ON THE SENSING PERIOD FOR OPPORTUNISTIC SPECTRUM ACCESS

By in-corporating the PU spectrum activities, we model and analyze the type-IImissed detection error which arises from the mismatch between the fixed SU sensing period and the PU ON/OFF

On The Sensing Period For Opportunistic

Spectrum Access

ZHENG WANG

A THESIS SUBMITTED FOR THE DEGREE OF

MASTER OF ENGINEERINGDEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

2013

I hereby declare that this thesis is my original work and it has beenwritten by me in its entirety I have duly acknowledged all the sources of

information which have been used in the thesis

This thesis has also not been submitted for any degree in any university

previously

Zheng Wang

12 August 2013

To my parents.

I would like to express my heartfelt gratitude to my supervisor, DrChew Yong Huat, for his continuous guidance and support during myM.ENG candidature His insights, knowledge, patience, and enthusiasmhave provided great inspirations and set an admirable example for me Hehas generously devoted his time and efforts to this thesis, without whichits completion would not be possible

1.1 Background 1

1.2 Cognitive Radio Technology 2

1.2.1 Opportunistic Spectrum Access Model 4

1.2.2 Spectrum Sensing Algorithms 4

1.2.3 Spectrum Detection Techniques 5

1.2.4 Modeling of Spectrum Holes 6

1.2.5 Spectrum Sensing Model and Sensing Errors 6

1.3 Motivations and Contributions 8

1.4 Thesis Organization 10

2 System Model 11 2.1 System Model 11

2.2 Performance Metrics for Spectrum Sensing 13

3 Modeling Type-II Missed Detection Error Under Given

3.1 Type-II Missed Detection Error Derivation 16

3.2 Exponential Ton and Tof f 18

3.3 Hyper-Erlang Ton and Tof f 19

3.4 Pareto Ton and Tof f 23

3.5 Comparing Exponential, Hyper-Erlang and Pareto PU ON/OFF Models 26

3.6 Simulations and Discussions 29

3.6.1 Type-II Missed Detection Error - Theory and Simu-lation 29

3.6.2 SU’s Saturated Throughput - Theory and Simulation 32 3.6.3 Type-II Missed Detection Error and SU Throughput - Light and Heavy PU Traffic Condition 36

3.7 Conclusion 39

4 On Discretizing Continuous Primary ON/OFF Activities 40 4.1 System Model of 2-state PU Discrete Markov Chain 41

4.2 Type-II Missed Detection Error for 2-state Discrete Markov Chain 42

4.3 Limiting the Discretization Error 44

4.4 Derivation of Secondary Arrivals Based on Continuous and Discrete PU ON/OFF Model 45

4.5 Conclusion 50

5 Conclusion and Future Work 51 5.1 Conclusion 51

5.2 Future Work 53

In the opportunistic spectrum access (OSA) model, it is paramountthat the primary users (PUs) transmissions are not significantly affected.Hence, accurate and efficient channel sensing by the secondary users (SUs)plays a key role in achieving this objective The motivation behind thiswork is the belief that it is insufficient to just consider the false alarmand missed detection errors when channel sensing is performed By in-corporating the PU spectrum activities, we model and analyze the type-IImissed detection error which arises from the mismatch between the fixed

SU sensing period and the PU ON/OFF activities Four spectrum ing performance metrics are identified, namely the probability of type-IImissed detection error, probability of missed SU transmission opportunity,probability of SU successful transmission and probability of SU blockedaccess We derive and validate the closed-form expressions for the perfor-mance metrics under a few common PU spectrum activity models, such

sens-as exponential model, hyper-Erlang model and Pareto model This thesisthen illustrates the trade-off relationship between aforementioned errorsand network throughput based on theory and computer simulation Howthe channel sensing rate is affected by the statistics of the PU spectrum ac-tivities is also studied Lastly, this thesis looks into how to approximate the

PU continuous ON/OFF process by a 2-state discrete Markov chain in thecontext of SU spectrum sensing More specifically, we investigate how toselect the time stamp and transition probability of discrete Markov chain,

so that discretizing the continuous PU ON/OFF process can be achievedwithout losing valuable information about the presence of type-II misseddetection error The accuracy of discretization is demonstrated throughextensive simulations

