Compressed channel sensing: A new approach to estimating sparse multipath channels

Waheed U. Bajwa, Jarvis Haupt, Akbar M. Sayeed, Robert Nowak

Research output: Contribution to journalArticlepeer-review

927 Scopus citations


High-rate data communication over a multipath wireless channel often requires that the channel response be known at the receiver. Training-based methods, which probe the channel in time, frequency, and space with known signals and reconstruct the channel response from the output signals, are most commonly used to accomplish this task. Traditional training-based channel estimation methods, typically comprising linear reconstruction techniques, are known to be optimal for rich multipath channels. However, physical arguments and growing experimental evidence suggest that many wireless channels encountered in practice tend to exhibit a sparse multipath structure that gets pronounced as the signal space dimension gets large (e.g., due to large bandwidth or large number of antennas). In this paper, we formalize the notion of multipath sparsity and present a new approach to estimating sparse (or effectively sparse) multipath channels that is based on some of the recent advances in the theory of compressed sensing. In particular, it is shown in the paper that the proposed approach, which is termed as compressed channel sensing (CCS), can potentially achieve a target reconstruction error using far less energy and, in many instances, latency and bandwidth than that dictated by the traditional least-squares-based training methods.

Original languageEnglish (US)
Article number5454399
Pages (from-to)1058-1076
Number of pages19
JournalProceedings of the IEEE
Issue number6
StatePublished - Jun 2010

Bibliographical note

Funding Information:
Dr. Bajwa received the Best in Academics Gold Medal and President’s Gold Medal in Electrical Engineering from the National University of Sciences and Technology (NUST) in 2001, and the Morgridge Distinguished Graduate Fellowship from the University of Wisconsin-Madison in 2003. He was Junior NUST Student of the Year (2000), Wisconsin Union Poker Series Champion (Spring 2008), and President of the University of Wisconsin-Madison chapter of Golden Key International Honor Society (2009). He is currently a member of the Pakistan Engineering Council and Golden Key International Honor Society.

Funding Information:
Dr. Nowak has served as an Associate Editor for the IEEE TRANSACTIONS ON IMAGE PROCESSING, the Secretary of the SIAM Activity Group on Imaging Science, and is currently an Associate Editor for the ACM Transactions on Sensor Networks. He was General Chair for the 2007 IEEE Statistical Signal Processing Workshop and Technical Program Chair for the 2003 IEEE Statistical Signal Processing Workshop and the 2004 IEEE/ACM International Symposium on Information Processing in Sensor Networks. He received the General Electric Genius of Invention Award in 1993, the National Science Foundation CAREER Award in 1997, the Army Research Office Young Investigator Program Award in 1999, the Office of Naval Research Young Investigator Program Award in 2000, and the IEEE Signal Processing Society Young Author Best Paper Award in 2000.

Funding Information:
Dr. Haupt has completed internships at Georgia Pacific, Domtar Industries, Cray, and L-3 Communications/Integrated Systems. He was the recipient of several academic awards, including the Wisconsin Academic Excellence Scholarship, the Ford Motor Company Scholarship, the Consolidated Papers Tuition Scholarship, the Frank D. Cady Mathematics Scholarship, and the Claude and Dora Richardson Distinguished Fellowship. He served as Co-Chair of the Teaching Improvement Program at the University of Wisconsin-Madison for two semesters, and was awarded Honorable Mention for the Gerald Holdridge Teaching Award for his work as a teaching assistant. Dr. Haupt is also a Certified Professional Locksmith.

Funding Information:
Dr. Sayeed is a recipient of the Robert T. Chien Memorial Award (1996) for his doctoral work at Illinois, the National Science Foundation CAREER Award (1999), the Office of Naval Research Young Investigator Award (2001), and the UW Grainger Junior Faculty Fellowship (2003). He is currently serving on the signal processing for communications technical committee of the IEEE Signal Processing Society. He also served as an Associate Editor for the IEEE SIGNAL PROCESSING LETTERS from 1999 to 2002, and as the Technical Program Co-Chair for the 2007 IEEE Statistical Signal Processing Workshop and the 2008 IEEE Communication Theory Workshop.


  • Channel estimation
  • Compressed sensing
  • Dantzig selector
  • Least-squares estimation
  • Multiple-antenna channels
  • Orthogonal frequency division multiplexing
  • Sparse channel modeling
  • Spread spectrum
  • Training-based estimation


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