The problem of decision fusion in a large wireless sensor system with many power-constrained distributed nodes is considered. The sensor network is assumed to be inhomogeneous. i.e. the channel statistics are not identical among the sensors. Assuming identical, binary local quantizing schemes at all the nodes, the optimal fusion scheme is derived. The large system performance of this optimal decision fusion detector is next analyzed. The asymptotic fusion performance is derived via the Lindberg-Feller central limit theorem for non-identical large samples. Numerical examples are used to show that the derived large system closed-form fusion error probability expressions provide a very close approximation to the exact finite-size sensor system fusion performance even for a relatively smaller number of nodes.