26 IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL …dpopescu/papers/WiMAX_LTE_JSTSP2012.pdf26 IEEE...

26 IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, VOL. 6, NO. 1, FEBRUARY 2012

Second-Order Cyclostationarity of Mobile WiMAXand LTE OFDM Signals and Application to Spectrum

Awareness in Cognitive Radio SystemsAla’a Al-Habashna, Octavia A. Dobre, Senior Member, IEEE, Ramachandran Venkatesan, Senior Member, IEEE,

and Dimitrie C. Popescu, Senior Member, IEEE

Abstract—Spectrum sensing and awareness are challengingrequirements in cognitive radio (CR). To adequately adapt to thechanging radio environment, it is necessary for the CR to detectthe presence and classify the on-the-air signals. The wirelessindustry has shown great interest in orthogonal frequency divisionmultiplexing (OFDM) technology. Hence, classification of OFDMsignals has been intensively researched recently. Generic signalshave been mainly considered, and there is a need to investigateOFDM standard signals, and their specific discriminating fea-tures for classification. In this paper, realistic and comprehensivemathematical models of the OFDM-based mobile WorldwideInteroperability for Microwave Access (WiMAX) and third-Gen-eration Partnership Project Long Term Evolution (3GPP LTE)signals are developed, and their second-order cyclostationarityis studied. Closed-from expressions for the cyclic autocorrelationfunction (CAF) and cycle frequencies (CFs) of both signal typesare derived, based on which an algorithm is proposed for theirclassification. The proposed algorithm does not require carrier,waveform, and symbol timing recovery, and is immune to phase,frequency, and timing offsets. The classification performance ofthe algorithm is investigated versus signal-to-noise ratio (SNR), fordiverse observation intervals and channel conditions. In addition,the computational complexity is explored versus the signal type.Simulation results show the efficiency of the algorithm is terms ofclassification performance, and the complexity study proves thereal time applicability of the algorithm.

Index Terms—Long-term evolution (LTE), mobile WorldwideInteroperability for Microwave Access (WiMAX), orthogonalfrequency division multiplexing (OFDM), signal classification,signal cyclostationarity.

I. INTRODUCTION

C OGNITIVE RADIO (CR) represents a promising solu-tion to the spectrum scarcity problem. There are many

potential commercial and military applications for CR. Using

Manuscript received March 30, 2011; revised August 08, 2011 andSeptember 25, 2011; accepted October 14, 2011. Date of publication December21, 2011; date of current version January 18, 2012. This work was supported inpart by the Natural Sciences and Engineering Research Council of Canada, andwas presented in part at the 2010 IEEE Global Communications Conference(Globecom). The associate editor coordinating the review of this manuscriptand approving it for publication was Prof. Philippe Ciblat.

A. Al-Habashna was with the Faculty of Engineering and Applied Science,Memorial University of Newfoundland, St. John’s, NL A1B 3X5, Canada. Heis now with Stratos Global, St. John’s, NL A1C 2G, Canada (e-mail: Ala’[email protected]).

O. A. Dobre, and R. Venkatesan are with the Faculty of Engineering and Ap-plied Science, Memorial University of Newfoundland, St. John’s, NL A1B 3X5,Canada (email: [email protected]; [email protected]).

D. C. Popescu is with the Department of Electrical and Computer En-gineering, Old Dominion University, Norfolk, VA 23529 USA (email:[email protected]).

Digital Object Identifier 10.1109/JSTSP.2011.2174773

CR, the spectrum utilization will be significantly improvedby opening the licensed bands to be exploited by other users,without interfering with the licensed users. CR dynamicallyaccesses the available spectrum, and adapts its transmissionparameters according to the changes in the radio environment.In order to acquire information on the surrounding, CR needsto detect and classify the on-the-air signals [1]–[3].

As orthogonal frequency division multiplexing (OFDM) hasbeen chosen for the physical layer of many wireless standards,intensive research has been done recently on the detection,classification, and parameter estimation of the OFDM signals[4]–[18]. Most of the classification methods are developedfor generic signals and rely on cyclostationarity, with some ofthem employing the detection of the cyclic prefix (CP)-inducedpeaks in the cyclic autocorrelation function (CAF) [5]–[9]. Inthese methods, the CAF magnitude is either searched over alarge delay range to find the peaks [5]–[8], which introducescomputational complexity, or the location of the peaks isassumed a priori known [9]. Although this location is knownfor standard signals, it can be unreliable for classification, asthe cognitive users sharing the spectrum may also employ theOFDM modulation with close useful symbol duration. Anothermethod is presented in [10] and [11], and uses the cyclostation-arity signatures intentionally embedded in the OFDM signals.The drawback of this method is the extra overhead that resultsfrom embedding such signatures. Furthermore, pilot-inducedcyclostationarity is exploited in [12] under the assumptionthat the pilot pattern repeats in time and frequency with somedistributions, and there are identical pilot symbols in eachsuch pattern group, having application to WiFi, Digital VideoBroadcasting- Terrestrial, and fixed Worldwide Interoperabilityfor Microwave Access (WiMAX) signals. In [13], the authorsexploit the second-order cyclostationarity to classify diverseIEEE 802.11 standard signals. A theoretical analysis of thesecond-order cyclostationarity induced by pilots, with appli-cation to the IEEE 802.11a signals is carried out in [14]. Anon-cyclostationarity approach is presented in [17], [18], basedon the kurtosis of the decoded symbols. The useful symbolduration, CP duration, carrier frequency offset, and time delayare jointly estimated by performing a search to minimize thiskurtosis, and the OFDM signal type is identified based on theuseful symbol duration estimate. As it was mentioned for thecyclostationarity-based approach, although the useful symbolduration is specific to diverse standards, this information canbe unreliable for classification.

1932-4553/$26.00 © 2011 IEEE

AL-HABASHNA et al.: SECOND-ORDER CYCLOSTATIONARITY OF MOBILE WIMAX AND LTE OFDM SIGNALS 27

Fig. 1. TDD frame structure for mobile WiMAX.

Fig. 2. OFDM frequency description [21].

In this paper, we provide realistic and comprehensive mathe-matical models of the mobile WiMAX OFDM and Long TermEvolution (LTE) OFDM signals, which take into account pream-bles, pilots, and reference signals (RS). We also study the pre-amble-, CP-, and RS-induced second-order cyclostationarity ofthese signals, and based on the findings, we propose an algo-rithm for signal classification in common frequency bands. Weshow that the phase offset has no effect on CAF, while the fre-quency and timing offsets affect only the CAF phase. The cyclefrequencies (CFs) are not affected by such signal impairments.Furthermore, the CAF-based statistics used for signal classifica-tion are independent of phase, frequency, and timing offsets. Theperformance of the proposed classification algorithm is studiedversus signal-to-noise ratio (SNR), for different observation in-tervals (number of samples) and channel conditions. Analysisof the computational complexity is performed versus the con-sidered signals and the number of samples. Apparently, there isa tradeoff between performance and complexity. Results show agood performance, as well as real-time applicability of the pro-posed algorithm. In addition, the proposed algorithm does notrequire carrier, waveform, and symbol timing recovery, and isimmune to phase, frequency, and timing offsets.

