Tracking Behavior of Adaptive Equalizers in Filtered Multitone Communication Systems Pooyan Amini and Behrouz Farhang-Boroujeny University of Utah e-mails: (amini,farhang)@ece.utah.edu Abstract— Although orthogonal frequency division multiplex- ing (OFDM) communication systems that uses inverse discrete Fourier (IDFT) for multicarrier modulation and discrete Fourier transform (DFT) for demodulation are dominantly adopted in the current broadband communication standards, there have been some reports in recent years that discuss the shortcomings of OFDM in highly mobile and/or multiple access environments. To resolve these problems, a number of authors have proposed a shift from OFDM to filterbank-based multicarrier (FBMC) techniques. In a recent work, we presented a thorough study of filtered multitone (FMT), a class of FBMC systems, in time-varying frequency selective channels. We derived close-form equations for the optimum parameters of per-tone fractionally spaced equalizers and also signal to interference plus noise ratio (SINR) and used these to evaluate FMT in typical wireless mobile environments. These results provide an upper limit to the performance of this class of FBMC systems. In this paper, we study the performance of an adaptive channel estimation algorithms that attempts to reach this upper limit. To further improve the channel estimate, the proposed method uses a minimum mean-square error (MMSE) channel estimator and considers the fact that the channel impulse response is limited in time. Keywords – multicarrier communication, OFDM, filtered multi- tone, equalization, channel estimation I. I NTRODUCTION Orthogonal frequency division multiplexing (OFDM) has been the dominant technology for multicarrier communica- tions over broadband wireless channels [2]–[4]. In frequency selective time invariant channels, OFDM offers a number of properties that make it the most attractive candidate for a variety of applications. In particular, the use of cyclic prefix (CP) samples, makes the task of channel equalization trivial; a single-tap equalizer per subcarrier channel suffices. How- ever, in time varying environments, the OFDM performance degrades due to high spectral leakage, [5], [6]. Also, OFDM may not be a good candidate in multiple access applications; particularly, in cognitive radios [7]. On the other hand, multicarrier modulation techniques that are based on filter banks have recently been emphasized as an alternative to OFDM, e.g., [7], [8], [10], [11]. Wang et al., [8], [9], particularly, have recently compared filtered multitone (FMT), one of a few variations of filter bank multicarrier This work has been supported by National Science Foundation under the award number 0801641. (FBMC) techniques, with OFDM and concluded that in fast fading channels FMT outperforms OFDM. In a recent work [1], we furthered the analysis of [8] and [9] by exploring the FMT performance when a multi-tap equalizer is used at each subchannel output of FMT. We derived close- form solutions for the optimum coefficients of a fractionally spaced equalizer and the signal to intersymbol interference plus noise ratio (SINR) at the equalizer output. We concluded that for normal speeds in an IEEE 802.16 environment, a single-tap equalizer performs almost as good as a multiple- tap equalizer. FMT has been extensively studied for application in digital subscriber lines (DSL) technologies, [12]–[14]. In such chan- nels, to improve on the bandwidth efficiency, it is proposed to use prototype filters that do not follow the conventional design of square-root Nyquist filters. The prototype filters are design for a very small excess bandwidth (say, 12.5%) and decision feedback equalizers (DFEs) are used to compensate for the non-Nyquist distortion introduced by the prototype transmitter and receiver filters. This idea does not work for wireless channels, where adaptation of DFEs and also error propagations in DFEs are serious problems. To resolve the problems associated with adaptation of equalizers in FMT, when applied to time-varying channels, we propose the following solution. We note that according to our earlier studies in [1] for typical wireless mobile channels single tap equalizers per subcarrier are sufficient. In such cases, the optimum equalizer setting is (almost) independent of the chan- nel noise and is equal to the inverse of the channel gain at each subcarrier. We thus take an indirect approach to setting the equalizers. We first identify the channel using the commonly known techniques from the OFDM literature, [15]. We also make use of the prior knowledge that the impulse responses of channels of interest are limited in time to smoothen the channel frequency responses. We show through numerical simulations that this method has excellent performance in typical mobile wireless channels of interest. II. CHANNEL MODEL The block diagram of an FMT system is shown in Fig. 1. In order to achieve intersymbol interference (ISI) free transmis- sion over each subcarrier band (which is approximated by a flat-fading time-invariant gain), the transmit filter and receive filter are designed such that their convolution makes a Nyquist pulse-shape. On the other hand, in order to achieve inter- channel interference (ICI) free transmission, the filters that are 903 978-1-4244-5827-1/09/$26.00 ©2009 IEEE Asilomar 2009