Angular Beamforming Technique for MIMO Beamforming System

Table 5

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

𝐛𝑡,𝐛𝑟	E1  (𝑙=1)	E2  (𝑙=2)	E3  (𝑙=3)	E4  (𝑙=4)	Beam; direction	Interelement phasing; (average)
Port 1; (𝑚=1)	1√4𝑒^∘𝑗158	1√4𝑒^∘𝑗25	1√4𝑒^∘−𝑗112	1√4𝑒^∘𝑗118	138°	−130°
Port 2; (𝑚=2)	1√4𝑒^∘−𝑗87	1√4𝑒^∘−𝑗137	1√4𝑒^∘𝑗176	1√4𝑒^∘𝑗137	105°	−42°
Port 3; (𝑚=3)	1√4𝑒^∘𝑗132	1√4𝑒^∘𝑗178	1√4𝑒^∘−𝑗139	1√4𝑒^∘−𝑗98	76°	50°
Port 4; (𝑚=4)	1√4𝑒^∘𝑗136	1√4𝑒^∘−𝑗90	1√4𝑒^∘𝑗40	1√4𝑒^∘𝑗176	42°	138°