ofdm 1

3410 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 7, SEPTEMBER 2009

Spectrum Sensing of OFDMA Systems forCognitive Radio Networks

Sheng-Yuan Tu, Kwang-Cheng Chen, Fellow, IEEE, and Ramjee Prasad, Fellow, IEEE

Abstract—To fully exploit wireless radio resource and, thus,increase spectrum efficiency, cognitive radios shall sense wire-less environments and identify interference to allow opportunis-tic transmissions for secondary systems. Based on Chen et al.in their work about a terminal architecture for cognitive radionetworks, by further obtaining transmission information with arate–distance nature that is extended from an overlay concept,secondary systems can even leverage busy duration of primarysystems to enhance the opportunity to use spectrum under de-rived tolerable interference to the primary orthogonal frequency-division multiple access (OFDMA) system. Our proposed novelmultistate (i.e., existence, activity, and data transmission rate)spectrum sensing can thus effectively acquire a set of cognitiveinformation for OFDMA mobile communication systems undera general system model. Through the received signal strengthindicator (RSSI), fundamental symbol rate, cyclic property ofthe OFDMA signal, and the control and management signal, wecan precisely determine the existence and activity of the primary(OFDMA) system within a subband via Neyman–Pearson (NP)criterion. With a priori knowledge of the frame structure ofpotential primary systems, communication parameters, includ-ing data transmission rate and resource allocation state, can beextracted by analyzing the frame header. Through appropriateparametric adjustments, our sensing procedure can be extendedto state-of-the-art OFDMA systems.

Index Terms—Cognitive cycle, cognitive radio, orthogonalfrequency-division multiple access (OFDMA), rate–distancerelationship, spectrum sensing.

I. INTRODUCTION

T REMENDOUS mobile communication standards andtechnologies have been developed to cope with different

applications, coverage, and transmission rates. Instead of devel-oping a universal air interface, software-defined radios (SDRs)[1] for reconfiguring communication by adjusting system pa-rameters are considered to be more feasible future mobilecommunication systems. In addition to low-cost highly flexibleradios, spectrum efficiency, which is driven by the need for

Manuscript received March 14, 2008; revised October 5, 2008. First pub-lished February 6, 2009; current version published August 14, 2009. This workwas supported in part by the National Science Council of Taiwan under contractNSC-95-2923-I-002-001-MY2. This paper was presented in part at the IEEEInternational Symposium on Personal, Indoor, and Mobile Radio Communi-cations, 2007. The review of this paper was coordinated by Dr. H. Jiang.

S.-Y. Tu is with the Institute of Communication Engineering, NationalTaiwan University, Taipei 10617, Taiwan (e-mail: [email protected]).

K.-C. Chen is with the Institute of Communication Engineering and theDepartment of Electrical Engineering, National Taiwan University, Taipei10617, Taiwan (e-mail: [email protected]).

R. Prasad is with the Center for TeleInFrastruktur, Aalborg University, 9220Aalborg, Denmark (e-mail: [email protected]).

Digital Object Identifier 10.1109/TVT.2009.2014775

multimedia wireless applications in limited radio resources, isanother important issue for state-of-the-art mobile communica-tion technologies. According to recent measurements from theFederal Communications Commission (FCC) [4], [5], spectrumutilization at any time is roughly 10%. This instance highlightspossible improvement of the current static spectrum allotmentpolicy. Further generalizing the SDR concept, Mitola pioneerlyproposed cognitive radios [2], [3], which sense and cognize en-vironments and then transmit data in idle/nonoccupied channelsto increase spectrum efficiency. Therefore, spectrum sensingand cognition are among major functions in cognitive radios[7]. Conventionally, spectrum sensing is implemented by anenergy detector, i.e., received signal strength indicator (RSSI)[10]–[14]. However, because of wireless fading channel andthe existence of other noncollaborative interference, a simpleenergy detector is not sufficient to determine system existenceand its operation state. Recently, Hsieh and Chen [31] haveproposed a method to identify a frequency-hopping system andwideband systems by unique characteristics in frequency andtime domains under maximum a posteriori criterion. However,this method is not enough for orthogonal frequency divisionmultiple access (OFDMA) and multicode code-division mul-tiple access (CDMA) [23] due to dynamic allocation of radioresources. Furthermore, the aformentioned methods only takeaccount of spectrum holes [7]. To explore the extreme of radioresource utilization or medium access control (MAC) [44],[45] in cognitive radio “networks” so that the packets canbe forwarded after using spectrum holes, we have to furtheridentify the activity and transmission rate of primary systems.Consequently, more appropriate spectrum sensing for OFDMAis required, as proposed in this paper.

Let us recall a very fundamental situation in modern mobilecommunications. Based on the received power level, modernsystems automatically adjust physical transmission rate ac-cordingly and, thus, throughput via MAC [40]. We observefrom a realistic operation of modern adaptive modulationand coding (AMC) [27] wireless systems such as the IEEE802.11a/g that the physical layer (PHY) selects higher spectralefficient modulations for stronger received power, which aregenerally more sensitive to interference, noise, and fading, toyield high throughput. At lower received power, PHY selectslower spectral efficient modulations, which are more resistibleto interference. We call such a nature as the rate–distancefeature of wireless communications as an extension of overlaysystems [8], [9]. Here, “distance” is considered as a measure ofreceived signal power rather than just Euclidean or propagationdistance. If we could guarantee “distance” between cognitiveradios and primary systems in the channels that are occupied by

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TU et al.: SPECTRUM SENSING OF OFDMA SYSTEMS FOR COGNITIVE RADIO NETWORKS 3411

Fig. 1. System model for OFDMA/OFDM broadband wireless systems.

transmissions of the primary link, cognitive radios can reuse thechannels and increase the opportunity to transmit. This featurehas hardly been explored in traditional cognitive radio spectrumsensing research that considers only spectrum holes. Therefore,our spectrum sensing procedure also provides a methodologyfor sensing radio resource in the busy duration of primarysystems.

In this paper, we focus on sensing OFDMA systems due totheir potential applications for future mobile communications.The rest of this paper is organized as follows. In Section II,we present the system model, a set of cognitive information,and cognitive cycle. In Section III, we provide a procedure foridentifying the existence and activity of the primary (OFDMA)system and design optimal detectors under a Neyman–Pearson(NP) criterion. Then, available radio resource to secondarysystems in occupied channels is determined in Section IV. Thespectrum sensing algorithm and block diagram are summarizedin Section V. Section VI presents numerical results and com-parisons. Concluding remarks are made in Section VII.

II. SYSTEM MODEL

A. Primary System

Consider a cell-structured OFDMA system. The base station(BS) lies at the center of cell with coverage radius R (seeFig. 1). Let W be the total bandwidth, which contains NF

subbands. One subband is allocated to one cell and is furtherdivided into N channels. Similarly, the timing axis is segmentedby the OFDMA symbol period. Then, the radio resource, whichis composed of channels and OFDMA symbols, is allocated toactive users in the cell. This information is usually specified ina frame header. Without loss of generality, we adopt the framestructure in IEEE 802.16 [6] as an example. The frame startswith a preamble, which is mainly used for synchronizationand channel estimation, followed by a frame header, includingDL_MAP and UL_MAP. In addition, the frame header alsodefines transmission parameters such as the forward error con-trol (FEC) code rate and the modulation in DL and UL bursts,respectively. To simplify the model without loss of generality,

assume that there are two data transmission rates, which isdetermined by AMC. Although the data transmission rate canadaptively be adjusted, the fundamental symbol rate is ratherfixed in most systems.

