION RESULTS

In order to verify our analysis, we have performed a simulation of the system using MATLAB. The

simulation is based on the system model described in Figures 1 and 2 for the primary and secondary

users. The two primary and secondary systems were run simultaneously for a long period of time and

the average overlapping and non-overlapping durations were computed. Figure 5 shows the users busy

overlapping time versus the SU transmission period for four different values of the SU idle intervals. The

mean values of the PU channel idle and busy periods are assumed to be TON = 1 and TOFF = 2 which

gives the ratio of 66% for the idle period. The false alarm and miss detection probabilities of the sensing

process are assumed to be respectively 0.1 and 0.2. The sensing duration of the SU is set to 0.01. The

four different values of the SU idle period are 0, 0.1,0.2 and 0.3. Using the same system parameters,

Figure 6 shows the non-overlapping time of the SU busy period versus the SU transmission duration.

In both figures, the dashed lines are the simulation results and the solid lines are the numerical results

based on the equations (7) and (14). The simulation results evidently show the accuracy of the derivedperformance equations.

VI. INFLUENCE OF THE SYSTEM PARAMETERS ON THE PERFORMANCE METRICS

In this section, we investigate the effect of the SU transmission and idle durations as our two main

intrusive system parameters on the performance metrics. The influence of the SU idle duration on the

system performance is our main point of interest. Figures 7 and 8 show the normalized overlapping and

non-overlapping times of the system versus the SU idle duration for different values of the channel sensing


10

error. The overlapping and non-overlapping times are normalized to their maximum values TON and TOFF.

In these figures the SU has a constant transmission time T = 0.2. The PU system parameters are set to

TON = 1 and TOFF = 2. The overall behaviors of Figures 7 and 8 do not change with the variations of

TON, TOFF or T . As shown in Figure 7, in the perfect sensing case (Pfa = Pm = 0), the users overlappingduration is constant for all values of the SU idle times (Tidle). On the other hand, in the same zero sensingerror case, the longer the SU idle length is, the smaller the amount of the non-overlapping time is (Figure8). Hence, the introduction of the SU idle period does not have any effect on the interference amount onthe PU while it decreases the SU data rate. Therefore, in the ideal perfect sensing case, it would be better

considering a scheme without an idle period for the SU(Tidle = 0) as discussed in [6], [7]. The situationhowever changes when we consider the possibility of error in sensing the channel. As it is obvious from

Figure 7, in the imperfect channel sensing cases, for near zero SU idle length, the overlapping time period

is relatively high and close to the maximum value (TON) which results in a great amount of interferenceon the PU. The introduction of a non-zero SU idle period, causes the interference to fall rapidly to a lower

amount. Although, we lose a small amount in the SU data rate whenever the SU idle period increases

(Figure 8), we show in the next section that there is an optimal non-zero value for the SU idle periodwhen the SU channel sensing is imperfect. A typical behavior of the performance metrics respect to the

SU transmission time, is also shown in the Figures 5 and 6 from the simulation section. It is clear that

the longer the SU transmission time is, the more the interference amount on the PU and the bit rate of

the SU would be. This is true for perfect or imperfect channel sensing and for any length of the SU idle

time.

VII. OPTIMIZATION OF THE SECONDARY USER TRANSMISSION AND IDLE PERIODS

In this section, we discuss how to find the optimum values for the SU transmission period (T ) and theSU idle length (Tidle) for given system parameters. We consider two optimization problems. In the firstoptimization problem, we find the values of T and Tidle which maximize the SU data rate while keeping the

average interference amount on the PU below a specified threshold. In the second optimization problem,

we investigate the values of T and Tidle which minimize the interference amount on the PU while achieving

a given SU data rate. Hence, The first optimization problem can be stated as maximizing Tnov with respect

to T and Tidle subject to the constraint that Tov = Tovth where Tovth is the threshold value set forthe overlapping time. Similarly, the second optimization problem can be stated as minimizing Tov with

respect to Tidle and T subject to the constraint that Tnov = Tnovth where Tnovth is the desired SUDownloaded from engine.lib.uwaterloo.ca on 20 July 2012 Page 10 of 19

11

data rate. Following the expressions derived in sections 3 and 4, it can be verified that solving these

optimization problems analytically is not tractable and we need to evaluate the optimum values of T and

Tidle numerically.

To solve the first optimization problem, we use equations (4)-(7) and the given overlapping time threshold,Tovth, to find the values of T and Tidle which satisfy the equality Tov = Tovth. For any value of Tidle, we

numerically search for the value of T such that Tov = Tovth. Figure 9(a) shows the result of this searchfor Tovth = 0.2 and Tovth = 0.4. The system parameters are set to TON = 1, TOFF = 2, Ts = 0.01 and

Pfa = Pm = 0.1. In the next step of solving our optimization problem, for each pair of (T, Tidle) presented

in Figure 9, we can calculate the corresponding non-overlapping time, Tnov, using (14). Figure 9(b) showsTnov as a function of Tidle for the same system parameters. As it can be seen, there is an optimum Tidle,

where, the value of the non-overlapping time is maximum. The corresponding value of T of this optimal

Tidle can be obtained using Figure 9(a). As a typical example, in Figure 9(b), for Tovth = 0.4, the optimumvalue of Tidle is 0.055, with the corresponding T value 0.273 from Figure 9(b). Hence, in this case, thepair (T, Tidle) of the SU parameters which is optimal for the system performance, would be (0.273, 0.055).

