Optimal detection for a distributed transmission array

Absrract We consider the problem of communication over the reachback channel: this channel arises in the context of wireless sensor networks, where multiple nodes pick up correlated samples of some spatial stochastic process, and seek to communicate their observations back to a remote receiver. In this paper we consider the problem of designing a suitable transmitter for reachback. We assume that all the nodes agree on a common bit of information to send, and that all sensor nodes cooperate to generate an aggregate signal. With a large number of cheap and unreliable transmitters, it seems unlikely that these transmitters will be able to achieve high precision in synchronizing their transmissions in the cooperative transmission step. We consider the effects of timing jitter on the correlation detector and observe that modelling timing jitter as a fading problem leads to interesting detector designs.