Signal cancellation in far field by feeding +180° copy of signal to adjacent patches?

Setup:
Patch array antenna fed with a signal F(t)=F1(t)+F2(t)+F3(t), in other words there are simultaneously three frequencies.
F2(t) signal component may be fed to each patch with arbitrary phase shift.

Question:
Is it possible to cancel out F2 frequency by feeding each odd-numbered patch with F2 signal shifted by 180°?
Each odd-element will be fed with F_cancellation(t)=F1(t)+F2(t+dt_180°)+F3(t).
Each even-numbered fed with F(t)=F1(t)+F2(t)+F3(t).
So at some distance from antenna F2 will be cancelled out.

I think that this may be possible, and best cancellation will be observed at boresight direction.
Then cancellation will degrade and it may be estimated using using beam steering / phase monopulse related formulas,

For example, with λ/2 spacing beam steering pointing to Theta=5 degree will require phase shift of 2*180*0.5*Sin(5)=15.6 [deg] between adjacent patches. Using this formulas backwards to estimate F2 signal cancellation effect.

at boresight (Theta=0) direction i expect to see cancellation >-20dB
Estimating cancellation by comparing waveform
F2_{nocancellation}(x)=Sin(x) and
F2_cancellation(x)=(Sin(x)+Sin(x+(180+15.6)*Pi/180)
which will lower F2 signal level by -6 to -12dB instead of -20dB


Is this even possible or something is not taken into account?

well, practically speaking, if you just flip an adjacent patch 180 degrees, won't you just be cancelling the desired signal too?

Yes, but my idea is to use separate mixer for each patch.