Orthogonal frequency division multiplexing (OFDM) systems based on discrete fractional Fourier transform (DFRFT) chirp basis replacing the complex exponential basis of discrete Fourier transform (DFT) is extensively studied in the literature. Authors of this paper have recently proposed fractional Fourier domain equalization (FFDE) for an OFDM system with a discrete cosine transform (DCT) multicarrier basis. The proposed DCT-OFDM system with FFDE nearly achieves the performance of the DFRFT-OFDM system without requiring any chirp rate feedback to the transmitter. This is enabled by separately performing the tasks of multicarrier modulation/demodulation with IDCT/DCT kernels at transmitter/receiver and FFDE using DFRFT/IDFRFT kernels both at the receiver. However, in the presence of a high value of CFO and also with higher modulation order, the residual interference power existing after channel equalization in fractional Fourier domain (FFD) using the channel decomposed with DFRFT significantly degrades the error rate performance. In this paper, the equalization and interference compensation is treated as a joint and linear problem in FFD after DFRFT at the receiver. Full compensation by performing direct matrix inverse can ensure the performance free from CFO for the DCT-OFDM system with both FDE and FFDE, but will drastically increase the computational cost to the $O(N^3)$ for implementing the joint equalizer at the receiver for N subcarriers. Therefore, low complexity joint equalization and interference compensation (JEIC) schemes are proposed for the DCT-OFDM system with FFD decomposition utilizing the banded implementation of joint ICI matrix after DFRFT at the receiver. The banded JEIC can closely preserve the interference-free performance and only requires operations in the $O(N)$ to implement the joint equalizer.

文献中广泛研究了基于离散分数傅立叶变换（DFRFT）线性调频基频的正交频分复用（OFDM）系统，以取代离散傅立叶变换（DFT）的复指数基础。本文的作者最近提出了基于离散余弦变换（DCT）多载波的OFDM系统的分数阶傅里叶域均衡（FFDE）。所提出的具有FFDE的DCT-OFDM系统几乎可以实现DFRFT-OFDM系统的性能，而无需向发射机发送任何线性调频速率反馈。通过在发送器/接收器上使用IDCT / DCT内核以及在接收器上使用DFRFT / IDFRFT内核分别使用FFDE分别执行多载波调制/解调任务，可以实现此功能。但是，在CFO值较高且调制阶数较高的情况下，在使用DFRFT分解的信道进行分数阶傅立叶域（FFD）信道均衡后，存在的残留干扰功率会大大降低误码率性能。在本文中，将均衡器和干扰补偿视为接收器进行DFRFT后的FFD中的联合和线性问题。通过执行直接矩阵逆的完全补偿可以确保对于同时具有FDE和FFDE的DCT-OFDM系统，没有CFO的性能，但将大大增加CFO的计算成本。在接收器进行DFRFT之后，均衡和干扰补偿被视为FFD中的联合和线性问题。通过执行直接矩阵逆的完全补偿可以确保对于同时具有FDE和FFDE的DCT-OFDM系统，没有CFO的性能，但将大大增加CFO的计算成本。在接收器进行DFRFT之后，均衡和干扰补偿被视为FFD中的联合和线性问题。通过执行直接矩阵逆的完全补偿可以确保对于同时具有FDE和FFDE的DCT-OFDM系统，没有CFO的性能，但将大大增加CFO的计算成本。$Ø（{ñ}^3）$用于在接收机处为N个子载波实现联合均衡器。因此，在接收器进行DFRFT之后，利用联合ICI矩阵的带域实现，针对具有FFD分解的DCT-OFDM系统，提出了低复杂度联合均衡和干扰补偿（JEIC）方案。带状的JEIC可以紧密保留无干扰的性能，只需要在$Ø（ñ）$ 实现联合均衡器。