This chapter considers the problem of data gathering in correlated wireless sensor networks with distributed source coding (DSC), and virtual multiple input and multiple output (MIMO) based cooperative transmission. Using the concepts of super and sub modularity on a lattice, we analytically quantify as how the optimal constellation size, and 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 virtual MIMO transmission case, the optimal number of cooperating nodes is a decreasing function of the correlation coefficient. We also prove that in a virtual MIMO based transmission scheme, the optimal constellation size adopted by each cooperating node is a decreasing function of 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. We also study numerically that for short distance ranges, SISO transmission achieves better energy-mutual information (MI) tradeoff. However, for medium and large distance ranges, the virtual MIMO transmission achieves better energy-MI tradeoff.
