**4.2 The simulation result of the multibeam cylindrical analog phased array of 32** � **10 elements**

When combining 10 rings of Section 4.1 in Z-axis with each ring spaced by λ/2 (half of wave length), we obtain the MC-analog-PA of 32 � 10 elements. The array factor of the MC-analog-PA of 32 � 10 elements is calculated [Eqs. (11) and (12)] and depicted in Cartesian coordinate as in **Figure 8** as follows.

From the result in **Figure 8**, we can see that the array can produce 32 independent beams symmetrical in azimuthal plane.

Since *HPBW<sup>θ</sup>* <sup>¼</sup> *HPBW<sup>φ</sup>* <sup>≈</sup>9*<sup>o</sup>* , the directivity of the MC-analog-PA of 32 � 10 elements can be approximated as

$$D\_{cylinder} = \frac{41253}{(9).(9)} \approx 509 \approx 27 dB \tag{14}$$

From the obtained results of the multibeam over azimuthal angle of 360° and directivity of the array, we may conclude that the MC-analog-PA of 32 � 10 elements can meet the requirements of multibeam, wide azimuthal coverage and high gain of 5G applications.

## **5. Multibeam cylindrical digital phased array (MC-digital-PA)**

Let us introduce the last array of this chapter, namely, multibeam cylindrical digital phased array (MC-digital-PA). The MC-digital-PA of M � N elements is the expanding of a MULA-digital-PA combing with a cylindrical geometry. Therefore, it has both the characteristics of multibeam and wide azimuthal coverage. Especially, not only the array structure follows the cylindrical geometry as described in Section 4 but also the digital beamforming is performed using DSP units or a strong computer accompany with beamforming algorithms.

Generally, if huge beams and 3600 azimuthal angle are required, the MC-digital-PA will become a promising candidate. The only shortcoming of the MC-digital-PA is the cost of intensive computations.

#### **6. Conclusions**

The analyses of MULA-analog-PA, MULA-digital-PA, MC-analog-PA, and MC-digital-PA show that all arrays could provide multibeam with different complexities and computations but MULA-analog-PA and MULA-digital-PA are with maximum 180° of azimuthal coverage; whereas MC-analog-PA and MC-digital-PA are with unlimited azimuthal angle. The simulations of the MC-analog-PA with 32 � 10 elements (10 rings with each ring of 32 elements) show that the array could provide 32 beams symmetrical over 360 azimuthal coverage with the directivity of 27 dB. In view of antenna design, those arrays are possible candidates for 5G applications.

#### **Acknowledgements**

This work is partially supported by the Vietnam National University, Hanoi (VNUH).

*Advanced Radio Frequency Antennas for Modern Communication and Medical Systems*