The rest of this paper is organized as follows. In Sections IIand III, we introduce the developed signal model and findingson the second-order cyclostationarity of mobile WiMAX andLTE OFDM signals, respectively. In Section IV we presentthe proposed cyclostationarity-based signal classification al-gorithm. We investigate the performance and computationalcomplexity of the proposed algorithm in Section V, followedby conclusions and final remarks in Section VI. Appendix Apresents fundamental concepts on the second-order signalcyclostationarity, Appendices B and C discuss proofs related

to the second-order cyclostationarity of mobile WiMAX andLTE OFDM signals, respectively, and Appendix D shows thatthe test statistics are independent of the phase, frequency, andtiming offsets.

II. MOBILE WiMAX OFDM SIGNAL MODEL AND ITS

SECOND-ORDER CYCLOSTATIONARITY

A. Mobile WiMAX OFDM Signal Model

Fig. 1 presents the IEEE 802.16e time-division duplex (TDD)frame structure, as per the current mobility certification profiles[19]–[21]. The standard frame duration can range from 2 ms to20 ms; however, all WiMAX equipments support only a 5-msframe [22]. The frame is divided into two subframes, one forthe downlink (DL) and another one for the uplink (UL). TheDL-to-UL subframe ratio is variable, to support different trafficprofiles. Transition gaps separate the adjacent DL and UL sub-frames. In Fig. 1, TTG represents the DL-UL gap and is referredto as the transmit/receive transition gap, while RTG representsthe UL-DL gap and is referred to as the receive/transmit tran-sition gap. Note that the terminology used here is according tothe IEEE 802.16e standard [20], [21]. The DL subframe startswith a preamble as the first symbol, which is used for timeand frequency synchronization and uniquely identifies a servingbase-station. Therefore, a cognitive user within the coveragearea of a base-station will periodically receive the same pre-amble.

The OFDM frequency-domain description is presented inFig. 2. One can note four types of subcarriers: data subcar-riers to transmit information, pilot subcarriers for estimationpurposes, null subcarriers for guard bands, and direct current(DC) subcarrier [21]. The first two types of subcarriers arecalled the used subcarriers. The pilot symbol on subcarrier isgenerated as where is a value taken from apseudorandom binary sequence that is different for each OFDMsymbol [21]. The distribution of the pilot subcarriers mightdiffer from one OFDM symbol to another in the frame, whilethis repeats every frame, i.e., it is the same for each th OFDMsymbol of a frame [19]–[21]. Note that for the preamblesymbol, for the DL OFDM symbols (excludingthe preamble), and for the ULOFDM symbols, with and as the number of OFDMsymbols in the DL (excluding the preamble) and in the frame,respectively. Note that more than one pilot distribution mightbe employed in the DL or UL subframes; each pilot distributionis used in a certain set of OFDM symbols in the DL or ULsubframes [19]–[21]. The pilot symbols are usually transmittedwith boosted power over the data symbols. The preamble con-tains only null subcarriers and subcarriers used for transmittingpreamble data. According to the standard, the preamble datasymbols are transmitted every third subcarrier out of the set ofsubcarriers, starting from thesubcarrier up towhere and is the number of the preambledata symbols [19]–[21]. Fig. 3 shows the frequency domaindescription of the preamble when .


Fig. 3. OFDM frequency description of the preamble symbol �� .

According to the above description, we express the discrete-time mobile WiMAX OFDM signal affected by noise as1

(1)

where and are the signal componentscorresponding to the preamble, and the DL (excluding the pre-amble) and UL subframes, respectively, and is the ad-ditive zero-mean Gaussian noise. Furthermore,and are given respectively as1

(1.a)

(1.b)

(1.c)

where and are the number of used subcarriers inthe preamble, DL, and UL symbols, respectively, and

are the amplitude factors equal to andrespectively, is the OFDM symbol period2 equal

to the useful OFDM symbol duration, plus the CP dura-tion, is th preamble data symbol transmitted in the

th subcarrier of the preamble, withas the position of the first subcarrier used to transmit pre-

amble data and and are the symbols(data and pilot) transmitted on the th subcarrier and within

1Note that the effect of phase, frequency, and timing offsets are not includedin the signal expressions to simplify and streamline presentation. However, theyare taken into account and their effect on the second-order signal cyclostation-arity is discussed in Section II-C.

2Note that durations are expressed in number of samples. For durations ex-pressed in time periods, we use the symbol � instead of �, e.g., �� and� � instead of �� and � , respectively.

TABLE IOFDM PARAMETERS FOR THE MOBILE WiMAX Signal [22]

the th 3 OFDM symbol which belongs to the DL and UL sub-frames, respectively (note that the distribution of pilot subcar-riers could be different for different groups of OFDM symbols),

is the number of OFDM symbols in the UL subframe,is the impulse response of the transmit and the receive

filters in cascade, and is the total dura-tion of the transition gaps within each frame, with and

as the TTG and RTG transition gaps, respectively. Thedata symbols are taken either from a quadrature amplitude mod-ulation (QAM) or phase shift keying (PSK) signal constellation,and are assumed to be zero-mean independent and identicallydistributed (i.i.d.) random variables. The fast Fourier transform(FFT) size for generating OFDM symbols is equal to the totalnumber of subcarriers (used and guard band subcarriers), andequals . To ease the understanding of the expressions for thesignal model, here we provide an explanation for the in(1.a). The inner summation on the right-hand side of (1.a) isover the number of data subcarriers, while the outer summationis over the OFDM symbol (preamble) index. Specific to (1.a) isthe position of the preamble, which appears at the beginning ofeach frame. As such, the preamble index, , is an integer multipleof the number of OFDM symbols in a frame .Furthermore, for the position of the preamble, we need to takeinto account the total duration of the transition gaps within eachframe, which yields the shift of and the exponential with

where provides the frame index. It is note-worthy that the data symbol on each subcarrier is the same forall preambles ( does not depend on the preamble index ).

The OFDM parameters for mobile WiMAX signals are pre-sented in Table I. As one can notice, the FFT size is scalablewith the bandwidth: when the available bandwidth increases,the FFT size also increases, such that the useful symbol duration(equal to the reciprocal of the subcarrier frequency spacing, )is fixed. This in turn leads to a constant useful OFDM symbolduration.

B. CAF and Set of CFs4 for the Mobile WiMAX OFDM Signals

According to derivations in Appendix B, the CAF and set ofCFs for the mobile WiMAX OFDM signals are as follows.

3Note that the OFDM symbol index, �, can be further expressed in terms of theframe index, �� with �� as the floor function, and OFDM symbol indexwithin a frame, �� with � � � �� . As such, � � �� .

4For the definition of CAF, � �� and set of CFs, �� the reader isreferred to Appendix A.


Fig. 4. CAF magnitude for the mobile WiMAX signal at � � � � ��

versus CFs.

Case (1): For delays equal to zero (due to the correlation ofthe signal with itself) and (CP-induced cyclostationarity)

(2)

(3)

where

with and 5 as thenumber of data and pilot subcarriers, and and

as the variance of data and pilot symbols in the thDL OFDM symbol (excluding the preamble), respectively,and and as their ULcounterparts. Noteworthy to mention that the CFs are integermultiples of the reciprocal of the frame duration, and notof the OFDM symbol duration, as one can expect based onthe analysis of generic OFDM signals [4]–[6]. This is dueto the existence of the transition gaps in the WiMAX frame.Nevertheless, we expect that the CAF magnitude at CFs closeto integer multiples of predominates, as the transitiongaps are small when compared with the frame duration. Fig. 4shows the CAF magnitude at delay versusCFs, with the signal parameters set as in Section V. One cansee that, indeed, although the CFs are integer multiples of thereciprocal of the frame duration, the CAF at integer multiplesof the symbol duration predominates.

