**3. Reconfigurable intelligent surface (RIS)**

Another possible scenario is the case when the initial source is located outside the surface, but far from the structure. Assume an ideal initial source located at the angle of ð Þ *θ<sup>s</sup>* ¼ *π=*6, *ϕ<sup>s</sup>* ¼ *π=*4 with respect to the surface normal far from the structure. Following the routine explains in Section 2.1 and 2.2, *E*ref, *E*obj, and the EM hologram patterns are calculated as shown in **Figure 7(a)**, **(b)**, and **(c)** respectively provided that the reflected beam is aimed to be pointed to ð Þ *θ<sup>m</sup>* ¼ *π=*3, *ϕ<sup>m</sup>* ¼ *π=*6 .

To translate this mechanism into a practical format, this is the case when the surface reflects the incoming waves from a far-located source to a desired direction. This is not a simple mirror reflection where there is no control over the angle of reflection; indeed, the reflection angle can be engineered in this case using the holography technique. This brings a new idea for the future generation of cellular networks.

Consider a case where there is a blind spot within the area under the coverage of a base station (BS). The conventional approach to providing coverage for this blind spot is to add a new BS in the network. However, this method can be expensive and sometimes very challenging regarding the environmental barriers in an area. The idea is to locate a surface in the line of sight (LoS) of the BS so that it can be illuminated by the BS. Then the receiving EM waves reflect back to that blind spot to recycle the waves and provide coverage without adding a new BS. It is possible to reconfigure the response of the surface by applying some components like Varactor or PIN diodes on each unit cell and recalculating the EM hologram for each state of reflection. Under this circumstance, the obtained structure is called a reconfigurable intelligent surface (RIS) [9]. This scenario is schematically shown in **Figure 8(a)**.

Note that holography is not the only technique to regulate the response of the RIS. The generalized Snell's law of reflection (GSR) can also be used in this regard [10]; a GSR-based RIS prototype [11] is shown in **Figure 8(b)**.

One of the biggest problems for RIS to be industrialized and practically applied in real-world networks is its very low aperture efficiency *η<sup>a</sup>* ð Þ. This will be more challenging for the uplink scenario when the user attempt to connect BS via RIS. To have a more clear idea about this problem, consider a rectangular reflecting surface with a planar dimension of *X* � *Y*, illuminated by a feed horn, distanced by *R* as presented in **Figure 9(a)**. The feeder's radiation pattern can be expressed by cos *qE* ð Þ*<sup>θ</sup>* and cos *qH* ð Þ*<sup>θ</sup>*

**Figure 7.**

*Recording process: (a) E*ref *with an ideal source at the angle of* ð Þ *θ<sup>s</sup>* ¼ *π=*6, *ϕ<sup>s</sup>* ¼ *π=*4 *with respect to the surface normal located far from the structure, (b) E*obj *in case the reflected beam is aimed to be pointed to* ð Þ *θ<sup>m</sup>* ¼ *π=*3, *ϕ<sup>m</sup>* ¼ *π=*6 *, and (c) the obtained EM hologram.*

#### **Figure 8.**

*(a) The coverage provisioning via reconfigurable intelligent surface (RIS) for a blind spot and (b) a prototype example of RIS [11].*

#### **Figure 9.**

*(a) The overall geometry of a reflective surface illuminated by a feeder, (b) the theoretical aperture efficiency when the feeder is not far from the aperture, (c) a schema of using reflective surfaces to provide the coverage for the user in the blind spot region of the BS, and (d) the theoretical aperture efficiency when the feeder is located relatively far from the aperture.*

at the E-plane and H-plane respectively. Product of the illumination *ηill* ð Þ and spillover *η<sup>s</sup>* ð Þ efficiencies is then defines *ηa*. In case of rectangular surfaces, *ηill* can be calculated by [12]:

