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


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
Publication statusPublished - 2011
EventIEEE 74th Vehicular Technology Conference, VTC Fall 2011 - San Francisco, CA, United States
Duration: 2011 Sept 52011 Sept 8

Publication series

NameIEEE Vehicular Technology Conference
ISSN (Print)1550-2252


OtherIEEE 74th Vehicular Technology Conference, VTC Fall 2011
Country/TerritoryUnited States
CitySan Francisco, CA

All Science Journal Classification (ASJC) codes

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


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