spectrum sensing in wideband ofdm cognitive radios-vl6

8/8/2019 Spectrum Sensing in Wideband OFDM Cognitive Radios-VL6

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IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 58, NO. 2, FEBRUARY 2010 709

Spectrum Sensing in WidebandOFDM Cognitive Radios

Chien-Hwa Hwang , Member, IEEE , Guan-Long Lai, and Shih-Chang Chen

Abstract In this paper, spectrum sensing of an orthogonal fre-quency division multiplexing (OFDM) based cognitive radio (CR)is addressed. The goal is to identify the portions of the spectrumthat are unused by primary user systems and other CR systems,called existing user (EU) systems altogether, with the emphasis onconquering the challenge imposed by multipath fading channel.The sensing of EU systems consists of two steps. In the rst step,the maximum likelihood (ML) estimates of the frequency bandsof EU systems are calculated; in the second step, detection is per-formed at each suspected band to decide whether an EU system istruly in operation. The idea is that an EU system appears at a seg-ment of continuous subcarriers. This fact can be exploited by em-ploying measurementsat a continual subcarriers and executing thesensing along the frequency domain. An autoregressive (AR)modelis adopted to track the variation of the received EU signal strengthalong frequencies. It is shown by simulations that the proposedspectrum sensing algorithm is robust in a severe frequency-selec-tive fading channel.

Index Terms Autoregressive model, cognitive radio (CR), dy-namic programming, orthogonal frequency division multiplexing(OFDM), spectrum sensing.

I. INTRODUCTION

R ADIO spectrum is the medium for all types of wirelesscommunications, such as cellular phones, satellite-basedservices, wireless low-powered consumer devices, and so on.Since most of the usable spectrum has beenallocated to existingservices, the radio spectrum has become a precious and scarceresource, and there is an urgent concern about the availability of spectrum for future needs. The solution to the spectrum scarcityproblem is dynamically looking for thespectrum whitespacesand using them opportunistically. Cognitive radio (CR) tech-nology, dened rst by Mitola [1], [2], is thus advocated as acandidate for implementing opportunistic spectrum sharing.

Manuscript received December 22, 2008; accepted August 19, 2009. Firstpublished September 18, 2009; current version published January 13, 2010. Theassociate editor coordinating the review of this manuscript and approving it forpublication was Prof. Hongbin Li. This research was supported in part by theNational Science Council, Taiwan, under Contract NSC-95-2219-E-007-005,and in part by Chung-Shan Institute of Science and Technology, Taiwan, underContract BU95W028.

C.-H. Hwang and are with the Institute of Communications Engineering, Na-tional Tsing Hua University, Hsinchu 30013, Taiwan (e-mail: [email protected]).

G.-L. Lai was with the Institute of Communications Engineering, NationalTsing Hua University, Hsinchu 30013, Taiwan (e-mail: [email protected]).

S.-C. Chen is with the Realtek Semiconductor Corporation, Hsinchu 300,Taiwan (e-mail: [email protected]).

Digital Object Identier 10.1109/TSP.2009.2032453

To achieve the goal of CR, it is a fundamental requirementthat the cognitive user performs spectrum sensing to identifythe portions of spectrum that are unused at a specic time. Thus,over various frequency bands, sensing of primary user systemsand other CR systems in operation should be performed reg-ularly. Each of the systems that have already been operatingin a particular band of interest is called an existing user (EU)system. Digital signal processing techniques can be employedto promote the sensitivity of the EU signal sensing. Three com-monly adopted methods are matched ltering, energy detection[3][9], and signal feature detection with the cyclostationaryfeature most widely adopted [10][13]. Moreover, cooperationamong cognitive users in spectrum sensing can not only reducethe detection time and thus increase the agility, but also alle-viate the problem that a cognitive user fails to detect EU signalbecause it is located at a weak-signal region [7][9], [14][18].For an overview of these approaches and their properties, see[19][21].