5Note that the number of pilot subcarriers, the variance of the data symbols,and the variance of the pilot symbols are the same in all the OFDM symbolsbelonging to the same group. For the convenience of notation, we provide here amore general case where these parameters are different for each OFDM symbol,�.

Fig. 5. CAF magnitude for the mobile WiMAX signal at � � ��

versus CFs.

Case (2): For delays andinteger and (structure and repetition of

the preamble induced-cyclostationarity), with denoting theceiling function

(4)

and the set of CFs is given by (3). As the preamble repeats everyframe, it is expected that the CFs are integer multiples of theframe duration. The CAF magnitude due to the preamble, atdelays is plotted versus CFs in Fig. 5.

Case (3): For delayswith as the difference between

two consecutive pilot subcarriers in DL (pilot induced-cyclo-stationarity)

(5)

where the CFs are given in (3), withand as the variances of the pilot and data symbols,

respectively, and represents the set of pilot subcarriers inDL. Similar expressions as in (5) can be also obtained for CAF atdelays

andand the same CFs. In the expressions for CAF at and

and are, respectively, replaced by their ULcounterparts, and .


Fig. 6. CAF magnitude for the mobile WiMAX signal at� � �� versus CFs.

Fig. 7. CAF magnitude for the mobile WiMAX signal at � � � � ��

versus CFs.

Fig. 6 displays the CAF magnitude atversus CFs. As the distribution of the pilot symbols repeats

every two DL OFDM symbols, one may expect that the CFs areinteger multiples of . Nevertheless, this periodicity does notappear in the UL OFDM symbols. Hence, the CAF has CFs at

integer. However, the CAF magnitude at CFs close tointeger multiples of predominates; this can be explainedbased on the relatively large number of DL OFDM symbols inthe frame.

Case (4): For delays equal to integer multiples of (repe-tition of the preamble induced-cyclostationarity)

(6)

and the set of CFs is given in (3). Fig. 7 shows the CAF mag-nitude due to the preamble at delay versusCFs. We should note that all previously mentioned results forthe estimated CAF agree with theoretical results; these are notpresented here due to space consideration.

Fig. 8. FDD DL frame structure in the LTE OFDM-based systems [24].

TABLE IILTE OPERATION MODES AND ASSOCIATED SIGNAL PARAMETERS

C. Effect of Phase, Frequency, and Timing Offsets on CAFand CF

For a received signal affected by phase, frequency, and timingoffsets, and , respectively, one can find the effect ofthese impairments on CAF and CFs by following the derivationsteps provided in Appendix B, as: the phase offset has noeffect on CAF; the frequency offset affects the phase ofCAF at delay and CF by ; the timing offsetaffects the phase of CAF at delay and CF by ; theCFs are not affected by phase, frequency, and timing offsets.

III. LTE OFDM SIGNAL MODEL AND ITS SECOND-ORDER

CYCLOSTATIONARITY

A. LTE OFDM Signal Model

Fig. 8 shows the frequency division duplex (FDD) DL framestructure used in the LTE systems [24]. The frame time durationis 10 ms, and each frame is divided into 20 slots, with the slotduration equal to 0.5 ms. Each slot contains OFDM sym-bols, where depends on the CP length and useful symbolduration (equal to the reciprocal of the subcarrier frequencyspacing) parameters of the OFDM signal. The LTE standard al-lows multimedia broadcast multicast services be performed ei-ther in a single cell mode or in a multi-cell mode. For the latter,transmissions from different cells are synchronized to form amulticast broadcast single frequency network (MBSFN) [24].Here, we consider the case where a single operational mode isemployed in each cell, i.e., either MBSFN or non-MBSFN [24].The LTE operation modes, along with the values of their param-eters, i.e., 2, are summarized in Table II.


Fig. 9. Slot structure and resource grid in the FDD DL frame [24].

The slot structure and associated resource grid used in theFDD DL frame are illustrated in Fig. 9. The slot can be repre-sented as a two dimensional resource grid consisting ofOFDM symbols in time domain and subcar-riers in frequency domain, with as the number of resourceblocks and as the number of subcarriers in a resourceblock. Note that represents the number of subcarriers in anOFDM symbol. A resource block is defined as consecu-tive OFDM symbols in time domain and consecutive sub-carriers in frequency domain. equals 12 and 24 for the LTEsignals with 15 kHz and 7.5 kHz subcarrier spacing, re-spectively. then depends on the signal bandwidth; for pos-sible values of this parameter the reader is referred to [25]. Thesmallest entity of the resource grid is called resource element; aresource block consists of resource elements.

Reference signals (RSs) are embedded in the resource blocksof the transmission frame for channel estimation and cell search/acquisition purposes [24]. An RS is assigned to each cell ofthe network and acts as a cell identifier. Therefore, the RS re-peats each DL frame. Here we study two types of RSs: thecell-specific RS associated with the non-MBSFN mode and theMBSFN RS associated with the MBSFN mode. Note that theterminology used here is according to [24]. The RSs are inter-spersed over the resource elements, usually transmitted on someof the subcarriers of one or two non-consecutive symbols ineach slot. Fig. 10 shows the distribution of the cell-specific RSfor short CP over one resource block and two consecutive slots( OFDM symbols per slot and subcar-riers per resource block): the cell-specific RS is transmitted onthe first and seventh subcarriers of the first OFDM symbol andon the fourth and tenth subcarriers of the fifth OFDM symbolin each slot. For the distribution of other RSs, one is referred to[24].

Following this description, we express the received LTEOFDM signal with short CP and corresponding RS distribution,which is affected by additive Gaussian noise as1

Fig. 10. Resource element mapping of cell-specific RS in LTE signal with non-MBSFN mode and short CP [24].

(7)

where is the amplitude factor equal to is the repe-tition period for the RS distribution (in number of OFDM sym-bols), which equals 7 in this case and corresponds to the numberof OFDM symbols in a slot, and arethe sets of subcarriers on which the RS is transmitted in cor-responding OFDM symbols, is the transmit pulse shapewindow (associated with the first symbol in the slot) and theimpulse response of the receive filter in cascade, is thetransmit pulse shape window (associated with remaining sym-bols in the slot) and the impulse response of the receive filterin cascade, and are the duration of the first OFDMsymbol in the slot, the duration of the remaining OFDM sym-bols in the slot, and the duration of the slot, respectively, and

are the data and RS symbols transmitted on the th subcar-rier and within the th OFDM symbol, respectively, and isthe additive zero-mean Gaussian noise. Note that the data sym-bols are taken either from a QAM or PSK signal constella-tion, while the RS symbols are taken from the BPSK signalconstellation. Data and RS symbols are zero-mean i.i.d. randomvariables. To ease the understanding of the expressions for thesignal model in (7), here we provide an explanation for that.


