On the scaling laws of multimodal wireless sensor networks

In this paper, we consider dense wireless sensor networks deployed to observe multiple random processes. The requirement is to reconstruct an estimate of each random process at the corresponding collector node. This leads to multiple many-to-one data gathering wireless channels that interfere with one another. We derive the transport capacity that the network can provide to each process and characterize an achievable rate region for the dense multimodal network. We further investigate the number of processes that can be observed simultaneously by the network. Specifically, we show that it is possible to observe O (N^β) processes simultaneously such that the transport capacity scales as Θ (log (N)) for each of the observed processes, with a large number of sensors A; and a fixed total average power. We show this result using a simple scheme based on antenna sharing. We then proceed to show that it is possible to simultaneously observe O (N^β) continuous, spatially bandlimited Gaussian processes using a fixed total average power, through a scheme composed of single dimensional quantization, distributed Slepian-Wolf source coding, and the proposed antenna sharing strategy.