Abstract
Orthogonal Chirp Division Multiplexing (OCDM) is a modulation scheme which outperforms the conventional Orthogonal Frequency Division Multiplexing (OFDM) under frequency selective channels by using chirp subcarriers. However, low complexity equalization algorithms for OCDM based systems under doubly selective channels have not been investigated yet. Moreover, in OCDM, the usage of different phase matrices in modulation will lead to extra storage overhead. In this paper, we investigate an OCDM based modulation scheme termed uniform phase-Orthogonal Chirp Division Multiplexing (UP-OCDM) for high-speed communication over doubly selective channels. With uniform phase matrices equipped, UP-OCDM can reduce the storage requirement of modulation. We also prove that like OCDM, the transform matrix of UP-OCDM is circulant. Based on the circulant transform matrix, we show that the channel matrices in UP-OCDM system over doubly selective channels have special structures that (1) the equivalent frequency-domain channel matrix can be approximated as a band matrix, and (2) the transform domain channel matrix in the framework of the basis expansion model (BEM) is a sum of the product of diagonal and circulant matrices. Based on these special channel structures, two low-complexity equalization algorithms are proposed for UP-OCDM in this paper. The equalization algorithms are based on block LDL factorization and iterative matrix inversion, respectively. Numerical simulations are finally proposed to show the performance of UP-OCDM and the validity of the proposed low complexity equalization algorithms. It is shown that when the channel is doubly selective, UP-OCDM and OCDM have similar BER performance, and both of them outperform OFDM. Moreover, the proposed low complexity equalizers for UP-OCDM both show better BER performance than their OFDM counterparts.
Highlights
In the last two decades, high-speed data communication over dispersive channels has been widely investigated
Based on the circulant transform matrix, we show that the channel matrices in UP-Orthogonal Chirp Division Multiplexing (OCDM) system over doubly selective channels have special structures that (1) the equivalent frequency-domain channel matrix can be approximated as a band matrix, and (2) the transform domain channel matrix in the framework of the basis expansion model (BEM) is a sum of the product of diagonal and circulant matrices
OCDM systems intersect the curve of orthogonal frequency division multiplexing (OFDM) at about SNR = 5 dB, which means uniform phase-Orthogonal Chirp Division Multiplexing (UP-OCDM) and OCDM will outperform OFDM when SNR is more than 5 dB, whereas, for the 16-QAM, the intersection is at SNR = 10 dB
Summary
In the last two decades, high-speed data communication over dispersive channels has been widely investigated. Division Multiplexing (FrFT-OFDM) is proposed in Reference [7], which is able to generate orthogonal chirp signals via fractional Fourier transform (FrFT). It is shown in Reference [7] that the performance of FrFT-OFDM is better than OFDM over varying Doppler spread factors. Based on the circulant structure, two low complexity equalization methods are proposed for UP-OCDM over doubly selective channels. We will show in this paper that the transform domain matrix channel of UP-OCDM can be represented as a sum of the product of several diagonal and circulant matrices.
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