My question is: Has there been any effort to improve or optimize the radiation patterns on the subsequent satellite navigation constellations (e.g. Glonass, Galileo, BeiDou-2) to facilitate trans-GEO navigation?
In a presentation entitled Enabling a Fully Interoperable GNSS Space Service Volume (slides 12, 24, 25, 26 are also shown below) some aspects of the possible use of GPS signals for navigation beyond Geosynchronous orbit are discussed.
While I have asked elsewhere about any actual navigation uses or tests of the GPS system, I am wondering now if this possibility was considered for other navigation constellations, e.g. Glonass, Galileo, or BeiDou-2.
Have the radiation patterns of the broadcast antennae on any of these satellite constellations been designed to provide additional power "over-the-limb" of the earth (see below)?
This answer has a great discussion (and nice plots!) of radiation patterns.
The AO-40 data show that the signals from the IIR Block satellites at large off-nadir angles are much larger than expected, and even at small angles are distinctly different than those of II and IIA Block satellites.
That suggests the possibility at least that the design was somehow modified to enhance the over-the-limb signal and improve the possibility of navigational use far from LEO.