B. Cognitive Radios

We categorize received signals at cognitive radios within asubband of the primary system into the following six classes:C0 : wLP (t) background noise;C1 : st(t) primary system traffic signal;C2 : sc(t) primary system control signal;C3 : is(t) interfering traffic signal with the same funda-

mental symbol rate as the primary system;C4 : i(t) interfering traffic signal without the same fun-

damental symbol rate as the primary system;C5 : ic(t) interfering control signal.Here, wLP (t) denotes the equivalent bassband (BB) additivewhite Gaussian noise (AWGN) with zero mean, and the two-sided power spectrum density, i.e., N0 and st(t), denotes thetraffic signal of the primary system. In addition, is(t)/i(t)denotes the traffic signal from an interfering system with andwithout the same fundamental symbol rate as the primarysystem and is assumed white within a subband. By the centrallimit theorem [37], traffic signals are modeled as independentcircular symmetric complex Gaussian processes. Finally, sc(t)and ic(t) denote control and management signals from theprimary and interfering systems, respectively, and are period-ically transmitted. In the following, we just denote “control andmanagement signals” by “control signal” for simplicity.

By analyzing the received signals, cognitive radios determinethe operation state of the primary system in the following fivepossible states:S0 nonexistent, i.e., neither C1 nor C2 exists;S1 existent and inactive, i.e., C2 exists, but C1 does not exist;S2 existent, active, and high rate, i.e., C1 exists, and traffic is

transmitted at a high rate in a channel;S3 existent, active, and low rate, i.e., C1 exists, and traffic is

transmitted at a low rate in a channel;S4 existent, active, and idle, i.e., C1 exists, and no traffic is

transmitted in a channel.In this paper, we further consider the state existent and

inactive, in which primary users will enter the primary network,or more aggressively, cognitive radios could adjust systemparameters and connect to the primary BS in cooperative com-munications. In addition, to find out potential radio resource ofsecondary systems within occupied subbands, we require in-formation about data transmission rate and subband utilization,which is governed by the MAC protocol.

C. Cognitive Cycle

The operation of cognitive radios can be viewed as a finite-state machine and, thus, be considered by cognitive cycle [3],[7]. We facilitate our cognitive cycle, as shown in Fig. 2,with two sensing paths. Path A is responsible for detecting theexistence and activity of the primary system, whereas Path B isused to decode the frame header and determine frequency–time



Fig. 2. Cognitive cycle.

utilization. For each OFDMA symbol, we establish twoNF × N tables—the channel-state table and the radio re-source table—where the (n,m)th element records the opera-tion state of the primary system and maximum transmissionpower at cognitive radios of the mth channel within the nthsubband, respectively. The networking terminal operator inFig. 2 collects sensing information and makes optimal decisionof the operating mode, including configuration of softwareand hardware in MAC [30] and SDR, network routing andhandoff, and maintenance of requirements from upper layerapplications. Based on this system architecture, cognitive radionetworks can practically be implemented in future mobilecommunications.

1) Cognitive Cycle—Path A: RSSI is a simple widely ap-plied method in spectrum sensing; however, it is impossible todistinguish the signal of the primary system C1 from interferingsignals, i.e., C3 and C4. For example, in a 2.4-GHz ISMband, large RSSI may result from a microwave inside theband rather than the IEEE 802.11b network. In addition, noiseuncertainty significantly degrades energy detector performance[15]. Therefore, we have to extract features of the traffic signalby transformation, which suppresses noise and interferencesignals. A fundamental symbol rate is invariant or belongs to afinite set (e.g., scalable WiMAX); thus, we model traffic signalsas cyclostationary processes, which are induced by pulse trains,and detect such a feature by the spectral correlation func-tion [24], [25]. Although preliminary spectrum sensing exists[16]–[18], we adopt a spectral-line generator to meet the needfor quickness in cognitive radios.

However, in our system model, C1 and C3 have the samefundamental symbol rates. By means of a cyclic prefix (CP)in OFDMA systems, we can precisely detect the existence ofthe active primary system. Finally, BSs periodically broadcasta control signal (e.g., a beacon in IEEE 802.11) to maintain

mobile network operation; thus, we could identify the existenceof the inactive primary system by this property.

2) Cognitive Cycle—Path B: In Path A, we determined thestate of the primary system: 1) nonexistent S0; 2) existent andinactive S1; and 3) existent and active S2, S3, S4. We furtherconsider the channels that are occupied by transmissions andapply rate–distance nature so that simultaneous communicationis possible. The information about channel occupation anddata transmission rate can be obtained by analyzing the frameheader after cognitive radios achieve synchronization with theprimary BS.

3) Cognitive Information: We summarize a set of cognitiveinformation in spectrum sensing under OFDMA systems asfollows:

• RF signal processing: includes (carrier) frequency,bandwidth, RSSI, signal-to-noise-and-interference ratio(SINR), and noise power;

• BB predetection signal processing: includes fundamentalsymbol rate, carrier and timing, pilot signal, and channelfading;

• BB post-detection signal processing: includes systemidentification, modulation parameters, and FEC typeand rate;

• Network processing information: includes multiple accessprotocol and radio resource allocation.

Suppose that cognitive radios know a priori informationabout potential primary systems that include frequency plan-ning, frame structure, subcarrier structure (e.g., fast Fouriertransform (FFT) size and pilot positions), transmission parame-ters (e.g., fundamental symbol rate, CP length, and FEC type),and tolerant interference of primary systems, because spectrumusage is regulated, and system specifications are well defined.



III. DISCRIMINATION OF THE STATE

OF THE PRIMARY SYSTEM

In this section, we propose a simple design to identify theexistence and activity of the primary (OFDMA) system withinone subband by the RSSI, fundamental symbol rate, cyclicproperty, and control signal of the primary system, where RSSIis simply an energy detector. In general, we do not know thea priori probability of existence of the primary system. Hence,we adopt an NP criterion [36] to design the spectrum-sensingprocedure.

A. Fundamental Symbol Rate

If there exists traffic signal from the primary system, thereceived signal at cognitive radios may be written as

z(t) =�{

ej2πfct

( ∞∑n=−∞

x(n)h(t − nTs) + wLP (t)

)}

=�{ej2πfct (st(t) + wLP (t))

}= �{y(t)} . (1)

Here, fc denotes the carrier frequency, Ts denotes the reciprocalof the fundamental symbol rate, h(t) denotes the pulse-shapingfilter, and x(n) denotes the transmitted data in time domain.Alternatively, we have (2), shown at the bottom of the page,wherein Xm(k) denotes modulated data at the kth subcarrier inthe mth OFDMA symbol, NFFT is the FFT size, and NCP isthe CP length. Without loss of generality, h(t) is assumed thesquare-root raised cosine filter with a roll-off factor less than100% [32], and (45) in Appendix A becomes

E[z2(t)

]≈ 1

2

(σ2

X

Ts+ σ2

w

)+

σ2X

Ts�{

Z1ej2π t

Ts

}(3)

where

Zm =12π

∞∫−∞

H(jω)H∗ (j(ω − 2πm/Ts)) dω. (4)

Noise power σ2w is shown in (44) in the Appendix, Z−m =

Z∗m, and Z0 = 1. Note that the component at the fundamen-

tal symbol rate is independent of noise power, and thus, thechallenge of noise uncertainty in an energy detector is released.However, the received signal power in the second term of (3)is reduced by factor Z1. Therefore, the performance of thedetector depends on Z1. Based on (4), we conclude that, if h(t)has larger bandwidth (i.e., a higher roll-off factor), the detectorhas better performance. A similar phenomenon happens intiming tracking systems [33], [34]. Furthermore, this algorithmcan be implemented at the radio frequency (RF) part in front ofan analog–digital converter (ADC); thus, it can be done quickly.

