As the software radio makes its transition from research to practice, it be
comes increasingly important to establish provable properties of the softwa
re radio architecture on which product developers and service providers can
base technology insertion decisions. Establishing provable properties requ
ires a mathematical perspective on the software radio architecture. This pa
per contributes to that perspective by critically reviewing the fundamental
concept of the software radio, using mathematical models to characterize t
his rapidly emerging technology in the context of similar technologies like
programmable digital radios. The software radio delivers dynamically defin
ed services through programmable processing capacity that has the mathemati
cal structure of the Turing machine. The bounded recursive functions, a sub
set of the total recursive functions, are shown to be the largest class of
Turing-computable functions for which software radios exhibit provable stab
ility in plug-and-play scenarios. Understanding the topological properties
of the software radio architecture promotes plug-and-play applications and
cost-effective reuse. Analysis of these topological properties yields a lay
ered distributed virtual machine reference model and a set of architecture
design principles for the software radio. These criteria may be useful in d
efining interfaces among hardware, middleware, and higher level software co
mponents that are needed for cost-effective software reuse.