Blind CFO Estimators for OFDM/OQAM Systems With Null Subcarriers Tilde Fusco and Mario Tanda Dipartimento di Ingegneria Elettronica e delle Telecomunicazioni, Universit` a di Napoli Federico II, via Claudio 21, I-80125 Napoli, Italy. E-mail: {tilfusco, tanda}@unina.it Abstract— This paper deals with the problem of blind carrier-frequency offset (CFO) estimation in OFDM sys- tems based on offset quadrature amplitude modulation (OFDM/OQAM) with null subcarriers. Specifically, by as- suming that the number of subcarriers is sufficiently large, the received signal is modeled as a complex Gaussian random vector (CGRV). Since the OFDM/OQAM signal results to be a noncircular (NC) process, by exploiting the generalized probability density function for NC-CGRVs, the unconditional maximum likelihood (ML) algorithm for CFO estimation in non dispersive channel is proposed. Moreover, a modified version of the unconditional ML CFO estimator is considered. The performance of the derived algorithms, assessed via computer simulation, is compared with that of recently proposed estimators exploiting the second-order cyclostationarity and with the Gaussian Cram´ er-Rao bound. Index Terms— Blind estimation, carrier-frequency offset, null subcarries, OFDM/OQAM systems. I. I NTRODUCTION Orthogonal frequency-division multiplexing (OFDM) modulation is well known for its robustness to multi- path channels. This is mainly due to the insertion of a guard interval (or cyclic prefix) that efficiently combat the intersymbol interference and the intercarrier interference in dispersive channels. However, the insertion of a guard interval is pure redundancy, and then it decreases the spectral efficiency. Therefore, it is interesting to study al- ternative OFDM modulation schemes, which can provide the same robustness without requiring a guard interval, offering a better spectral efficiency. For this purpose, recently, a new efficient OFDM scheme based on offset quadrature amplitude modulation (OFDM/OQAM) has been developed (see [1]- [5] and references therein). Moreover, OFDM/OQAM systems with null (or virtual) subcarriers have also been investigated by the IEEE 802.22 working group [6]. However, like all the other multicarrier modulation schemes, OFDM/OQAM systems are in general more sensitive to frequency synchronization errors than single- carrier systems, [7] and [8]. In particular, a carrier- frequency offset (CFO) induces an amplitude reduction of the transmitted signal and provokes intersymbol and This work was supported in part by the Italian Ministry of University (MIUR) project S.Co.P.E. intercarrier interference [9]. Therefore, accurate CFO syn- chronization schemes must be designed for these systems. In [10] a blind CFO estimation algorithm has been derived by exploiting the conjugate second-order cyclo- stationarity of the received OFDM signal in the case of noncircular transmissions. In [5] this method, designed for standard OFDM systems, has been extended and analyzed in the context of OFDM/OQAM transmissions. However, the derived estimator assures a satisfactory performance only when a large number of OFDM symbols is con- sidered. The second-order conjugate cyclostationarity has been also exploited in [11] while in [12] a blind joint CFO and symbol timing estimator based on the unconjugate cyclostationarity property of the OFDM/OQAM signal has been derived. This paper, by considering the study addressed in [13], proposes blind CFO estimation algorithms for OFDM/OQAM systems with virtual subcarriers. Specif- ically, by assuming that the number of subcarriers is sufficiently large, the received signal is modeled as a complex Gaussian random vector (CGRV). Moreover, it is shown that the OFDM/OQAM signal results to be a noncircular (NC) (or improper [14]) process (i.e., its conjugate correlation function is different from zero [5]). Therefore, by exploiting the generalized probability density function (pdf) for NC-CGRVs reported in [15] and under the hypothesis of a non dispersive channel, the unconditional maximum likelihood (ML) algorithm for CFO estimation is derived. Moreover, a modified version of the unconditional ML CFO estimator is considered. The performance of the derived algorithms, assessed via computer simulation, is compared with that of the estima- tors proposed in [12] and in [5], exploiting the second- order cyclostationarity, and with the Gaussian Cram´ er- Rao bound. The organization of this paper is as follows. In Section II we describe the considered system model. Section III deals with the ML CFO estimation algorithm. The GCRB is derived in Section IV and numerical results are presented and discussed in Section V. Finally, conclusions are drawn in Section VI. Notation: j △ = √ −1, superscript (·) ∗ denotes the complex conjugation, ℜ[·] real part, ℑ[·] imaginary part, |·| absolute value and arg[·] the argument of a complex number in [0, 2π). Moreover, (·) T indicates transpose, JOURNAL OF COMMUNICATIONS, VOL. 2, NO. 3, MAY 2007 17 © 2007 ACADEMY PUBLISHER