# A Low-Complexity Pilot-Based Frequency-Domain Channel Estimation for ICI Mitigation in OFDM Systems
###### Abstract  
A low-complexity pilot pattern and a frequency-domain channel estimation method for Inter-Carrier Interference (ICI) mitigation is proposed for Orthogonal Frequency Division Multiple Access (OFDM) systems. The proposed method exploits the band structure of the coupling matrix to perform an ICI-free channel estimation in the frequency domain. This ICI-free estimation relies on some conditions imposed over the pilot pattern that simplify the complexity of channel estimation significantly, since its complexity is the same as classical least squares (LS) channel estimation used in low mobility scenarios. Then, the ICI is removed by using a modified version of Minimum Mean Square Error (MMSE) equalization, which reduces the computational complexity considerably. This modified MMSE equalization relies on the sparse and banded structure of the coupling matrix and on a low complexity variant of the Cholesky decomposition, which is named \(LDL^{H}\) factorization. It is shown that the proposed method greatly improves the Bit Error Rate (BER) in the high Signal-to-Noise Ratio (SNR) regime. ICI mitigation; OFDM; high mobility; channel estimation; pilot patterns +
Footnote †: journal: 10 June 2021  
linear fashion during a symbol period, the output/input relationship between transmitted and received OFDM symbols can be expressed as a diagonal-dominant sparse matrix (i.e., banded matrix). This matrix is known in the literature as subcarrier coupling matrixand it has dimensions \(N\times N\), being \(N\) the fast Fourier transform (FFT) size. This band structure of the coupling matrix is used to reduce the complexity of the matrix inversion required to perform equalization, since the inversion of a \(N\times N\) matrix is reduced to \(N-2Q\) inversions of \(2Q\times 2Q\) matrices, being \(Q\) the number of non-zero diagonals. This complexity reduction is further improved on [6], using Jacobi stationary iterative algorithm, and [7], which uses low complexity \(LDL^{H}\) factorization for minimum mean square error (MMSE) equalization. The linear model for the time variation of the CIR is also exploited in [8]. In this work, the channel matrix is split into two components: mid-point and slope of the CIR that are estimated separately. Then, two methods are proposed to estimate the slope, which are based on the redundancy of the cyclic prefix (CP) and on the information of two OFDM symbols, respectively. However, the proposed method is still complex since it requires to perform several matrix inversions, FFT operations and channel interpolations to estimate the transmitted sequence. A novel pilot pattern and channel estimation method for ICI mitigation is proposed in [9]. The proposed pilot pattern is a combination of comb-type and grouped patterns that allows ICI mitigation with a small pilot density. Nevertheless, that scheme is numerically complex since it requires to obtain the most significant paths of the CIR, FFT operations and an iterative process to obtain the data. Iterative interference cancellation [10; 11; 12; 13; 14; 15] has been also widely investigated, since it has the potential to exploit the temporal diversity of the time varying channel to improve the performance. Nevertheless, the cost to pay is a higher computational complexity than linear equalizers like least squares (LS) and MMSE. Finally, ICI self-mitigation is a promising approach that has attracted research interest in the last years. In [16; 17; 18], a time domain window is applied on the received OFDM symbols to concentrate the ICI power on the main diagonal of the coupling matrix. Recently, in [19] an adaptive windowing technique is proposed. This scheme is able to track directly an optimal receiver window in terms of average signal-to-interference and noise (SINR) ratio, requiring only linear complexity. Other schemes reduce the ICI power instead of concentrating it. A correlative precoding scheme is proposed on [20] to offer a balance between ICI self-mitigation, spectral confinement and peak-to-average power ratio (PAPR) reduction.