# A Low-Complexity Pilot-Based Frequency-Domain Channel Estimation for ICI Mitigation in OFDM Systems
###### Abstract
In [21] a mapping of each data symbol onto several sub-carriers with proper weighting coefficients is proposed to reduce the ICI power although the spectral efficiency is also reduced. In [22; 23], an appealing scheme involving a linear combination of the ISI-free part of the OFDM symbols is proposed to suppress the ICI power. This scheme, which was treated heuristically in above works, is analyzed mathematically on [24], to derive the optimum weights for the combination of the ISI-free part. Although the complexity of this scheme is reduced compared to other approaches, its performance is severely degraded if the delay spread is close to the CP length, since the ISI-free part is reduced. Although the ISI-free part might be increased by extending the CP length, it should be noted that this method leads to an undesired reduction in the spectral efficiency. As can be noticed from the literature review, ICI mitigation is a challenging task, where finding an appropriate balance between receiver complexity, spectral efficiency, and bit error rate (BER) is complicated. On the one hand, iterative interference cancellation approaches offer a high performance in terms of BER at the expense of a prohibitively receiver complexity for many applications. ICI self-mitigation schemes greatly reduce the receiver complexity. However, they either require a pre-processing that is incompatible with existing communication standards, such as 4G Long Term Evolution Advance (LTE-A) or 5G New Radio (NR) [20; 21], or they reduce the spectral efficiency [22; 23; 24]. On the other hand, linear equalization has been proven to achieve a good performance with low complexity MMSE equalization [7], and it can be implemented with existing communication standards. However, channel estimation is in this case challenging since ICI and channel variations between pilot symbols in the time domain may lead to outdated and noisy estimated channel samples [25]. In addition, sophisticated channel estimation schemes can increase the receiver complexity, and the pilot pattern must be carefully devised to avoid reducing the spectral efficiency. All these issues motivated us to investigate channel estimation and linear equalization for ICI mitigation with reduced complexity. In this paper we propose a low-complexity pilot pattern and a novel frequency domain coupling matrix estimation for ICI mitigation in OFDM systems. The proposed method uses a pilot pattern with some reserved sub-carriers to avoid ICI in the estimation of the channel matrix. Then, a low complexity \(LDL^{H}\) factorization is used to mitigate the ICI through MMSE equalization. It is shown that the proposed method achieves a great improvement in terms of Bit Error Rate (BER) in the high Signal-to-Noise Ratio (SNR) regime, compared to existing approaches of similar complexity, which are based on classical 1-tap zero forcing. The rest of the paper is structured as follows. The system model that considers the definition of sub-carrier coupling matrix, the OFDM modulation and classical channel estimation, interpolation and equalization, is presented in Section 2. The proposed pilot pattern and low complexity channel estimation is described in Section 3. Next, the low complexity channel equalization that relies on the band structure of the channel coupling matrix is presented in Section 4. Finally, numerical results showing the benefits of the proposal and the conclusions drawn from this work are detailed in Sections 5 and 6, respectively. Notation: Matrices and vectors are represented in bold. The \((i,j)\)-th element (i.e., \(i\)-th row and \(j\)-th column) of a given matrix, \(\mathbf{B}\), is represented as \(\mathbf{B}(i,j)=B_{i,j}\). The same holds for vectors, e.g, \(\mathbf{X}\in\mathbb{C}^{N\times 1}\) and \(\mathbf{X}(k)=X_{k}\). Transpose and conjugate transpose operations are represented as \((\,\boldsymbol{\cdot}\,)^{T}\) and \((\,\boldsymbol{\cdot}\,)^{H}\) respectively. Being \(\mathcal{P}\) a set, \(|\mathcal{P}|\) represents its number of elements.