Impact of Data Retrieval Pattern on Homogeneous Signal Field Reconstruction in Dense Sensor Networks

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Abstract
We analyze the impact of data retrieval pattern on the reconstruction performance of a one-dimensional homogeneous random field measured by a large-scale sensor network. From a networking perspective, we connect data retrieval protocols and different sampling schemes. Specifically, we show that the data retrieval pattern affects the efficiency of reconstruction; as the number of received packets M increases, the deterministic retrieval pattern that schedules sensors to transmit from equally spaced locations results in a faster decay of distortion than the random pattern does. In particular, we show that the ratio of the excess reconstruction distortion under the random retrieval pattern to that under the deterministic one grows as logM+O(loglogM). Comparing the reconstruction performance directly, we further show that, in the high measurement signal-to-noise ratio (SNR) regime, the benefit from carefully scheduling sensor transmissions from specific locations instead of collecting in a random fashion is substantial. In the low SNR regime, however, using the random pattern results in little reconstruction performance loss. Finally, as Mrarrinfin, we show the strong convergence property of reconstruction distortion under the random pattern

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