Your plot suggests your antenna is acting an omni, and not directional.
He gets the back-side planes via reflections of something in front of his window (a high-rise building?).
Possibly, but being close to a south window would also explain the greater number of planes to the south.
It’d take a well designed reflector to give such good performance!
RF at 1 GHz tends to quite reflective (even more so at higher frequencies) so getting it to “bounce” off
a surface is actually easier than one might think.
Building materials that offer little or no attenuation to HF or VHF RF energy start to behave differently above
~400 MHz. At 1 GHz, metallic window screen looks more like a solid sheet of metal than it does a
surface with many small openings in it. (e.g. the “screen” in a microwave oven door)
Other building materials, i.e sheetrock (drywall) lumber, concrete, et al, have higher attenuation
characteristics at 1 GHz than they do at lower frequencies.
A building can act like a Faraday cage (RF shield), a reflective (or directive) element of an antenna,
resonant cavity, attenuator or a combination of any of these characteristics.
With such a short overall (wave)guide length, the main lobe beam width will be quite wide.
As was pointed out at the top of the thread, it seems to be a common misconception that a waveguide length of 3/4λ is sufficient. The ARRL antenna book suggests that a waveguide of 2 or 3 guide lengths would offer much better performance. The larger the waveguide diameter, the more pronounced the effect.