List of Figures

1.1 Spectrum holes illustration 3

1.2 Structure of SU sensing frame 7

2.1 PU 2-state ON/OFF process 12

2.2 SU missed opportunity 14

2.3 Type-II missed detection error 14

3.1 Remaining time T∗ on and T∗ of f 17

3.2 Type-II missed detection error under exponential PU ON/OFF model 31

3.4 Type-II missed detection error under Pareto PU ON/OFF model 31

3.3 Type-II missed detection error under hyper-Erlang PU ON/OFF model 32

3.5 SU’s saturated throughput under exponential PU ON/OFF model 33

3.6 SU’s saturated throughput under hyper-Erlang PU ON/OFF model 34

3.7 SU’s saturated throughput under Pareto PU ON/OFF model 35 3.8 SU’s successful transmission probability Pt in light PU traffic 35 3.9 Type-II missed detection error in light PU traffic 36

3.10 Type-II missed detection error in heavy PU traffic 37

3.12 SU’s saturated throughput in heavy PU traffic 37

3.11 SU’s saturated throughput in light PU traffic 38

4.1 The 2-state continuous Markov ON/OFF process to describe the PU spectrum activities 41

LIST OF FIGURES

4.2 The 2-state discrete Markov ON/OFF process to describethe PU spectrum activities 424.3 Remaining time Tof fg ∗ 434.4 Type-II missed detection errors under continuous and dis-crete PU ON/OFF models 464.5 A snapshot of continuous PU ON/OFF spectrum activitiesand secondary arrivals 474.6 A snapshot of discrete PU ON/OFF spectrum activities andsecondary arrivals 474.7 Probability of n secondary arrivals under continuous PUON/OFF model - theoretical result and simulation result 484.8 Probabilities of n secondary arrivals under continuous anddiscrete PU ON/OFF models - theoretical results 50

Pof f PU transition probability from ON-state to OFF-state

Ton time duration of PU ON-state

Tof f time duration of PU OFF-state

T∗

on remaining time of PU in ON-state

T∗

of f remaining time of PU in OFF-state

E{·} expected value

f (·) probability density function

Pe type-II missed detection error

Pm missed opportunity error

Pt successful transmission probability

Pb blocked access probability

δt simulation time stamp

λon rate parameter for exponentially distributed Ton

λof f rate parameter for exponentially distributed Tof f

λarr rate for Poisson secondary arrivals

ζ error bound between continuous and discrete PU

ON/OFF models

A report published by Spectrum Policy Task Force (SPTF), under eral Communication Commission (FCC) of the United States, shows thatthe inflexible spectrum regulation policy, rather than the physical limita-tion of spectrum bandwidth, is the main cause for the shortage of spectrumresource [2] The field measurement results, conducted by the SPTF as well

Fed-as other agencies, shows that the actual utilization of spectrum resource

CHAPTER 1 Introduction

can be highly inefficient [3, 4] In Singapore, a study conducted by stitute for Infocomm Research (I2R) demonstrates that the efficiency ofspectrum utilization can be as low as 5% in certain spectrum bands in cityarea [5] All the measurements and investigations shed light on the exist-ing problem of spectrum under-utilization With the continuous growth ofwireless service demand and the emergence of new wireless communicationsystems, spectrum scarcity is bound to be more severe in future Hence,new spectrum allocation scheme must be developed to remove the rigidregulatory and meet the compelling need for improving the efficiency inspectrum utilization

Cognitive radio (CR) technology emerges as a novel solution to thespectrum under-utilization problem and addresses the exclusive spectrumaccess problem The concept of CR was first introduced by Joseph Mitola

in his dissertation [6] CR is described as a reconfigurable wireless devicewhich has sufficient intelligence to be aware of the environment and beable to automatically adjust its operating parameters in response to theenvironment changes By dynamically tuning the transmission parame-ters, such as transmit power, operating frequency and modulation scheme,

