# Manifold-Based System for Passive-Active Spectrum Sharing

#### Abstract

A feasibility study for an automated scheme for spectrum sharing between passive and active users is presented. The needs of spectrum users can be represented by manifolds in a Euclidean hyperspace called *electrospace* which has 7 dimensions: frequency (*f*); Cartesian coordinates (*x*,*y*,*z*); angular coordinates (*θ*,*φ*), and time (*t*). The entire globe is tessellated into geographical areas containing spectrum users, called user domains. Each user domain is recursively tessellated into smaller user domains, or subdomains. A computer cluster, or broker, in each smallest subdomain performs the calculations necessary to determine if a particular user in the subdomain experiences interference. Throughout this thesis, the Chicago Loop (area of 4.09 sq km, population ∼ 21,000) is taken to be the representative example of a smallest subdomain.

Within each subdomain, the number of users served by a broker is reduced to a manageable number by the process of *culling*. There are three orders of culling. In first-order culling, subdomain pairs without line of sight and not close enough to mutually interfere are culled, or removed from further consideration for interference calculations. In second-order culling, within each subdomain an intersection test of the electrospace manifolds of all user pairs is performed. User pairs whose manifolds do not intersect are culled. In third-order culling a Friis calculation is performed for all remaining user pairs. The output of third-order culling is an RFI flag bit for each user indicating whether interference is present or not. The computational complexity of first-, second-, and third-order culling calculations was determined.

Three representative user classes will be discussed: WiFi access points, Terminal Doppler Weather Radars, and passive EESS satellites. The manifold descriptor language (MDL) for each of the three user classes was described. The computational complexity of broker calculations to determine electrospace parameters from the MDL was determined. Using this complexity and the complexity of culling calculations, the total computational requirements for a broker in a representative subdomain is determined in GFLOPS (Giga Floating Point Operations Per Second).

*This paper has been withdrawn.*