beams. However, it remains a major technological challenge to provide sufficient flexibility to achieve multiple beam directions with an analog beamforming system.
Phased arrays are inherently suited for producing single beams. Because one signal is fed to all of its elements, a phased array constitutes only one antenna port per beam. The beam is steered to follow the intended user by controlling the values of its phase shifters. Some sacrifices have to be made to produce individually steerable multiple beams with a phased array. They include partitioning the array aperture for different beams; and, hence, this limits the overall performance of each generated beam. In the following subsections, we present two multiple analog beamforming techniques that are currently popular for cellular systems: Butler matrices, and Luneburg lenses.
1.4.1 Butler Matrix
One traditional method of producing multiple beams is to utilize Butler matrices [14]. These multiple beams can be steered together in principle, but not independently. Therefore, Butler matrices are almost exclusively used for fixed beams. A Butler matrix is an RF circuit consisting of couplers, delay lines, crossovers, and transition parts. An n‐way Butler matrix has n inputs and n outputs. A signal applied to a given input will lead to outputs of equal amplitude but with a uniform phase gradient, thus leading to a single steered beam. The phase increment between adjacent outputs is a multiple of
Figure 1.7 Typical implementation of a 4 × 4 Butler matrix (BM) connected to 4 radiating elements and the 4 beams it produces.
Unfortunately, multiple beamforming employing a Butler matrix has a number of disadvantages. First, the beams are fixed. Consequently, it is only a switched beam solution for tracking mobile users. Second, owing to the losses in the Butler matrix’s circuits, a major challenge for large antenna arrays is keeping the overall losses small, especially at millimeter‐wave frequencies. Third, a 2D Butler matrix would be required for two‐dimensional (2D) beamforming. However, the conventional structure is generally too bulky and too lossy owing to the complicated requisite crossovers. Fourth, a complete system engineering approach is required to achieve wideband operation with a Bulter matrix. These issues are only some of the challenges facing the antenna research community. They and some recently developed solutions will be addressed in several later chapters.
1.4.2 Luneburg Lenses
A simple, yet powerful, analog method to create steerable and multiple beams is to employ a spherical Luneburg lens. A Luneburg lens in its simplest form consists of a radially inhomogeneous sphere with a well‐defined graded dielectric constant that varies from 2.0 at the center of the sphere to 1.0 at its outer surface. The gradation is given by the equation:
Figure 1.8 Illustration of Luneburg lenses. (a) Spherical. (b) Cylindrical.
The beamwidth of a Luneburg lens is approximately the same as that of a linear array whose length equals the diameter of the lens. Nevertheless, the nulls are considerably deeper. If one places a number of feeds along the surface of a Luneburg lens, one can produce a multiple beam antenna, one beam per feed. These multi‐beam antennas can be employed for data distribution or broadcasting in 5G networks.
It is very difficult and very costly to produce an ideal Luneburg lens. As a practical alternative, one can employ several separate shells to replace the theoretical continuous gradation of the dielectric constant with a discrete approximation to it. Many such versions have been deployed in a variety of current systems.
The main advantages of Luneburg lenses over antenna arrays based on beamforming networks can be summarized as follows [14]:
A great simplification in component count and inherent low passive intermodulation (PIM).
Reduction of network losses.
Beam crossover levels can be selected arbitrarily by choosing the spacing of the source elements.
Isolation between elements is generally superior to that obtained with beamforming networks.
The relative disadvantage of a Luneburg lens antenna is its three‐dimensional bulk compared with planar forms of the array antennas. Nevertheless, some mobile operators are currently showing strong interest in Luneburg lenses due to their low cost in hardware and low energy consumption.
1.5 Millimeter‐Wave Antennas
To date, every new generation of mobile wireless communication has been allocated its own dedicated spectrum. This is again true for 5G networks. Given the fact that the radio spectrum is a worldwide limited resource, the mobile wireless communication industry has been “forced” to start using the mm‐wave spectrum to accommodate some portion of its 5G networks, known as 5G mm‐wave. Application examples include small cells for data‐hungry hot spots and fixed wireless access services where line of sight (LoS) propagation is easier to be guaranteed. Moving forward to 6G, it is expected that some airborne and satellite systems will also embrace the mm‐wave spectrum. Compared with the microwave frequency bands, the propagation of mm‐waves is negatively impacted by higher attenuation rates and severe weather.
To emphasize this issue, Figure 1.9 shows the attenuation of electromagnetic waves from DC into the low terahertz (THz) range as functions of the propagation distance, altitude, and weather conditions. Notice that there are some windows in these spectra where the atmospheric attenuation is high, such as around 60 GHz, and, conversely, much lower. The former are clearly not suitable for long‐distance communication. The latter are targeted
