Guiding Wireless Signals with Arrays of Metallic Linear Fresnel Reflectors: A Low-cost, Frequency-versatile, and Practical Approach

We employ multiple specialized metallic LFR arrays designed to guide signal wavefronts back into the environment and toward a desired location. As can be seen from Figure 2, each of our reflector arrays comprises many individual units, referred to as tiles. These tiles have the ability to rotate independently, allowing for the manipulation of the signal wavefront reflection.

Our objective is to optimize signal strength at the UE position. This involves maximizing the number of transmission paths from the AP to the UE through the adjustment of metallic LFR arrays. Our approach focuses on aligning each reflector’s tile to create a path from the AP to the central point of the tile and subsequently to the UE location. This strategy guarantees the existence of at least one reflected path from the AP to the UE for every tile on the reflector array. Additionally, as the number of tiles on the reflector increases, so does the quantity of reflected paths available.

Without constraints on rotation angles, we have the flexibility to select rotation angles for the reflector’s tiles without limitations. By applying Snell’s law, which governs that the angle of incidence equals the angle of reflection, our objective is to manipulate the normal of the material’s surface to achieve these equal angles. For clarity, we introduce some annotations: point A represents the center of a reflector tile, point B denotes the location of the AP, point C is the UE location, and $\vec{n}$ is the normal of the material’s surface (Figure 3).

We can find the normal $\vec{n}$ of the surface that satisfies Snell’s law by using (1).

Initially, the tile is positioned flat on the xy-plane with its normal directed upwards along the positive z-axis. We use the standard transformation from the Cartesian coordinate system to the spherical coordinate system to determine both angles, $\theta$ and $\phi$ using (2), (3), and (4).

where $x$, $y$, and $z$ are coordinates of the normal $\vec{n}$, $r$ is the length of the normal $\vec{n}$, $\theta$ is the elevation angle, $\phi$ is the azimuth angle, and $\text{sgn}(\cdot)$ is the signum function.

Our work utilizes ray tracing method, which mimics real-world scenarios where a tranmission source emits numerous rays that interact with surrounding objects, bouncing off them indefinitely until losing intensity.

We make an assumption that upon encountering an object, a ray undergoes specular reflection back into the environment (Figure 3). Each successive reflection diminishes the signal power, a reduction governed by a reflection coefficient. This coefficient is determined by both the ray’s direction and the material composition of the surface it impinges upon [13]. Furthermore, the ray tracing method incorporates diffraction phenomenon [14, 15] to improve the simulation accuracy.

Several other assumptions are made. Firstly, all device positions are predetermined at the start of the simulation, a condition that can be realized in practical scenarios using tracking technologies such as Ultra Wideband (UWB) [16]. Additionally, we assume precise control over all tiles of a reflector device without addressing practical limitations. This enables us to freely adjust reflector tile rotation angles in the simulation to enhance UE path gains.

We investigate the downlink scenario, where an AP transmits information to a UE at a frequency of 28GHz. In this study, we leverage an open-source simulation wireless software library, Sionna by NVIDIA [17], to maximize received power at the UE location in 3D models. The software offers ray tracing simulations to generate coverage maps within a given geometry. The maximization of UE path gain, which is directly related to received power, is achieved by placing LFR devices at suitable locations. Based on a predefined configuration of AP, UE, and reflector devices, a 3D modeling software, particularly Blender [18], can produce a desired 3D model. The geometry is then imported into the simulation software to generate coverage maps.

In our simulation, we predefined the properties of each component of the 3D model. We configured a metallic LFR array consisting of 7x10 tiles (Figure 2). Each metal tile measures 20 cm by 20 cm, resulting in a total device size of 1.4 m by 2.0 m. The walls, ceiling, and floor are made of concrete.

