## Compressed Sensing and Its Application in Large Wireless Networks

Wednesdays@NICO Seminar, Noon, May 27 2009, Chambers Hall, Lower Level

Prof. Dongning Guo, Northwestern University

**Abstract**

The Nyquist/Shannon sampling theorem states that any band-limited analog signal can be represented without any loss by its discrete samples taken at a frequency twice of its bandwidth, whereas lower sampling rate induces irrecoverable loss. Intuitively, an analog signal of bandwidth B has at most 2B degrees of freedom per second, which implies that at least 2B measurements per second is necessary. What is ignored is the fact that most useful signals have sparse representation in certain domain, and apparently much fewer degrees of freedom. In this talk, we discuss the new compressed sensing paradigm where a few random linear measurements of a sparse signal is shown to be sufficient for recovering the signal. As an application, we show that neighbor discovery in large wireless networks is a compressed sensing problem by nature. Besides the fundamental limits on the number of transmissions for accurate discovery, we show a simple and effective non-coherent compressed sensing scheme, which requires much fewer transmissions than conventional random-access schemes.

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