CR devices can greatly enhance the flexibility of spectrum allocation andimprove the spectrum utilization efficiency This work lays the foundationfor the current opportunistic spectrum access model In [7], the authorintroduced the concept of interference temperature and then initiated theidea of interference-temperature-based CR This paper paves the way tothe current spectrum sharing model Although the exact definition of CR

is still evolving, CR can be generally categorized into two operation models

- opportunistic spectrum access (OSA) model and spectrum sharing (SS)model The radios in CR network can be categorized into two groups aswell In the CR network, the radios which are licensed to use a particularspectrum band are referred as primary users (PUs) The radios which donot own any channel, but intend to transmit are referred as secondary users(SUs) When a spectrum band, which is exclusively assigned to a PU sys-

CHAPTER 1 Introduction

tem, is not being utilized within a particular geographic location and time,

a spectrum hole is said to present [7], as illustrated in Fig 1.1 The idea

of CR is to allow SUs to take the spectrum for transmission even though

it is not licensed to them, while protecting the interest of PUs Depending

on the different operating model, PUs and SUs share the same spectrumband in different manners In the OSA model, SU system can dynamicallyuse the temporally unoccupied and intermittently available spectrum holesfor its own transmission To avoid causing excessive interference to the PUsystem, SU has to periodically sense the surrounding environments Once

SU senses the presence of PU on the same frequency, it is required to stopits own transmission to vacate the spectrum immediately to avoid affectingPU’s transmission However, in the spectrum sharing model, SU system

is allowed to transmit concurrently with PU system using the same nel, given that interference caused by SU is within a tolerable threshold.This can be realized by imposing the interference power constraint on SU’stransmission, so that the interference power received at PU’s receiver isbelow a pre-defined limit In the following, a detailed introduction of theOSA model is presented

chan-Fig 1.1: Spectrum holes illustration

CHAPTER 1 Introduction

The key concept of OSA is to open licensed spectrum to SUs whileprotecting the PU system from interferences caused by SUs Communica-tion systems adopting the OSA model have been under extensive researchand development in recent years The neXt-Generation (XG) program, un-der the Defense Advanced Research Projects Agency (DARPA), developed

a XG radio system focusing on intelligent policy-based negotiation andgrouping in order to enable PUs and SUs to share the usage of spectrum[8,9] The IEEE 802.22 working group was formed to work on developing

a standard for unlicensed access to TV spectrum on a non-interfering basis

in wireless regional area networks (WRAN) [10]

As SUs are only granted lower access priority and rely on temporalspectrum holes for transmission in the OSA model, the statistics of the PUspectrum activities have significant impact on SU’s transmission There-fore, the performance of spectrum sensing and modeling of spectrum holesboth play a very important role in the OSA model The performance ofspectrum sensing decides whether the spectrum holes can be used efficiently

by the SU system and whether the priority of the PU system can be fectively protected Extensive research has been performed to study thespectrum detection techniques, spectrum sensing performances and mod-eling of spectrum holes

There have been a few spectrum sensing algorithms under extensiveresearch, which include wide-band and narrow-band sensing, as well ascooperative sensing

Narrow-band spectrum sensing usually involves sensing and detection

of the spectrum activities in one single spectrum band by a single radio.The objective is to maximize the discovery possibility of spectrum opportu-nities and minimize the delay in locating an available channel In [11], theauthors formulated a periodic sensing scheme for each spectrum sub-band

as a partially observable Markov decision decision process (POMDP) andderived the sensing period using linear programming techniques However,the analysis was restricted to slotted access models of PU and SU systems

When there are multiple SUs in one cognitive network, a more tive approach has been proposed as cooperative spectrum sensing [17–21].Cooperative spectrum sensing requires multiple SUs concurrently sensingfor spectrum opportunities at different geographical locations The detec-tion results are centralized and analyzed for decision making to achievebetter detection accuracy By exploiting spatial diversity, the hidden nodeproblem can be alleviated through cooperative sensing, as demonstrated

effec-by recent research work [19,20,22] However, better performance of erative sensing is also achieved at the expense of additional computationalcomplexity and overhead traffic, since SUs have to exchange and fuse theirdetection results There are other advanced sensing algorithms to improvethe sensing performance for different scenarios, such as [23–28]

