Shannon Meets Nyquist: Capacity Limits of Sampled Analog Channels

Details Shannon Meets Nyquist: Capacity Limits of Sampled Analog Channels Shannon Meets Nyquist: Capacity Limits of Sampled Analog Channels

2011-09-25

arxiv.org/abs/1109.5415v1

Computer Science

Information Theory

submitted to IEEE Transactions on Information Theory, 66pages

Scientific paper

We explore two fundamental questions at the intersection of sampling theory and information theory: how is channel capacity affected by sampling below the channel's Nyquist rate, and what sub-Nyquist sampling strategy should be employed to maximize capacity. In particular, we first derive the capacity of sampled analog channels for two prevalent sampling mechanisms: filtering followed by sampling and sampling following filter banks. Connections between sampling and MIMO Gaussian channels are illuminated based on this analysis. Optimal prefilters that maximize capacity are identified for both cases, as well as several kinds of channels for which these sampling mechanisms are optimal to maximize capacity at sub-Nyquist rates. We also highlight connections between sampled analog channel capacity and minimum mean squared error estimation from sampled data. In particular, it is shown that for both filtering and filter-bank sampling strategies, the filters maximizing capacity and minimizing mean squared error are equivalent. We also investigate a more general sampling strategy by adding modulation banks to filter-bank sampling. This general sampling method subsumes most nonuniform sampling techniques applied in both theory and practice. We also show a connection between this general sampling method and MIMO Gaussian channels. We then identify the optimal sampling strategy for piece-wise flat sampled channels to be a single branch of modulation and filtering. These results demonstrate the tradeoffs between channel capacity and sampling rate, illustrate the interplay between sampling techniques and capacity of sampled analog channels, and identify a simple optimal sampling strategy to maximize capacity for a large class of channels.

Affiliated with

Also associated with

No associations

Rating

Shannon Meets Nyquist: Capacity Limits of Sampled Analog Channels does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Shannon Meets Nyquist: Capacity Limits of Sampled Analog Channels, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Shannon Meets Nyquist: Capacity Limits of Sampled Analog Channels will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-685398