  We consider the detection and estimation of a zero-mean Gaussian signal in a
wireless sensor network with a coherent multiple access channel, when the
fusion center (FC) is configured with a large number of antennas and the
wireless channels between the sensor nodes and FC experience Rayleigh fading.
For the detection problem, we study the Neyman-Pearson (NP) Detector and Energy
Detector (ED), and find optimal values for the sensor transmission gains. For
the NP detector which requires channel state information (CSI), we show that
detection performance remains asymptotically constant with the number of FC
antennas if the sensor transmit power decreases proportionally with the
increase in the number of antennas. Performance bounds show that the benefit of
multiple antennas at the FC disappears as the transmit power grows. The results
of the NP detector are also generalized to the linear minimum mean squared
error estimator. For the ED which does not require CSI, we derive optimal gains
that maximize the deflection coefficient of the detector, and we show that a
constant deflection can be asymptotically achieved if the sensor transmit power
scales as the inverse square root of the number of FC antennas. Unlike the NP
detector, for high sensor power the multi-antenna ED is observed to empirically
have significantly better performance than the single-antenna implementation. A
number of simulation results are included to validate the analysis.