B. CP of OFDMA Signal

The initial setup for detecting the existence of CP is similar to[38]. Collect 2NFFT + NCP samples with sampling rate 1/Ts

and assume that this region contains one complete OFDMAsymbol. The detection problem becomes

H0 :r(n)= w0(n), n=0, 1, . . . , 2NFFT+NCP−1H1 :r(n)= s(n)+w1(n), n=0, 1, . . . , 2NFFT+NCP−1.

Under H1, there exist timing offset (TO) θ and frequency offsetε due to the lack of synchronization. Then, the traffic signal ofthe primary system becomes

s(n) = x(n − NCP − θ)ej2πεn/NFFT . (5)

Let I and I be two sampling intervals, which contain the CPand its replica, respectively, i.e.,

I = {θ, θ + 1, . . . , θ + NCP − 1}I = {θ + NFFT, θ + NFFT + 1, . . . , θ + NB − 1}

where NB = NFFT + NCP. If there exists the primary system,the samples in the CP and their copies are correlated [38], or

E [r(n)r∗(n + m)|H1] =

⎧⎨⎩σ2s + σ2

w, m = 0σ2

se−j2πε, m = NFFT, n ∈ I0, otherwise.

(6)

We model w1(n) as a white Gaussian process with zero meanand variance σ2

w, and E[|s(n)|2] = E[|x(n)|2] = σ2s . On the

other hand, w0(n) denotes the superposition of interfering sig-nals and background noise and is modeled as a white Gaussianprocess with zero mean and variance σ2 = σ2

s + σ2w, i.e.,

E [r(n)r∗(n + m)|H0] ={

σ2 m = 00, otherwise.

(7)

We assume that the total powers under both hypotheses are thesame, which leads to the worst case, because the energy detectordoes not work. Then, the likelihood ratio test (LRT) becomes(see Appendix B)

M(r) = |S(θ)| cos (2πε + ∠S(θ)) − ρ

2P (θ)

H1≥<H0

τCP (8)

where

S(θ) =∑n∈I

r(n)r∗(n + NFFT) (9)

P (θ) =∑n∈I

[|r(n)|2 + |r∗(n + NFFT|2)

](10)

ρ = SINR/(SINR + 1) (11)

x (n + (NFFT + NCP)m) =

{1√

NFFT

(∑NFFT−1k=0 Xm(k)ej2π kn

NFFT

), if n ∈ {0, 1, . . . , NFFT − 1}

x (n + (NFFT + NCP)m + NFFT) , if ∈ {−NCP,−NCP + 1, . . . ,−1}, m ∈ Z (2)



and SINR = σ2s/σ2

w. The decision metric M(r) only dependson the samples in the CP and their copies whose energy P (θ)and correlation S(θ) are considered.

With the unknown parameters (i.e., θ, ε, σ2, and SINR) in (8),it becomes a composite detection problem, which is desirablefor finding the uniformly most powerful (UMP) test [36]. How-ever, the UMP test does not exist, because the decision regiondepends on θ. In the absence of the UMP test, generalized LRT(GLRT) can be applied. We assume that the SINR is known andhas (see Appendix B)

M(r) =∑

n |r(n)|2∑n |r(n)|2 − 2ρ

1−ρ2 maxθ

{|S(θ)| − ρ

2P (θ)} H1≥<H0

τCP.

(12)

Note that this detector is just the ratio of estimations of the totalenergy under two hypotheses, and the frequency offset does notaffect (12). In addition, we evaluate the probability of a falsealarm in Appendix C and have

PF =

∞∫τCP

f (M(r)|H0) dM ≈ Q

(−μ1 − μ2√

σ21 + σ2

2

)(13)

where f(·) is a probability density function, Q(x) denotesthe right-tail probability of a Gaussian random variable withzero mean and unit variance [36], and (14)–(17), shown atthe bottom of the page, holds. By taking the inverse of Q(x),we can obtain the optimal threshold under the NP criterion.Next, we investigate a special case, i.e., ρ = 0, which resultsin the detection of a white random signal under AWGN withunknown noise power, and the decision metric in (12) becomesM(r) = 1. This case explains why a simple energy detectordoes not work with unknown noise power.

Finally, to deal with unknown SINR, note that (12) and (13)depend on SINR via ρ, and we design a robust CP detector at thetarget SINR SINR. The parameters ρ and τCP can be calculatedin advance by (11) and (13), with SINR = SINR. Furthermore,this detector explores the CP property of the target OFDMAsystem; thus, it can be used to recognize among OFDM-basedsystems with different system parameters NFFT and NCP (e.g.,IEEE 802.11a and IEEE 802.16 in a 5-GHz unlicensed band).

C. Control and Management Signal

We do not specify control signals of potential primary sys-tems but model them as white Gaussian processes. Therefore,

this detector is robust to system variation. The control signal ofthe primary system is modeled as a zero-mean white Gaussianprocess with transmission-period MC samples and duration NC

samples. To detect the control signal, we collect MC samplesand assume that this interval contains one control signal period.The detection problem turns out to be

H0 : r(n) = w(n), n = 0, 1, . . . ,MC − 1

H1 : r(n) ={

w(n), n /∈ Jsc(n) + w(n), n ∈ J

where J denotes the sampling interval, which contains thecontrol signal, or J = {φ, φ + 1, . . . , φ + NC + 1}, where φdenotes the TO of the control signal. Note that the frequencyoffset is ignored, because it contributes phase shift, but onlya magnitude of the received signal provides information in alikelihood function. In addition, the statistics of the receivedsignal under hypotheses are shown as follows:

E [r(n)r∗(n + m)|H1] =

⎧⎨⎩σ2s + σ2

w, m = 0, n ∈ Jσ2

w, m = 0, n /∈ J0, otherwise

(18)

E [r(n)r∗(n + m)|H0] ={

σ2w, m = 0

0, otherwise.(19)

The GLRT becomes

M(r) = maxφ

⎧⎨⎩φ+NC−1∑

n=φ

|r(n)|2⎫⎬⎭

H1≥<H0

τC . (20)

This detector finds the TO and measures the energy of thereceived signal in the interval of the control signal. Next, werelease the assumption of knowing noise power, which occurs indetecting the superposition of the control signal of the primarysystem and noncollaborative interference or background noisewith unknown power. In addition to noise power, signal poweris another unknown parameter under H1. Then, we have (seeAppendix D)

M(r)=maxφ

{MC ln

(∑n

|r(n)|2)

− NC ln

(∑n∈J

|r(n)|2)

−(MC − NC) ln

(∑n/∈J

|r(n)|2)} H1

≥<H0

τC . (21)

μ1 = (2NFFT − NCP)(1 − τCP) (14)

σ21 = (2NFFT − NCP)(1 − τCP)2 (15)

μ2 = 2NCP − 2NCP − ρ√

πNCP

1 − ρ2τCP (16)

σ22 = 2NCP

(1 − 2

1 − ρ√

π(√

NCP + 1 −√

NCP)1 − ρ2

τCP +1 + 2ρ2(1 − π/4) − 2ρ

√π(√

NCP + 1 −√

NCP)(1 − ρ2)2

τ2CP

)(17)



