Complex Grassmannians in the wild
#math #signalprocessing #manifold #optimization
There is a neat approach to wireless communication based on Grassmann manifolds over the field of complex numbers. It's an idea about 20 years old and it's easy to explain. Here is how it goes:
1/๐
#math #signalprocessing #manifold #optimization
There is a neat approach to wireless communication based on Grassmann manifolds over the field of complex numbers. It's an idea about 20 years old and it's easy to explain. Here is how it goes:
1/๐
Comments
2/n
๐ฆ=๐ป๐ฅ+๐
where Z is iid complex Gaussian random vector...
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Turns out that adding more antennas has benefits that have to do with the fact that the high dimensional normal random vectors tend to concentrate on the sphere.
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The way it currently works is we first estimate H by sending pilot signals known to both sides...
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Do you see the problem?
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Is there a better way?
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