Distributed Parameter Detection in Massive MIMO Wireless Sensor Networks Relying on Imperfect CSI

Abstract

Distributed parameter detection is conceived for massive multiple-input multiple-output (MIMO) wireless sensor networks (WSNs), where multiple sensors collaborate to detect the presence/ absence of a spatially correlated parameter. Neyman-Pearson (NP) and generalized likelihood ratio test (GLRT)-based detectors are developed at the fusion center (FC) for known and unknown parameter detection scenarios, respectively. More explicitly, the GLRT detector also has to estimate the unknown parameter value. Closed-form expressions are derived for the probabilities of detection (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> ) and false alarm (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FA</sub> ) in order to characterize the performance of the proposed schemes. Furthermore, the optimal sensor transmit gains are determined for maximising the detection performance attained. An asymptotic performance analysis is carried out for determining the gain scaling laws for the massive MIMO WSN considered, when the number of antennas tends to infinity. The proposed framework is also extended to the realistic imperfect channel knowledge scenario at the FC, followed by the development of the associated fusion rules and analytical results to characterize the performance. Our simulation results closely tally the theoretical findings.