Finally, consider a situation where a nontarget system existsand broadcasts control signal. If cognitive radios only measurethe received energy, they fail to discriminate between thissystem and the primary system. Alternatively, it is reasonableto assume that periods of the control signal from differentsystems are distinct, because each standard is designed forspecific purposes (e.g., coverage and data rate), which resultsin individual timing parameters. Then, cognitive radios cantrack the period of the control signal from the primary systemto detect the control signal. We rewrite the control signal asfollows:

r(n) = sc(n)∞∑

m=−∞g(n − mMC) + w(n)

n = 0, 1, . . . , LMC − 1 (22)

where

g(n) ={

1, n = 0, 1, . . . , NC − 10, otherwise

(23)

and L denotes the number of periods that we observe. To trackthe period of the control signal, we adopt an approach similarto fundamental-symbol-rate tracking, i.e., squaring the receivedsignal and then extracting the magnitude at the fundamentalfrequency of the control signal 1/MC by Fourier transform. Itis easy to show that

E[|r(n)|2

]= σ2

s

∞∑m=−∞

g(n − mMC) + σ2w

n = 0, 1, . . . , LMC1. (24)

We observe that (24) is a periodic function with period MC , orspecifically, the magnitude at frequency 1/MC is

Lsin πNC/MC

sinπ/MCσ2

s . (25)

To provide high throughput, the control signal is not frequentlytransmitted, and thus, MC is large, which leads to long sensingduration. However, the primary BSs are reasonably assumed tobe fixed; thus, this process is only initially taken.

Furthermore, this detector can also be used to detect OFDM-based signal with zero padding in the prefix, such as multi-band OFDM. However, in detecting the control signal bythe received energy, we assumed that the observation intervalcontains one control signal period, which is true if MC NC . For OFDM-based signals, MC = NFFT + NCP, NC =NFFT, and the aforementioned condition is not satisfied. Tosolve this problem, we could collect 2NFFT + NCP sam-ples, as we did in the CP detector, and the optimal detec-tor has similar structure as in (21). Alternatively, we coulddetect such OFDM-based signals by tracking the symbolperiod similar to the method in detecting the fundamentalsymbol rate.

IV. AVAILABLE RADIO RESOURCE TO

SECONDARY SYSTEMS

To take advantage of the rate–distance nature, we reconsiderthe distance relation in Fig. 1 and the primary communicationlink to utilize some channel. Let SINRmin be the minimumSINR at which the primary receiver Rx1 maintains the currentlink quality. Note that this value will depend on the modula-tion scheme and the FEC type and rate. Thus, we obtain aninequality, i.e.,

SINR1 =G11P1

G21P2 + N1≥ SINRmin (26)

where Pi denotes the transmission power at Txi, Ni denotes thenoise power at Rxi, and Gij denotes the power loss from Txi toRxj . Then, we have

P2,max =1

G21

(G11P1

SINRmin− N1

)=

ICR

G21(27)

where ICR denotes the maximum-tolerance interference ofthe primary system at the channel. ICR depends on the sig-nal quality of the primary communication link; thus, we canroughly infer it from the transmission rate and assume that itis known. In addition, “distance” is actually a measure of thereceived signal power; thus, we have to specify the relationbetween received power and propagation distance. Without lossof generality, we adopt large-scale path loss that includes log-distance path loss and log-normal shadowing [28], becausespectrum sensing does not treat instantaneous signal reception.The power loss between two nodes G is given by

G = Kd−α10β/10 (28)

where K is a normalization constant, d is the distance betweenthese two nodes, α is a path-loss exponent, and β is a shadowingparameter, which is modeled as a Gaussian random variablewith zero mean and variance σ2

β . In the following, we condi-tionally determine the radio resource on whether informationabout the distance between Tx2 and Rx1r is available or not,which corresponds to uplink and downlink environments.

A. Radio Resource: Uplink

In uplink, Rx1 is the primary BS, and cognitive radios cantrace its location by the received signal strength of a preamble.Then, we get the following inequality:

KP2r−α10β/10 ≤ ICR. (29)

Due to shadowing factor β, the interference level is a randomvariable and, hence, can only be guaranteed in probabilitysense. The optimal criterion is maximum transmission powersuch that the probability of interfering with the primary systemis less than ξ, i.e.,

P2,max = arg maxP2

{Pr

(KP2r

−α10β/10 > ICR

)≤ ξ

}.



This criterion has the same concept as in the NP criterion, andwe have

PUL2,max =

ICRrα

K10−σβQ−1(ξ)/10. (30)

Note that PUL2,max is proportional to ICR.

B. Radio Resource: Downlink

In downlink, Rx1 becomes the primary mobile station (MS),and it is hard for cognitive radios to estimate the location ofthe MS. It is reasonable to assume that MSs are uniformlydistributed around a coverage region; thus, by the Bayesianapproach, we have

Pr{P2G21 > ICR} =

∞∫0

Q

(1σβ

10 log10

(ICRrα

P2K

))dF (r)

(31)where

F (r) =

{AH(r,c,D)

πD2 , high-rate regionAL(r,c,D,R)π(R2−D2) , low-rate region.

(32)

In (32) (see Appendix E), we have

AH(r, c,D)=

⎧⎨⎩πr2U(D−c), 0≤r< |D−c|θ2r

2+θ1D2−cv, |D−c|≤r<D+c

πD2, D+c≤r

(33)

AL(r, c,D,R)= AH(r, c, R)−AH(r, c,D) (34)

where U(x) is the unit step function. In addition

u =c2 + D2 − r2

2c(35)

v =√

D2 − u2 (36)

θ1 = cos−1(u/D) (37)

θ2 = cos−1 ((c − u)/r) (38)

and θ1, θ2 ∈ [0, π]. Then

PDL2,max = arg

P2

⎧⎨⎩∞∫

0

Q

(1σβ

10 log10

(ICRrα

P2K

))dF (r) = ξ

⎫⎬⎭(39)

and can numerically be obtained. By similar procedures, we caneasily generalize to multilevel data transmission rates.

We now acquire a rough range of ICR from a priori infor-mation; however, it could dynamically be calculated accordingto the instantaneous link quality of the primary system. Ifcognitive radios can exchange information with the primarysystem, i.e., collaborative coexistence [29], after achievingsynchronization with the primary BS, they can more efficientlysqueeze the radio resource and further achieve channel capacity.

V. SPECTRUM-SENSING PROCEDURE

The spectrum sensing algorithm serially senses the wholespectrum subband by subband. To quickly acquire spectrumutilization within a subband, we discriminate the traffic signalof the primary system from noise and interference by receivedenergy and extracting signal feature, including the fundamentalsymbol rate and CP, and then assure the existence of the activeprimary (OFDMA) system. We then consider the existenceof the inactive primary system by means of control signalunder three conditions: 1) background noise C0; 2) interferingtraffic signal C3 and C4; and 3) interfering control signal C5.Although there exists an active primary system, we acquire theutilization status of each channel along the time axis to furtherincrease spectrum efficiency by decoding the frame headerand then determining the radio resource to secondary systems.This general sensing algorithm, which can be applied to IEEE802.16 and other OFDMA systems by adjusting the system pa-rameters Ts, NFFT, NCP,MC , NC , is summarized as follows.

1) Initially, set the channel-state table as S0 and reset theradio resource table.

2) For n = 1 to NF (subband), do the following substeps.Then, go to step 3.a) Measure the RSSI and distinguish the hypothesis test.

H0: traffic signals do not exist.H1: traffic signals exist.If H0 is true, go to step 2.f; otherwise, go tostep 2.b.

b) Track the fundamental symbol rate of the primarysystem.