Similarly, in order to solve the second optimization problem for the same system parameters, first, by

using (14), we find the pairs of (T, Tidle) which satisfy the equality Tnov = Tnovth. The result is shownin Figure 10(a). The corresponding overlapping time of each of these pairs is calculated form equations(4)-(7) and shown in Figure 10(b). The value of Tidle and its corresponding value of T which minimizethe overlapping period are our desired optimal SU system parameters. In Figure 10, for Tnovth = 1.7,

the pair Tidle = 0.082 and T = 0.133 result in the minimum overlapping time between the users busy

periods.

We have also investigated the variation of the optimum SU idle length with the variation of the proba-

bilities of error in sensing in Figure 11.The optimum value of the SU idle length decreases for higher

probabilities of false alarm and increases for higher probabilities of miss detection. This is because, for

a fixed probability of miss detection, with a higher false alarm probability, the SU loses its transmission

opportunity and a higher idle period leads to a lower data rate without any effective impact on the

interference amount on the PU. On the other hand, for a fixed probability of false alarm, with a higher

miss detection probability, the SU idle length avoids more interference on the PU due to the sensing miss

detection without degrading the SU data rate.


12

VIII. CONCLUSION

We analyzed a practical overlay cognitive radio system. We considered a medium access layer scheme

in which the secondary user imperfectly senses the channel and transmits data if it senses a free channel or

goes through an idle interval otherwise. The analytical expressions of the interference on the primary user

and the overall data rate of the secondary user were derived and compared with the simulations results. The

results showed that introducing the idle interval for the secondary user improves the system performance

in imperfect sensing. We described algorithms to find the optimum secondary user transmission and idle

durations which minimize the interference on the primary user in order to achieve a particular secondary

user data rate or maximize the data rate of the secondary user while keeping the interference on the

primary user below a specified threshold.

APPENDIX

OBTAINING THE INTERFERENCE OCCURRENCE PROBABILITIES, P1 AND P2

In the case of collision type I, we have zero interference on the PU, if we have a series of one or more

than one incorrect sensing outcomes instantly before the PU switches to its busy mode. This series of

imperfect sensing outcomes may start exactly T seconds before the PU idle time ends, may start after

the last non interfering transmission of the SU or may start at the beginning of the PU idle duration (incase that 1 < T ). Our goal is to evaluate the probability of the occurrence of this event. Suppose thelength of the SU transmission time is greater than its idle period (T Tidle). We assume that the bunchof wrong sensing outcomes start at a point x, which is 1 seconds before the beginning of the PU busy

period. Hence 1 = 1 x. Since 0

1 T , its cumulative distribution function can be derived as

P (1 x <

1|1 x < T ) =1 exp(

1

TOFF)

1 exp( TTOFF

). (15)

This result can also be obtained using the memoryless property of the exponential distribution. Therefore,

the probability density function of 1 would be1

TOFFexp(

1

TOFF)

1exp( TTOFF

)for 0 6 1 6 T . According to our scenario,

all the sensing outcomes in 1 interval are wrong. Each incorrect sensing of the SU results in an idle

duration Tidle. The number of incorrect sensing outcomes during

1, is[

1

Tidle

]+ 1, where [] is the integer

part of the fraction. Hence, the probability of no occurrence of the series of wrong sensing outcomes


13

event or the probability of the interference event would be simply

P1 = 1 T

0

P

[

1

Tidle

]+1

fa

1TOFF

exp(

1

TOFF)

1 exp( TTOFF

)d

1. (16)

Now we consider the case in which the SU transmission time length is smaller than its idle duration

(T < Tidle). In this case, if we have a wrong sensing at most Tidle seconds before the PU idle period ends,we have zero interference on the PU. Therefore, the interference on the PU occurs, if we have a series of

one or more than one successful sensing outcomes which extend to the PU busy time. We assume that

this series of correct sensing outcomes start at a point y, which is 2 seconds before the beginning of the

PU busy period. Clearly, we have 2 = 1 y and 0

2 Tidle. Based on the aforementioned argument

and the memoryless property of the exponential distribution, the probability density function of 2 would

be1

TOFFexp(

2

TOFF)

1exp(TidleTOFF

)for 0 6 2 6 Tidle. Therefore, in this case, with the same discussions as the previous

case, the probability of having the series of correct sensing outcomes before the beginning of the PU busy

time or the probability of having the interference on the PU would be derived as

P2 = Tidle

0

(1 Pfa)

[

2

T

]+1 1

TOFFexp(

2

TOFF)

1 exp( TidleTOFF

)d

2. (17)

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[5] Yang, Q. Xu, S. Kwak, K.S, Outage Performance of Cognitive Radio with Multiple Receive Antennas, IEICE TRANSACTION ONCOMMUNICATIONS, vol. E91-B, pp.85-94, Jan 2008.