It is concluded in [22] that orthogonal-frequency-divisionmultiplexing (OFDM) is the best physical layer candidate fora CR system since it allows easy generation of spectral signalwaveforms that can t into discontinuous and arbitrary-sized

spectrum segments. Besides, OFDM is optimal from the view-point of capacity as it allows achieving the Shannon channelcapacity in a fragmented spectrum. Owing to these reasons, inthis paper, we consider the problem of spectrum sensing in anOFDM based CR system.

Themain concern of this paper is to develop spectrum sensingalgorithms that are robust to multipath fading channels. Oneof the main challenges in performing reliable spectrum sensingarises from the fading channel of a wireless link. There are twotypes of fading, i.e., shadowing fading and multipath fading.The former does not cause large uctuations in signal strengthover small changes of receivers location, while the latter gen-erally results in signicant variations of signal strength with asmall change of location [23]. To alleviate the difculties re-sulting from fading channels, it is advantageous to make use of diversity gains in various domains. Concerned with shadowingfading, cooperative spectrum sensing among cognitive users sit-uated at different locations can be employed, which is the usercooperation diversity. Regarding multipath fading (the concernof this work), since channels may be quite different even for twoclosely located receivers, a spectrum sensing device equippedwith multiple antennas is able to exploit the spatial diversity.Moreover, particularly convenient for OFDM based CR, spec-trum sensing using observations along the frequency domaincan take advantage of the fact that, once an EU system appears,

several subcarriers ina row are interfered simultaneously. Thus,1053-587X/$26.00 2010 IEEE

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spectrum sensing can be transformed into the model change de-tection [24], which aims at detecting changes in the characteris-tics of physical systems and is an important practical problem.However, due to frequency selectivity of multipath fading, thereceived EU signal strength may vary with frequencies. Part of the band of the EU system may be deeply faded, making it dif-

cult to detect its presence. A remedy is to endow the spec-trum sensing device with the capability of tracking EU signalstrength variation in the frequency domain. In so doing, eventhough some portion of the band is severely faded, weak signalsat this region can still be identied as a part of the entire signal.

In this paper, it is assumed that an unknown number of EUsystems are operating in the spectrum segment under sensing.The detection of EU systems is composed of two stages: i) es-timating the most likely bands of EU systems, and ii) for eachsuspected band, testing whether or not an EU system is reallyin operation. For the rst stage, an autoregressive (AR) modelis adopted to track the changes of signal magnitude in the fre-quency domain, and the maximum likelihood (ML) estimates of the parameters of concern are calculated. It turns out that a hugenumber of search is required for estimating the frequency bandsof EU systems. A dynamic programming (DP) technique is em-ployed to reduce the complexity in searching. For the secondstage, due to insufcient knowledge of statistics of EU signals,an energy detector is employed. In each of stages i) and ii), bothsingle antenna and multiple antennas are considered.

The organization of this paper is summarized as follows. InSection II, the problem statement as well as the signal model of a CR OFDM system interfered by an EU signal are described.Two stages of spectrum sensing, i.e., estimation and detection,are given in Section III when the sensing device has a single

antenna. In Section IV, results of Section III are extended to thecase that multiple antennas are equipped. Simulation results of the proposed algorithm are demonstrated in Section V. Finally,we conclude this paper in Section VI.

II. PROBLEM STATEMENT

Consider awideband cognitive OFDM system with sub-carriers. It is required that the CR system identies the portionsof the spectrum that are unused at a specic time. Thus, overvarious frequency bands, sensing of primary user systems andother CR systems in operation is performed regularly. Each of the systems that have already been functioning within a bandof interest is called an EU system. The CR system performingsensing is wideband in the sense that its bandwidth can accom-modate more than one EU systems.

When a sensing of EU systems is performed, the CR OFDMsystemceases transmission.Thereceivedsignal is ampliedandfrequency down-converted from the radio frequency (RF) undersensing to the baseband. After analog-to-digital (A/D) conver-sion, cyclic prex removal and some necessary processing, theoutput signal is passed through a -point discrete Fourier trans-form (DFT). If an EU signal is present at the frequency of sub-carrier , the th DFT output corresponding to the th OFDMsymbol is given by

(1)

where and are the complex-valued contri-butions resulting from EU signal and additive white Gaussiannoise (AWGN), respectively.