H0: traffic signals with the fundamental symbol rateof the primary system do not exist.H1: traffic signals with the fundamental symbol rateof the primary system exist.If H0 is true, go to step 2.g; otherwise, go tostep 2.c.

c) By the CP of the OFDMA signal, separate the non-collaborative interference and traffic signal from theprimary system.

H0: traffic signals with the CP property of theprimary system do not exist.H1: traffic signals with the CP property of theprimary system exist.If H0 is true, go to step 2.g; otherwise, go tostep 2.d.

d) Synchronize with the primary BS, including carrierand timing synchronization, and channel estimationby the preamble [39]. Then, go to step 2.e.

e) Decode the frame header (DL_MAP and UL_MAPin this case) and obtain the transmission parame-ters of the primary system, including the FEC rate,modulation scheme, and resource allocation. Theseparameters are used to set the nth row of the channel-state table from S2 to S4. Then, go to step 2.i.

f) Measure the energy of the control signal and detect thehypothesis test.

H0: control signals do not exist.H1: control signals exist.



Fig. 3. Sensing tree of the proposed spectrum sensing procedure.

If H0 is true, go to step 2.i; otherwise, go tostep 2.h.

g) Extract the control signal of the primary system fromnoncollaborative interference.

H0: the control signal of the primary system doesnot exist.H1: the control signal of the primary system exists.If H1 is true, set the nth row of the channel-statetable as S1. Then, go to step 2.i.

h) Track the period of the control signal and discriminatebetween control signals from the primary system andother systems.

H0: the control signal of the primary system doesnot exist.H1: the control signal of the primary system exists.If H1 is true, set the nth row of the channel-statetable as S1. Then, go to step 2.i.

i) (optional) Identify the system by the fundamentalsymbol rate, cyclic properties of OFDMA systems,and control signal. This step is critical information incognitive and cooperative networking [26]. Then, goto step 2.

3) According to the channel-state table, set the radio re-source table by (30) and (39). Then, end the sensingprocedure.

In steps 2.4 and 2.5, if synchronization or packet decodingcannot be achieved due to the lack of frame information, thisinstance leads to a degenerative case, in which S2, S3, andS4 merge to one state, and we only need two NF × 1 tables.To illustrate the spectrum sensing procedure, we establish asensing tree as shown in Fig. 3. Here, we assume that thecontrol signal and traffic signal of a system cannot exist atthe same time. Then, there are 15 possible combinations ofreceived signal at cognitive radios as follows:

Π1 =C0 Π2 = C1 ∩ C0 Π3 = C2 ∩ C0

Π4 =C3 ∩ C0 Π5 = C4 ∩ C0 Π6 = C5 ∩ C0

Π7 =C1 ∩ C3 ∩ C0 Π8 = C1 ∩ C4 ∩ C0

Π9 =C1 ∩ C5 ∩ C0 Π10 = C2 ∩ C3 ∩ C0

Π11 =C2 ∩ C4 ∩ C0 Π12 = C2 ∩ C5 ∩ C0

Π13 =C3 ∩ C4 ∩ C0 Π14 = C1 ∩ C3 ∩ C4 ∩ C0

Π15 =C2 ∩ C3 ∩ C4 ∩ C0.

As shown in the figure, there may be several possiblesignals that belong to the same state. Transmission of otherpotential systems should be honored; thus, a similar sensingprocedure can also be applied to other potential systems.By combining these channel-state tables and radio resourcetables, we obtain complete information of spectrum usageand corresponding maximum transmission power. Finally, tofulfill this sensing/cognition cycle, the spectrum sensing blockdiagram is illustrated in Fig. 4. The functionalities are labeledin corresponding blocks.

VI. NUMERICAL RESULTS

A. Detector of the State of the Primary System

To illustrate detector performance, we show the probabilityof detection PD versus the SINR under constraint on theprobability of false alarm PF < 0.05 in AWGN and frequency-selective fading channels. We adopt SUI-3 Channel [42], whichis the channel model for IEEE 802.16. We develop the theoryfor spectrum sensing, but it is still effective for multipathchannels by simulation. In addition, to protect the primarysystem, the probability of detection must be high enough,e.g., 0.95. Therefore, we also investigate the required sensingduration to achieve system requirement, PF < 0.05, PD >0.95, at SINR = 0 dB. According to IEEE 802.16, we set thefundamental symbol rate to 20 MHz, FFT size NFFT = 1024,and CP length NCP = NFFT/32 = 32.

1) Fundamental-Symbol-Rate Detector: We first showspectrum magnitude with a roll-off factor equal to 0.35 and0.55, respectively, in Fig. 5(a). It is easy to observe the tone atthe fundamental symbol rate. As our analytical result, noisedoes not affect magnitude at the fundamental symbol rate butonly at the DC component, and the one with the larger roll-offfactor has larger magnitude at the fundamental symbol rate.However, note that spectrum magnitude below 10 MHz is largeto a certain degree, which comes from the Signal × Signalterm due to the randomness of the signal and is called selfnoise [35]. Therefore, to design a multisymbol-rate detector,asymmetric mutual interference between decision metricsmust be considered. This task is similar to [43], where thenumber of active users in CDMA systems is identified, andtherefore, subspace signal processing and the multiple signalclassification algorithm can be applied.



Fig. 4. Spectrum sensing block diagram of OFDMA systems.

Fig. 5(b) shows the probability of detection versus SINR andsensing duration (T2 in Fig. 4) in AWGN and SUI-3 fadingchannels. We observe that a larger roll-off factor outperforms.We also note that the fading channel does not much degradedetector performance, particularly in a large roll-off factor,because the periodicity of pulse trains is retained under thefading channel. Although the fading channel makes approxi-mate white OFDMA signal to colored signal, if pulse shapinghas a larger roll-off factor, the colored part can be ignored,like what we did in Appendix A. Therefore, the detector isrobust to fading channels. In addition, note that the probabilityof detection in the fading channel approaches that in AWGNwhen the roll-off factor = 0.35 when SINR is below −3 dB,

because noise dominates detector performance at low SINR.In addition, to achieve system requirement, sensing durationis equal to 1.6 μs when the roll-off factor = 0.55. This resultreveals the quickness of this detector.

2) CP Detector: The probability of detection versus SINRand effective sensing duration NCP under AWGN and SUI-3fading channels are depicted in Fig. 6. We compare the CPdetector with a known total power, i.e., (8), and robust CP de-tector, i.e., (12), with SINR equal to 0 dB, and observe that theyhave the same performance in the AWGN channel. Therefore,the robust CP detector shows its robustness to noise and SINRuncertainty. However, in a fading channel, the robust CP de-tector experiences more degradation than the CP detector with



Fig. 5. Fundamental symbol rate detector. (a) Spectrum magnitude aftersquarer. (b) Probability of detection versus SINR and sensing duration underconstraint PF < 0.05.

known total power, because the energy estimator in the robustCP detector cannot work well in fading channels. To achievesystem requirement in fading channels, NCP has to be largerthan 104 samples, or we have to collect four complete OFDMAsymbols. However, if there is constraint on sensing duration,exploring spatial diversity by multiple-input–multiple-output(MIMO) or cooperative spectrum sensing [19]–[22] is a feasiblesolution.

We also investigate the effect of the TO estimation errorin the top figure in Fig. 6. Although detector performancedegrades below SINR = 0 dB, the probabilities of detection ofthese two detectors approach one at SINR = 2 dB. Therefore,our CP detectors are robust to timing error.

