Biquad antenna reflector design: Does it need to be a groundplane or float?

I am unclear from the various designs put out on the web. To me it appears
that if the reflector itself is connected to the coaxial cable, it then
becomes a part of a semi-dipole that now forms between the 2 antenna
terminals. One leg of the dipole is the reflector and the other is the other
signal terminal.
So we have a case of a biquad and this qasi dipole being in parallel?

 

Nope. Two random twisted pieces of metal do NOT magically make a
usable dipole antenna. The biquad is basically two full wave loops in
parallel, with a reflector behind it. The reflector is usually
grounded to the coax cable shield, although it will work equally well
if it were floating. For example, this reflector is not grounded and
works acceptably:
<http://802.11junk.com/jeffl/antennas/biquad2/index.html>

More:
<http://802.11junk.com/jeffl/antennas/Biquad/index.html>

 

Thanks Jeff. Just to be clear, what I meant by the 2 dipoles: One leg of the dipole: The complete biquad itself and the 2nd leg of the dipole: The reflector itself since it is electrically joined to the other antenna-wire terminal. Yr point taken on the reflector being fully functional even if it is floating....but I wonder why most designs use the reflector as a ground plane. Did they find any improvement while doing that?

Addition on October 6, 2015: It is my understanding now that if the reflector is not made into a ground plane (ie connected to one limb of the antenna), the signal is balanced and that may necessitate a balun functionality at the receive end. To that end it looks like such a connection to the ground plane may be necessary. I will really appreciate views on this. Many thanks in advance.