Optimization and Performance of Metamaterial- Based Electromagnetic Scattering Sheet for Coverage Improvement in 28 GHz Band

Fifth generation (5G) mobile communication systems have been deployed in the millimeter wave (mmWave) band. Since electromagnetic (EM) waves in this band exhibit high propagation loss and antennas are highly directive, the performance of wireless communications is largely degraded in a non-line-of-sight (NLOS) area, resulting in a limited coverage area. To improve the performance and increase the coverage area, a metamaterial-based electromagnetic scattering sheet (EMSS) with broad scattering characteristics is proposed in this paper. We also introduce fast design and optimization methods using equivalent circuits of metamaterials, antenna array theory, and the genetic algorithm (GA). The diffusion coefficient is used as a fitness value to evaluate the scattering characteristics of the EMSS generated by GA. The broad scattering characteristics of the designed EMSS are experimentally confirmed. We clarified that the optimized EMSS has a higher diffusion coefficient than a metal plate of the same size. Finally, we demonstrated improved wireless communication performance in an NLOS area by diffusing the incoming EM fields using our designed EMSS.

SECTION I. Introduction

Fifth generation (5G) mobile communication systems have been developed for use in the millimeter wave (mmWave) frequency band [1], [2]. Highly directive antennas are often used to compensate for the high attenuation of electromagnetic (EM) waves owing to the propagation and atmospheric absorption in this band [3]. It has been shown [4] that when a cement wall or cement floor is illuminated by an EM wave at 28 GHz, which is one of the 5G frequency bands in operation worldwide, scattering mainly occurs in a specular direction with a small portion of diffusive components. Therefore, when a receiving antenna is placed in a non-line-of-site (NLOS) area, as illustrated in Fig. 1, wireless communication quality is largely degraded [5], [6]. One technique to improve the signal quality in a coverage hole area is to use a distribution antenna system (DAS) [7] at the expense of an increased budget for multiple microwave components such as amplifiers, demodulators, and antennas. The other promising solution for addressing this problem is to use metamaterial reflectors or metasurfaces to enhance the scattered EM field in the desired direction and provide alternative wireless propagation paths [8], [9]. Many types of metamaterial reflector have been proposed. They are placed on building structures such as walls, windows, and roofs to improve the coverage area, and some field experiments have been demonstrated in the literature [10]. In [11], a dual-band metamaterial reflector for frequencies of 28 and 39 GHz was designed, and the received power distribution on a test field was measured and evaluated. Kitayama et al. designed a metasurface transparent at 28 GHz for installation on existing walls or glass windows [12] In [13], a metasurface reflector array for near-field focusing was proposed. These initial studies have demonstrated the benefits of using metamaterial reflectors to improve the coverage area by designing the desired propagation of self-scattering waves without external power. Compared with a DAS, these metamaterial reflectors are lightweight and thin. In addition, they do not require a power source, but the scattering is intended to be in a specifically designed direction. Therefore, when the propagation environment changes, the reflector should be redesigned.

FIGURE 1.

Deterioration of millimeter-wave wireless communication performance in various scenarios.

Many types of reconfigurable intelligent surface (RIS) have been proposed to deal with a dynamic propagation environment [13], [14], [15], [16], [17], [18]. An RIS consists of a large number of passive elements, where the electrical contact or dielectric properties of substrates at each element can be actively controlled by changing the bias voltage at varactor diodes or liquid crystals, respectively. In [19] and [20], a comparison between active and passive RISs in terms of energy efficiency was reported. H. Zhang et al. proposed an intelligent omni-surface (IOS) to serve mobile users on both sides of the surface and to achieve full-dimensional wireless communications [21]. The reflection characteristics of an RIS can be dynamically changed in response to a changing environment. However, a large number of active elements (e.g., varactor diodes, which increase the fabrication cost) and an external power supply to apply voltage bias are required at each element.

