Here's an opinion from an (anonymous) friend on the antennas
On Fri, Nov 21, Thane Plambeck writes ...
Thane> Any comments...
You're in trouble because I'm not really an antenna guy. Of course, I do have an opinion ...
There are a few key parameters of an antenna that determine its performance (I'm going to describe them in terms of reception, but all of the statements have a corresponding transmission formulation). The first parameter is effective aperture (units of m^2). Effective aperture is not the same as the physical area of an antenna, but it's very closely related. The antenna's job is to collect RF energy in the form of a flux density (Watts/m^2) from space. Physically small antennas have small effective apertures; tiny antennas can't collect as much energy as big antennas regardless of whether they're made from clever space-filling curves or coat hangers. The second two parameters are radiation and circuit impedance, and respectively describe how efficiently antennas couple RF energy into free space and between their terminals and some other circuit. These are quantities that are functions of antenna geometry and materials. If fractal designs have any fundamental efficiency benefits to offer, it is in the area of antenna geometry.
One issue that antenna manufacturers face is that the coupling efficiency and directivity (radiation pattern) of a particular antenna design is a function of wavelength (among other things). For relatively broadband applications, e.g., for UHF televsion which operates at frequencies from 470-890 MHz in the US, special geometries are used to provide efficiency across a broad range of operating frequencies. These antennas have self-similar structure resulting in efficient reception across a wide range of frequencies; the most familiar example is a log-periodic antenna which you would recognize by sight if not by name (see, e.g., http://www.ramayes.com/Log_Periodic_Antennas.htm). The self-similar structure of various fractal curves might also have good properties in this regard, but I can't immediately think of any physical reason why they would have exceptional performance as compared to the alternatives.
Another fractal antenna claim is that by "folding" the array geometry, an antenna can be made small (retain its effective aperture) while maintaining performance. I've been approached by other people working with folded antennas, e.g., http://www.skycross.com, and the problem always seems to be that these types of antennas are inefficient in coupling energy to a transmitter or receiver.
Finally, regarding the claims of enabling fast algorithms for beamforming, there are probably some clever recursive algorithms that one can develop for an array with fractal geometry. The real question is whether the algorithms are less computationally intensive than standard techniques (which typically require only the solution of a linear system of equations of order equal to the number of elements in the array) for arrays of realistic size.
So, I'm suspicious. Without giving the subject the thought that it no doubt deserves, my intuition is that there are some nice mathematical/algorithmic properties of arrays with fractal geometry but that the arrays being proposed by these people have no significant performance advantage relative to the other self-similar and folded designs that are well known in the industry.