There are three common spectrum detection techniques: energy tion [29, 30], matched-filter detection [31, 32] and cyclostationary featuredetection [33, 34] Each of the three spectrum detection techniques has itsown pros and cons Because of the low computational complexity, energydetection is the most widely adopted spectrum detection technique Un-fortunately, it is not the optimal approach for detecting signals Matched-filter detection is optimal as it can achieve maximum Signal-to-Noise Ra-tio (SNR) given the background noise is stationary Gaussian However,matched-filter detection requires prior knowledge of PU’s signal, which may

detec-CHAPTER 1 Introduction

not be available in the practical situation When noise level is high, stationary feature detection can perform very well by exploiting the certaindegree of correlation among signals, given the fact there is usually no corre-lation between signals and noise The minimum number of samples requiredfor cyclostationary feature are a lot more compared to energy detection andmatched-filter detection There are also some advanced spectrum detectiontechniques proposed recently by researchers, such as eigenvalue-based [35]and covariance-based detection [36] The aforementioned spectrum detec-tion techniques can be adopted to make decision of the channel status based

cyclo-on the observaticyclo-on by individual SUs

Although modeling of spectrum holes is crucial for the OSA model,limited work has been done to study this topic Some of the importantwork can be found in [37–39] In [37], the authors modeled the duration ofwhite spaces for individual WLAN channels in the 2.4GHz ISM band It hasbeen concluded that the hyper-Erlang distribution works best to describethe duration of white spaces for each channel In [38], by adopting a slottedaccess model for the SU, the authors described the duration of white spacesfor a channel in terms of the number of time slots which are not occupied by

PU The duration of white spaces for each channel was then approximated

by a geometric distribution Extensive measurements were performed bythe Dutch Radio Regulatory Body over twelve Netherlands cities in year

2002 and the findings were presented in [39] The measurements were taken

at 10s interval over a 24-hour time span and were performed in steps of100kHz from 400MHz to 1GHz It was found that the PU activities in eachspectrum band can be approximately modeled as a 2-state exponentialON/OFF process

Spectrum sensing plays an important role in the performance of theOSA model In the OSA model, periodic spectrum sensing is usuallyadopted by SUs The sensing frame comprises of two slots - a sensingslot and a data transmission slot, as illustrated in Fig 1.2 Suppose the

CHAPTER 1 Introduction

sensing duration is Td and sensing period is Ts, Ts − Td is the durationfor SU to transmit data given that the channel is vacant Suppose SU isinterested in a frequency band with carrier frequency fc and bandwidth W ,the number of samples of received signal is determined by sensing duration

Td and SU’s sampling frequency fs In general, longer sensing duration Td

makes SU’s spectrum sensing more accurate but inevitably leads to shortertransmission time, which results in lower SU’s throughput This tradeoff

is termed as sensing throughput tradeoff This tradeoff was defined andinvestigated in [40] For cooperative sensing and wide-band sensing, thesescenarios were investigated in [41] and [42], respectively

Fig 1.2: Structure of SU sensing frame

As spectrum sensing is subject to sensing errors in the practical tion, extensive research has been done to investigate the spectrum sensingerrors There are two common performance metrics to quantify the per-formance of the spectrum sensing - probability of missed detection andprobability of false alarm [30] Probability of missed detection is defined asthe probability of failing to detect the presence of PU when PU is occupyingthe spectrum; while probability of false alarm is defined as the probability

situa-of falsely declaring the presence situa-of PU when spectrum is actually vacant

A lot of research has been done to study these two spectrum sensing formance metrics and to improve the accuracy of spectrum sensing [43–45].Different sensing schemes are developed as a result, catering to differentrequirements and situations [46]

per-In the OSA model, missed detection and false alarm errors affect the

PU system as well as the SU system From the perspective of PU, thelower the probability of missed detection, the better protection it can re-

CHAPTER 1 Introduction

ceive From the perspective of SU, the lower the probability of false alarm,there are more chances for SU to make use of vacant spectrum bands fortransmission In the literature, the analytical results for missed detec-tion and false alarm errors have been presented based on different channelfading environment and detection techniques For example, assuming the

SU spectrum sensing is performed using energy detection techniques in arayleigh fading environment, the false alarm error and missed detectionerror can be expressed as [17]:

λ¯λ2(1 + ¯λ)

k!

