Performance analysis of probabilistic transmission control for distributed estimation in wireless sensor networks

This paper presents a probabilistic transmission control technique for the distributed estimation in WSNs. The presented technique is based on a novel transmission control which is to minimize a mean squared error of estimation by increasing the packet transmission success probability of only sensors having the high observation SNR. In the presented method, the transmission of sensors is probabilistically decided whether the SNR of sensor is greater than the threshold whereas the transmission of sensors is deterministically decided in the conventional method. To achieve the presented method, we introduce a probabilistic transmission control function that gives each sensor a probabilistic value (from 0 to 1) as the transmission probability. Also, since the presented method can allows sensors to retransmit messages, it can be expected that the reliability of estimate increases. We employed the collision channel model where the transmission from the sensor to the FC is successful only when no other sensors are transmitting in the same time slot. Also, we assume that each sensor observe unknown at the beginning of the limited observation period, and each sensor can transmits observation only the limited retransmission time. Based on the model, theoretical packet transmission success probability of the presented and conventional method is derived. Numerical results are presented to valid the effectiveness of the presented method.