Open-Loop Beamforming Technique for MIMO System and Its Practical Realization

Table 2

Element phasing, beam direction, and interelement phasing for the Butler matrix shown in Figure 4 (manufactured).

𝜃𝑘𝑙	E1 (𝑙=1)	E2 (𝑙=2)	E3 (𝑙=3)	E4 (𝑙=4)	Beam direction	Inter-element phasing (average)
Port 1 (k = 1)	158°	25°	−112°	118°	138°	−130°
Port 2 (k = 2)	−87°	−137°	176°	137°	105°	−42°
Port 3 (k = 3)	132°	178°	−139°	−98°	76°	50°
Port 4 (k = 4)	136°	−90°	40°	176°	42°	138°