In this paper we provide a study of channel-aware decision fusion (DF) over a "virtual" multiple-input multipleoutput (MIMO) channel in the large-array regime at the DF center (DFC). The considered scenario takes into account channel estimation and inhomogeneous large-scale fading between the sensors and the DFC. The aim is the development of (widely) linear fusion rules, as opposed to the unsuitable optimum loglikelihood ratio (LLR). The proposed rules can effectively benefit from performance improvement via a large-array, differently from existing sub-optimal alternatives. Performance evaluation, along with theoretical achievable performance and complexity analysis, is presented. Simulation results are provided to confirm the findings. Analogies and differences with uplink communication in a multiuser (massive) MIMO scenario are underlined. Index Terms-Decision fusion, distributed detection, largescale MIMO, wireless sensor networks. Recently, DF over MACs is becoming increasingly attractive, since it exploits both the interfering nature of the broadcast wireless medium (for spectral-efficiency purposes) and the correlated nature of decisions, all regarding the same unknown event being observed. Also, deep fading scenarios

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Abstract-We tackle distributed detection of a non-cooperative target with a Wireless Sensor Network (WSN). When the target is present, sensors observe an (unknown) deterministic signal with attenuation depending on the distance between the sensor and the (unknown) target positions, embedded in symmetric and unimodal noise. The Fusion Center (FC) receives quantized sensor observations through error-prone Binary Symmetric Channels (BSCs) and is in charge of performing a more-accurate global decision. The resulting problem is a two-sided parameter testing with nuisance parameters (i.e. the target position) present only under the alternative hypothesis. After introducing the Generalized Likelihood Ratio Test (GLRT) for the problem, we develop a novel fusion rule corresponding to a Generalized Rao (G-Rao) test, based on Davies' framework, to reduce the computational complexity. Also, a rationale for thresholdoptimization is proposed and confirmed by simulations. Finally, the aforementioned rules are compared in terms of performance and computational complexity.

We consider a decentralized multi-sensor estimation problem where L sensor nodes observe noisy versions of a correlated random source vector. The sensors amplify and forward their observations over a fading coherent multiple access channel (MAC) to a fusion center (FC). The FC is equipped with a large array of N antennas, and adopts a minimum mean square error (MMSE) approach for estimating the source. We optimize the amplification factor (or equivalently transmission power) at each sensor node in two different scenarios: a) with the objective of total power minimization subject to mean square error (MSE) of source estimation constraint, and b) with the objective of minimizing MSE subject to total power constraint. For this purpose, based on the well-known favorable propagation condition (when L ≪ N) achieved in massive multiple-input multiple-output (MIMO), we apply an asymptotic approximation on the MSE, and use convex optimization techniques to solve for the optimal sensor power allocation in a) and b). In a), we show that the total power consumption at the sensors decays as 1/N , replicating the power savings obtained in massive MIMO mobile communications literature. We also show several extensions of the aforementioned scenarios to the cases where sensor-to-FC fading channels are correlated, and channel coefficients are subject to estimation error. Through numerical studies, we also illustrate the superiority of the proposed optimal power allocation methods over uniform power allocation.