(1.2)

with λ and ¯λ are the SNR ratio and the average SNR ratio, respectively

m is known as the time-bandwidth product, which is the product of theobservation bandwidth W and sensing duration Td Note that false alarmerror and missed detection error are related to sensing duration Td only,but not the sensing period Ts

The performance of spectrum sensing is crucial in CR system design

as it will determine whether the spectrum holes can be efficiently utilizedand whether the PU’s transmission can be effectively protected Althoughmissed detection and false alarm errors are two important performance met-rics to quantify the performance of the SU spectrum sensing in traditionalradio networks, we argue that it is not sufficient to only consider thesetwo errors in a more complicated setup of CR When designing a spectrumsensing algorithm for CR networks, it is crucial to incorporate the statis-tics of the PU spectrum activities More specifically, we need to consider

CHAPTER 1 Introduction

the errors arising from the mismatch between the SU sensing period and

PU ON/OFF spectrum activities However, so far there is no literature tomodel and study the errors arising from the mismatch between the fixed SUsensing period and PU 2-state ON/OFF spectrum activities Although thestatus of channel is only known by the SU at the sensing epoch, PU can be-come active and access its licensed spectrum band at any time Therefore,even channel is sensed correctly by the SU at the sensing epoch, collision

of transmission may still happen and will cause throughput degradation ofthe CR network if PU becomes active before SU’s next channel sensing isperformed This spectrum sensing error must be taken into consideration

It is named as type-II missed detection error in this thesis So far only

a few works have included the statistics of PU spectrum activities in thedesign [40, 47] In [40], the author studied the optimal sensing period for

a fixed SU sensing duration But no effort is made to study the trade-offrelationship among the errors arising from the mismatch between fixed SUsensing period and the PU ON/OFF spectrum activities In [47], the au-thors studied the optimal sensing period and sensing duration to maximizethe SU sensing efficiency, defined as the ratio of the available transmissiontime to the sensing period But, the trade-off relationship among the errorswere not examined

Most of the works, such as [40, 47], are based on the exponential PU2-state ON/OFF model While exponential distribution allows easy deriva-tions and analytical tractability, recent studies have revealed that the PUON/OFF spectrum activities exhibit “heavy-tail” characteristics, whichcan be modeled by the hyper-Erlang distribution [48], and the Pareto dis-tribution [37] These characteristics indicate that there’s higher probabilitythat the channel could be “ON” or “OFF” for longer time durations thanexponential distribution model Therefore, the SU performance could differsignificantly under different PU ON/OFF models

The contribution of this thesis is three-fold Firstly, we will derivethe closed-form expression of the performance metrics for the SU spec-trum sensing under three PU ON/OFF activity models, namely exponen-tial model, hyper-Erlang model and Pareto model The correctness of theclosed-form expressions is verified through extensive simulations Moreover,the trade-off relationship of SU’s sensing performance and throughput is

CHAPTER 1 Introduction

analyzed in depth In particular, we compare the type-II missed detectionerrors based on aforementioned PU ON/OFF activity models and showthat the Pareto distributed ON/OFF model leads to the highest proba-bility of PU interference Lastly, we also investigate how to discretize thecontinuous PU ON/OFF Markov process model by appropriately choosingthe time stamp and transition probabilities of discrete ON/OFF Markovchain model to preserve the valuable information of type-II missed detec-tion error In general, this thesis provides a complete overview about theperformance metrics for the SU spectrum sensing in the OSA model of

CR It can serve as a reference for spectrum sensing design of future CRcommunication systems