Suppose there are EU systems operating in the frequencyband of interest, with the th system occupyingthe band extending from the th to the th subcarriers of

the CR OFDM system. It is assumed that the frequency bandsof EU systems, i.e., with , are disjointand the knowledge of the number of EU systems and their fre-quency bands are unknown to the sensing device. The sensingalgorithm addressed in this paper decides how many EU sys-tems and where they are based on the observation

with denoting the observationlength at each subcarrier.

III. SENSING OFEU SYSTEMS IN ACOGNITIVEOFDM SYSTEM

The observation is processed in two steps. Werst performestimation for the most likely values of and

, and we next execute adetection for each suspectedband to decide whether or not an EU system is truly in op-eration. The estimation and detection procedures are to bediscussed in Sections III-A and B, respectively.

A. Estimating Frequency Bands of EU Systems

For each , we build an observation fromsuch that the estimation of the frequency bands of

EU signals is based on the measurements along the frequencydomain. Assume it is known that the variances of in thereal and imaginary parts are both . We choose

(2)

with . It is seenis the periodogram of the received signal at the th subcarrieraveraged over OFDM symbols, and the periodogram is anestimate of the true spectrum of a signal. The observation for EUsystem frequency bands estimation is , where we dene

.

We rst consider the case that there is one EU system, i.e.,, operating in the target band, and then we extend theresult to the more practical situation that there are unknownnumber of EU systems in the band.

Supposethat an EU system is present at subcarriers .We assume that correlation exists among with neigh-boring subcarrier indices. A rst-order autoregressive (AR)model is adopted to t the signal .That is,

(3)

where and are model parameters, and is a whiteGaussian random process with variance . All of , , andare unknown. If there is no EU signal in subcarriers ,



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Fig. 2. An EU system operates at subcarriers[ a ; b ] , and M is set as 2. The received EU signal strength is plotted as the shaded region. (a) A deep fade occurs athe middle region of the band, and the result of band estimation is[ a ; c ] and [ d ; b ] , and (b) deep fade occurs at the border, and the estimated bands are[ a ; c ] and[ b + 1 ; d ] .

alarmed band in Fig. 2(b) can be correctly identiedas a band of AWGN.

The goal is to test whether an EU system is truly present in

each of the suspected bands found in the estimation stage. Fornotational simplicity, we address the detection of EU signal in. Commonly adopted detection algorithms in CR contain

matched ltering, energy detection, and cyclostationary signalfeature detection [19]. However, due to the lack of knowledgeabout EU signals, energy detection becomes the only choiceamong the three. Actually, this is a very natural selection as thereceiver structure of an OFDM based CR is convenient for theimplementation of an energy detector.

The detector is designated as

where represents EU signal is absent, and otherwise.Under , the scaled test statistic is a central chi-squared distribution with degree of freedom ,i.e., . Using the NeymanPearson philosophy, thedetection threshold is set as

(25)

with the target false alarm probability , where isthe inverse function of the right-tail probability evaluated at

for distribution .Suppose that an EU system is present, and its average powerat the th subcarrier is denoted by , given as

The test statistic can be expressed as

where by the central limit theorem, the distributions of thesecond and third terms at the right-hand side can be approx-imated as and

, respectively. Thus, given a threshold, the probability of detection is

(26)

where is the right-tail probability of evaluated at. To relate the probability of miss and the probability

of false alarm, we approximate the test statistic under asGaussian, and the threshold in (25) has

(27)Plugging (27) back to (26) and by some manipulations, we ob-tain

(28)where is the averageSNR of the EU signal in the band.

IV. MULTIPLE ANTENNAS

To improve the performance of spectrum sensing, we mayequip the sensing device with ( ) receive antennas.We suppose that, under , each antenna observes the sameEU transmission, and the channels from an EU to all antennasare independent. The output of each antenna is processedindividually by a DFT. In the presence of an EU signal, let

stand for the th symbol DFToutput of the th receive antenna at subcarrier , whereand are contributions from EU signal and AWGN,respectively. In the following, the superscript is afxed toa notation of single-antenna to represent the counterpart of thenotation in the th antenna for the multiantenna case. If noambiguity occurs, new notations augmented with superscript

will not be dened again.



