In this case we must consider time varying signals, which have phase.
Signals from source 1 and 2 received on each patch with some phase shift. Here is simplified example:
Two patches example
Assume we have two patches, signal source 1 is to the left , and signal source 2 is on the right, placed symmetrically at the same angle.
Patch 1 receives signal 1 with phase shift 0 deg, signal 2 with phase shift 90 deg
Patch 2 receives signal 1 with phase shift 90 deg, signal 1 with phase shift 0 deg.
Configuring phase shifters:
Phase shifter 1: + 90deg
Phase shifter 2: + 0deg
After phase shifters:
signal 1 patch 1: 90deg
signal 1 patch 2: 90deg
signal 2 patch 1: 180 deg
signal 2 patch 2: 0 deg
after power combiner:
signal 1: summed in-phase 2x amplitude
signal 2: summed out-of-phase (0deg, 180deg) , results in zero amplitude
Phase is relative to global time.
Random example for eight patches:
1) patch 1, signal source 1 is received with phase shift of 10 deg, source 2 is received with phase shift of 60 deg
2) 13 deg / 57 deg
3) 16 deg / 54 deg
4) 19 deg / 51 deg
5) 22 deg / 48 deg
6) 25 deg / 45 deg
7) 28 deg / 42 deg
8) 31 deg / 39 deg
Phase shifters are configured to form beam in source 1 direction, so each patch provides copy of signal 1 with the same phase
For example, each phase shifter provides phase shift:
1) phase shifter 1 provides shift of -3 deg, source 1 signal phase after phase shifter: 10-3=7deg
2) phase shifter 2 provides shift of -6 deg, source 1 signal phase after phase shifter: 13-6=7deg
3) phase shifter 3 provides shift of -9 deg, source 1 signal phase after phase shifter: 16-9=7deg
4) ... -12 deg, source 1 signal phase after phase shifter: 19-12=7deg
5) ... -15 deg, source 1 signal phase after phase shifter: 22-15=7deg
6) ... -18 deg, source 1 signal phase after phase shifter: 25-18=7deg
7) ... -21 deg, source 1 signal phase after phase shifter: 28-21=7deg
8) ... -24 deg, source 1 signal phase after phase shifter: 31-24=7deg
After phase shifting there is power combiner, adding 8 copies of signal 1 in power combiner provides signal with 8x amplitude received by single patch, because
we have the same sinusoidal signal and relative phase shift is 0 deg (7deg - 7deg = 0 deg)
Signal from source 2 while beam is directed to source 1,
1) 60 deg - 3 deg = 57 deg
2) 57 deg - 6 = 51
3) 54 deg - 9 = 45
4) 51 deg - 12 = 39
5) 48 deg - 15 = 33
6) 45 deg - 18 = 27
7) 42 deg - 21 = 21
8) 39 deg - 24 = 15
Signals from source 2 after phase shifting are more out of phase after shifting.
To get best results of suppressing unwanted directions each patch also may be equipped with variable power attenuator.