Agile Communications in Adaptively Defined, Orthogonal Subspaces

Opportunistic airwave access using agile communications simultaneously solves the problems of interference, jamming, and access to the increasingly congested radio spectrum. We have invented a generalized mathematical framework based on adaptive, orthogonal subspaces, for analyzing and designing agile link schemes that goes well beyond the limitations imposed by Fourier representations of the radio spectrum. Using this framework, we have formally defined and solved the technical optimization problems of agile links. Our solutions provide templates for creating and evaluating sub-optimal, but fast and efficient, algorithmic approximations suitable for implementation in existing software radios. The benefits of our approach include formal mathematical structures for organizing, defining and attacking the engineering challenges of optimal agile communications and ad hoc networking. The initial designs suggested by this framework are surprisingly straightforward, numerically efficient, and extremely agile, when confronted by a statistically non-stationary, wideband channel. Our approach is easily implemented and requires no measurements other than the received signals. Our methods address several of the concerns raised by the Defense Science Board and the Congressional Budget Office (and others) about the challenges of providing sufficient network throughput in currently funded military radio programs.