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In the estimation stage, the observation from the th antennais

Consider that there is one EU system operating in theband. Let the likelihood function at the th antenna be

. We assume the noisevariances and are common at all antennas, andand are distinct for different s. Since the received sig-nals at antennas are mutually independent, the joint likelihoodis given by

(29)

We estimate the unknowns individually at each an-

tenna, and and are estimated from the combined obser-vations of all antennas. By following the same steps in the caseof single antenna, it can be shown the optimization presented in(16)(18) still applies except that and shouldbe revised as

(30)

and [see (31), shown at the bottom of the page], respectively. Onthe other hand, in the case that there may be arbitrary number

of EU systems in the band, the algorithm of Fig. 1 still holdsexcept that and in (23) and (24) are replaced with(30) and (31), respectively, and the initial condition of isrevised to be .

In the detection stage, to perform detection at the band, the test statistic is

where is somewhat different in the form from its counterpartin single antenna to take into account thedistinct noise variances

at antennas. With a target false alarm rate , thethreshold is given as

By thecentral limit theorem, the test statistic is distributed as

Fig. 3. Performance of an energy detector with the processing gainD = K N ( q 0 q + 1 ) .

under and as

under . It can be shown the rates of miss and false alarm arerelated by

(32)

where

Compare (28) and (32), we can see the effective observationlength is times that of the single antenna case; thus, theadoption of multiple antennas decreases the probability of misswhich often results from deep channel fade. The performanceof energy detection is plotted in Fig. 3 with processing gain

.

V. SIMULATION RESULTSThroughout the simulations, an OFDM CR with the number

of subcarriers is adopted, and the observation lengthis set as . The fading channels used in simulations are

(31)



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Fig. 4. Performance of the estimation stage with respect to the average SNRof EU signal, frequency selectivity of fading channels, and the number of EUsystems. The length of observation isN = 1 0 0 . The value of m is correctlychosen, and the estimator has single antenna.

Fig. 5. Performance of the estimation stage with respect to the average SNR of EU signal, the number of antennas, and the number of EU systems. The lengthof observation isN = 1 0 0 . The value of m is correctly chosen, and the numberof channel paths is equal to 16.

multipath Rayleigh with uniform power delay proles. Each of the gures and tables is generated by Monte Carlo simulationswith 1000 runs. The channels change from one Monte Carlo runto another. When multiple antennas are used, channels from anEU to different antennas are independent. Thus, diversity gainis obtained by the combining across antennas. We rst showthe performance at the estimation stage in Figs. 4 and 5 andTable I and then the overall performance of spectrum sensing,i.e., composite of estimation and detection, in Tables II and III.

Beforepresenting theperformanceof theestimation stage,wegive the denition ofa hit. We use and todenotethetruenumber of EU systems and thechosen number in running (22),

respectively. As is the upper bound of , we always have. Given the true EU bands

and the estimates of EU bands . A hithappens if each EU band is equal to some estimatedEU band with one-subcarrier estimation error toler-ance at both sides. That is, for each , one can ndsome such that and .

In Figs. 4 and 5, we depict the performance of the estimation

stage when the value of (number of EU systems operating inthe band) is correctly chosen in running (22). Fig. 4 comparesthe performance of the EU band estimator for fading channelswith different frequency selectivitywhen the numberof antenna

. The numbers of multipaths in comparison are 4 and 16,and we consider number of EU systems 1, 2, and 3. EUsystems #1, #2, and #3 appear at subcarriers ,and , respectively. They allhave bandwidths equal to15.When , #1 EU system is in the band; when , sys-tems #1 and #2 exist, and so on. Every EU system has the sameaverage power. The horizontal axis of Fig. 4 is the ratio of theaverage power of an EU signal to AWGN; the vertical axis is theprobability of hit. It is seen that the performance of estimationdegrades as the number of EU systems increases, and the fre-quency selectivity of the channel deteriorates the performanceas well. Fig. 5 compares the performance of the EU band esti-mator for the number of antennas and number of EU systems . The number of multipaths is equalto 16. The frequency bands of EU systems are the same as thoseset in Fig. 4. It is shown that the performance of estimation im-proves with the increase of .

