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The Impact of MAC Design on Estimation of Spacial Markov Process in Sensor Networks

We consider the problem of reconstructing a signal field measured by a large scale sensor network with mobile agents. Sensors transmit packets containing measurement data to mobile agents using a specified medium access control (MAC) schemes, and the signal field is reconstructed by mobile agents that minimize the mean square error of the reconstruction. For the one-dimensional Gauss-Markov field, we investigate the impact of MAC scheme design on the signal reconstruction performance. Two types of MAC schemes are considered: random access MAC and deterministic MAC schemes. We show that the deterministic MAC with uniform packet reception, i.e., the successfully received packets are from uniformly spaced locations, is favored in such signal reconstruction applications. Specifically, for noiseless measurements, we show that the reconstruction distortion ratio between random access MAC and deterministic MAC with uniform packet reception grows as , where is the number of received packets.