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

Table 1

Element phasing, beam direction, and interelement phasing for the Butler matrix shown in Figure 3 (conceptual).

𝜃𝑘𝑙	E1 (l = 1)	E2 (l = 2)	E3 (l = 3)	E4 (l = 4)	Beam direction	Inter-element phasing
Port 1 (k = 1)	−45°	−180°	45°	−90°	138.6°	−135°
Port 2 (k = 2)	0°	−45°	−90°	−135°	104.5°	−45°
Port 3 (k = 3)	−135°	−90°	−45°	0°	75.5°	45°
Port 4 (k = 4)	−90°	45^o	−180°	−45°	41.4°	135°