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Compressive Multiplexing of Correlated S...
Ahmed, Ali...

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Compressive Multiplexing of Correlated Signals by Ahmed, Ali ( Author )
Lemonjar Open Access
Australian National University
25-08-2023
We present a general architecture for the acquisition of ensembles of correlated signals. The signals are multiplexed onto a single line by mixing each one against a different code and then adding them together, and the resulting signal is sampled at a high rate. We show that if the $M$ signals, each bandlimited to $W/2$ Hz, can be approximated by a superposition of $R < M$ underlying signals, then the ensemble can be recovered by sampling at a rate within a logarithmic factor of $RW$ (as compared to the Nyquist rate of $MW$). This sampling theorem shows that the correlation structure of the signal ensemble can be exploited in the acquisition process even though it is unknown a priori. The reconstruction of the ensemble is recast as a low-rank matrix recovery problem from linear measurements. The architectures we are considering impose a certain type of structure on the linear operators. Although our results depend on the mixing forms being random, this imposed structure results in a very different type of random projection than those analyzed in the low-rank recovery literature to date.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1308.5146
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