**4. Multibeam cylindrical analog phased array (MC-analog-PA) of M** � **N elements**

The objectives in many designs for 5G antenna are multiple independent beams (approximately dozens or hundreds of beams), wide azimuthal coverage (approximately 360**°**), and high gain (>20 dB). A MC-analog-PA of M � N elements has both the characteristics of multibeam and wide azimuthal coverage since it exploited the characteristics of not only of MULA-analog-PA but also of cylindrical geometry, that is, perfect symmetrical over Z-axis. However, since the array relies on analog technology, the number of beams is limited by the number of phase shifters. The geometry of a MC-analog-PA of M � N elements is shown in Cartesian coordinate in **Figure 6** as follows.

*Phased Antenna Arrays toward 5G DOI: http://dx.doi.org/10.5772/intechopen.93058*

**Figure 6.** *The geometry of MC-analog-PA of M* � *N elements (each ring has M elements).*

In this case, the array factor is given by [16].

$$AF\_{cylinder}(\varphi,\theta) = AF\_{ring}(\varphi,\theta)AF\_{linear}(\varphi,\theta) \tag{11}$$

where *AFring* ð Þ *φ*, *θ* is the array factor of the circular array [17] in XOY plane and *AFlinear*ð Þ *φ*, *θ* is the array factor of ULA-analog-PA in Z-axis.

Generally, the array factor of an array having *M* elements in space is given by

$$AF(\varphi, \theta) = I\_1 e^{-j\beta \Delta r\_1} + \dots + I\_M e^{-j\beta \Delta r\_M} = \sum\_{k=1}^{M} I\_k e^{-j\beta \Delta r\_k} \tag{12}$$

where Δ*rk* ¼ *rk:ar* ¼ *xk* cos *θ* sin *φ* þ *yk* sin *θ* sin *φ* þ *zk* cos *φ* is the phase difference of the *K*th element to the reference element, *Ik* is the excited current of the *K*th element, *rk* is position vector of the *K*th element, and *α*<sup>r</sup> is directional unit vector.

The directivity of an antenna can be approximated as [16].

$$D\_{\text{max}} = \frac{4\pi}{\text{HPBW}\_{\theta}.\text{HPBW}\_{\text{g}}} \approx \frac{41253}{\text{HPBW}\_{\theta}.\text{HPBW}\_{\text{g}}} \tag{13}$$

where half power beam width in Ѳ plane, *HPBWθ*, is perpendicular to the half power beam width in ϕ plane, *HPBWφ*.

#### **4.1 The simulation result of the multibeam circular analog phased array of 32 elements**

To illustrate the performance of MCr-analog-PA, we do some simulations. First, isotropic antenna elements are arranged symmetrical in a circular with the reservation of the Nyquist condition of the distance between two consecutive elements.

Therefore, the output of DSP is

three MULA-digital-PAs.

**Figure 5.**

*A typical MULA-digital-PA.*

**of M** � **N elements**

coordinate in **Figure 6** as follows.

**70**

*Yn*ð Þ¼ *<sup>θ</sup>* <sup>W</sup>*<sup>H</sup>*

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

The advantage of MULA-digital-PA is that performing the beamforming is a more flexible and versatile approach. However, the array still has limited azimuthal coverage which cannot be greater than 180° since it is one of the theoretical limitations of ULA. In order to cover the azimuthal angle of 360°, we have to use at least

The objectives in many designs for 5G antenna are multiple independent beams (approximately dozens or hundreds of beams), wide azimuthal coverage (approximately 360**°**), and high gain (>20 dB). A MC-analog-PA of M � N elements has both the characteristics of multibeam and wide azimuthal coverage since it

exploited the characteristics of not only of MULA-analog-PA but also of cylindrical geometry, that is, perfect symmetrical over Z-axis. However, since the array relies on analog technology, the number of beams is limited by the number of phase shifters. The geometry of a MC-analog-PA of M � N elements is shown in Cartesian

Finally, other constrains on the output of DSP is performed.

**4. Multibeam cylindrical analog phased array (MC-analog-PA)**

*<sup>n</sup> X* (10)

Second, uniform currents are excited for all elements then the array factor of MCr-analog-PA of 32 elements is calculated (Eq. (12)) and depicted in Cartesian coordinate in **Figure 7** as follows.

**4.2 The simulation result of the multibeam cylindrical analog phased array**

and depicted in Cartesian coordinate as in **Figure 8** as follows.

*Dcylinder* <sup>¼</sup> <sup>41253</sup>

dent beams symmetrical in azimuthal plane.

Since *HPBW<sup>θ</sup>* <sup>¼</sup> *HPBW<sup>φ</sup>* <sup>≈</sup>9*<sup>o</sup>*

elements can be approximated as

high gain of 5G applications.

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)]

From the result in **Figure 8**, we can see that the array can produce 32 indepen-

From the obtained results of the multibeam over azimuthal angle of 360° and

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

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

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

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

This work is partially supported by the Vietnam National University, Hanoi

with maximum 180° of azimuthal coverage; whereas MC-analog-PA and MC-digital-PA are with unlimited azimuthal angle. The simulations of the

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

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

computer accompany with beamforming algorithms.

is the cost of intensive computations.

candidates for 5G applications.

**Acknowledgements**

(VNUH).

**73**

**6. Conclusions**

, the directivity of the MC-analog-PA of 32 � 10

ð Þ <sup>9</sup> *:*ð Þ <sup>9</sup> <sup>≈</sup> <sup>509</sup><sup>≈</sup> <sup>27</sup>*dB* (14)

**of 32** � **10 elements**

*Phased Antenna Arrays toward 5G*

*DOI: http://dx.doi.org/10.5772/intechopen.93058*

**Figure 7.** *The array factor of MCr-analog-PA of 32 elements.*

**Figure 8.** *The array factor of MC-analog-PA of 32 10 elements.*

Second, uniform currents are excited for all elements then the array factor of MCr-analog-PA of 32 elements is calculated (Eq. (12)) and depicted in Cartesian

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

coordinate in **Figure 7** as follows.

**Figure 8.**

**72**

**Figure 7.**

*The array factor of MC-analog-PA of 32 10 elements.*

*The array factor of MCr-analog-PA of 32 elements.*