The remainder of the thesis is organized as follows Chapter2presentsthe system model and elaborates several performance metrics for the SUspectrum sensing, including type-II missed detection error, in the context ofthe OSA model This chapter lays the foundation for our further discussions

in the following chapters In Chapter 3, based on the different statisticalmodels of PU ON/OFF spectrum activities, the closed-form expressions

of sensing performance metrics are derived The trade-off relationship,between sensing accuracy and SU’s saturated throughput, is discussed indepth based on the simulation results obtained under different primarytraffic conditions In Chapter 4, considering the case of discrete computersimulation, we illustrate how to use geometrically distributed PU ON/OFFMarkov chain model to approximate the continuous PU ON/OFF model bykeeping the type-II missed detection error within an error bound Chapter

5 concludes this thesis and discusses the future work

In the OSA model, SUs perform sensing to detect the channel status.

If a certain spectrum band is detected to be left unoccupied by PU, SUwill transmit over the spectrum; otherwise, SU will continue sensing until itdiscovers a vacant spectrum band The concurrent transmission of PU and

SU using the same channel is not allowed in the OSA model Therefore,SU’s transmission will commence only when spectrum holes are detected.After SU’s transmission starts, SU continues to perform spectrum sensing

to monitor the presence of PU, who may require the channel for sion at any time Once PU is detected, SU must cease transmission togive the priority to PU’s transmission The process to scan over a range oftarget spectrums and determine the existence of spectrum holes is termed

transmis-as spectrum sensing

Extensive measurement performed by the Dutch Radio RegulatoryBody in Netherland showed that PU’s activities across the spectrum can

CHAPTER 2 System Model

be approximately modeled by a 2-state exponential ON/OFF process [39].Based on this finding, the PU activities in each frequency band can bejustified to be modeled as a 2-state ON/OFF process, where the “ON-state”corresponds to the situation that the licensed spectrum band is occupied by

a PU and the “OFF-state” corresponds to the situation that the licensedspectrum band is vacant, as shown in Fig 2.1

The transition probabilities from “ON-state” to “OFF-state” and from

“OFF-state” to “ON-state” are denoted by Pof f and Pon, respectively Thedurations that PU stays in “OFF-state” and in “ON-state” are denoted by

Tof f and Ton, respectively Ton and Tof f are independent random variables,whose probability density functions are denoted by fT on(t) and fT of f(t),respectively

Fig 2.1: PU 2-state ON/OFF process

In the OSA model, SUs are granted lower access priority and canonly utilize temporal spectrum holes to transmit Furthermore, we assumethat at any instance of time, only one SU can access a detected spectrumhole for transmission Therefore, the coexistence of multiple SUs in onevacant spectrum band is not allowed In the practical situation, the SU

is unable to perform channel sensing and data transmission concurrently

We assume all the SUs can be synchronized in time and perform periodicchannel sensing with fixed sensing period as Ts At the beginning of thesensing period, the SU requires sensing duration, Td, to sense and processchannel information If the channel is deemed to be vacant by SU based

on the channel information collected in Td, the SU will transmit within theremaining duration of Ts− Td Data transmission stops at the next channel

CHAPTER 2 System Model

sensing epoch and the SU will start sense the channel again In the practicalsituation, Td is usually small enough so that the probability of PU behaviorchange within the sensing duration can be negligible Generally speaking,the reliability and accuracy of spectrum sensing depend on the conditions

of the radio environment, the SU’s detection techniques and the number ofsamples collected within the sensing duration Td

Most of the works, such as [40, 47], were based on the exponential

PU ON/OFF model Other work were also performed based on the Erlang and Pareto PU ON/OFF model [37, 48] As SU’s sensing perfor-mance could differ significantly under different PU ON/OFF models, theanalytical derivations of performance metrics for the SU spectrum sens-ing are illustrated for all three aforementioned statistical models of PUON/OFF spectrum activities in Chapter 3 The analytical results are alsocompared and verified against simulation outcomes