The relative permittivity and conductivity of all materials used in our simulation are specified according to guidelines provided by the International Telecommunications Union (ITU). Based on measurement data, the ITU derives frequency-dependent values for the real part of the relative permittivity, $\eta^{\prime}$, and conductivity, $\sigma$, for many groups of materials[13]. Properties of materials that we use in our simulation are calculated as follows.

where $\eta^{\prime}$ is dimensionless, $\sigma$ is in S/m, and $f$ is frequency in GHz. The values of $a,b,c$ and $d$ are presented in I.

We examine two primary cases: an L-shaped hallway and a T-shaped hallway (see Figure 4). In both cases, the location of the AP remains fixed at the same location. We adjust the position of the UE to move through sections of the hallway where direct line-of-sight (LOS) paths are absent. The AP position is depicted in blue, whereas the locations of UEs are illustrated in green.

The L-shaped case (Figure 4(a)) is designed as a fundamental case study to evaluate the efficacy of a single mechanical reflector array. Within the L-shaped case, we analyze three sub-cases: (1) a scenario without any reflector, (2) a scenario with a simple reflector, and (3) a scenario focusing on the beam-focusing technique. The first sub-case, without any reflector devices, establishes a baseline, representing a typical environment where no supporting devices are utilized to improve the received power at the UE. In contrast, the second and third sub-cases involve the placement of reflector devices at the hallway corner. In the simple reflector sub-case, all tiles within the reflector array rotate solely around the z-axis, each with an identical rotation angle of $45^{o}$. Conversely, the beam-focusing sub-case concentrates on creating multiple reflected paths through the reflector array, namely the AP-Reflector-UE paths. Through adjustments in the rotation angle of its tiles using the technique discussed in Section II-B, the reflector array can establish numerous reflected paths to the UE, thereby guiding various beams toward a specified location.

We expand our simulation to include a more complex layout, namely the T-shaped hallway, in which we incorporate two reflector arrays, as illustrated in Figure 4(b). Similar to the analysis conducted for the L-shaped hallway, we explore the coverage maps for three different sub-cases: (1) without any reflector, (2) with two simple reflector arrays, and (3) emphasizing our beam-focusing technique. The configurations for all scenarios mirror those of the L-shaped hallway. In both the second and third scenarios, two reflector arrays are employed, one positioned at the hallway corner and the other facing the extended corridor. In the second sub-case, which involves two simple reflectors, the reflector tiles are rotated by $45^{\text{o}}$ around the z-axis. On the other hand, the objective of the third sub-case is similar to that of the L-shaped layout, striving to establish multiple reflected paths between the AP and UE through the utilization of two reflector arrays. As the UE relocates, we adjust the configuration of the two arrays to ensure that each tile of the two arrays establishes at least one reflected path from the AP to the UE. This involves conducting two consecutive bisector calculations, detailed in Section II-B while accounting for specular reflection.

We generate various scenarios and geometrical adjustment of all objects. Guided by predefined parameters of the scenario such as the locations of AP and UE, along with desired techniques and scene configurations, we proceed with the adjustment of reflector arrays. Primarily, this involves calculating the rotation angle of tiles comprising reflector arrays. These adjustments are made prior to exporting the scene for coverage map simulation.

Following the setup with Blender, each scenario is subsequently simulated using Sionna, which offers ray tracing simulation for wireless communication. Internally, Sionna uses Monte Carlo approximation to calculate the received signal power of an area. It creates a 2D grid at a height of 1.5m above the ground. This grid contains many small units, called cells, each of which is used to accumulate all received power values at the cell’s center point. For example, when a ray hits a cell within a grid, the received power is calculated and accumulated in the cell. The process of calculation and accumulation happens until the maximum bounce is reached or the ray does not hit any objects in the scene. In the end, all received power values in a cell are summed to produce a single value at the center of that cell.

