The Karhunen-Loève expansion of 1D and 2D OFDM channel responses

Ming-Xian Chang, Ren Shian Chen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The discrete Karhunen-Loeve expansion (KLE) of a random vector x uses the orthonormal eigenvectors of the correlation matrix of x as the basis vectors. In the KLE we have uncorrelated random coefficients in the expansion. We can apply the KLE in the feedback and estimation of channel responses (CRs). In this paper, we study the KLE of CRs in the orthogonal frequency-division multiplexing (OFDM) system.We first consider the KLE for one-dimensional (1D) blocks of OFDM CRs across time slots and subchannels, respectively. We further derive the KLE for the two-dimensional (2D) blocks of OFDM CRs. Based on the Kronecker products, we show that the orthonormal matrices, which are served as the basis functions in the 2D KLE, can be obtained from the basis vectors in the KLEs for the two 1D blocks of CRs. We apply the KLE in the pilotassisted CR estimation for the OFDM systems, including both 1D and 2D blocks of CRs. The numerical results show that the meansquares errors (MSEs) of the KLE-based CR estimation approach the performance lower bounds. The KLE-based estimation for the 2D block of CRs has lower MSE than the MSE lower bound for the 1D block of CRs.

Original languageEnglish
Title of host publication2011 IEEE Vehicular Technology Conference Fall, VTC Fall 2011 - Proceedings
DOIs
Publication statusPublished - 2011 Dec 23
EventIEEE 74th Vehicular Technology Conference, VTC Fall 2011 - San Francisco, CA, United States
Duration: 2011 Sep 52011 Sep 8

Publication series

NameIEEE Vehicular Technology Conference
ISSN (Print)1550-2252

Other

OtherIEEE 74th Vehicular Technology Conference, VTC Fall 2011
CountryUnited States
CitySan Francisco, CA
Period11-09-0511-09-08

Fingerprint

Karhunen-Loève Expansion
Orthogonal Frequency Division multiplexing (OFDM)
Orthogonal frequency division multiplexing
Orthonormal matrix
Lower bound
Kronecker Product
Random Coefficients
Orthonormal
Correlation Matrix
Random Vector
Response Time
Eigenvector
Eigenvalues and eigenfunctions
Basis Functions

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Applied Mathematics

Cite this

Chang, M-X., & Chen, R. S. (2011). The Karhunen-Loève expansion of 1D and 2D OFDM channel responses. In 2011 IEEE Vehicular Technology Conference Fall, VTC Fall 2011 - Proceedings [6093037] (IEEE Vehicular Technology Conference). https://doi.org/10.1109/VETECF.2011.6093037
Chang, Ming-Xian ; Chen, Ren Shian. / The Karhunen-Loève expansion of 1D and 2D OFDM channel responses. 2011 IEEE Vehicular Technology Conference Fall, VTC Fall 2011 - Proceedings. 2011. (IEEE Vehicular Technology Conference).
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Chang, M-X & Chen, RS 2011, The Karhunen-Loève expansion of 1D and 2D OFDM channel responses. in 2011 IEEE Vehicular Technology Conference Fall, VTC Fall 2011 - Proceedings., 6093037, IEEE Vehicular Technology Conference, IEEE 74th Vehicular Technology Conference, VTC Fall 2011, San Francisco, CA, United States, 11-09-05. https://doi.org/10.1109/VETECF.2011.6093037

The Karhunen-Loève expansion of 1D and 2D OFDM channel responses. / Chang, Ming-Xian; Chen, Ren Shian.

2011 IEEE Vehicular Technology Conference Fall, VTC Fall 2011 - Proceedings. 2011. 6093037 (IEEE Vehicular Technology Conference).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Chang M-X, Chen RS. The Karhunen-Loève expansion of 1D and 2D OFDM channel responses. In 2011 IEEE Vehicular Technology Conference Fall, VTC Fall 2011 - Proceedings. 2011. 6093037. (IEEE Vehicular Technology Conference). https://doi.org/10.1109/VETECF.2011.6093037