Wang Xin, Jiang Zhe, Shen Xiao-Hong
School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China.
Sensors (Basel). 2020 Jun 1;20(11):3125. doi: 10.3390/s20113125.
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 H 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.
正交啁啾分割复用（OCDM）是一种调制方案，它通过使用啁啾子载波在频率选择性信道下优于传统的正交频分复用（OFDM）。然而，针对双选信道下基于OCDM的系统的低复杂度均衡算法尚未得到研究。此外，在OCDM中，调制中使用不同的相位矩阵会导致额外的存储开销。在本文中，我们研究了一种基于OCDM的调制方案，称为均匀相位 - 正交啁啾分割复用（UP - OCDM），用于双选信道上的高速通信。配备均匀相位矩阵后，UP - OCDM可以降低调制的存储需求。我们还证明，与OCDM一样，UP - OCDM的变换矩阵是循环矩阵。基于循环变换矩阵，我们表明双选信道上UP - OCDM系统中的信道矩阵具有特殊结构：（1）等效频域信道矩阵可以近似为带状矩阵，（2）在基扩展模型（BEM）框架下的变换域信道矩阵是对角矩阵和循环矩阵乘积的和。基于这些特殊的信道结构，本文为UP - OCDM提出了两种低复杂度均衡算法。均衡算法分别基于块LDL H分解和迭代矩阵求逆。最后进行了数值模拟，以展示UP - OCDM的性能和所提出的低复杂度均衡算法的有效性。结果表明，当信道为双选信道时，UP - OCDM和OCDM具有相似的误码率性能，并且它们都优于OFDM。此外，所提出的UP - OCDM低复杂度均衡器的误码率性能均优于OFDM对应的均衡器。
