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The authors present inner and outer bounds of the rate region for the multiple-input-multiple-output mutiple access channel with imperfect channel estimates. They then employ them to compare different channel estimation techniques. They show that the benefit of using traditional compressed sensing recovery techniques, specifically orthogonal matching pursuit, for multipath wireless channels is dominant for high signal to noise ratio regimes, but does not provide a good performance for low signal to noise ratio regime. There is a growing interest in understanding Multiple-Input-Multiple-Output (MIMO) Multiple Access Channels (MAC) for which channel estimates are imperfect.
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