Advances in Array Optimization

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 formula:

$$D(\theta,\varphi) = \frac{1 + \cos\left(\pi\cos\theta\right)}{\sin\theta} \ast \sum\_{n=1}^{8} \left[\frac{1}{\sqrt{8}} \sum\_{m=1}^{6} e^{-j\frac{2\pi}{N}(m-1)(n-1)}\right] e^{j\frac{2\pi}{\epsilon}n\frac{j\_0}{2}\cos\varphi} \tag{7}$$

4. A general analysis of radiation pattern sensitivity

delay lines has been widely used [17–20].

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

the sensitivity analysis is also necessary.

where Δφ is the phase shift in degrees.

are shown in Figures 9–11, correspondingly.

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

well-known formula:

Table 2.

119

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

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

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,

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

Δt ¼ Δφ= 360f <sup>c</sup>

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

Phase shift 22.5° 45.0° 67.5° 90.0° Time delay 1.55 ps 3.1 ps 4.65 ps 6.2 ps

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

(8)

Equation (7) is fundamental for further modeling.

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 Figure 8.

To summarize, the following outcomes could be concluded:


Figure 8. Radiation pattern of RS antenna system in the azimuth plane.

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