TABLE IIIOFDM PARAMETERS FOR THE LTE SIGNALS [24]

In all terms on the right hand-side of (7), the inner summationis over the number of subcarriers, while the outer summation isover the OFDM symbol index. The first two terms model the firstOFDM symbol in the slot, which includes data and RS symbols,respectively. The first term represents the subcarriers where datasymbols are transmitted, while the second term represents thosewhere RS symbols are transmitted. Furthermore, for the positionof the first symbol in the slot, we need to take into account theduration of the preceding slots, which yields the shift ofand by with providing theslot index. Similarly, the third and fourth terms model the fifthOFDM symbol in the slot, which includes data and RS sym-bols. Furthermore, for the position of the fifth symbol in theslot, we need to take into account the duration of the precedingslots, as well as the duration of the preceding OFDM symbolsin the same slot, which are the first OFDM symbol in the slot,

(which is longer than the other symbols) along with otherthree OFDM symbols, . This yields the shift of and

by . The fifth term expresses theremaining OFDM symbols where only data symbols are trans-mitted. Here, for the position of the OFDM symbol in the slot,we need to take into account the duration of the preceding slots,as well as the duration of the preceding OFDM symbols in thesame slot, which are the first OFDM symbol in the slot,along with other OFDM symbols, . This yieldsthe shift of and by .Similar signal models can be written for long CP with differentoperation modes and frequency separations. In this case, allsymbols have the same duration , and the signalmodels can be easily obtained.

The OFDM parameters for LTE signals are presented inTable III. As one can notice, the FFT size is scalable with thebandwidth: when the available bandwidth increases, the FFTsize also increases such that the useful symbol duration andthe subcarrier spacing are fixed. As previously mentioned, twodifferent values are used for the subcarrier spacing with theLTE signal ( kHz and 15 kHz), and this results in twodifferent values for the useful OFDM symbol duration (133.33

s and 66.67 s, respectively).

B. CAF and Set of CFs for LTE OFDM Signals

According to derivations in Appendix C, the CAF and set ofCFs for the LTE OFDM signals with short CP are as follows.


(8)

(9)

where represents the variance of RS and data symbols.Case (2): For delays equal to integer multiples of (RS-

induced cyclostationarity)

(10)

at the CFs in (9). Here represents the number of subcarrierson which RS are transmitted in each OFDM symbol which in-cludes RS; as noted in Section II.B, this is equal for and .

Similarly, one can show that CAF and set of CFs for LTEOFDM signals with long CP are as follows.


(11)

integer (12)

Case (2): For delays equal to integer multiples of (RS-induced cyclostationarity)

(13)

at the CFs in (9). Here and are the sets of the OFDMsymbols in which the RSs are transmitted, which is differentthan for the LTE OFDM signals with short CP [24].

It is worth noting that the CFs are integer multiples of forshort CP in all cases and long CP only at delays integer multiplesof while the CFs are integer multiples of for long CPat delays equal to zero and due to the same duration of allOFDM symbols in the frame.

The theoretical CAF magnitudes for the LTE signal withnon-MBSFN mode and short CP and non-MBSFN mode andlong CP at [Case (1)] are presented versus CFs inFigs. 11 and 12, respectively. The signal parameters are setas in Section V. The range corresponding to the first fourpositive and negative CFs is shown. As one can notice, the CAFmagnitude is lower for the LTE signal with the non-MBSFN


Fig. 11. CAF magnitude for the LTE signal with non-MBSFN mode and shortCP at � � � � �� versus CFs.

Fig. 12. CAF magnitude for the LTE signal with non-MBSFN mode and longCP at � � � � �� versus CFs.

mode and short CP; this is due to a lower in such acase. Additionally, the CAF magnitude at CFs close to integermultiples of predominates, as the duration of the firstsymbol in the slot is only slightly different when compared withthe duration of the remaining symbols. The theoretical CAFmagnitude for the LTE signal with non-MBSFN mode and shortCP, with non-MBSFN mode and long CP, and with MBSFNmode and long CP ( kHz) at is presentedversus CFs in Figs. 13–15, respectively. As one can see, theCAF magnitude is higher in case of MBSFN mode. This canbe easily explained, as the MBSFN RS is induced on moresubcarriers when compared with the cell-specific RS for thenon-MBSN mode. Furthermore, due to diverse RS distributionsfor different transmission modes, the CF values depend on themode. We would also like to note that results for estimatedCAF agree with theoretical results; these are not presented heredue to space consideration. Furthermore, the effect of phase,

Fig. 13. CAF magnitude for the LTE signal with non-MBSFN mode and shortCP at � � � � �� versus CFs.

Fig. 14. CAF magnitude for the LTE signal with non-MBSFN mode and longCP at � � � � �� versus CFs.

Fig. 15. CAF magnitude for the LTE signal with MBSFN mode and � � ��

kHz at � � � � �� versus CFs.

frequency, and timing offsets on CAF and CFs is as presentedin Section II-C for mobile WiMAX OFDM signals.


IV. PROPOSED CLASSIFICATION ALGORITHM BASED

ON CP-, PREAMBLE-, AND RS-INDUCED

SECOND-ORDER CYCLOSTATIONARITY

As previously discussed, both mobile WiMAX and LTEOFDM signals exhibit CP-induced cyclostationarity. However,this information can be unreliable for identifying primaryWiMAX and LTE signals, as the cognitive users sharingthe spectrum may employ OFDM signals with close usefulsymbol durations. Hence, the distinctive preamble-inducedcyclostationarity of the mobile WiMAX OFDM-based signals(Cases (2) and (4) in Section II) and the distinctive RS-inducedcyclostationarity of the LTE OFDM-based signals (Case (2) inSection III) are used in addition to the CP-induced cyclosta-tionarity for signal classification. We propose a classificationalgorithm for these signals, which makes use of their CP-,preamble-, and RS-induced cyclostationarity. The distinctivefeatures of the mobile WiMAX signals used with this algorithmare the non-zero CAF at: CF and delay(Case (1)); CF and delay[Case (2)]; CF and delay[Case (4)]. Note that only is used at as otherCFs depend on the CP length, which is unknown. Also notethat the pilot-induced cyclostationarity is not used here, asdifferent pilot distributions result in different locations for thepeaks, and the distribution is not a priori known. On the otherhand, the distinctive features of the LTE signals used with theproposed algorithm are the non-zero CAF at: CF

and delay [Case (1)]; CF and delay[Case (2)]. Note that only is used at

for the same reason as for the WiMAX signals. Also note thatonly is used at as other CFs depend on the RSdistribution, which is not a priori known. This characteristiccan be employed to further identify the operation mode; thistopic is beyond the scope of the paper.

A. Description of the Proposed Algorithm

The proposed classification algorithm is a binary tree classi-fier, as depicted in Fig. 16.

At Node 1, we decide whether or not the received signal isWiMAX based on the previously mentioned distinctive features.The cyclostationarity test proposed in [26] is applied to checkthat is a CF at (with s).2 In addi-tion, the test in [27], which represents an extension of the onein [26] to multiple CFs, is applied to check that a frequency

is a CF at and ,respectively (with s and ms).2 Both testsmake a decision on the existence of a CF at a certain delay bycomparing a CAF-based statistic with a threshold; details on thetests are provided in next section. If the tested ’s are decidedto be CFs at the corresponding delays, the decision is mobileWiMAX. Otherwise, the classification algorithm performs fur-ther testing at the next node.

