A JANUS-Based Consensus Protocol for Parametric Modulation Schemes

JANUS, the first digital underwater acoustic communications standard, is robust to noise in low SNR situations, but offers very limited data rate. A primary use of JANUS is thus that of a first-contact language in underwater networking, and may be laddered by a network as a means to decide in a distributed and collaborative manner which communication scheme and modulation parameters should be used after the first contact. Deciding this distributedly implies then negotiating a common choice, likely suboptimal for the individual node, but better holistically. This paper proposes, mathematically analyses and tests in simulation such a distributed modulation parameters negotiation protocol based on an ad-hoc consensus paradigm. In this, the nodes start with already estimated locally optimal modulation parameters (an estimation step outside the scope of this paper), and then exchange opportune series of opportunely crafted JANUS messages that bring nodes to a global consensus on such parameters. Besides proposing this protocol, we describe a necessary and sufficient convergence criterion under the assumption that the channel coherence time is large. In practice, we show that convergence is ensured as soon as the coherence time of the link reliability is much longer than the convergence time for the proposed negotiation process. We test, using simulations implemented in UnetStack, how often the protocol successfully achieves consensus in other realistic situations, and find that convergence may be achieved with a consensus error rate on the order of one per thousand in a three-node network, and an error rate on the order of one percent in a seven-node network with weak links.