1. Introduction

Wireless communication technologies have experienced a constant and rapid development over the past few decades. This has resulted in communication systems that need to fulfill increasing tighter requirements with the goal of improving their performance and quality. In particular, future developments and integration of 5G technologies for terrestrial and space communications [1] represent a great challenge. Specifically, the antenna is an important subsystem for wireless communications, since it is the device that converts the guided waves into propagating waves in free space and vice versa. Different parameters of the antenna may be optimized depending on the application, such as size, radiation pattern, matching, etc. In many cases, a shaped-beam pattern is necessary to adequately redirect power to the desired area. For instance, direct-to-home (DTH) applications need a contoured-beam footprint to match some specific geographic area on the surface of the Earth [2]. Also, an interesting feature for base stations for wireless communications is to provide constant power over a certain angular range. This may be achieved with a shaped-beam

squared-cosecant pattern [3]. Traditionally, shaped parabolic reflectors or phased arrays have been employed for these applications [2, 3]. However, shaped parabolic reflectors are bulky and expensive to manufacture, while phased arrays require complex feeding networks which introduce high losses. Nonetheless, with the popularization of the microstrip technology, reflectarray antennas have become a potential substitute to parabolic reflector dishes and phased arrays.

design and optimization methodology using the generalized IA. Section 4 contains the results regarding the two reflectarray designs for advanced wireless communi-

Before describing in detail the optimization algorithm, we will establish the different pattern requirements that can be imposed in the optimization procedure and how they are implemented in the generalized IA. For the case of radiation pattern optimization, the requirements may be imposed in the copolar and crosspolar components. When performing a POS, only copolar requirements are considered due to the simplifications in the analysis of the unit cell [9]. However, a direct optimization of the layout may consider both copolar and crosspolar requirements. In the generalized IA, the copolar requirements are given by means of two mask templates, which impose the minimum (Tmin) and maximum (Tmax) values that the far field must achieve. Thus, if Gcp is the copolar gain, it should fulfil

where u ¼ sin θ cos φ and v ¼ sin θ sin φ are the angular coordinates where the far field is computed. Figure 1 shows an example of typical copolar requirement templates for a squared-cosecant pattern and a sectored-beam pattern in a plane, where Tmin and Tmax are the minimum and maximum specifications between which the copolar pattern must lie. Alternatively, these requirements can be provided in

On the other hand, there are several methodologies to implement crosspolar requirements. A typical approach is to minimize the crosspolar far field component by means of templates [16], similarly to the procedure followed with the copolar pattern. However, the crosspolar pattern does not need a lower bound in the

superscript indicates that the mask is applied to the crosspolar pattern, fulfilling

<sup>G</sup>xpð Þ u, v <sup>≤</sup>Txp

Typical requirement templates for (a) squared-cosecant pattern and (b) sectored-beam pattern.

Tminð Þ u, v ≤ Gcpð Þ u, v ≤Tmaxð Þ u, v , (1)

max is needed in this case, where the

maxð Þ u, v : (2)

2. Optimization framework for electrically large reflectarrays

cations. Finally, Section 5 contains the conclusions.

DOI: http://dx.doi.org/10.5772/intechopen.88909

terms of minimum gain and maximum ripple.

optimization. Thus, only the maximum mask Txp

Figure 1.

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2.1 Pattern requirements in the optimization procedure

Reflectarray Pattern Optimization for Advanced Wireless Communications

The concept of reflectarray antenna was first introduced in 1963 [4] as a type of antenna that combines the simplicity of reflectors and the versatility of arrays, using waveguides as the reflecting element. This resulted in a bulky and expensive structure. However, reflectarrays were not widely studied until the development of low-profile printed antennas in the 1980s, when the printed planar reflectarray was developed [5]. It consists of an array of radiating elements that are spatially fed by a primary feed, which is usually a horn antenna. Its working principle is based on altering the properties of the electromagnetic field impinging from the feed. By adjusting the dimensions of the reflectarray elements, a phase shift is introduced in the impinging field [6], allowing to obtain the desired radiation pattern.

Although designing reflectarrays for high-gain pencil beam patterns at a certain direction may be achieved with analytical equations [5], the synthesis of noncanonical beams is a challenging task and requires the use of an optimization algorithm, especially in cases with tight requirements, such as space applications [2]. Since reflectarrays are usually comprised of hundreds or even thousands of elements, the employed algorithm must be computationally efficient. Until recently, the dominant approach was the phase-only synthesis (POS) [5], which employs a simplified analysis of the unit cell. This results in an extremely efficient synthesis [7–9] but has no control over the cross-polarization performance. The first approach to the crosspolar direct optimization of reflectarray antennas was presented in [10], using a method of moments based on local periodicity (MoM-LP) for the analysis of the unit cell. However, the algorithm was slow and only handled 1 polarization and small reflectarrays (225 elements). Other approaches for the minimization of the crosspolar component of the far field include a proper arrangement of the elements [11] and the minimization of the undesired tangential field adjusting the dimensions of the element [12] or through rotation [13]. These techniques are faster, but they work at the element level and thus provide suboptimal results.

In this chapter, we present a general framework for the efficient and accurate pattern optimization of reflectarray antennas for advanced wireless communications, including copolar and crosspolar specifications. It is based on the use of the generalized intersection approach (IA) algorithm [14] for the optimization and a MoM-LP [15] for the accurate characterization of the reflectarray unit cell. The design procedure is divided in several stages. First, a phase-only synthesis (POS) is carried out, to efficiently obtain the desired copolar pattern. Then, by using a zerofinding routine and the MoM-LP, the layout of the reflectarray is obtained adjusting the dimensions of each unit cell. Finally, an optional stage to improve the crosspolarization performance may be carried out. It employs the MoM-LP directly in the optimization loop to accurately characterize the crosspolar pattern. Both the POS and direct layout optimization are carried out with the generalized IA, demonstrating the versatility of the algorithm. Two relevant examples are provided to demonstrate the capabilities of the proposed framework. First, a shaped-beam reflectarray for future 5G base stations at millimeter waveband is proposed. It radiates a sectored-beam pattern in azimuth and a squared-cosecant pattern in elevation. The second example is a very large contoured-beam, spaceborne reflectarray for direct-to-home (DTH) broadcasting based on a real space mission.

The rest of the chapter is divided as follows. Section 2 introduces the optimization framework based on the generalized IA algorithm. Section 3 describes the

design and optimization methodology using the generalized IA. Section 4 contains the results regarding the two reflectarray designs for advanced wireless communications. Finally, Section 5 contains the conclusions.