At Node 2, we decide whether or not the received signal isLTE with kHz. For that we use the previously men-tioned distinctive features of the LTE signals ( kHz).The cyclostationarity test in [26] is employed to check whetheror not is a CF for delays equal to and respec-tively (with s and ms).2 The decision that

Fig. 16. Flowchart of the proposed cyclostationarity-based signal classificationalgorithm.

the LTE signals with kHz (MBSFN or non-MBSFN)is present is made if is found to be a CF at both delays.Otherwise, further testing is carried out at the next node.

Finally, at Node 3, we decide whether or not the receivedsignal is an LTE signal with kHz. The cyclostation-arity test in [26] is employed to check whether or not isa CF for delays equal to and , respectively (with

s and ms)2. The decision that the LTE signalwith this subcarrier spacing is present is made if is foundto be a CF at both delays. Otherwise, the decision that othersignals are present in the environment is made. For the clas-sification of other signals, such as single carrier linearly digi-tally modulated signals, cyclically prefix linearly digitally mod-ulated signals, and other OFDM signal types, further nodes canbe added [27].

We note that the CP- induced cyclostationarity based featuresare stronger than the preamble- and RS-induced cyclostation-arity-based features (see Figs. 4, 5, 7, 11–14). In addition, pre-amble- and RS-induced cyclostationarity-based features (Case(4) for WiMAX and Case (2) for LTE) require at least a twoframe observation interval for estimation. When the statisticscorresponding to the latter features do not pass the cyclostation-arity tests, e.g., because the observation interval is too short6, theclassification algorithm can still provide an indication based onthe CP-induced cyclostationarity. We would like to reiterate thatsuch a decision is not fully reliable (only one out of the three andtwo CAF-based statistics pass the test at Nodes 1, and Nodes 2and 3, respectively), as OFDM with close useful symbol dura-tion can be employed by CR users, as well.

B. Cyclostationarity Tests for Decision-Making

The cyclostationarity tests in [26] and [27], which are usedfor decision-making with the proposed algorithm, are describedbelow. With the test in [26], the presence of a CF is formulated

6One can go even further, and if the CP-induced cyclostationarity-based fea-ture fails the test, the kurtosis-based algorithm in [17], [18] can be triggered,which can provide the partial information with a very short observation time, atthe price of increased computational complexity.


as a binary hypothesis-testing problem, i.e., under hypothesisthe tested frequency is not a CF at delay and under

hypothesis the tested frequency is a CF at delay . Thetest consists of the following three steps:

— The CAF of the received signal, is estimated(from samples) at tested frequency and delay

and a vector is formed aswith and as

the real and imaginary parts, respectively, andas the estimate of .

— A statistic is computed for the tested frequency and

delay as with the su-perscripts and denoting the matrix inverse and trans-pose, respectively. is an estimate of the covariance ma-trix of

(14)

where the covariances and are given, for zero-meanprocess, respectively by [26]

(15)

(16)

with as the cumulant operator andas the second-order lag product.

The estimators for the covariances and are given,respectively, by [26]

(17)

(18)

where is a spectral window of length and.

— The test statistic is compared against a threshold,for decision making. If , we decide that the testedfrequency is a CF at delay . The threshold is set fora given probability of false alarm, which is defined as theprobability to decide that the tested frequency is a CF atdelay when this is actually not. This can be expressedas . By using that the statisticshas an asymptotic chi-square distribution with two degreesof freedom under the hypothesis [26], the thresholdis obtained from the tables of the chi-squared distributionfor a given value of this probability.

The cyclostationarity test proposed in [27] represents an ex-tension of the one presented previously to multiple CFs. In thiscase, the test statistic is with as the set oftested frequencies and at each tested frequency calculatedas previously explained. The threshold is similarly set, based onthe asymptotic distribution of the test statistic under the hy-pothesis . As shown in [27], this is a chi-square distributionwith degrees of freedom, where represents the numberof tested frequencies. Apparently, for this test reducesto the one proposed in [26].

Effect of Phase, Frequency, and Timing Offsets on the TestStatistics: By considering the effect of these signal impairmentson CAF (see Sections II-C and III-B), along with (14), (17), and(18), and after tedious trigonometric calculations, one can showthat and thus are independent of these impairments (seeAppendix D for proof).

Comment on the Asymptotic Algorithm Performance: Ac-cording to Section IV-A, three statistics are tested at Node 1,while two statistics are tested at Nodes 2 and 3; the thresholdsare set according to a certain as stated above. Hence, asymp-totically, the probability to decide that a signal is WiMAX whenit is not (Node 1) equals while the probability to decide thata signal is LTE with kHz and kHz when it isnot (Nodes 2 and 3) equals and ,respectively.

V. CLASSIFICATION PERFORMANCE AND COMPUTATIONAL

COMPLEXITY OF THE PROPOSED ALGORITHM

A. Simulation Setup

The signals are simulated with 5 MHz double-sided band-width. For WiMAX, the number of subcarriers is 512, whilefor LTE this is 512 with kHz and 1024 with

kHz. For the mobile WiMAX signal equals 1/8,while for the LTE signal both long ) and short( for the first symbol in the slot and

for the remaining symbols) CPs are employed. For bothWiMAX and LTE signals, QAM with 16 points and unit vari-ance of the signal constellation is used to modulate the datasubcarriers. The pilot subcarriers in mobile WiMAX are mod-ulated according to the IEEE 802.16e standard [21]. A raisedroot cosine pulse shape window is used at the transmitter witha roll-off factor of 0.025. For the WiMAX signal, the numberof symbols in the UL and DL subframes equals 35 and 12, re-spectively, and the RTG duration is 60 s whereas the TTG du-ration equals 107.225 s [19]. The sampling frequency at thereceiver is set to 8.4 MHz, and the signal is affected by a phaseoffset uniformly distributed in a timing offset uni-formly distributed in a carrier frequency offset

. The AWGN and ITU-R pedestrian and vehicular A fadingchannels are considered. The maximum delay spreads for theITU-R pedestrian and vehicular A fading channels are 410 nsand 2.51 s, respectively. For details on the power-delay pro-files of the fading channels one is referred to [29]. The max-imum Doppler frequency equals 7.28 Hz and 145.69 Hz for theITU-R pedestrian and vehicular A fading channels, respectively.At the receive-side, a filter is used to remove the out-of-band


Fig. 17. Probability of correct classification versus SNR for the signals of in-terest.

noise, and the SNR is set at the output of this filter. The proba-bility of correct classification is used as performancemeasure, with mobile WiMAX signals, LTE signals with

kHz (non-MBSFN mode and long CP, non-MBSFNmode and short CP, and MBSFN mode) and LTE signals with

kHz (MBSFN mode). Note that the LTE signalwith non-MBSFN mode and long CP is referred to LTE in fig-ures, for the convenience of notation. This probability is esti-mated based on 1000 Monte Carlo simulation trials. The Kaiserwindow with parameter 10 is used in (17) and (18), with

. Unless otherwise mentioned, the observation interval is30 ms (equivalent to six WiMAX frames and three LTE frames),the thresholds used with the cyclostationarity tests correspondto a probability of false alarm of , and the channel isAWGN.

