Effect of MAC design on source estimation in dense sensor networks

We investigate the impact of medium access control (MAC) design on the reconstruction performance of a 1D random signal field measured by a large scale sensor network. Assuming the sensor density goes to infinity, we show that MAC design affects the decay rate of reconstruction distortion, and thus the efficiency of reconstruction, as the number of received packets M increases. Using a deterministic MAC with uniform spatial sampling, i.e., scheduling sensor transmissions from uniformly spaced locations, results in a faster decay rate of distortion than that using an ALOHA-like random access MAC. In particular, the ratio of the excess reconstruction distortion under random access MACs to that under the MAC with uniform sampling grows as log M+O(log log M). We further show that in the high measurement SNR regime, the benefit from carefully scheduling transmission, instead of random access, is substantial. In the low SNR regime, however, using random access MACs results in little reconstruction performance loss.