Low complexity joint equalization and interference compensation in fractional Fourier domain for DCT-OFDM system with CFO

Abstract

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(N3) 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.