B. Classification Performance of the Proposed Algorithm

The performance of the proposed algorithm is investigated interms of the probability of correct classification. Fig. 17 showssimulation results for this probability versus SNR for mobileWiMAX, LTE with kHz (non-MBSFN mode andlong CP, non-MBSFN mode and short CP, and MBSFN mode)and LTE signals kHz (MBSFN mode). One can seethat among the LTE signals, the best results are achieved for theLTE signals with the MBSFN mode, while lower performanceis achieved for the LTE signals with the non-MBSFN mode andlong CP, and the lowest performance is attained for the LTE sig-nals with non-MBSFN mode and short CP. Also, the perfor-mance for WiMAX signals is relatively close to that of the LTEsignals with non-MBSFN mode and short CP. Note that this isexpected, being in agreement with CAF values used for discrim-ination, as per Sections II and III. We should also mention that aprobability of deciding that other signals, such as single carrierlinearly digitally modulated (SCLD) signals, are present, whenindeed this is the case, is almost 1 under the investigated condi-tions. This is expected, as per the discussion on the asymptoticperformance analysis in Section IV-B. A confusion matrix isprovided in Fig. 18, for dB SNR. As expected based on the

value, there are basically no cases in which the algorithmdecides that a signal is of one of the types of interest (mobile

Fig. 18. Confusion matrix for �� dB SNR and 30 ms observation interval.

WiMAX and LTE), if it is not of that specific type; if the algo-rithm fails in classifying the signal of interest, the decision ispractically “Other signals.”

Figs. 19 and 20 show the simulation results for the proba-bility of correct classification versus SNR for mobile WiMAXand LTE with the non-MBSFN mode and long CP (LTE ), re-spectively, with different observation intervals (minimum twoWiMAX and LTE frames, respectively), and diverse thresholdsused for decision-making. With respect to the thresholds usedfor decision making, corresponds to an asymptotic prob-ability of false alarm of 0.01 (this equals 9.21 for 1 CF and16.812 for 3 CFs), and to an asymptotic probability of falsealarm of 0.005 (this equals 10.597 for 1 CF and 18.548 for 3CFs). As expected, a higher probability of correct classificationis achieved with a lower threshold. Furthermore, an improvedperformance is achieved with increased observation interval (in-creased number of samples, L) for all signals. We note that atleast two frames are needed to estimate CAF at (10 ms forWiMAX and 20 ms for LTE signals); even with such a short ob-servation interval, a probability of almost 1 is achieved at 3 dBSNR for WiMAX and dB SNR for LTE signals, respec-tively.

According to Section IV, the CP-induced cyclostationaritycan provide a partial indication to the CR for lower SNRs, andshorter observation intervals. Simulation results show that with20 ms and 30 ms observation intervals, the statistics associatedto these features pass the cyclostationarity test with probabilityapproaching 1 at SNRs above dB and dB for the mobileWiMAX signal (Node 1), dB and dB for the LTEsignal with non-MBSFN mode and long CP and MBSFN modewith kHz, dB and dB for the LTE signalwith non-MBSFN mode and short CP (Node 2), and dBand dB for the LTE signal with MBSFN mode and

kHz (Node 3). Moreover, for a shorter observation intervalof 10 ms, these statistics pass the test at dB SNR for themobile WiMAX signal (Node 1), dB for the LTE signal withnon-MBSFN mode and long CP and MBSFN mode with

kHz, dB for the LTE signal with non-MBSFN mode and


Fig. 19. Probability of correct classification of mobile WiMAX signalsversus SNR with various observation intervals and thresholds used for deci-sion-making.

Fig. 20. Probability of correct classification of LTE signals (non-MBSFN modewith long CP) versus SNR with various observation intervals and thresholdsused for decision-making.

short CP (Node 2), and 9 dB for the LTE signal with MBSFNmode and kHz (Node 3).

The algorithm proposed in [17] and [18] also provides partialinformation to the CR based on the useful symbol duration.To estimate this duration, the authors perform a minimizationof the kurtosis of the decoded symbols over the useful andCP durations, as well as frequency and timing offsets. Whencompared to the CP-induced cyclostationarity approach, thismethod has the advantage that it does not depend on the CPduration. On the other hand, this comes at the price of increasedcomputational complexity, as it involves an exhaustive searchover four parameters, including timing and frequency offsets,whereas the CP-induced cyclsotationarity (zero CF) tests onlythe peak which corresponds to the useful symbol duration for acertain standard signal and is immune to frequency and timingoffsets. When the observation interval and CP duration are veryshort, the kurtosis-based method in [17], [18] provides betterperformance. For example, for a 5 OFDM symbol observationinterval and 4 dB SNR, the partial information on mobileWiMAX signal is provided with a probability approaching 1with the kurtosis-based method, whereas CP-induced cyclosta-tionarity gives around 0.95 probability when

Fig. 21. Probability of correct classification of mobile WiMAX signals versusSNR under different channel conditions.

Fig. 22. Probability of correct classification of LTE signals (non-MBSFN modewith long CP) versus SNR under different channel conditions.

and essentially fails for [17]. However,when and the observation interval is longer,e.g., 300 OFDM symbols at 0 dB SNR, the classificationperformance of the two methods becomes comparable [18].

Figs. 21 and 22 show the simulation results for the proba-bility of correct classification versus SNR for mobile WiMAXand LTE with the non-MBSFN mode and long CP (LTE1), re-spectively, with AWGN, and ITU-R pedestrian and vehicular Achannels. One can notice that for all cases, the correct classifica-tion performance degrades at lower SNRs under the ITU-R ve-hicular channel. An increase of 2 dB in SNR is needed to achievea probability of almost 1 in such a channel.

We reiterate that all previous results are obtained for a phaseoffset uniformly distributed in a timing offsetuniformly distributed in and a carrier frequency offset

. Simulations were run, and showed that theseresults are essentially identical to those achieved for the casewhen the signal is not affected by such impairments. Further,diverse other values were considered for the carrier frequencyoffset, e.g., and for which the sameresults hold. This is in agreement with the theoretical findings,according to which the test statistics are independent of such


TABLE IVNUMBER OF OPERATIONS REQUIRED TO JOINTLY DETECT AND ESTIMATE EACH

CONSIDERED SIGNAL FOR 20 ms AND 30 ms OBSERVATION INTERVALS

signal impairments, and, thus, these do not affect the classifi-cation performance.