Below, we investigate the performance at the estimation stagewhen the value of in (22) is incorrectly specied, i.e.,

. Table I shows the performance of the estimation stage whenand . The EU system is located

at subcarriers , and the number of multipaths is equal to16. Since , the estimator returns the resultand . For each , there contain four columns. Therst column denotes hit. Note that, since , we haveone falsely alarmed band when a hit occurs. However, simu-lation results indicate that the bandwidth of a falsely alarmedband is generally small (two or three subcarriers). The second(miss of type-I) and third (miss of type-II) columns denote theprobabilities that the situations illustrated in Fig. 2(a) and (b),respectively, happen. The fourthcolumn is the sum of thevaluesof the rst three columns. It is seen that the sums are in generalclose to 1, meaning that hit and miss of types I and II encompassmost situations. We observe that, as the average SNR of the EUsignal increases, the probability of hit decreases; regarding theprobability of miss, type-I increases with the average SNR, andtype-II tends to increase as well but not so obvious as type-I.This is explained as follows. When a deep channel fade occurs,the increase of average SNR magnies the channel frequencyselectivity; the portion of the band not experiencing deep fadetends to be tted by an AR model, and the portion under deepfade is modeled by AWGN. The EU system band is thus torninto pictures of Fig. 2(a) and (b), and the probability of hit isdecreased with the increase of SNR. We also nd that the ten-dencies of increase/decrease of probabilities of hit and miss be-come more and more evident when the number of antennas is

raised from to . This is because, with the increaseof the number of antennas, it is easier to identity the band of EU



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TABLE IPERFORMANCE AT THEESTIMATION STAGE WHEN ONE EU SYSTEMIS PRESENT ATSUBCARRIERS[ 3 5 ; 4 9 ] ( m = 1 ) BUT M = 2 . THE NUMBER OFMULTIPATHS

IS EQUAL TO16, AND THEOBSERVATION LENGTH IS N = 1 0 0 . THE DATA ARE GENERATED BY THEMONTE-CARLO SIMULATION WITH 1000 RUNS

TABLE IIPROBABILITY OFDETECTION OFSPECTRUMSENSING FOR( m ; M ) 2 f ( 1 ; 1 ) ; ( 2 ; 2 ) ; ( 3 ; 3 ) g AND K 2 f 1 ; 2 ; 3 g . THE NUMBER OFMULTIPATHS IS EQUAL TO16,

AND THEOBSERVATION LENGTH IS N = 1 0 0 . THE RESULTS ARE GENERATED BY THEMONTE-CARLO SIMULATION WITH 1000 RUNS

TABLE IIIPROBABILITY OFDETECTION OFSPECTRUMSENSING FOR( m ; M ) 2 f ( 1 ; 2 ) ; ( 1 ; 2 ) ; ( 2 ; 3 ) g AND K 2 f 1 ; 2 ; 3 g . THE NUMBER OFMULTIPATHS IS EQUAL TO16,

AND THEOBSERVATION LENGTH IS N = 1 0 0 . THE RESULTS ARE GENERATED BY THEMONTE-CARLO SIMULATION WITH 1000 RUNS

system, or equivalently, the band without EU system. However,due to the incorrect value of , the band of EU is to bedetected as two, leading to type-I miss.

In the following, the overall performance of spectrumsensing, i.e., concatenation of estimation and detection stages,is demonstrated. Let denote thenal result of spectrum sensing. We have described in the rstparagraph of Section III-B how the set is ob-tained. Detection occurs if each EU band is coveredby some with one-subcarrier tolerance at both ends.That is, we say the EU bands are detected if, for each EU band

, , one can nd some such that. Note that the denitions of

hit and detection are somewhat different. In the former, it isrequired that the estimated band is equal to the true band (withone-subcarrier tolerance); while in the latter, we require onlythe estimated band to be a subset of a true band. Thus, in caseof detection, there may be some falselyalarmed subcarriers.However, simulation results indicate that the number of suchfalselyalarmed subcarriers is generally small.

