## 1 Introduction  
Due to the OFDM system's high spectral efficiency and simple equalization, it has been widely adopted by many digital communication standards, such as Long-term evolution (LTE), LTE-Advanced and Worldwide Interoperability for Microwave Access (WiMAX). However, its performance suffers severely from inter-carrier interference (ICI) caused by the Doppler effect. The ICI can be effectively eliminated by introducing short OFDM symbols. However, the spectral efficiency is reduced due to more cyclic-prefixes (CPs) being required. In order to address this issue, several equalization techniques ranging from linear (zero-forcing (ZF) and minimum mean square error (MMSE)) to non-linear ones (successive interference cancellation (SIC) and (Maximum a priori probability (MAP)) have been proposed. A simple frequency domain ZF equalizer using the banded channel structure has been proposed in [1]; recursive MMSE filters with decision feedback equalization and matched filter bound (MFB) (perfect removal of ICI cancellation) [2; 3] have been investigated, and the bound can be considered as the performance benchmark for ICI cancellation algorithms. In [4; 5], the authors, using time-domain receiver windowing, further exploited the banded channel matrix in the frequency domain to design the serial and block equalizers with low complexity. Another method, based on the modified banded structure in the time or the frequency domain, estimates the symbols using a sequential least-square QR (LSQR) algorithm with selective parallel interference cancellation (PIC) [6]. Furthermore, the authors in [7; 8] proposed two pre-equalizers to mitigate the effects of time variations and to obtain a diagonal channel matrix. One in [7] developed a partial FFT (PFFT) method to reduce the size of receive signal vectors for simple equalization, and the other in [8] has formulated the pre-equalizer based on ICI power minimization. In [9], ICI is modeled using derivatives of the channel amplitude, and an iterative decision feedback equalizer (DFE) was used to derive a single tap equalizer in the frequency domain. A similar idea is implemented in [10] to obtain the diagonal matrix using mean values of transmit symbols based on log-likelihood ratio (LLR) values from the channel decoder. Some other iterative processing techniques employing a novel LLR criterion, hybrid processing or multiple cancellation orders are presented in [11; 12; 13]. Additionally, a low-complexity sequential MAP detector using the Markov chain Monte Carlo (MCMC) algorithm for mobile OFDM can be found in [14] with a successively-reduced search dimension using soft ICI cancellation, which is a variant of ICI cancellation with the aid of MAP detection. However, by introducing the Gibbs sampler, the complexity of generating samples for MAP detection is almost the same as that of tens of sequential ICI cancellations with a relatively large channel matrix. Besides the MCMC-MAP equalizer mentioned above, the authorsin [3,15] further investigate the reduced state MAP equalization techniques for uncoded and coded OFDM systems to achieve the benchmarking performance with hardware-realizable complexity. Due to the difficulty of estimating the rapidly varying channel, some joint receiver designs incorporating channel estimation have been proposed for OFDM systems in [16, 17, 18]. The authors of [16] propose a successive interference cancellation (SIC) scheme based on a group of subcarriers, namely match filter (MF)-SIC, with iterative single-burst channel estimation (SBCE), but its working scenario is limited to relatively low normalized Doppler frequencies due to the channel estimation error and the residual ICI inside the band. The work presented in [18] is relatively robust to channel time variation, but it requires a higher complexity than others. The recent work in [17] suggests an alternative way of estimating time varying channels in multi-segmental form with soft PIC, which can extend the operation of OFDM systems to higher Doppler frequencies.