3) Control Signal Detector: The period of control signalMC is relatively large (on the order of frame period) in practice;thus, we only show the effectiveness of the detector and setMC = 512 and NC = 16. Similar to the CP detector, the prob-ability of detection versus SINR and effective sensing duration

Fig. 6. Probability of detection versus SINR and sensing duration underconstraint PF < 0.05 for the CP detector with known total power and robustCP detector.

NC under AWGN and SUI-3 fading channels are illustratedin Fig. 7. We compare the control signal detector with andwithout knowledge of noise power, i.e., (20) and (21), and thereis observable degradation due to the lack of knowledge of noisepower. We also show the performance of detecting the controlsignal by tracking the period of the control signal and the effectof observation interval (the number of periods L). Simulationresults are presented in Fig. 7(b). The result with a longerobservation interval has better performance but experiencesmore performance degradation in the fading channel.

B. Radio Resource to Secondary Systems

In this section, we normalize the cell coverage of the primarysystem R to unity and combine normalization factor and K totransmission power at cognitive radio. We set the radius of thehigh-rate region D = 0.4, the distance between the cognitiveradio transmitter Tx2 and Tx1c = 0.5, path loss exponent α =4.725, and the variance of shadowing parameter σ2

β = 8.2. Theparameters are set according to terrain type B (intermediatepath loss) [42], with the height of the BS being equal to 20 m.

In the top row of Fig. 8(a), we present the relation betweenthe scaled transmission power at Tx2P2 and the probability ofinterfering with the primary system ξ under different tolerantlevels ICR in uplink. The normalized distance between theprimary BS and Tx2 is set to be 0.5. Simulation and analyticalresults are consistent, and ξ dramatically increases under toughconstraint (i.e., a lower tolerance level). The same relationis illustrated in the downlink environment in the bottom rowof Fig. 8(a), where high- and low-rate regions are shown forcomparison. It is interesting to observe that ξ more graduallyincreases when the primary MS lies in the low-rate region. Inaddition, Fig. 8(b) illustrates the maximum transmission powerP2,max at Tx2 if ξ is constrained to 0.1. The results show thatcognitive radios deliver more radio resource in uplink wherecognitive radios know the distance of the primary receiver Rx1

and Tx2, particularly at a high-tolerance level. In addition, note



Fig. 7. Control signal detector. (a) Probability of detection versus SINR andsensing duration under constraint PF < 0.05 for control signal detector withand without noise power. (b) ROCs of control signal period tracking.

that as our derivation that radio resource to secondary systems islinearly proportional to a tolerable interference level. In down-link, cognitive radios can utilize more radio resources whenthe primary MS lies in a low-rate region, because there is ahigher possibility for the primary MS in a low-rate region to beapart from the cognitive radio transmitter. These results suggestthat the radio resource to secondary systems heavily dependson the information available to cognitive radios; therefore, indownlink, utilization in the spatial domain should be exploitedby MIMO or cooperative spectrum sensing.

VII. CONCLUSION

To achieve effective spectrum sensing for cognitive radionetworks (beyond traditional cognitive radio links) by takingadvantage of the rate–distance nature, we have proposed toacquire a set of cognitive information for OFDMA systems.To avoid interfering with the overlay primary system, cognitiveradios could determine the operation state of the primary sys-

Fig. 8. (a) Scaled transmission power at the cognitive radio versus theprobability of interfering with the primary system. (b) Tolerable interferenceto the primary system versus available radio resource to the secondary system.

tem, including the frequency band, existence, activity, resourceallocation, and data-transmission rate. Spectrum sensing hastherefore been generalized to multistate discrimination and isillustrated in a sensing tree. Elaborating on existing energydetection and cyclostionary feature detection, we have designedthe optimal detectors to recognize the operation state of theprimary system in the generalized system model. Simulationresults showed that these detectors satisfactorily achieve systemrequirements (i.e., PF < 0.05, PD > 0.95, SINR = 0 dB) inAWGN and frequency-selective fading channels by increasingsensing duration.

After identifying the operation state of the primary sys-tem, we have generalized the conventional cognitive radio andpioneerly sensed the radio resource in the busy duration ofthe primary system by considering the rate–distance natureto improve the opportunity to use spectrum. We have shownthat radio resource to secondary systems critically depends onthe information (e.g., the link quality of the primary systemand distance information) available to cognitive radios and islinearly proportional to the tolerable interference level of theprimary system.



Furthermore, these methodologies can be applied to systemidentification, which is critical information in cognitive andcooperative networking. By adjusting the sensing parametersof the cognitive radio, our proposed sensing procedure can beextended to state-of-the-art OFDMA systems and even to mostmobile communication systems, along with MIMO processingtechnologies.

APPENDIX ADERIVATION OF (3)

By the circular symmetric property, we have

E[z2(t)

]= 1/2E

[|y(t)|2

]= 1/2E

[|st(t)|2 + |wLP (t)|2

].

(40)

The second equality comes from the independence betweenst(t) and wLP (t). The randomness of st(t) comes from datax(n); thus, we first find out the statistical characteristics ofx(n). Let

Rxx(n1, n2,m1,m2) = E [x(n1 + NBm1)x∗(n2 + NBm2)](41)

where NB = NFFT + NCP. By the existence of the CP,we have

Case 1 : n1, n2 ∈ [0, NFFT − 1]

Rxx(n1, n2,m1,m2) = σ2Xδm1m2δn1n2

Case 2 : n1, n2 ∈ [−NCP,−1]

Rxx(n1, n2,m1,m2) = σ2Xδm1m2δn1n2

Case 3 : n1 ∈ [−NCP,−1], n2 ∈ [0, NFFT − 1]

Rxx(n1, n2,m1,m2) = σ2Xδm1m2δn1+NFFT,n2

Case 4 : n1 ∈ [0, NFFT − 1], n2 ∈ [−NCP,−1]

Rxx(n1, n2,m1,m2) = σ2Xδm1m2δn1−NFFT,n2

where σ2X = E[|X(k)|2]. The autocorrelation function of x(n)

depends on the absolute value of the time index; thus, theoutput signal of the OFDMA system is not a stationary process[37]. However, the nonstationary property can be ignored byconsidering (42), shown at the bottom of the page. Note thatthe second term comes from the nonstationary property of theOFDMA signal. In the case where the pulse-shaping filter isa raised-cosine filter, h(t) has fast decay outside Ts in the timedomain. As a result, its contribution can be ignored. Then, usingPoisson’s sum formula [32], we have

∞∑m=−∞

|h(t − mT )|2 =1Ts

∞∑n=−∞

Znej2πnt/Ts (43)

where Zn is shown in (4). On the other hand, it is obvious that

E[|wLP (t)|2

]= σ2

w = N0W/NF . (44)

By inserting (42)–(44) into (40), we can get

E[z2(t)

]≈ σ2

X

2Ts

∞∑m=−∞

Zmej2π mtTs +

σ2w

2. (45)

APPENDIX BLRT AND GLRT OF THE CP DETECTOR

The likelihood function under two hypotheses can be writ-ten as

f(r|H0) =∏n

f (r(n)|H0) (46)

f(r|H1) =∏n∈I

f (r(n), r(n + NFFT)|H1)∏

n/∈I,I

f (r(n)|H1)

(47)

where

f (r(n)|Hi) =exp

(−|r(n)|2σ2

s+σ2w

)π (σ2

s + σ2w)

, i = 0, 1 (48)

and

f(r(n), r(n+NFFT)|H1)

=exp

(− (|r(n)|2+|r(n+NFFT)|2)−2ρ�{ej2πεr(n)r∗(n+NFFT)}

(1−ρ2)(σ2s+σ2

w)

)π2(1−ρ2)(σ2

s +σ2w)

.

