This will stimulate your imagination
Interesting concept.
In today's RW there was an article about Crossed Field Antennas. Apparently CFA, Ltd. will be submitting documentation for certification to the FCC in 4 months. These antennas are intriguing because the use no ground radials, are short and require comparatively little space.
It would be interesting to see if the design could be made part 15 compliant. Check out this site where you can see these squat beasts in action:
http://www.crossedfieldantenna.com/
For 20 years, the crossed field antenna promoters have been saying that they are going to do something very soon, but then nothing happens. The performance of this antenna is based on the same principle as the long ground lead in Part 15 AM, i.e. some radiating element that is not counted toward the length of the antenna.
In 2006, Prof. Valentin Trainotti published a thorough theoratical analysis of the crossed field anrenna in the IEEE Transactions on Broadcasting, called "On the Crossed Field Antenna Performance." A copy of the article can be obtained by clicking on the link in the references of the wikipedia article on the crossed field antenna.