## 1 Introduction  
Wireless communications within the 3 rd Generation Partnership Project (3 GPP) 5G New Radio (NR) paradigm have introduced new concepts and technologies, including ultra-dense networking, massive machine communications, all-spectrum access, full-duplexing, and massive MIMO [1, 2], for applications in the industry 4.0 [3], smart cities [4], Internet of Things (IoT) [5], precision agriculture [6], and self-driving cars [7], among others [8]. These applications require higher data rates, higher channel capacity, and lower latency than those achieved with previous generations of mobile networks [9]. To that end, the 3 GPP 5G NR technical specification [10] identifies two frequency ranges (FR) for the implementation of the 5G networks, namely, FR1 (0.41-7.125 GHz) and FR2 (24.25-71 GHz), each of them divided into several bands. From the point of view of frequency allocation, the FR1 spectrum is already very crowded, by now providing services that range from cellular and satellite communications, to wireless local area networks [9]. Thus, the mm-wave ranges provided by the FR2, with their readily available wide spectrum, have become increasingly interesting for the deployment of 5G NR networks. In particular, there is special interest in the three lower bands in FR2, n257 (26.5-29.5 GHz), n258 (24.25-27.5 GHz), and n261 (27.5-28.35 GHz) since they have been released by the most countries, including the United States, the European Union, China, Japan, and South Korea [9]. However, the use of frequencies in the FR2 presents some challenges, such as path loss due to higher losses and shadowing due to blockage by physical objects that act as barriers for the propagating wave [11]. To overcome these issues, the use of femtocells with increased line of sight connectivity [12; 13] has been proposed as a means of enhancing the cellular coverage while offloading the macro cell traffic in places with higher density. Spatially fed arrays have been proposed within the intelligent reflective surface (IRS) paradigm [14; 15; 16], specifically reflectarray antennas for both indoor [17] and outdoor scenarios [18]. Transmitarrays have also been proposed as a solution to provide coverage in indoor femtocells [19; 20]. In order to improve the coverage in indoor scenarios for transfer of information, power, or both simultaneously, near field beam-shaping techniques for the enlargement of coverage areas have been proposed. For instance, in [17] a phase-only synthesis (POS) based on the generalized intersection approach [21] was carried out to design two reflectarray antennas, one providing coverage in an outdoor scenario by considering a squared-cosecant beam in elevation and sectorial beam in azimuth, while the other reflectarray provides coverage in an indoor scenario. In [19], a novel near field POS algorithm was developed in which the far field resulting from the truncated near field according to specifications is computed as an intermediate step before recovering the field at the aperture by means of the fast Fourier transform (FFT). It was employed to design a 3D-printed dielectric transmitarray antenna that provides a very narrow coverage area. This algorithm was later extended [22] to include simultaneous near and far field constraints. Another near field POS is carried out in [20] to enlarge the coverage area provided by a multi-fed transmitarray antenna. The techniques employed in the previous works are very efficient for the near field beam-shaping of spatially fed arrays at a single frequency. However, they present some shortcomings. One common characteristic of the previous works is that they perform a POS, where a phase-shift for each array element is obtained at a single frequency such that the array radiates the desired near field. From those phases, the chosen unit cell is tuned in such a way that it produces the required phase-shift [23]. One obvious limitation of such an approach is the narrow bandwidth nature of the obtained arrays.