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On the Channel Estimation Effort for Analog Computation over Wireless Multiple-Access Channels

This letter studies a multiple-access transmission scheme that exploits interference for an efficient function computation in sensor networks. The central question is how much channel knowledge is generally needed and how the channel estimation effort can significantly be reduced. It is first shown that the channel magnitude at the transmitters is sufficient to achieve the same performance as with full channel state information. It is further shown that for a wide range of fading distributions, no channel state information is needed at the transmitters, provided that the receiver has access to some statistical channel knowledge and is equipped with multiple antennas.