Table II gives the performance when with, and and . When , the

EU system is located at ; when , EU systems areat and ; when , a system at isadded. The number of channel paths used in simulations is 16.Foreach pair of , each column shows the detection prob-ability ofEUsystem(s) at a specic value of . We observe that,for each , the probability of detection is proportional tothe number of antennas and the average SNR, and the detec-tion probability is inversely proportional to the number of EUsystems. Table III shows the performance of the proposed spec-trum sensing algorithm when with ,

and , and . The environments of sim-ulations are the same as those of Table II. Compare the resultsat and with that of inTable II, it is observed that the detection probability gets worsewith the increase of discrepancy between and . The sameinference is reached when comparing the result of

in this table and the result of in Table II.Moreover, the second column of Table III gives the overall de-tection performance for , while Table I showsthe probabilities of hit and misses of types I and II at the esti-mation stage with the same . Compare Table I and thesecond column of Table III, we can see the probability of de-



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tection shown in the latter is generally higher than the columnSum in the former with the same . This is mainly becausesome unfound EU bands at the estimation stage belong to nei-ther type I nor type II misses, but they are recovered at the de-tection stage.

VI. CONCLUSIONIn this paper, the problem of EU signal sensing in an OFDM

based CR system is addressed, where the number of EU sys-tems in operation and their frequency bands are all unknown.Our main idea is that, once an EU system appears, several sub-carriers in a row are interfered. To exploit this fact, observationsalong the frequency domain are employed. The emphasis of thiswork is on combating the challenge resulting from a severe fre-quency selective fading channel. We use an AR model to trackthe variation of the received EU signal strength along the fre-quency axis. When a deep fade occurs at part of the band of anEU system, tracking enables the sensing device to identify theweak signal under deep fade as a part of the entire signal. Wealso investigate the scenario of multiple antennas to enhance theperformance of spectrum sensing.

The task of spectrum sensing is composed of two stages: es-timation and detection. In the estimation stage, due to the lackof precise knowledge of EU signals statistics, it is hard to ob-tain an accurate estimate for the number of EU systems in op-eration. We assume the knowledge of an upper bound of thenumber of EU systems, denoted by , is known, and we calcu-late the ML estimates of the bands of EU systems. In the de-tection stage, energy detection is performed individually at eachof bands, including estimated bands and re-maining bands. Detection is executed at the remainingbands because some of them are unfound bands due to deepchannel fade. The nal result of spectrum sensing is the union of the bands that are judged to be EU system present by energydetection. Simulations result demonstrate that the composite of theestimation anddetection is robust under the ill condition thatthe correct number of EU systems cannot be found.

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Chien-Hwa Hwang (M00) received the B.S. andM.S. degrees from the National Taiwan University,Taiwan, in1993and 1995, respectively, andthe Ph.D.degree from the University of Southern California,Los Angeles, in 2003, all in electrical engineering.

In August 2003, he joined the Institute of Com-munications Engineering of the National Tsing HuaUniversity, Taiwan, as an Assistant Professor. His

research interests include random matrix theory andstatistical signal processing.

Guan-Long Lai received the B.S. degree from theDepartment of Electrical Engineering at the NationalChung Hsing University, Taichung, Taiwan, in 2007and the M.S. degree from the Institute of Communi-cations Engineering, National Tsing Hua University,Hsinchu, Taiwan, in 2009.

Shih-ChangChen received the B.S. degree from theDepartment of Electrical Engineering and the M.S.degree from the Institute of Communications Engi-neering, both in the National Tsing Hua University,Hsinchu, Taiwan, in 2005 and 2007, respectively.

He is currently an Engineer at the Digital IC De-sign Department of Realtek Semiconductor Corpora-tion, Hsinchu, Taiwan.

spectrum sensing in wideband ofdm cognitive radios-vl6

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