(49)

As a result, the LRT becomes

K1 exp[K2

(S(θ) cos (2πε + ∠S(θ)) − ρ

2P (θ)

)] H1≥<H0

τ

(50)

where K1 and K2 are constants, which are independent of thereceived signal. Finally, by discarding constants, we can get (8).

If there are unknown parameters, we have to derive theGLRT. Under H0, the maximum likelihood estimation (MLE)of the total power can easily be derived as

σ20 =

12NFFT + NCP

∑n

|r(n)|2 . (51)

E[|st(t)|2

]= σ2

X

∞∑m=−∞

[|h(t − mT )|2 + 2�

{ −1∑n=−NCP

h (t − (n + NBm)Ts) × h∗ (t − (n + NBm + NFFT)Ts)

}](42)



Under H1, the MLE of θ and ε have been derived in [38], or

θML = arg maxθ

{|S(θ)| − ρ

2P (θ)

}εML = − 1

2π∠S(θML).

With some algebraic manipulations, we can get the MLE of thetotal power under H1. We have

σ21 =

∑n�∈I,I

|r(n)|2 +P (θML)−2ρ|S(θML)|

1−ρ2

2NFFT + NCP. (52)

Note that the second term in the numerator is an energy estima-tor of the correlated signal. Finally, the GLRT becomes

f(r|σ21 , θML, εML,H1)f(r|σ2

0 ,H0)=(

11−ρ2

)NCP(

σ20

σ21

)2NFFT+NCPH1≥<H0

τ.

(53)

With further simplification, we can obtain (12).

APPENDIX CPROBABILITY OF A FALSE ALARM IN (13)

To derive the probability of a false alarm in (13), we firstderive the statistics of a|S(θ)| + bP (θ), where a and b areconstants, whereas S(θ) and P (θ) are shown in (9) and (10).

1) Mean: We have

E [a |S(θ)| + bP (θ)] = aE [|S(θ)|] + bE [P (θ)] . (54)

Thus, we separately derive the mean as follows. Under H0,{r(n), n = 1, 2, . . . , 2NFFT + NCP} are independent identi-cally distributed (i.i.d.) Gaussian random variables with zeromean and variance σ2. In the first term, S(θ) is the sum of NCP

i.i.d. random variables, and we can approximate it as a Gaussianrandom variable by the central limit theorem. The mean andvariance of S(θ) are

E [S(θ)] =∑n∈I

E [r(n)r∗(n + NFFT)] = 0 (55)

Var (S(θ)) =∑n∈I

Var (r(n)r∗(n + NFFT)) = NCPσ4. (56)

Therefore, |S(θ)| is a Rayleigh random variable, and

E [|S(θ)|] =√

πNCP

2σ2. (57)

In terms of P (θ), the observation spaces are 2NFFT +NCP i.i.d. Gaussian random variables with zero mean andvariance σ2; thus, {|r(n)|2, n = 1, 2, . . . , 2NFFT + NCP} arei.i.d. exponential random variables [37] with parameter 1/σ2.Then, P (θ) is a Gamma random variable with parameter(2NCP, σ2), and

E [P (θ)] = 2NCPσ2. (58)

By inserting (57) and (58) into (54), we have

E [a |S(θ)| + bP (θ)] =(

a

√πNCP

2+ 2bNCP

)σ2. (59)

2) Variance: Similarly, we have

Var (a |S(θ)| + bP (θ)) = a2Var (|S(θ)|)+ b2Var (P (θ)) + 2abCov (|S(θ)| , P (θ)) . (60)

Thus, we discuss these three terms, respectively. For the firsttwo terms, from the last part, we have

Var (|S(θ)|) = NCP

(1 − π

4

)σ2 (61)

Var (P (θ)) = 2NCPσ4. (62)

For the last term, by definition [37], we have

Cov (|S(θ)| , P (θ)) = E [|S(θ)|P (θ)] − E [|S(θ)|] E [P (θ)] .(63)

In (63), the second term is the product of (57) and (58), and wederive the first term in the following equation:

E [|S(θ)|P (θ)] =∑m∈I

E

[ ∣∣∣∣∣∑n∈I

r(n)r∗(n + NFFT)r2(m)

∣∣∣∣∣+

∣∣∣∣∣∑n∈I

r(n)r∗(n + NFFT)r2(m + NFFT)

∣∣∣∣∣]. (64)

Similarly, we can get

E

[∑n∈I


]= 0 (65)

Var

(∑n∈I


)= 2(NCP + 2)σ8. (66)

However, it is hard to specify the joint PDF of this variable,which is a product of the correlated Gaussian and exponen-tial random variable. By adjusting the coefficients, we canapproximate

E [|S(θ)|P (θ)] ≈ NCP

√π(NCP + 1)σ4. (67)

Finally, by inserting (57), (58), (61), (62), and (67) into (60),we have

Var (a |S(θ)| + bP (θ)) = NCPσ4[a2(1 − π/4) + 2b2

+ 2ab√

π(√

NCP + 1 −√

NCP)]. (68)

Based on (12) and (13), we have

PF = Pr

⎛⎝ ∑n/∈I,I

|r(n)|2 + P (θ)∑n/∈I,I

|r(n)|2 + P (θ)1−ρ2 − 2ρ|S(θ)|

1−ρ2

> τCP|H0

⎞⎠= Pr(X + Y > 0|H0) (69)



where

X = (1 − τCP)

∑n/∈I,I

|r(n)|2

σ2(70)

Y =2ρτCP

(1 − ρ2)σ2|S(θ)| +

(1 − τCP

1 − ρ2

)P (θ)σ2

. (71)

The summation intervals of X and Y are nonoverlapping; thus,X and Y are independent random variables. Based on (69),X is the sum of i.i.d. random variables; thus, its distributioncan be approximated by Gaussian. In terms of Y , although itis the weighted sum of a Rayleigh random variable S(θ) and aGamma random variable P (θ), this term is dominated by P (θ).P (θ) is also the sum of i.i.d. random variables; thus, the ran-dom variable Y can also be approximated by Gaussian. Then,we have

X|H0 ∼ N(μ1, σ

21

); Y |H0 ∼ N

(μ2, σ

22

)where μ1, μ2, σ2

1 , and σ22 are shown in (14)–(17). Finally, we

have (13).

APPENDIX DGLRT OF THE CONTROL SIGNAL DETECTOR

The likelihood functions can be written as

f(r|H0) =∏n

exp(−|r(n)|2

σ2w

)πσ2

w

(72)

f(r|θ,H1) =∏n∈J

exp(− |r(n)|2

σ2s+σ2

w

)π (σ2

s + σ2w)

∏n/∈J,J

exp(−|r(n)|2

σ2w

)πσ2

w

.

(73)

Under H0, the MLE of the noise power has been shown in (51)with 2NFFT + NCP = MC . Under H1, we can get the MLEsof the noise power and signal power as follows:

σ21 =

1MC − NC

∑n/∈J

|r(n)|2 (74)

σ2s =

1NC

∑n∈J

|r(n)|2 − σ21 . (75)

Then, by inserting (51), (74) and (75) into a likelihood ratiofunction, we can get the GLRT as

f(r|σ2

1 , σ2s , φML,H1

)f(r|σ0

2,H0

) =maxφ

{ (σ2

0

)MC

(σ21+σ2

s)NC (σ21)MC−NC

}H1≥<H0

τ.

(76)

In the implementation, we avoid power functions due to largeMC and NC in practice and take logarithm on both sides. Withsome algebraic manipulations, it yields (21).

