  In this paper we investigate fusion rules for distributed detection in large
random clustered-wireless sensor networks (WSNs) with a three-tier hierarchy;
the sensor nodes (SNs), the cluster heads (CHs) and the fusion center (FC). The
CHs collect the SNs' local decisions and relay them to the FC that then fuses
them to reach the ultimate decision. The SN-CH and the CH-FC channels suffer
from additive white Gaussian noise (AWGN). In this context, we derive the
optimal log-likelihood ratio (LLR) fusion rule, which turns out to be
intractable. So, we develop a sub-optimal linear fusion rule (LFR) that weighs
the cluster's data according to both its local detection performance and the
quality of the communication channels. In order to implement it, we propose an
approximate maximum likelihood based LFR (LFR-aML), which estimates the
required parameters for the LFR. We also derive Gaussian-tail upper bounds for
the detection and false alarms probabilities for the LFR. Furthermore, an
optimal CH transmission power allocation strategy is developed by solving the
Karush-Kuhn-Tucker (KKT) conditions for the related optimization problem.
Extensive simulations show that the LFR attains a detection performance near to
that of the optimal LLR and confirms the validity of the proposed upper bounds.
Moreover, when compared to equal power allocation, simulations show that our
proposed power allocation strategy achieves a significant power saving at the
expense of a small reduction in the detection performance.
