Information, Energy and Density for Ad Hoc Sensor Networks over   Correlated Random Fields: Large Deviations Analysis
  Using large deviations results that characterize the amount of information per node on a two-dimensional (2-D) lattice, asymptotic behavior of a sensor network deployed over a correlated random field for statistical inference is investigated. Under a 2-D hidden Gauss-Markov random field model with symmetric first order conditional autoregression, the behavior of the total information [nats] and energy efficiency [nats/J] defined as the ratio of total gathered information to the required energy is obtained as the coverage area, node density and energy vary. 
Youngchul Sung, H. Vincent Poor and Heejung Yu