C. Computational Complexity of the Proposed Algorithm

For the computational complexity of the proposed al-gorithms, we are interested in the computation of the teststatistics. For a certain delay and tested frequency , oneneeds the estimate of the covariance matrix and the estimateof the vector to calculate the statistic . Whentesting multiple frequencies at a certain delay , a statistic iscalculated for each frequency and their sum is used as a teststatistic . We first obtain the number ofcomplex multiplications and additions needed to calculate .Then, based on the number of delays and tested frequenciesat each delay which are used for considered signals, one canobtain the number of complex operations required to obtain theperformance presented in Section V-B for a certain observationinterval (number of samples). When using the time domaindecimation FFT, based on (14), (17), (18), and the expressionof in Section IV-B, one can find that the number of com-plex multiplications and additions needed to calculate is

and ,respectively. Given that is usually a fraction of , e.g.,

the order of complexity of the algorithm canbe given as where represents the bignotation. With the parameters considered for the simulationsetup and an observation interval of 20 and 30 ms, respectively,the numbers of complex operations required with the proposedalgorithm are listed in Table IV. Note that with a micropro-cessor that can execute up to 107.55 billion floating pointoperations (flops) per second,7 the highest number of complexcomputations required to make a decision (as considered inTable IV) can be performed in approximately 2.3 ms (this isobtained assuming that 1 flop involves either a real multipli-cation or a real addition [30]). Apparently, there is a tradeoffbetween complexity and performance, according to results inSections V-B and C. Also, the number of operations needed to

7[Online]. Available: http://ark.intel.com/Product.aspx?id=47932&pro-cessor=i7-980X&spec-codes=SLBUZ

discriminate WiMAX and LTE signals is different for the sameobservation interval, as different signal features are employedand diverse steps are required (see Section IV-A). However, thecomputation time is short when compared to the observationtime, and it does not add much to the overall time needed tomake a decision.

VI. CONCLUSION AND FINAL REMARKS

In this paper, the mathematical models and second-ordercyclostationarity of OFDM-based signals employed in twopopular wireless technologies, namely, the mobile WiMAXand third Generation Partnership Project Long Term Evolution(3GPP LTE), are derived. Furthermore, the second-order cyclo-stationarity of these signals is exploited to develop an algorithmfor their classification. The proposed algorithm provides a goodperformance at low SNRs, with short observation intervals,and under diverse channel conditions. In addition, it does notrequire carrier, waveform, and symbol timing recovery, and isimmune to phase, frequency, and timing offsets. The algorithmcan be implemented in real time, with a tradeoff betweencomplexity and performance, i.e., a longer observation intervalleads to an improved performance but also to an increase in thenumber of operations. However, the processing time is shortwhen compared with the observation time, and it does not addmuch to the overall decision time. In further work, we willinvestigate other efficient methods for the implementation ofthe proposed algorithm, e.g., the Goertzel method, as well asclassification of single carrier signal employed by the WiMAXand LTE standards.

APPENDIX ASECOND-ORDER SIGNAL CYCLOSTATIONARITY: DEFINITIONS

A random process is said to be second-order cyclosta-tionary if its mean and autocorrelation are almost periodic func-tions of time [31]. The latter is expressed as a Fourier series as[31]

(19)

where is the CAF at CF and delay , andrepresents the set of CFs. The CAF can

be estimated based on samples, as [31]

(20)

APPENDIX BDERIVATION OF THE ANALYTICAL EXPRESSIONS

FOR THE CAF AND CFS CORRESPONDING TO THE

MOBILE WiMAX OFDM SIGNALS

Using the signal model in (1.a)–(1.c), one can express theautocorrelation function of as the sum of auto-correlation functions corresponding to the signal components,


signal and noise, and only noise. We expect that non-zero sig-nificant values of are attained at certain delays, forwhich we subsequently study and its representation asa Fourier series, and further determine the expressions for theCAF at CF and these delays, and set of CFs, .

Case (1): of mobile WiMAX signals is non-zero atdelays equal to zero (due to the correlation of the signal with it-self) and (due to the CP). Assuming that the symbols on eachsubcarrier are i.i.d. and mutually independent for different sub-carriers, one can easily see that onlyand are non-zero at such delays, and this occurswhen and . Based on the aboveand considering the data and pilot symbols separately in eachOFDM symbol in the DL and UL subframes, one can show that

(21)

where denotes convolution. By expressing asand using that in (21), applying the Fouriertransform, and employing the convolution theorem and the iden-tity one canfurther obtain

(22)

As one can easily see from (22), is non-zeroonly for with as an integer. By using the inverseFourier transform of (4), one can further observe thathas a Fourier series representation. This means that the CF do-main is discrete, and the CAF at CF and delay , and the setof CFs are given as in (2) and (3), respectively.

Case (2): We investigate for delays equal to in-teger multiples of plus and

, respectively, at which we expect havenon-zero values due to the structure of the preamble and itsrepetition every frame. Without considering its particular posi-tion in the frame, a preamble symbol can be expressed in timedomain as

(23)

Without loss of generality, we consider a rectangular window.According to [23], such a preamble consists of three consecu-tive sequences that are highly correlated waveforms, and can bewritten as

(24)where and with

and . As such,one can see that there is a non-zero autocorrelation of atdelays equal to given by

(25)

Similarly, one can show that there is a non-zero autocorrela-tion of at delays equal to as given in(25). Furthermore, by considering the other components of themobile WiMAX signal within a single frame, one can show thatthe only non-zero component of the autocorrelation function atdelays equal to and , respectively, isdue to the preamble. With multiple framesand based on the time-domain repetition property of the pre-amble, one can further show that the values of for de-lays equal to and integerand are equal to those at and re-spectively. With andinteger, and can be shown to be

(26)


By following the same steps as in Case (1), one can furthershow that the CAF at the above delays and the set of CFs aregiven as in (4) and (3), respectively.

Case (3): We investigate for delays equal toand andand at

which we expect have non-zero values due to thetransmission of boosted pilot symbols every th and thsubcarriers in the DL and UL OFDM symbols, respectively.As in Case (2), we consider a single DL OFDM symbol,which includes both data and pilot subcarriers; without lossof generality, this is a DL symbol, and a rectangular windowis assumed. The pilot symbols are transmitted every thsubcarrier, and are boosted over the data symbols. The timedomain representation of such a DL OFDM symbol is

(27)

where is the (data/pilot) symbol transmitted on the th sub-carrier. The DL OFDM symbol can be further expressed as thesum of two parts: a first part which corresponds to symbolsover all subcarriers, whose variance is and a second partwhich corresponds to symbols only over the pilot subcarriers,whose variance is i.e.,

with

(28)

(29)

where and are the symbols with variance and, respectively, is the number of subcarriers used

for pilot transmission in the considered DL OFDM symbol, andis the position of the first subcarrier where a pilot

symbol is transmitted.Apparently, Case (3) can be treated similarly to Case (2),

where is replaced by , and , withand

, respectively. By following the same proce-dure as in Case (2), one can obtain the expressions for the CAFand set of CFs in (5) and (3), respectively.

Case (4): We further investigate for delays equal tointeger multiples of . At these delays, one can easily showthat the only non-zero term corresponds to when

8Note that, for simplicity, we assume that one set of pilot symbols are trans-mitted in an OFDM symbol. In case that another set is transmitted with dif-ferent distribution, simply, another term e.g., � �� can be added to representany additional set. The analysis for � �� also applies for � �� with CAFbeing the summation of results for all terms.

which is due to the time repetition of the pre-amble every frame. Thus, for such delays becomes

(30)

where . Note that at these delaysunless

(otherwise the pulses do not overlap, yieldingzero product). Based on the above observation, by using that

and after some mathematical manipulations,(30) can be re-expressed as

. Furthermore, by following the same stepsas in Case (1), one obtains the CAF and set of CFs as in (6) and(3), respectively.

