## 1 Introduction
All of the techniques discussed above consider only the dominant ICI terms inside the band; the rest of the ICI outside the band is treated as white noise. However, the ICI terms outside the band are not properly modeled as white noise, but correlated. Hence, the autocorrelation function of the ICI outside the band has been discussed in [19] to design a pre-whitener to compensate ICI outside the band, the autocorrelation matrix of which can also be applied to the likelihood function for more accurate LLR computations. However, this makes the LLR computations not a desirable feature for soft ICI cancellation. In this paper, we first discuss the matched filter-based multiple PIC (MF-PIC), and then, we employ multi-feedback ICI cancellation matched filter in a sequential form (MF-SIC). It is worth to noting that the matched filter is used for the proposed methods throughout the paper unless otherwise specified. The original idea is motivated by [20], which proposes multi-feedback (MB) cancellation for MIMO systems to approximate the ML solution by selecting one SIC solution out of multiple candidates. Unlike the work in [14,16,17,20], the proposed multi-feedback matched filter (MBMF) strategy has been employed to approximate the residual ICI induced by soft cancellation and to obtain more reliable LLR values of transmitted bits. We propose two generation mechanisms for the multi-feedback strategy: Gibbs sampling-based generation (GSG) and tree search-based generation (TSG). Note that the generation of feedback candidates by GSG is performed bit by bit independently, unlike the recursive implementation described in [21,22]. Furthermore, it does not require a burn-in period to reach its stationary distribution [14] and the removal of repetitions [23]. For TSG-based on the conventional Bayesian framework, it builds up a tree structure-like breadth-first search algorithm [24] and searches for the most likely candidates given the probability of bits. Hence, the contribution of this paper can be summarized as:  
* The effectiveness of MF-PIC and MF-SIC using the banded channel matrix is analytically validated in terms of signal-to-interference-plus-noise-ratio (SINR). * We propose two generation mechanisms for the multi-feedback strategy: Gibbs sampling-based generation (GSG) and tree search-based generation (TSG). * The SINR ordering is also discussed to further remove the error floor induced by the ICI. * With the aid of the autocorrelation of the residual ICI, analytical derivation of the bit error rate (BER) performance with the proposed MBMF scheme is given. * The derivation of the proposed channel estimation (Multi-segment channel estimation (MSCE)) and the lower MSE performance bound have been presented. The proposed ICI cancellation algorithms incorporating MSCE show the robustness to the time-varying channels and better performance than other cancellation techniques. The paper is organized as follows. Section 2 states the system model and receiver structure. Section 3 discusses conventional PIC and SIC for OFDM systems over time-varying channels. Section 4 formulates the problem of multiple interference cancellation and derives its LLR computation. The multi-feedback generation mechanism is presented in Section 5, and the analytical derivation of the BER performance is presented in Section 6. The SINR ordering for MBMF-SIC is in Section 7. Followed by Section 7, the MSCE and the lower bound are investigated in Section 8. In Section 9, the complexity requirement of the interference cancellation and channel estimation algorithms is presented. The simulation results are given in Section 10, and Section 11 draws the conclusions.