Sens-ing

From the system model mentioned above and assuming perfect trum sensing without traditional missed detection error and false alarmerror, there are four scenarios which may happen to the SU, when SUperforms periodic spectrum sensing in one unlicensed PU spectrum band:

spec-• Data transmission is successful

• Channel access is blocked

• Spectrum hole is missed for transmission

• PU’s transmission is interfered by SU’s transmission

Scenarios 3 and 4 are illustrated in Fig 2.2 and 2.3, respectively InFig 2.2, the channel is sensed to be occupied by PU during the sensingduration Td Hence, SU’s access is blocked for the remaining time of Ts−Td.During this time, PU may cease transmission and leave this channel, whichinevitably leads to missed opportunity for the SU to transmit SU can

CHAPTER 2 System Model

only acknowledge the spectrum hole after sensing is performed at the nextsensing epoch, given that PU remains inactive throughout the time span.Type-II missed detection error is illustrated in Fig 2.3 During thesensing duration Td, SU senses the channel to be vacant and decides totransmit However, there’s a possibility that PU becomes active againwithin the SU’s transmission duration before next spectrum sensing starts

As SU has no knowledge on the presence of PU, it will keep transmittingthroughout the rest of the sensing period Hence, PU’s transmission andSU’s transmission inevitably collides Although the cause of collision isdifferent, scenario 4 leads to the same result as the conventional misseddetection error So we name it as type-II missed detection error Onlywhen PU remains inactive throughout the sensing period, SU can transmitsuccessfully without interfering with PU’s transmission

Fig 2.2: SU missed opportunity

Fig 2.3: Type-II missed detection error

From the system model, we can see that Ts must be carefully sen in order to minimize the probability of type-II missed detection error

cho-CHAPTER 2 System Model

However, if Ts is too short, the throughput of SU transmission will be promised because less time can be utilized by the SU for data transmis-sion Moreover, it is generally desirable to reduce the probability of missedopportunity to make SU to fully utilize the spectrum hole Meanwhile,lower probability of blocked SU access and higher probability of successful

com-SU transmission are also desirable, which generally leads to higher com-SU’sthroughput In Chapter 3, we will discuss the trade-off relationship andthe effect of sensing period selection in detail

Chapter 3

Modeling Type-II Missed

Detection Error Under Given Primary ON/OFF Activities

In this chapter, we derive the closed-form expressions of type II misseddetection error and other sensing performance metrics in the OSA model,assuming that PU’s activities can be described as a 2-state continuousON/OFF Markov process [39]

Deriva-tion

Denote Ton and Tof f as the time durations of PU’s “ON” and “OFF”state, respectively Then denote E(Ton) and E(Tof f) as the mean timedurations of PU’s “ON” and “OFF” state, respectively If E(Ton+ Tof f) <

∞, from the results of renewal theory [49], we can express:

Pof f = E(Tof f)

E(Ton) + E(Tof f) (3.1)

Pon = E(Ton)

E(Ton) + E(Tof f) (3.2)

CHAPTER 3 Modeling Type-II Missed Detection Error Under Given Primary ON/OFF Activities

Note that Ton and Tof f need not follow any particular distribution for(3.1) and (3.2) to be hold Pon can be also used as the PU activity factor

to indicate how frequently PU will occupy its licensed spectrum band.Denote T∗

on as the remaining time duration of PU being “ON”, after

it is sensed to be “ON” by the SU Denote T∗

of f as the remaining timeduration of PU being “OFF” after it is sensed to be “OFF”, as shown inFig 3.1

Fig 3.1: Remaining time T ∗

Pe = Pof f× P (T∗

of f < Ts) = Pof f ×

Z T s 0

fT ∗

of f(t)dt (3.5)

A missed SU transmission error occurs when the channel is sensed to

be occupied but the PU cease transmission before SU performs channelsensing at the start of next sensing period If we denote the probability ofmissed opportunity is denoted by Pm, we can express Pm as:

CHAPTER 3 Modeling Type-II Missed Detection Error Under Given Primary ON/OFF Activities

CHAPTER 3 Modeling Type-II Missed Detection Error Under Given Primary ON/OFF Activities

and λon and λof f are the rate parameters associated with the exponentiallydistributed Ton and Tof f, respectively

