IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 58, NO. 5, MAY 2010 2783 Pilot-Aided Carrier Frequency Estimation for Filter-Bank Multicarrier Wireless Communications on Doubly-Selective Channels Vincenzo Lottici, Ruggero Reggiannini, and Michele Carta Abstract—Multicarrier modulation techniques are currently the key technology in the area of high-data-rate transmission over wireless fading channels. Their considerable vulnerability to car- rier frequency offsets, however, hinders their appealing features and demands adequate countermeasures. This paper contributes with a class of frequency estimation algorithms intended for filter bank burst-mode multicarrier transmission over time-frequency selective fading channels. All algorithms are derived from the maximum likelihood principle, exhibit a feedforward structure and are based on the use of pilot symbols scattered throughout the burst. The accuracy of the proposed schemes is investigated in typical mobile wireless scenarios, showing that they outperform maximum likelihood non-data-aided frequency recovery in spite of a substantially lower computational requirement. Index Terms—Filter bank multicarrier transmission, frequency recovery, pilot-aided synchronization, time-frequency selective channels. I. INTRODUCTION T HE area of high-data-rate transmission over both wired and wireless channels has been marked in the last decades by an ever increasing interest on multicarrier (MC) modulation techniques [1], [2]. In the form of orthogonal-frequency-divi- sion-multiplexing (OFDM) modulation, MC schemes have been embedded in several standards, such as terrestrial digital audio broadcasting (DAB) and video broadcasting (DVB-T), IEEE 802.11 Wi-Fi indoor wireless LANs, IEEE 802.16 Wi-MAX fixed broadband wireless access, and asymmetric digital sub- scriber lines (ADSL) for digital services over twisted-pair chan- nels [3]–[7]. Recently, the class of orthogonal MC systems has been generalized with the introduction of filter bank multicar- rier (FBMC) modulations for very-high-speed wired access net- works [8]. In FBMC-based systems the data symbols are fre- quency-multiplexed over contiguous subchannels after proper pulse shaping. Compared with conventional OFDM, the pulse waveforms are significantly longer than the subchannel symbol Manuscript received January 18, 2009; accepted December 16, 2009. Date of publication January 29, 2010; date of current version April 14, 2010. The as- sociate editor coordinating the review of this manuscript and approving it for publication was Prof. Gerald Matz. This paper was presented in part at the In- ternational Conference on Communications, June 2007. The authors are with the Department of Information Engineering, University of Pisa, I-56122 Pisa, Italy (e-mail: vincenzo.lottici@iet.unipi.it; ruggero.reg- giannini@iet.unipi.it; michele.carta@iet.unipi.it). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSP.2010.2041872 interval, and thus overlap in time. Conversely, the spectra of data signals on the available subcarriers are bandlimited and, de- pending on the prototype filter employed in the filter bank, they are either nonoverlapping in frequency, as in filtered multitone (FMT) [8], or marginally overlapping, as in discrete wavelet multitone (DWMT) [9]. The spectral constraint imposed on the subchannels makes FBMC an efficient alternative to conven- tional OFDM signalling with a number of appealing features such as [8]: i) reduced sensitivity to narrowband interferers, ii) higher flexibility to allocate groups of subchannels to dif- ferent users, iii) mitigation of inter-carrier interference (ICI) on severely time-frequency selective wireless channels, iv) pulse shaping and subcarrier spacing can be selected to improve spec- tral efficiency, v) absence of any cyclic extension, vi) simple fre- quency-domain equalization. Further, whenever adopted in con- junction with offset QAM modulation (OQAM) in the form of OFDM/OQAM, it enables high throughput efficiency [10]. The above qualities explain why FBMC schemes have been adopted for a number of wireless standards as well, such as the return channel of terrestrial DVB (DVB-RCT) [11] and the second re- lease of the terrestrial trunked radio (TETRA) enhanced data system (TEDS) air interface [12]. The interest surrounding FBMC is also demonstrated by a number of significant works on the topics of channel equaliza- tion and signal synchronization [13]–[22]. In [13], per-subcar- rier equalization structures are proposed each comprising the cascade of an allpass filter and a linear-phase finite impulse response (FIR) filter for separately adjusting signal amplitude and phase, whereas in [14], fractionally spaced linear and deci- sion feedback equalizers are designed and evaluated. The timing synchronization problem specific to FBMC-based systems is studied in [15]–[18]. In particular, the bit-error-rate sensitivity to timing errors is assessed in [15]. In [16] and [17] simple data-aided and decision-directed timing error detectors are pre- sented, while [18] discusses an iterative blind, or non-data-aided (NDA), 1 closed-loop scheme. The issue of carrier frequency offset (CFO) recovery for FBMC is also treated in the litera- ture [19]–[22]. The scheme in [19] addresses blind timing and frequency synchronization by exploiting the cyclostationary na- ture of the FBMC signal, while that in [20] again relies on the specific statistical properties of the FBMC signal and is de- rived from the best linear unbiased estimation (BLUE) prin- ciple. With a different yet more accurate approach, the max- imum-likelihood (ML) criterion is applied in [21] under the as- sumption of low signal-to-noise-ratio (SNR) to obtain a closed- 1 This indicates a synchronization algorithm that does not rely on pilot or training sequences. 1053-587X/$26.00 © 2010 IEEE