Wireless Aggregation at Nearly Constant Rate

TL;DR

This paper demonstrates that wireless network aggregation can be achieved at nearly constant rates even in arbitrary networks under interference, by optimal power control and scheduling, improving previous bounds significantly.

Contribution

It establishes tight bounds on the achievable aggregation rate in wireless networks, showing constant or near-constant rates are possible with proper power control and scheduling.

Findings

Optimal rate is effectively constant under interference.

Power control is crucial for achieving high aggregation rates.

Bounds are tight; no better rate is possible with fixed power.

Abstract

One of the most fundamental tasks in sensor networks is the computation of a (compressible) aggregation function of the input measurements. What rate of computation can be maintained, by properly choosing the aggregation tree, the TDMA schedule of the tree edges, and the transmission powers? This can be viewed as the convergecast capacity of a wireless network. We show here that the optimal rate is effectively a constant. This holds even in \emph{arbitrary} networks, under the physical model of interference. This compares with previous bounds that are logarithmic (e.g., $\Omega(1/\log n)$). Namely, we show that a rate of $\Omega(1/\log^* \Delta)$ is possible, where $\Delta$ is the length diversity (ratio between the furthest to the shortest distance between nodes). It also implies that the \emph{scheduling complexity} of wireless connectivity is $O(\log^* \Delta)$. This is achieved using the natural minimum spanning tree (MST). Our method crucially depends on choosing the appropriate power assignment for the instance at hand, since without power control, only a trivial linear rate can be guaranteed. We also show that there is a fixed power assignment that allows for a rate of $\Omega(1/\log\log \Delta)$. Surprisingly, these bounds are best possible. No aggregation network can guarantee a rate better than $O(1/\log\log \Delta)$ using fixed power assignment. Also, when using arbitrary power control, there are instances whose MSTs cannot be scheduled in fewer than $\Omega(1/\log^* \Delta)$ slots.