Continuous compressed sensing and its applications to communication
An examination of continuous compressed sensing is made beginning with Lipschitz functions. The theory of Gersgorin discs is used to make proofs that sensing matrices satisfy the restricted isometry property become intuitive. A connection of the analysis to traditional wireless communication systems is made by adopting the sinc function as the impulse response of the pulse shaping filter. The application of the results for deterministic signals to signals that are bandlimited WSS random processes follows directly. The issue of synchronization and timing in practical systems is introduced to bridge the gap between practical systems and theoretical analysis. A sparse OFDM receiver is simulated, and an implementation with a field programmable gate array (FPGA) is examined. The work concludes with two examples, CSMA for multiuser mobile environment, and the study of a sensing matrix that is built with a PN code.
Lehnert, Purdue University.
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