APPENDIX CDERIVATION OF THE ANALYTICAL EXPRESSIONS FOR THE CAF

AND CFS CORRESPONDING TO THE LTE OFDM SIGNALS

By using the signal model in (7), the autocorrelation func-tion of can be expressed as the sum of the autocorrelationfunctions corresponding to any two signal components, signaland noise components, and noise component. We expect thatnon-zero significant values of are attained at certaindelays, for which we subsequently study and its rep-resentation as a Fourier series, and determine the expressionsfor the CAF at CF and these delays, and set of CFs,

.Case (1): We expect that non-zero significant values of

are attained for delays equal to zero (due to the cor-relation of the signal with itself) and (due to the existenceof the CP). Assuming that the symbols on each subcarrier arei.i.d. and mutually independent for different subcarriers, andconsidering that the number of RS subcarriers is equal forand and the symbol variances satisfyby following the same procedure as in Case (1) for WiMAXsignals, one can show that

(31)


and the CAF at CF and delay and the set of CFs are given,respectively, in (8) and (9).

Case (2): We expect that non-zero significant values ofare also attained for delays equal to integer multi-

ples of (due to the repetition of the RS every frame). Atthese delays, one can show that the only non-zero terms in

are due to the repetition of the RS, and correspond towhen and

with as an integer and as the number of OFDM symbolsin the transmission frame. By taking this into account and fol-lowing the same procedure as for Case (1) of WiMAX signals,after several mathematical manipulations, one can show that

(32)

where represents the number of RS subcarriers, which isequal in and . Hence, the CAF at CF and delay andthe set of CFs are given, respectively, as in (8) and (9). Similarly,one can show that for the LTE signals with long CP, non-zero

is attained for delays equal to zero and [Case (1)]and integer multiples of [Case (2)]. The CAF at CF anddelay and the set of CFs can be similarly shown to be givenas per Section III-B.

APPENDIX DEFFECT OF PHASE, FREQUENCY, AND TIMING

OFFSET ON TEST STATISTICS

According to results provided in Sections II.C and III-B, thephase offset does not affect the CAF and CFs of the mobileWiMAX and LTE OFDM signals. Hence, the CAF-basedtest statistics used for classification, which are given inSection IV-B, are independent of the phase offset. On the otherhand, the frequency and timing offsets, and , affect thephase of CAF at CF and delay by and ,respectively; the CAF magnitude and CFs are not affected. Toemphasize the effect of and on the CAF phase, we ex-press CAF as , where represents theCAF of the signal unaffected by these signal impairments, and

. As such, when the signal is affectedby and becomes

and, by using the expressionof and (17) and (18), one can see that the effect on

is multiplication by while there is no effect on

. By employing these results with (14), is calculated,and after tedious trigonometric calculations, one finds that thetest statistic is independent of and . Furthermore, it isthen straightforward that is also independent of these signalimpairments.

ACKNOWLEDGMENT

The authors would like to thank the anonymous reviewers andthe Editor, Dr. P. Ciblat, for their constructive comments on thepaper.

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stationary time-series, Part I: Foundation and Part II: Developmentand applications,” IEEE Trans. Signal Process., vol. 42, no. 12, pp.3387–3429, Dec. 1994.

Ala’a Al-Habashna received the B.S. degree (withexcellent assessment) in computer engineering fromMu’tah University, Karak Governorate, Jordan,in 2006, and the M.S. degree in electrical andcomputer engineering from Memorial University ofNewfoundland, St. John’s, NL, Canada, in 2010. Hereceived the fellowship of school of graduate studiesat Memorial University of Newfoundland.

He is currently with Stratos Global, St. John’s, asa Technical Communications Specialist. His researchinterests include signal detection and classification,

cognitive radio systems, communication networks architecture and protocols,and communication networks security.

Octavia A. Dobre (M’04–SM’07) received theDipl.Ing. and Ph.D. degrees in electrical engineeringfrom Politehnica University of Bucharest (formerlythe Polytechnic Institute of Bucharest), Bucharest,Romania, in 1991 and 2000, respectively. In 2000she was the recipient of a fellowship at WestminsterUniversity, U.K., and in 2001 she held a Fulbrightfellowship at Stevens Institute of Technology,Hoboken, NJ.

Between 2002 and 2005, she was a Research As-sociate with the Department of Electrical and Com-

puter Engineering, New Jersey Institute of Technology, Newark. In 2005, shejoined the Faculty of Engineering and Applied Science at Memorial Univer-sity of Newfoundland, St. John’s, NL, Canada, where she is currently an Asso-ciate Professor. Her research interests include blind signal recognition, cogni-tive radio systems, cooperative communications, network coding, and resourceallocation in emerging wireless networks.

Dr. Dobre is an Associate Editor for the IEEE COMMUNICATIONS LETTERS

and has served as the technical program chair for the signal processing and mul-timedia symposium of the IEEE Canadian Conference on Electrical and Com-puter Engineering (CCECE) 2009 and the signal processing for communica-tions symposium of the International Conference on Computing, Networking,and Communications (ICNC) 2012.

Ramachandran Venkatesan (M’78–SM’92) re-ceived the M.S. and doctoral degrees from theUniversity of New Brunswick, Saint John, NB,Canada.

He is the Dean Pro Tempore and a Professor ofComputer Engineering in the Faculty of Engineeringand Applied Science of Memorial University ofNewfoundland, St. John’s, NL, Canada. His researchinterests include architecture and application of par-allel processing structures, wireless sensor networks,underwater acoustic communications, error control

codes, and digital design.He is member of the Professional Engineers and Geoscientists of Newfound-

land and Labrador. For over ten years he has held several academic adminis-trative positions including the Chair of Electrical and Computer Engineering,Associate Dean of Graduate Studies and Research, Associate Dean of Under-graduate Studies, and Acting Dean of Engineering.

Dimitrie C. Popescu (S’98–M’02–SM’05) receivedthe Engineering Diploma and M.S. degrees inelectrical engineering from the Polytechnic Instituteof Bucharest, Bucharest, Romania, in 1991, and thePh.D. degree in electrical and computer engineeringfrom Rutgers University, New Brunswick, NJ, in2002.

From 2002 to 2006, he was with the Departmentof Electrical and Computer Engineering, The Univer-sity of Texas at San Antonio. He has also worked forAT&T Labs, Florham Park, NJ, on signal processing

algorithms for speech enhancement, and for Telcordia Technologie, Red Bank,NJ, on wideband CDMA systems. He is currently with the Department of Elec-trical and Computer Engineering, Old Dominion University, Norfolk, VA. Heis the coauthor of a monograph book on Interference Avoidance for WirelessSystems (Kluwer, 2004). His current research interests are in the areas of wire-less communications and cognitive radio systems and include spectrum manage-ment and dynamic spectrum access, transmitter/receiver optimization to supportquality of service, and spectrum sensing and modulation classification.

Dr. Popescu has served as the Technical Program Chair for the vehicular com-munications track of the IEEE Vehicular Technology Conference (VTC) 2009Fall, the Finance Chair for the IEEE Multiconference on Systems and Control(MSC) 2008, and a Technical Program Committee member for the IEEE GlobalTelecommunications Conference (GLOBECOM), the IEEE International Con-ference on Communications (ICC), the IEEE Wireless Communications andNetworking Conference (WCNC), and VTC conferences. He was the recipientof the Second Prize Award at the AT&T Student Research Symposium (an ACMregional competition) in 1999 for his work on interference avoidance and dis-persive channels.

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