  This paper analyzes a broadcasting technique for wireless multi-hop sensor
networks that uses a form of cooperative diversity called opportunistic large
arrays (OLAs). We propose a method for autonomous scheduling of the nodes,
which limits the nodes that relay and saves as much as 32% of the transmit
energy compared to other broadcast approaches, without requiring Global
Positioning System (GPS), individual node addressing, or inter-node
interaction. This energy-saving is a result of cross-layer interaction, in the
sense that the Medium Access Control (MAC) and routing functions are partially
executed in the Physical (PHY) layer. Our proposed method is called OLA with a
transmission threshold (OLA-T), where a node compares its received power to a
threshold to decide if it should forward. We also investigate OLA with variable
threshold (OLA-VT), which optimizes the thresholds as a function of level.
OLA-T and OLA-VT are compared with OLA broadcasting without a transmission
threshold, each in their minimum energy configuration, using an analytical
method under the orthogonal and continuum assumptions. The trade-off between
the number of OLA levels (or hops) required to achieve successful network
broadcast and transmission energy saved is investigated. The results based on
the analytical assumptions are confirmed with Monte Carlo simulations.