Coverage maps display path gain through a color map. As illustrated in Figure 5, our simulation results indicate the efficacy of our reflector array. Figure 5(a) demonstrates that the signal strength remains unchanged regardless of the UE’s position since there are no devices or objects to guide the signal transmission. Given the UE position in Figure 5(a), the path gain at the UE is measured at -125.61 dB. On the other hand, Figure 5(b) illustrates a marginal improvement of path gain at the UE to -99.54 dB, when employing a simple reflector.

Figure 5(c) demonstrates a significant enhancement in the path gain at the UE through the utilization of individual control for each tile on the reflector. With this approach, we improve the UE’s path gain to -72.57 dB. This path gain, achieved with our technique, surpasses that of both the scene without any devices and the scene featuring a simple reflector. It is crucial to clarify the alteration in color observed in this specific scenario. The depiction of the coverage map represents a 2D x-y plane positioned at an elevation of 1.5 meters above ground level, while the surrounding environment exhibits 3D characteristics. Signals reflect off both the lower and the upper section of the array, ultimately converging at the UE location, precisely at a height of 1.5 meters. This convergence phenomenon leads to a significant amplification in path gain (resulting in color change) along the trajectories of all focused beams.

Similar to the findings from the L-shape hallway scenario, our simulation outcomes for the T-shaped hallways confirm the effectiveness of our reflector device, as depicted in Figure 6. Figure 6(a) demonstrates that without any supporting devices, the path gain at the UE is estimated to be -156.35 dB. Meanwhile, Figure 6(b) demonstrates an improvement in path gain at the UE with the integration of two simple reflectors, resulting in an increase to -109.20 dB. On the other hand, Figure 6(c) depicts a substantial increase in path gain at the UE when complex reflectors are used. With the individual control of each tile to guide signal beams, we improve the UE’s path gain to -68.88 dB.

As evident from Figure 5 and Figure 6, the individual control of each tile in a reflector demonstrates the effectiveness in enhancing the path gain at the UE’s location. The results, showing the proficiency of our method to track the UE’s position while simultaneously improving its path gain, is presented at [19].

Figure 7 presents a comparative analysis of RSS, measured in dBm, when employing a transmitter with 10 watts transmit power across four distinct scenarios at nine predetermined locations within the area of interest, as depicted in Figure 4. Notably, in Figure 7(a), the employment of a beam-focusing reflector array significantly enhances RSS across all locations, surpassing even free space transmission outcomes. Figure 7(b) displays similar findings, with two exceptions at locations 2 and 5, where RSS with beam-focusing reflector arrays is lower than RSS under free space conditions. This discrepancy is currently attributed to certain multipath components destructively interfering with each other at these specific locations, resulting in reduced RSS with the beam-focusing reflector. Further investigation into this phenomenon is planned for future work. Lastly, it is noteworthy that even a simple specular reflective surface can have a non-negligible impact on RSS.

While the results of our proposed method are anticipated even without extensive research, this study employs simulations to quantify the path gain improvements achieved by using reflectors for beam focusing. The simulations show a path gain increase of at least 50 dB in both scenarios, indicating that this approach is promising for enhancing received signal strengths at the UE. Additionally, it has the potential to reduce power consumption in indoor environments, particularly for home users with stationary receiving devices, as it does not consume power once the reflector device is configured. Therefore, comparing our proposed method with conventional RIS implementations is not appropriate due to the latter’s higher power consumption requirements.

To implement our reflector, we are investigating the use of MEMS mirrors as the primary tiles for the device. Each MEMS mirror tile is controlled by simple motors that allow limited movement in both horizontal and vertical directions. Specifically, each tile can adjust its orientation within a 20-degree range in both axes. The reflective surface of the MEMS mirrors is made of aluminum, which is cost-effective to manufacture and provides sufficient reflective properties for efficient beam-focusing. In addition, the quick response times and precise control capabilities of the MEMS mirrors make them ideal for dynamic beam steering, further enhancing the performance and adaptability of our reflector system. This approach aims to optimize the device’s functionality while maintaining low production costs and ensuring easy integration into existing indoor environments.