Majority decision sensor networks composed of binary tree fading links

In the binary tree network composed of a binary symmetric channel (BSC), the bit error probability of majority decision at the fusion center is found to be almost constant regardless of a network size. In this paper, we consider a fading channel for BSC in the binary tree network. In the fading channel, the error probability becomes a random variable. 2nd-order moments of error probability are derived by an iterative calculation of correlation matrix. Numerical results show that the mean and variance of error probability does not affected by the network size and keeps constant.