Compressed Sensing with Rank Deficient Dictionaries

Thomas Lundgaard Hansen, Daniel Højrup Johansen, Peter Bjørn Jørgensen, Kasper Fløe Trillingsgard, Thomas Arildsen, Karsten Fyhn, Torben Larsen

Research output: Contribution to journalConference article in JournalResearchpeer-review

3 Citations (Scopus)
760 Downloads (Pure)


In compressed sensing it is generally assumed that the dictionary matrix constitutes a (possibly overcomplete) basis of the signal space. In this paper we consider dictionaries that do not span the signal space, i.e. rank deficient dictionaries. We show that in this case the signal-to-noise ratio (SNR) in the compressed samples can be increased by selecting the rows of the measurement matrix from the column space of the dictionary. As an example application of compressed sensing with a rank deficient dictionary, we present a case study of compressed sensing applied to the Coarse Acquisition (C/A) step in a GPS receiver. Simulations show that for this application the
proposed choice of measurement matrix yields an increase in SNR performance of up to 5 − 10 dB, compared to the conventional choice of a fully random measurement matrix. Furthermore, the compressed sensing based C/A step is compared to a conventional method for GPS C/A.
Original languageEnglish
JournalGlobecom. I E E E Conference and Exhibition
Pages (from-to)3594-3599
Number of pages6
Publication statusPublished - 2012
EventIEEE Globecom 2012: Globecom Communications Conference - Disneyland Hotel, Anaheim, California, United States
Duration: 3 Dec 20127 Dec 2012


ConferenceIEEE Globecom 2012
LocationDisneyland Hotel
Country/TerritoryUnited States
CityAnaheim, California


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