*Holographic Beamforming DOI: http://dx.doi.org/10.5772/intechopen.112467*

$$
\eta\_{\rm ill} = \frac{I^2}{\mathfrak{s}\varPi}.\tag{7}
$$

where *s* ¼ *X* � *Y* and

$$\begin{split} I &= \int\_{\mathbf{x} = -X/2}^{X/2} \int\_{\mathbf{y} = -Y/2}^{Y/2} \left\{ \frac{1}{\sqrt{R^2 + \mathbf{x}^2 + \mathbf{y}^2}} \left[ \left( \frac{R}{\sqrt{R^2 + \mathbf{x}^2 + \mathbf{y}^2}} \right)^{q\_x + 2} \frac{\mathbf{y}^2}{\mathbf{x}^2 + \mathbf{y}^2} \right. \\ & \left. + \left( \frac{R}{\sqrt{R^2 + \mathbf{x}^2 + \mathbf{y}^2}} \right)^{q\_H + 1} \frac{\mathbf{x}^2}{\mathbf{x}^2 + \mathbf{y}^2} \right] \right\} dyd\mathbf{x}, \end{split} \tag{8}$$

with

$$\begin{split} II &= \int\_{x=-X/2}^{X/2} \int\_{y=-Y/2}^{Y/2} \left[ \left( \frac{R}{\sqrt{R^2 + \varkappa^2 + y^2}} \right)^{2q\_E} \frac{y^2}{\varkappa^2 + y^2} \\ &+ \left( \frac{R}{\sqrt{R^2 + \varkappa^2 + y^2}} \right)^{2q\_E} \frac{\varkappa^2}{\varkappa^2 + y^2} \right] \frac{R}{\left( \sqrt{R^2 + \varkappa^2 + y^2} \right)^3} dy d\varkappa. \end{split} \tag{9}$$

Under this circumstance, *η<sup>s</sup>* reads:

$$
\eta\_s = \frac{\text{II}}{\text{III}},
\tag{10}
$$

with

$$\text{III} = \pi \left( \frac{1}{1 + 2q\_E} + \frac{1}{1 + 2q\_H} \right). \tag{11}$$

Now consider the rectangular aperture of **Figure 6**(a). Recall that the physical size of the aperture is *s* ¼ 1*:*65 m � 1*:*25 m at 3.5 GHz. With a symetrical radiation pattern at the feeder, *q* ¼ *qE* ¼ *qH* and *ηill* and *η<sup>s</sup>* are obtained by (7) and (10) respectively, followed by calculation of *η<sup>a</sup>* ¼ *ηill* � *ηs*. The result is shown in **Figure 9(b)** for different values of *q* ¼ 10 � 80 and *R* ¼ 0*:*5 � 3 m. This shows that it is possible to realize optimum values of *q* and *R* to use a specific feed horn and locate it at a specific distance from the surface to obtain the maximum possible *ηa*. This is a routine step of designing reflectarray antennas and metasurface reflectors. However, in the case of RIS where there is no control on *q* and *R*, it is not possible to customize the structure to reach the optimum *ηa*.

**Figure 9(c)** shows a schema of applying the surface of **Figure 6(a)** for coverage provisioning purposes. Note that this surface has a very large size comparing to the operating wavelength which can potentially be a positive factor for *ηa*. We repeat the same calculation, but this time the distance range is expanded to *R* ¼ 0*:*5 � 50 m. The result is shown in **Figure 9(d)**. As it is clear, a massive region of this plot shows a very low *η<sup>a</sup>* which can make the structure impractical for real-world applications. This will be more challenging when we pay attention to two factors, 1st: in cellular networks,

the cell radius is much longer than 50 m, this means that the situation is even worse than **Figure 9(d)**; 2nd: for the uplink connection, the user equipment (UE) will have a very low gain (or low *q*) which will make the connection very challenging if not impossible (see **Figure 9(d)** for low values of *q* and high *R*). Finally, it should be noted that these are all theoretical calculations; when it comes to practice, the obtained *η<sup>a</sup>* is expected to be relatively lower than the theory. This is also true even for reflectarray antennas where the feeder is optimized.