Fig. 9. Intersection area of a high-rate region and a circle with the center atcognitive radio with radius r.

APPENDIX EDERIVATION OF (32)

Assume that the coordinates of the primary BS and cognitiveradio transmitter are (0, 0) and (0, c), respectively. Without lossof generality, we assume c > 0. We first derive the F (r) whenthe primary MS lies in a high-rate region and then apply theresults to a low-rate region. The derivation mainly refers to[41]. We assume that MSs are uniformly distributed; thus, F (r)in a high-rate region is the ratio of an intersection area to anarea of a high-rate region πD2. We compute the intersectionarea, depending on the location of the cognitive radio, which isshown in Fig. 9. We have

Case 1 : 0 < c < D

Case (i) : 0 ≤ r < D − c

AH(r, c,D) = πr2

Case (ii) : D − c ≤ r < D + c

AH(r, c,D) = θ2r2 + θ1D

2 − cv



Case (iii) : D + c ≤ r

AH(r, c,D) = πD2

Case 2 : D ≤ c

Case (i) : 0 ≤ r < c − D

AH(r, c,D) = 0

Case (ii) : c − D ≤ r < D + c

AH(r, c,D) = θ2r2 + θ1D

2 − cv

Case (iii) : D + c ≤ r

AH(r, c,D) = πD2

where (u, v) is cross point of these two circles by solving{u2 + v2 − D2 = (u − c)2 + v2 − r2

u2 + v2 = D2(77)

and is shown in (35)–(38). Combining these two cases, we get(33). On the other hand, if MS lies in a low-rate region, theintersection area is the difference between the intersection withan outer circle and the intersection with an inner circle, i.e.,

AL(r, c,D,R) = AH(r, c, R) − AH(r, c,D). (78)

Then, F (r) in a low-rate region is obtained by dividing theintersection area by the area of a low-rate region and is shownin (32).

ACKNOWLEDGMENT

The authors would like to thank the anonymous reviewers fortheir constructive comments that helped improved this paper.

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Sheng-Yuan Tu received the B.S. degree in elec-trical engineering and the M.S. degree in com-munication engineering from the National TaiwanUniversity, Taipei, Taiwan, in 2005 and 2007,respectively.

He is currently a Research Assistant with theWireless Broadband Communication System Lab-oratory, National Taiwan University. His researchinterests include cognitive radio networks and statis-tical signal processing.

Kwang-Cheng Chen (M’89–SM’93–F’07) receivedthe B.S. degree from the National Taiwan University,Taipei, Taiwan, in 1983 and the M.S. and Ph.D.degrees from the University of Maryland, CollegePark, in 1987 and 1989, respectively, all in electricalengineering.

From 1987 to 1998, he worked with SSE,COMSAT; IBM Thomas J. Watson Research Cen-ter, Yorktown Heights, NY; and the National TsingHua University, Hsinchu, Taiwan, where he dealtwith mobile communications and networks. He held

visiting/guest positions with the Hewlett-Packard Laboratories, USA; DelftUniversity of Technology, Delft, Netherlands; and Aalborg University, Aalborg,Denmark. Since 1998, he has been with the Institute of CommunicationEngineering and the Department of Electrical Engineering, National TaiwanUniversity, where he is also the Distinguished Professor and the Irving T. HoChair. He actively participates in various wireless international standards. Hehas authored or coauthored over 200 technical papers and 18 granted U.S.patents. He coedited (with R. DeMarca) the book Mobile WiMAX (Wiley, 2008),authored the book Principles of Communications (River, 2009), and coauthored(with R. Prasad) another book Cognitive Radio Networks (Wiley, 2009). Hisresearch interests include wireless communications and networks, cognitivescience, and nanocomputation/communication.

Dr. Chen was a recipient of a number of awards and honors. He is ac-tively involved with the technical organization of numerous leading IEEEconferences, including Technical Program Committee (TPC) Chair for the1996 IEEE International Symposium on Personal Indoor Mobile Radio Com-munications, TPC Cochair for the 2002 IEEE Global TelecommunicationsConference, General Cochair for the 2007 IEEE Mobile WiMAX Symposium,Orlando, FL, the 2009 IEEE Mobile WiMAX Symposium, Napa Valley,CA, and the General Chair for the IEEE 2010 Spring Vehicular TechnologyConference. He has served editorships with several IEEE journals and manyinternational journals and has served in various IEEE positions.

Ramjee Prasad (F’09) is currently the Director ofthe Center for Teleinfrastruktur, Aalborg University,Aalborg, Denmark, where he holds the chair of wire-less information and multimedia communications.He is the Coordinator of the European CommissionSixth Framework Integrated Project My personalAdaptive Global NET Beyond (MAGNET Beyond).He was involved in the European ACTS projectFuture Radio Wideband Multiple Access Systems(FRAMES) as the Project Leader. He is also theproject leader of several international industrially

funded projects. He has published over 500 technical papers, contributed toseveral books, and authored, coauthored, and edited 19 books. His latest bookis Introduction to Ultra Wideband for Wireless Communications. He is alsothe Coordinating Editor and the Editor-in-Chief of the Springer InternationalJournal on Wireless Personal Communications.

Prof. Prasad has served as a member of the advisory and program committeesof several IEEE international conferences. He has also presented keynotespeeches and delivered papers and tutorials on wireless personal multimediacommunications (WPMC) at various universities, technical institutions, andIEEE conferences. He was also a member of the European cooperation inthe scientific and technical research (COST-231) project, which dealt with theevolution of land mobile radio (including personal) communications, as anexpert for The Netherlands, and he was a member of the COST-259 project.He was the Founder and the Chairman of the IEEE Vehicular Technology/Communications Society Joint Chapter, Benelux Section, where he is nowthe Honorary Chairman. He is also the Founder of the IEEE Symposium onCommunications and Vehicular Technology (SCVT) in the Benelux, and he wasthe Symposium Chairman of SCVT’93. He is currently the Chairman of theIEEE Vehicular Technology/Communications/Information Theory/Aerospaceand Electronics Systems/Society Joint Chapter, Denmark Section. He wasthe Technical Program Chairman of the 1994 International Symposium onPersonal, Indoor, and Mobile Radio Communications held in The Hague,The Netherlands, on September 19–23, 1994 and of the Third CommunicationTheory Mini-Conference in conjunction with the 1994 IEEE Global Telecom-munications Conference held in San Francisco, CA, on November 27–30, 1994.He was the Conference Chairman of the 50th IEEE Vehicular TechnologyConference and the Steering Committee Chairman of the Second Interna-tional Symposium on WPMC, both held in Amsterdam, The Netherlands, onSeptember 19–23, 1999. He was the General Chairman of WPMC’01, whichwas held in Aalborg on September 9–12, 2001 and of the first InternationalWireless Summit, also held in Aalborg, on September 17–22, 2005. He is theGeneral Chair of the First International Conference on Wireless Communica-tion, Vehicular Technology, Information Theory, and Aerospace and ElectronicSystems Technology, which will be held on May 17–20, 2009, also in Aalborg.He was also the Founding Chairman of the European Center of Excellencein Telecommunications (HERMES), of which he is currently the HonoraryChairman. He is a Fellow of the Institution of Electronics and Telecommunica-tion Engineers, a Fellow of the Institution of Electrical Engineers, a member ofThe Netherlands Electronics and Radio Society, and a member of the DanishSociety of Engineers. He is an advisor to several multinational companies. Hewas a recipient of several international awards, the latest being the “TelenorNordic 2005 Research Prize.”


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reconfiguring communication

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spectrum efficiency

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sensing procedure

aalborg university