The expectation of Ton and Tof f can then be expressed as:

on(t) =

fT on(t) and fT ∗

of f(t) = fT of f(t) Substitute (3.9) and (3.10) into (3.5) to (3.8)and after some algebraic simplification, the closed form expressions for thedesired probabilities are:

CHAPTER 3 Modeling Type-II Missed Detection Error Under Given Primary ON/OFF Activities

P2

i=1αi = 1,P2

i=1βi = 1 mi and ki are called the shape parameters ofhyper-Erlang distribution and must be positive integers for all i ni and riare called the scale parameters of hyper-Erlang distribution and must bepositive real numbers

The expectation of Ton and Tof f can be expressed as:

P2 i=1αimini+P2

i=1βikiri

(3.21)

Pof f =

P2 i=1βikiri

P2 i=1αimini+P2

fT ∗

on(t) = 1 −

Rt

−∞fT on(x)dxE(Ton)

CHAPTER 3 Modeling Type-II Missed Detection Error Under Given Primary ON/OFF Activities

Gamma function [50] By substituting (3.19), we can obtain:

fT ∗

on(t) = 1 −

P2 i=1αiΓ(m(mii−,t/n1)!i)

P2 i=1αimini

P2 i=1βikiri

, t > 0 (3.25)From (3.24) and (3.25), the performance metrics can be expressed as:

Pe = Pof f× P (T∗

of f < Ts) = Pof f ×

Z T s 0

fT ∗

of f(t)dt

=

RT s 0



1 −P2 i=1βiΓ(ki ,t/r i ) (k i − 1)!

dt

Pm = Pon× P (T∗

on < Ts) = Pon×

Z T s 0

fT ∗

on(t)dt

=

RT s 0



1 −P2 i=1αiΓ(m(mii,t/n− 1)!i)

dtE(Ton) + E(Tof f) (3.27)

0



1 −P2 i=1βiΓ(k(kii−,t/r1)!i)

dtE(Ton) + E(Tof f) (3.28)

0



1 −P2 i=1αiΓ(m(mii,t/n− 1)!i)

dtE(Ton) + E(Tof f) (3.29)

To obtain a closed-form expression, Γ(s, x) can be re-written as [50]:

CHAPTER 3 Modeling Type-II Missed Detection Error Under Given Primary ON/OFF Activities

fT ∗

on(t) =

1 −P2 i=1αi

h

1 − e− t/n iPm i − 1

l=0

(t/n i ) l l!

i

P2 i=1αimini

, t > 0 (3.31)

fT ∗

of f(t) =

1 −P2 i=1βih1 − e− t/r iPk i − 1

l=0

(t/r i ) l l!

i

P2 i=1βikiri , t > 0 (3.32)

We can rewrite (3.26) to (3.29) using (3.31) and (3.32) to obtain moretractable, closed-form expressions for Pe, Pm, Pt and Pb , respectively As

an example, we show the mathematical derivation for Pe as:

Pe =

RT s 0



1 −P2 i=1βi(1 − e− t/r iPk i − 1

l=0

(t/r i ) l l! )dtE(Ton) + E(Tof f)

=

RT s 0



1 −P2 i=1βi(1 − e− t/r iPk i − 1

l=0

(t/r i ) l l! )dt

P2 i=1αimini+P2

CHAPTER 3 Modeling Type-II Missed Detection Error Under Given Primary ON/OFF Activities

i=1βikiri (3.35)

Pm = Ts−

P2 i=1αi

h

Ts− niPmi

− 1 l=0



1 − e− Ts

ni Pl j=0

1 j!(Ts

n i)ji

P2 i=1αimini+P2

CHAPTER 3 Modeling Type-II Missed Detection Error Under Given Primary ON/OFF Activities

must be positive integers Their reciprocals 1q and 1s are known to mine the shape of the Pareto distributed Ton and Tof f, respectively Theexpectation of Ton and Tof f can then be expressed as:

of f(t) From the renewal theory[49], we can obtain (3.3) as:

s−1

rs , 0 < t < r (3.47)The correctness of (3.46) and (3.47) can be verified by checking that

R∞

0 fT ∗

on(t)