Channel Capacity under Sub-Nyquist Nonuniform Sampling
arXiv:1204.6049 · doi:10.1109/TIT.2014.2323406
Abstract
This paper investigates the effect of sub-Nyquist sampling upon the capacity of an analog channel. The channel is assumed to be a linear time-invariant Gaussian channel, where perfect channel knowledge is available at both the transmitter and the receiver. We consider a general class of right-invertible time-preserving sampling methods which include irregular nonuniform sampling, and characterize in closed form the channel capacity achievable by this class of sampling methods, under a sampling rate and power constraint. Our results indicate that the optimal sampling structures extract out the set of frequencies that exhibits the highest signal-to-noise ratio among all spectral sets of measure equal to the sampling rate. This can be attained through filterbank sampling with uniform sampling at each branch with possibly different rates, or through a single branch of modulation and filtering followed by uniform sampling. These results reveal that for a large class of channels, employing irregular nonuniform sampling sets, while typically complicated to realize, does not provide capacity gain over uniform sampling sets with appropriate preprocessing. Our findings demonstrate that aliasing or scrambling of spectral components does not provide capacity gain, which is in contrast to the benefits obtained from random mixing in spectrum-blind compressive sampling schemes.
accepted to IEEE Transactions on Information Theory, 2014
References in corpus (6)
- Multichannel Sampling of Pulse Streams at the Rate of Innovation
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- Riesz bases of exponentials on multiband spectra
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Cited by in corpus (6)
- On the Information Bottleneck Problems: Models, Connections, Applications and Information Theoretic Views
- Distortion-Rate Function of Sub-Nyquist Sampled Gaussian Sources
- Shannon Meets Nyquist: Capacity of Sampled Gaussian Channels
- Analog-to-Digital Compression: A New Paradigm for Converting Signals to Bits
- Channel Capacity under General Nonuniform Sampling
- Nonuniform Sampling for Random Signals Bandlimited in the Linear Canonical Transform Domain