Please see comments below...
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"Reg Edwards" wrote (in part):

Simultaneous transmission of vertical and and horizontal polarised
signals from a single antenna system is impossible without upsetting
the desired radiation coverage pattern.

Sorry, but that statement is incorrect as it applies to FM broadcasting, at
least. There are many commercial FM broadcast transmit antenna designs
capable of doing so, for example the cavity-backed radiator (CBR) introduced
by Harris Corporation in the U.S, and used for simultaneous transmission of
8-10 FM channels in r.h. circular polarization at 100kW ERP each. Examples
are the Senior Road Tower Group in Houston, and Master FM sites in Miami and
St Louis.

The CBR is a panel type antenna designed to mount on and around the faces of
a tower, and has azimuth pattern circularity and axial ratio of less than
~1.5dB on a tower of ~2 meter face width. Other OEMs such as Kathrein,
SIRA, ERI, Dielectric etc supply other designs nearly as good.

As Cecil says, nobody gains anything power-wise. For the same
transmitter radiated power everybody's signals are 3 dB down
(half-power) relative to simple linear polarision when both transmitting
and receiving antennas have the same polarisation.

Incorrect again, at least in the US, where FM broadcast ERP is defined only
for horizontally polarized radiation. Therefore the output power of the
transmitter itself is raised 3dB so that the station's full, authorized ERP
is produced in all radiation planes. In theory, a r.h. CP receiving antenna
actually will receive 3dB MORE signal from CP transmission than when linear
polarization is used. For CP transmit and linear receive, received field
strength would be the same as if the transmit antenna also was linear, with
the same ERP in the same plane.

The advantage of circular polarisation is that it doesn't matter which
polarisation your antenna is orientated because, in practice, when
erecting it, the polarisation received by your antenna is usually a matter
of guesswork anyway. Only with relatively-rare, direct line-of-sigh
it broadcasting propagation is there any certainty in the polarisation
of received signals.

The full benefit of CP transmission is realized only when a CP receive
antenna is used. A CP receive antenna will tend to reject reflections of
the transmitted signal (multipath), because the physics of producing the
reflection causes a reversal of its polarization sense -- which the CP
receive antenna will reject. Reduced multipath content makes for "cleaner"
reception. Not too practical in automobiles, though, where it is most
needed.

RF (retired broadcast engineer - RCA and Harris Corp)

Visit http://rfry.org for FM broadcast RF system papers.