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Top1. Introduction
Modern communication systems are expected to provide high data rates, up to many Gbps as in 5G systems. Multicarrier (MC) schemes might be the best choice for wideband transmission. They convert a frequency selective channel into a set of parallel frequency flat channels. One of the most important schemes of MC systems is CP-OFDM which is used in many applications, such as digital television, audio broadcasting (Alard & Lassalle, 1987) and 4G mobile communications. It is combined with MIMO in IEEE802.11n in order to increase the bit rate and to provide a better use of the channel spatial diversity (Pajouhi, Fakhraie, & Jamali, 2008). However, OFDM suffers from some drawbacks such as: low spectral efficiency due to the Cyclic Prefix (CP) as it contains redundant information (Qinwei, Schmeink, 2015); high sensitivity to frequency offset and high out-of-band emission due to the rectangular prototype filter used in CP-OFDM which has poor frequency localization and high side-lobes level (Vahlin & Holte, 1996). To overcome these drawbacks, FBMC/OQAM scheme was suggested as an appropriate alternative to CP-OFDM scheme (Siohan, Siclet, & Lacaille 2002). This modulation is being studied and considered nowadays in recent research projects as a key for next generation 5G mobile communications (Xu, Zhang, Lu, Wang, Guidotti, & Chang, 2016). Indeed, FBMC /OQAM does not need any CP so it exhibits better spectrum shape compared with CP-OFDM and enables better spectrum usage. FBMC allows the use of different time-frequency prototype filters which are well localized in the time-frequency domain such as PHYDYAS prototype filter (Siohan & Roche, 2000; Du, & Signell, 2007) and Isotropic Orthogonal Transform Algorithm (IOTA) prototype filter (Bellanger, 2001), so the out of band emission and sensitivity to frequency offset can be reduced.
All these advantages reflect negatively on the complexity of the equalizer, since CP is not used to reduce Inter-Symbol Interference (ISI), so one tap equalizer per subchannel is not sufficient for highly frequency selective channels as in OFDM (Marijanovic, Schwarz, & Rupp, 2016), so the equalization problem in FBMC systems is still the subject of current research.
Many equalization schemes have been proposed in literature. A low complexity frequency sampling equalizer is proposed in (Ihalainen, Stitz, Rinne, & Renfors, 2006) to equalize the frequency response of the sub-channel at a number of frequencies equal to the number of equalizer’s coefficients, but equalizing the frequency response does not provide a direct control of the residual interference in the output signal. An efficient linear minimum mean square error (MMSE) per-subcarrier equalizer has been derived in (Waldhauser, Baltar, & Nossek, 2008), which takes into account Inter-Carrier Interference (ICI) coming from adjacent subchannels. This equalizer has been enhanced in (Ikhlef & Louveaux, 2009) by using a two stage MMSE equalizer. In the first stage, an ordinary MMSE equalizer is applied to the received signal. In the second stage, the decisions on the received symbols at the output of the first stage are used by an interference canceller to remove the term corresponding to ICI from the received signal for each subchannel. In this manner, the second stage deals only with signal that is mainly corrupted by ISI and additive noise. An attempt to also remove ISI from the received signal does not help to improve the performance due to the error propagation phenomenon. Actually, estimated errors in the current FBMC symbol at the output of the first stage would increase the interference after the interference canceller for the symbols that follow.
Error propagation phenomenon can be overcome in Bit Interleaved Coded Modulation (BICM) system (Caire, Taricco, & Biglieri, 1998) by using the decisions on the received symbols at the output of the channel decoder instead of the output of the equalizer. Our previous work (Assimi, Poulliat, & Fijalkow, 2008a; Assimi, Poulliat, & Fijalkow, 2008b) on turbo-equalization for finite-length packets using single carrier show that the channel decoder improves the reliability of estimated symbols while residual errors are decorrelated by the interleaver.