Low Complexity Equalization of Orthogonal Chirp Division Multiplexing in Doubly-Selective Channels
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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-06-01
|
| Series: | Sensors |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1424-8220/20/11/3125 |
| _version_ | 1827715772162506752 |
|---|---|
| author | Xin Wang Zhe Jiang Xiao-Hong Shen |
| author_facet | Xin Wang Zhe Jiang Xiao-Hong Shen |
| author_sort | Xin Wang |
| collection | DOAJ |
| description | 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<inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mi>H</mi> </msup> </semantics> </math> </inline-formula> 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. |
| first_indexed | 2024-03-10T19:26:37Z |
| format | Article |
| id | doaj.art-4b0618fa9d0f42b18fc113824b2c301f |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-10T19:26:37Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-4b0618fa9d0f42b18fc113824b2c301f2023-11-20T02:28:07ZengMDPI AGSensors1424-82202020-06-012011312510.3390/s20113125Low Complexity Equalization of Orthogonal Chirp Division Multiplexing in Doubly-Selective ChannelsXin Wang0Zhe Jiang1Xiao-Hong Shen2School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, ChinaSchool of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, ChinaSchool of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, ChinaOrthogonal 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<inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mi>H</mi> </msup> </semantics> </math> </inline-formula> 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.https://www.mdpi.com/1424-8220/20/11/3125OCDMdoubly-selective channelschannel equalizationBEMunderwater acoustic communications |
| spellingShingle | Xin Wang Zhe Jiang Xiao-Hong Shen Low Complexity Equalization of Orthogonal Chirp Division Multiplexing in Doubly-Selective Channels Sensors OCDM doubly-selective channels channel equalization BEM underwater acoustic communications |
| title | Low Complexity Equalization of Orthogonal Chirp Division Multiplexing in Doubly-Selective Channels |
| title_full | Low Complexity Equalization of Orthogonal Chirp Division Multiplexing in Doubly-Selective Channels |
| title_fullStr | Low Complexity Equalization of Orthogonal Chirp Division Multiplexing in Doubly-Selective Channels |
| title_full_unstemmed | Low Complexity Equalization of Orthogonal Chirp Division Multiplexing in Doubly-Selective Channels |
| title_short | Low Complexity Equalization of Orthogonal Chirp Division Multiplexing in Doubly-Selective Channels |
| title_sort | low complexity equalization of orthogonal chirp division multiplexing in doubly selective channels |
| topic | OCDM doubly-selective channels channel equalization BEM underwater acoustic communications |
| url | https://www.mdpi.com/1424-8220/20/11/3125 |
| work_keys_str_mv | AT xinwang lowcomplexityequalizationoforthogonalchirpdivisionmultiplexingindoublyselectivechannels AT zhejiang lowcomplexityequalizationoforthogonalchirpdivisionmultiplexingindoublyselectivechannels AT xiaohongshen lowcomplexityequalizationoforthogonalchirpdivisionmultiplexingindoublyselectivechannels |