Massive MIMO for wireless sensing with a coherent multiple access channel

Abstract—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 detec-tion problem, we study the Neyman–Pearson (NP) detector and en-ergy detector (ED) and find optimal values for the sensor transmis-sion gains. For the NP detector, which requires channel state infor-mation (CSI), we show that detection performance remains asymp-totically 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 minimummean-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 an-tennas. Unlike the NP detector, for high sensor power, themulti-an-tenna ED is observed to empirically have significantly better per-formance than the single-antenna implementation. A number of simulation results are included to validate the analysis. Index Terms—Distributed detection, distributed estimation, large scale antenna systems, massive MIMO, wireless sensor networks