Minimum Energy Data Gathering in Correlated Sensor Networks with Cooperative Transmission

We consider combination of distributed source coding (DSC) and cooperative transmission techniques to improve energy efficiency in sensor networks. To start with we formulate the data gathering problem in correlated wireless sensor networks with cooperative multiple input and multiple output (MIMO) transmission at the physical layer and DSC at the application layer. Using the concepts of super and sub modularity on a lattice, we analytically quantify as how the optimal constellation size and the optimal number of cooperating nodes vary with respect to the correlation coefficient. In particular, we show that the optimal constellation size is an increasing function of the correlation coefficient. For the MIMO transmission case, the optimal number of cooperating nodes is a decreasing function of the correlation coefficient. We also prove that in a MIMO transmission based scheme the optimal constellation size adopted by each cooperating node is a decreasing function of the number of cooperating nodes. Also, it is shown that the optimal number of cooperating nodes is a decreasing function of the constellation size adopted by each cooperating node. Finally through our numerical results, it is shown that significant energy savings can be obtained if correlation in the network is exploited. Also, when the desired probability of error is small MIMO transmission can lead to large scale energy savings.