**2.2 The simulation result of the ULA phased array 1 4 elements using advanced design software (ADS)**

When using ADS software to design a ULA-analog-PA of 1 4 elements in X-axis, we obtain the radiated field pattern E as in **Figure 3** as follows [15].

After the analysis and some illustrations of ULA-analog-PA, we may conclude that a ULA-analog-PA could provide only one main beam and some side lobes at a time.

**2.3 Multibeam ULA analog phased array (MULA-analog-PA)**

progressive for the corresponding ULA-analog-PA.

*<sup>φ</sup>nm* � *<sup>φ</sup>n m*ð Þ �<sup>1</sup> ¼ � <sup>2</sup>*π<sup>d</sup>*

consecutive elements, *d*, has to be satisfied. The Nyquist condition is

Therefore, there is a little result for this kind of the array. Besides, the

**3. Multibeam ULA digital phased array (MULA-digital-PA)**

MULA-digital-PA is shown in **Figure 5** as follows.

W ¼

where the component weighting is given by

W*<sup>n</sup>* ¼ 1, exp *j*

W1 W2 ⋮ W*<sup>M</sup>*

2*π <sup>λ</sup> <sup>d</sup>* cos *<sup>θ</sup>*

W, which can be written as follows:

the received vector

**69**

**Figure 4** as follows.

*Phased Antenna Arrays toward 5G*

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

the nth beam is given by

Now that the ULA-analog-PA has been introduced let us generalize to the construction of a MULA-analog-PA. A typical ULA-analog-PA is indicated as in

In principle, a MULA-analog-PA could provide *N* independent beams in space. In order to drive the nth beam toward Ѳ direction, it is necessary to make phase

In another statement, the phase difference between two consecutive elements of

To avoid grating lobe, the Nyquist condition for the distance between two

*d*< *λ*

MULA-analog-PA has to deal with the problem of the limited azimuthal coverage which cannot be greater than 180°. It is one of the theoretical limits of ULA.

The disadvantage of a MULA-analog-PA is the limit of number of independent beams due to the complexity of a matrix of N � M phase shifters or attenuators.

In contrast to analog beamforming, the digital beamforming is performed without phase shifters or attenuators. MULA-digital-PA relies on a digital processing unit such as digital signal processing (DSP) or a strong computer in order to process the digital data that are the outputs of analog to digital converters (AD) and accompany with beamforming algorithms [13, 14]. The diagram of a typical

The principle of a MULA-digital-PA is that the collection of M antenna produces

Then, at the DSP unit, the received vector is multiplied by a matrix of weighting,

� �, <sup>⋯</sup>, exp *<sup>j</sup>*

*X* ¼ ½ � *x*1,*x*2, ⋯*xM* , *m* ¼ 1, 2, … , *M* (7)

2*π*

*<sup>λ</sup> nd* cos *<sup>θ</sup>*

(8)

W1⋯W1*<sup>M</sup>* W2 ⋮ ⋮

W*M*⋯W*NM*

� � � � (9)

*<sup>λ</sup>* cos *<sup>θ</sup>n*, *<sup>m</sup>* <sup>¼</sup> 2, … , *<sup>M</sup>* (5)

<sup>2</sup> (6)

**Figure 3.**

*The radiated field pattern of the ULA-analog-PA of 1 4 elements in X-axis.*

**Figure 4.** *A typical MULA-analog-PA.*

**2.2 The simulation result of the ULA phased array 1 4 elements using**

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

When using ADS software to design a ULA-analog-PA of 1 4 elements in X-axis, we obtain the radiated field pattern E as in **Figure 3** as follows [15].

After the analysis and some illustrations of ULA-analog-PA, we may conclude that a ULA-analog-PA could provide only one main beam and some side lobes at

**advanced design software (ADS)**

*The radiated field pattern of the ULA-analog-PA of 1 4 elements in X-axis.*

a time.

**Figure 3.**

**Figure 4.**

**68**

*A typical MULA-analog-PA.*

#### **2.3 Multibeam ULA analog phased array (MULA-analog-PA)**

Now that the ULA-analog-PA has been introduced let us generalize to the construction of a MULA-analog-PA. A typical ULA-analog-PA is indicated as in **Figure 4** as follows.