[6] Bastami B.A, Saberinia E, Optimal Transmission Time of Secondary User in an Overlay Cognitive Radio System, Electronics andTelecommunications Quarterly, Vol 55, issue 2, 2009.

[7] Bastami B.A, Saberinia E, Optimal Transmission Time of Secondary User in an Overlay Cognitive Radio System, Proceedings ofthe 2009 Sixth International Conference on Information Technology: New Generations, pp. 1269-1274, 2009.

[8] Huang S, Liu X, Ding Z, Optimal Transmission Strategies for Dynamic Spectrum Access in Cognitive Radio Networks, IEEETransactions on Mobile Computing, Vol 8, issue 12,pp. 1636 - 1648 , Dec 2009.


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[9] Huang S, Liu X, Ding Z, Optimal Sensing-Transmission Structure for Dynamic Spectrum Access,Proceedings of INFOCOM 2009.The 28th Conference on Computer Communications. IEEE , pp. 2295 - 2303 , 2009.

[10] Huang S, Liu X, Ding Z, Opportunistic Spectrum Access in Cognitive Radio Networks,Proceedings of INFOCOM 2008. The 27thConference on Computer Communications. IEEE , pp. 1427 - 1435 , 2008.

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Fig. 3. Typical time lines of the primary and secondary users.

Fig. 4. Joint timing between the primary and the secondary user.


16

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

T

T ov

Tidle=0

Tidle=0.1

Tidle=0.2

Tidle=0.3

Fig. 5. The values of the overlapping time versus the SU transmission duration for various SU idle periods. The simulation and analyticalresults are respectively shown by the dashed and the solid lines. The system parameters are TON = 1,TOFF = 2 ,Ts = 0.01, Pfa = 0.1,Pm = 0.2 . The four different values of the SU idle period are 0, 0.1,0.2 and 0.3.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

T

T no

v

Tidle=0

Tidle=0.1Tidle=0.2

Tidle=0.3

Fig. 6. The values of the non-overlapping time versus the SU transmission duration for various SU idle periods. The simulation andanalytical results are respectively shown by the dashed and the solid lines. The system parameters are TON = 1,TOFF = 2 ,Ts = 0.01,Pfa = 0.1, Pm = 0.2 . The four different values of the SU idle period are 0, 0.1,0.2 and 0.3.


17

0 0.05 0.1 0.15 0.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Tidle

T ov/T

ON

Pe=0

Pe=0.05

Pe=0.1

Pe=0.15

Pe=0.2

Fig. 7. The normalized overlapping time versus the SU idle duration for different values of the channel sensing error. The SU transmissionperiod is set to T = 0.2. The system parameters are TON = 1,TOFF = 2 ,Ts = 0.01, Pfa = Pm = Pe.

0 0.05 0.1 0.15 0.20.7

0.75

0.8

0.85

0.9

0.95

1

Tidle

T no

v/TO

FF

Pe=0

Pe=0.05

Pe=0.1

Pe=0.15

Pe=0.2

Fig. 8. The normalized non-overlapping time versus the SU idle duration for different values of the channel sensing error. The SUtransmission period is set to T = 0.2. The system parameters are TON = 1,TOFF = 2 ,Ts = 0.01, Pfa = Pm = Pe.


18

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

0.2

0.4

0.6

0.8

Tidle

T

(a)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

1.4

1.6

1.8

2

Tidle

T no

v

(b)

Tovth=0.4

Tovth=0.2

Fig. 9. (a) The pairs of the SU idle and transmission periods for fixed overlapping times.(b) The non-overlapping duration versus the SUidle period for fixed overlapping times. The system parameters are TON = 1,TOFF = 2 ,Ts = 0.01, Pfa = Pm = 0.1.

0 0.05 0.1 0.15 0.20

0.2

0.4

0.6

0.8

Tidle

T

(a)

0 0.05 0.1 0.15 0.20

0.2

0.4

0.6

0.8

Tidle

T ov

(b)

Tnovth=1.7

Tnovth=1.8

Fig. 10. (a) The pairs of the SU idle and transmission periods for fixed non-overlapping times.(b) The overlapping duration versus the SUidle period for fixed non-overlapping times. The system parameters are TON = 1,TOFF = 2 ,Ts = 0.01, Pfa = Pm = 0.1.


19

0

0.1

0.2

00.050.10.15

0.20

0.1

0.2

0.3

0.4

Pm

Pfa

opt

imum

SU

idle

tim

e

Fig. 11. The optimum value of the SU idle length versus the sensing probability of false alarm and probability of miss detection. Thesystem parameters are TON = 1,TOFF = 2 ,Ts = 0.01.


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Optimal Transmission Strategy in a Practical Overlay Cognitive Radio System