We previously proposed a scattering surface (hereafter called an electromagnetic scattering sheet (EMSS)) that exhibits broad scattering characteristics. Our design also took into account the location and radiation pattern of an illuminating EM source or a transmitting antenna [22]. The advantages of the proposed EMSS were that it only required optimization during its fabrication/configuration process and did not require real-time reconfiguration. In addition, no external power supply was needed to deal with a dynamic propagation environment. The proposed EMSS was constructed by combining two regions of metal with different heights corresponding to two different reflection phases, namely, 180° and 0°, at the same reference plane. The height difference must be $0.25\lambda$ , where $\lambda$ is the wavelength of the design frequency. We also provided a fast design method using the genetic algorithm (GA), which is an optimization method inspired by natural selection [23]. We used GA to find an optimized combination pattern [24]. Since a different in the path length of $0.25\lambda$ is always required, the height of the EMSS must be larger than $0.25\lambda$ .

In this study, we propose a metamaterial-based EMSS for improved coverage at 28 GHz. By using metamaterials, the thickness of the EMSS can be made the same as that of the substrates, typically less than $0.1\lambda$ . A fast design method that combines equivalent circuits of a metamaterial unit-cell structure, array antenna theory, and GA is proposed. The concept of the EMSS and design method is presented in detail in Section II. Design and optimization methods are described in Section III. The optimized structure is discussed in Section IV. In Section V, we experimentally demonstrate the improvement of the coverage area using the designed EMSS. Finally, conclusions are drawn in Section VI.

SECTION II. Proposed EM Scattering Sheet

The EMSS can be constructed by altering the reflection phase at each subregion. In the literature, the reflection phase is randomized to achieve diffusive scattering in a terahertz frequency range [25]. By using a random phase, the rapid design of the surface is possible, but the number of combinations of random phase metasurfaces is large, making the optimization slow. In addition, although an optimized structure may be obtained for a certain angle of incidence, it may create a specular reflection at another incident angle or frequency when using a random phase method. A simpler structure to achieve diffusive scattering is a metasurface composed of two types of unit cell with different reflection phases, called a “coding metasurface” [26]. The configuration of the metasurface is coded and optimized using a two-dimensional binary code. The structure can be optimized by evolutional algorithms such as particle swarm optimization. However, high fabrication accuracy is required to satisfy the phase difference condition using two types of unit cell, especially at mmWave frequencies and above. To alleviate the phase condition, an EMSS using only one type of metamaterial structure is proposed in this paper. As shown in Fig. 2, the EMSS comprises two subregions, one metal and the other metamaterial, corresponding to 180° and 0° reflection phases, respectively. With the metamaterial structure, a low-profile surface with a thickness of less than $0.1\lambda$ can be achieved.

FIGURE 2.

Design methodology of metamaterial-based EM scattering sheet.

SECTION III. Design and Optimization Methodologies

Fig. 3 shows the design methodology for our proposed metamaterial-based EMSS. The metamaterial used in this study was a square patch. Initially, we chose dimensions of the patch element, namely, the spacing between the patches, the side length, and the thickness of the substrate, which can provide a reflection phase of 0° at the reference plane at the design frequency. The reflection phase was calculated via equivalent circuit theory [27], [28], [29]. The microstrip patch array can be considered as a strip grating structure with a strip width equal to that of the patch. Details of the equivalent circuit for the strip grating structure are described in Appendix. After the dimensions of unit cells are determined, optimization is required to find the best configuration for a specific size of the EMSS. Essentially, to optimize the overall structure of the EMSS, it is necessary to analyze all combinations of metal plates and metamaterials. However, the number of trials increases exponentially with the number of subregions of metal plates and metamaterials, resulting in a high computation time and cost. To reduce the computation time and cost, we apply GA, in which a pattern of the EMSS is coded into a sequence of 1-bit patterns depending on the subregion (metal or metamaterial). The metamaterial and metal, having reflection phases of 0° and 180°, are replaced with the codes “1” and “0”, respectively. The number of bits is the same as the number of subregions. Therefore, a sequence of 1-bit patterns corresponds to one configuration of the EMSS. Several randomly initiated sequences of 1-bit patterns are produced and evolved in accordance with the genetic process (selection, crossover, and mutation). Then, the scattering pattern for each configuration is calculated using array antenna theory [30], and the scattering characteristics are evaluated using the diffusion coefficient defined in Section V-B. The optimization loop is continued until the maximum number of generations is reached, as shown in Fig. 3. Our proposed method searches for theoptimal structure of the EMSS having the largest diffusion coefficient averaged over many different incident angles. Therefore, the proposed EMSS does not require reconfiguration when the position or location of the transmitter or EMSS is altered. The disadvantage of the proposed method is that the optimization only treats the problem from the viewpoint of the transmitter side and neglects the impact of the receiver channel. This issue requires more experimental investigation and will be studied in the future.