In principle, a MULA-analog-PA could provide *N* independent beams in space. In order to drive the nth beam toward Ѳ direction, it is necessary to make phase progressive for the corresponding ULA-analog-PA.

In another statement, the phase difference between two consecutive elements of the nth beam is given by

$$
\rho\_{nm} - \rho\_{n(m-1)} = -\frac{2\pi d}{\lambda} \cos \theta\_n, \quad m = 2, \ldots, M \tag{5}
$$

To avoid grating lobe, the Nyquist condition for the distance between two consecutive elements, *d*, has to be satisfied. The Nyquist condition is

$$d < \frac{\lambda}{2} \tag{6}$$

The disadvantage of a MULA-analog-PA is the limit of number of independent beams due to the complexity of a matrix of N � M phase shifters or attenuators. Therefore, there is a little result for this kind of the array. Besides, the MULA-analog-PA has to deal with the problem of the limited azimuthal coverage which cannot be greater than 180°. It is one of the theoretical limits of ULA.

### **3. Multibeam ULA digital phased array (MULA-digital-PA)**

In contrast to analog beamforming, the digital beamforming is performed without phase shifters or attenuators. MULA-digital-PA relies on a digital processing unit such as digital signal processing (DSP) or a strong computer in order to process the digital data that are the outputs of analog to digital converters (AD) and accompany with beamforming algorithms [13, 14]. The diagram of a typical MULA-digital-PA is shown in **Figure 5** as follows.

The principle of a MULA-digital-PA is that the collection of M antenna produces the received vector

$$X = [\mathbf{x}\_1 \mathbf{x}\_2, \dots, \mathbf{x}\_M], \quad m = 1, 2, \dots, M \tag{7}$$

Then, at the DSP unit, the received vector is multiplied by a matrix of weighting, W, which can be written as follows:

$$\mathbf{W} = \begin{bmatrix} \mathbf{W}\_1 \\ \mathbf{W}\_2 \\ \vdots \\ \mathbf{W}\_M \end{bmatrix} = \begin{bmatrix} \mathbf{W}\_1 \cdots \mathbf{W}\_{1M} \\ \mathbf{W}\_2 & \vdots \\ \vdots \\ \mathbf{W}\_M \cdots \mathbf{W}\_{NM} \end{bmatrix} \tag{8}$$

where the component weighting is given by

$$\mathbf{W}\_{\pi} = \left[ \mathbf{1}, \exp\left( \begin{array}{c} j\frac{2\pi}{\lambda} d\cos\theta \end{array} \right), \dots, \exp\left( \begin{array}{c} j\frac{2\pi}{\lambda} nd\cos\theta \end{array} \right) \right] \tag{9}$$

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

**Figure 5.** *A typical MULA-digital-PA.*

Therefore, the output of DSP is

$$Y\_n(\theta) = \mathbf{W}\_n^H \mathbf{X} \tag{10}$$

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

*AF*ð Þ¼ *φ*, *θ I*1*e*

vector.

**71**

**Figure 6.**

*Phased Antenna Arrays toward 5G*

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

*AFlinear*ð Þ *φ*, *θ* is the array factor of ULA-analog-PA in Z-axis.

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

*AFcylinder*ð Þ¼ *φ*, *θ AFring* ð Þ *φ*, *θ AFlinear*ð Þ *φ*, *θ* (11)

�*jβ*Δ*rM* <sup>¼</sup> <sup>X</sup>

<sup>≈</sup> <sup>41253</sup> *HPBWθ:HPBW<sup>φ</sup>*

*M*

�*jβ*Δ*rk* (12)

(13)

*k*¼1 *Ike*

where *AFring* ð Þ *φ*, *θ* is the array factor of the circular array [17] in XOY plane and

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

�*jβ*Δ*r*<sup>1</sup> <sup>þ</sup> <sup>⋯</sup> <sup>þ</sup> *IMe*

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

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

*HPBWθ:HPBW<sup>φ</sup>*

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

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

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.

*<sup>D</sup>*max <sup>¼</sup> <sup>4</sup>*<sup>π</sup>*

power beam width in ϕ plane, *HPBWφ*.

**of 32 elements**

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

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 three MULA-digital-PAs.
