On the effectiveness of multiple antennas in distributed detection over fading MACs

A distributed detection problem over fading Gaussian multiple-access channels is considered. Sensors observe a phenomenon and transmit their observations to a fusion center using the amplify and forward scheme. The fusion center has multiple antennas with different channel models considered between the sensors and the fusion center, and different cases of channel state information are assumed at the sensors. The performance is evaluated in terms of the error exponent for each of these cases, where the effect of multiple antennas at the fusion center is studied. When there is channel information at the sensors, the gain in error exponent due to having multiple antennas at the fusion center is shown to be limited to a factor of 8/π for Rayleigh fading channels between the sensors and the fusion center, and independent of the number of antennas at the fusion center. Simple practical schemes and numerical methods using semidefinite relaxation techniques are presented that utilize the limited possible gains available. Simulations are used to establish the accuracy of the results.