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Cognitive Radios observe the spectral environment through spectrum estimation. In particular, reconfigurable Software Defined Radio architectures generate large amounts of sample data, which can be computationally expensive to analyze. Compression by time-shifted random pre-integration prior to spectrum estimation reduces the amount of data to be processed. It is simple to implement and scalable. This paper shows that linear compression with time-shifted random pre-integration is equivalent to compressed sensing with Toeplitz-structured random matrices and preserves autocorrelation properties, which allows for efficient joint compressed spectrum estimation and compressed signal detection in Cognitive Radio terminals.
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