Inherence of Hard Decision Fusion in Soft Decision Fusion and a Generalized Radix-2 Multistage Decision Fusion Strategy

We consider the problem of decision fusion for binary event detection using a sensor network of nodes with non-identical detection and false-alarm probability pairs. We show that a soft decision fusion rule that is used to make a binary decision inherently possesses a hard decision fusion (HDF) part. Revelation of HDF part within the soft decision fusion rule, on the one hand, shows a connection between the two approaches and, on the other hand, enables straightforward computation of network-level detection and false-alarm probabilities. We consider the optimal soft decision fusion rule that minimizes the total probability of error and reveal its inherent HDF part for a network of two nodes. We subsequently use it to develop a radix-2 multistage decision fusion strategy for larger networks since revelation of HDF part for them is quite time-consuming. We consider spectrum sensing by a cognitive radio-enabled wireless sensor network to demonstrate the effectiveness of the proposed strategy. We show that the error performance of the proposed strategy is close to that exhibited by the optimal soft decision fusion rule and is better than many suboptimal hard and soft decision fusion strategies. The overall detection and false-alarm probabilities can be easily computed using the proposed strategy. We also show that the EXOR and EXNOR binary fusion rules are never optimal in minimizing the probability of error in decision making.