4. A general analysis of radiation pattern sensitivity

where f is the signal frequency inside the operating frequency range of 37–43,5 GHz, c is the light speed in vacuum, λ<sup>0</sup> is the wavelength corresponding to the center frequency of the operating frequency range, and An is amplitudephase distribution generated by the Butler matrix and determined according to Eq. (2). Thus, the six-beam radiation pattern of single PAA is described by the

> X 8

1 ffiffiffi 8 <sup>p</sup> <sup>X</sup> 6

Note that to ensure the required coverage in the elevation plane, the PAA panels have to be tilted to the ground at an angle near 45°. The unidirectional coverage provided in the azimuth plane by four sub-arrays of antenna system is illustrated in

• The Butler matrix is more suitable for the formation of a multipath radiation pattern in comparison with the Blass matrix because of its simpler design,

• The use of six central beams, generated by the eight-channel Butler matrix, provides a coverage sector of about 50° and does not create a significant level

• The omnidirectional coverage of the service area is provided by using halfwave dipoles as elements of the one-dimensional PAA, providing coverage of 78° in elevation angle and an antenna system of four linear PAA, providing

m¼1 e �j 2π <sup>N</sup>ð Þ m�1 ð Þ n�1

" #

e j 2πf c n λ0

<sup>2</sup> cos <sup>φ</sup> (7)

n¼1

formula:

Figure 8.

Figure 8.

118

Dð Þ¼ θ, φ

Advances in Array Optimization

1 þ cosð Þ π cos θ sin <sup>θ</sup> <sup>∗</sup>

of interference beyond its limits.

overall coverage of 360° in azimuth.

Radiation pattern of RS antenna system in the azimuth plane.

Equation (7) is fundamental for further modeling.

To summarize, the following outcomes could be concluded:

fewer components, and better C-SWAP characteristics.

Due to the difficulty in providing time delays between PAA elements, phase shifters usually control the steering signal instead of using actual time delays, because their realization in RF band is much simpler, especially in the case of limited bandwidth. However, a phenomenon called "beam squint" leads to an error in the direction of the maximum of the PAA pattern and also to a certain increase in the level of the side lobes. Nevertheless, as known, a BFN based on phase shifters has become widespread in relatively narrowband RF-band PAAs with a fractional bandwidth, commonly not exceeding 10%, depending on the criterion used [16]. Though, the development of a key trend for 5G NR networks associated with the implementing the mmWave in the wireless frontend has led to a change in the design principle of the access network's RS, whose antenna pattern was steered using photonics technique. At the same time, due to the more complexity for the implementation of fundamentally narrowbandwidth phase shifters in the optical range, the so-called true -time delay (TTD) concept based on wideband optical delay lines has been widely used [17–20].

Thus, when the fractional bandwidth of the BFN under design exceeds the 10% as noted above, it is required to determine the optimal approach by analyzing the sensitivity of the radiation pattern to the frequency change in the entire specific RF range. We previously performed this procedure for the mmWave PAA with singlebeam photonics BFN operating in the 57–76 GHz RF band (fractional bandwidth of 28.6%) [10]. As a result of the direct comparison, the TTD approach was unambiguously selected, since using phase shifters in the BFN produced more than 10% shift in the azimuth angle for the main lobe of the NRP, as well as increase in the side lobes level by almost 10 dB. This chapter discusses a mmWave multiple-beam photonics BFN operating in the 37–43.5 GHz band (fractional bandwidth of 16%), for the implementation of which the Butler matrix (see Figure 3) is preselected (see section 3). In its scheme, to ensure the required phase shifts, optical delay lines of constant length are usually used [21]; therefore, prior to designing the specific BFN, the sensitivity analysis is also necessary.

In the process of simulation using MATLAB software, the sensitivity of the PAA's NRP is examined for the example of a linear equidistant array of eight ideal isotropic elements designed for operation at the center (40.25 GHz) and two extreme (37.0 and 43.5 GHz) frequencies of the specified RF range. The BFN diagram was drawn based on the 8�8 Butler matrix according to Figure 3 with the replacement of phase shifters with ideal equivalent delay circuits, in which the constant delay Δt was calculated at the center RF frequency fc using the following well-known formula:

$$
\Delta \mathbf{t} = \Delta \boldsymbol{\rho} / \left( \mathbf{360} \mathbf{f}\_c \right) \tag{8}
$$

where Δφ is the phase shift in degrees.

Table 2 lists the calculation results for phase shift (see Figure 3).

The results for MATLAB calculations of NRP using Eq. (7) at the center RF, lower RF, and upper RF in the azimuth angles range of �50° from PAA broadside are shown in Figures 9–11, correspondingly.


#### Table 2.

Time delays of the equivalent delay circuits of 8�8 Butler matrix.

Figure 9.

NRP at the center RF of 40.25 GHz using phase matrix (top) or time delay matrix (bottom).

To summarize, the following outcomes could be concluded.

NRP at the upper RF of 43.5 GHz using phase matrix (top) or time delay matrix (bottom).

Design of Reconfigurable Multiple-Beam Array Feed Network Based on Millimeter-Wave…

DOI: http://dx.doi.org/10.5772/intechopen.89076

Figure 11.

121

the neighboring beams still remains at 4 dB from the maximum.

wavelength corresponding to the center frequency.

millimeter-wave array beamformers

5. Design principles and ways of integrated photonics-based

• According to [1], a Butler matrix provides a predetermined phase distribution at its outputs within the operating frequency band of its constituent components, such as quadrature hybrids and phase shifters. In it, when the RF deviates from the central one, the effect of beam squint is observed. The set of the beams narrows at the upper frequency and expands at the lower one, but the intersection point of

• When used in the matrix, some delay elements with the values given in Table 2, the effect of the beam squint is not observed, and the positions of the maxima do not change with RF, but the radiation patterns lose orthogonality, and the beams

have a greater overlap at the lower frequency and less at the highest one.

• Despite visible deviations in the shape of radiation patterns, the simulation results demonstrate the possibility of using delay elements in the Butler matrix to ensure uniform coverage of the sector 50° in the 37–43.5 GHz operating frequency range when the antenna elements are spaced through half the

In general, photonics-based BFNs for PAAs have many potential advantages over their electrical counterparts [18, 19, 22], such as small size, low weight, no

Figure 10. NRP at the lower RF of 37.0 GHz using phase matrix (top) or time delay matrix (bottom).

Design of Reconfigurable Multiple-Beam Array Feed Network Based on Millimeter-Wave… DOI: http://dx.doi.org/10.5772/intechopen.89076

Figure 11. NRP at the upper RF of 43.5 GHz using phase matrix (top) or time delay matrix (bottom).

To summarize, the following outcomes could be concluded.