FIGURE 3.

Design methodology of metamaterial-based EM scattering sheet. $N_{max}$ is the maximum number of generations.

A. Optimization Based on Genetic Algorithm

After the structure of the metamaterial with the 0° reflection phase is determined, an EMSS is then constructed by combining the metamaterial and metal subregions. However, there are many possible combinations; for example, if an EMSS is divided into $N_{l}$ subregions, where each subregion may be metal or metamaterial, then the number of possible combinations becomes $2^{N_{l}}$ . Here, we use GA to reduce the number of trials and to efficiently search for the combination that provides the best broad scattering characteristics. GA contains the following four steps. (1) Generation of codes or 1-bit patterns: each code represents an individual EMSS structure comprising a combination of metal and metamaterial subregions as described above. (2) Calculation and evaluation of the scattering pattern for each generated structure or code. (3) Selection and crossover between selected candidate codes: the selection is conducted in proportion to the diffusion coefficient; a code with a large diffusion coefficient has a high probability of being selected as a candidate. (4) Mutation: every code generated by “crossover” is mutated at a certain rate to avoid a “local minima” case. The evaluation, crossover, and mutation procedures are repeated until the number of generations reaches the maximum defined in the optimization process.

B. Calculation and Evaluation of Scattering Pattern

The scattering pattern of a defined EMSS configuration is calculated using array antenna theory [30]. Fig. 4 shows the parameters of the EMSS used in the calculation of the scattering pattern. An EMSS with $N_{l}$ subregions can be considered as an array antenna with $N_{l}$ separate antenna elements. When the number of metal subregions is $M$ , the remaining $N_{l}-M$ subregions are metamaterial subregions.Each subregion is sequentially aligned with a separation of $w_{d}$ and has a radiating phase constant equal to the reflection phase, which can be 0° (metamaterial) or 180° (metal). $w_{d}$ is determined as a multiple of the periodicity $p$ of the metamaterial unit cell, as described in Section V. $w_{d}$ can be chosen arbitrarily but, empirically, it should be larger than $4p$ to consider the mutual interactions between the metamaterial elements. In our design, $w_{d}$ is set to ten times the periodicity ($10p$ ). In array antenna theory, the scattering pattern $E_{\mathrm {s}}\left ({\theta,\theta ^{\mathrm {inc}}}\right)$ of an EMSS with a transmitting antenna located at distance $L$ and at angle $\theta ^{\mathrm {inc}}$ from the center of the EMSS, as shown in Fig. 4, can be derived as

$$\begin{align*} E_{\text {s}}\left ({\theta, \theta ^{\text {inc }}}\right)&=\sum _{l=1}^{N_{l}} F_{l} D_{l}(\theta) \exp \left ({j k(l-1) w_{d} \sin \theta }\right), \tag{1}\\ D_{l}(\theta)&=\begin{cases} \displaystyle \frac {\sin \left [{\frac {k}{2} w_{d} \sin (\theta)}\right]}{\frac {k}{2} w_{d} \sin (\theta)} { \text {for metal subregion, }} \\ \displaystyle \sin ^{n}(\theta) \quad { \text {for metamaterial subregion, }} \end{cases} \\ F_{l}&=A_{l}^{\text {feed }} \exp \left \{{j\left ({\delta _{l}^{\text {feed }}+\delta _{l}^{\text {inc }}+\delta _{l}^{r}}\right)}\right \}, \tag{2}\\ A_{l}^{\mathrm {feed}}&=\left |{R\left ({\theta _{l}^{\prime }}\right)}\right |, \tag{3}\\ \delta _{l}^{\mathrm {feed}}&=\angle R\left ({\theta _{l}^{\prime }}\right)-k\left ({L-L_{l}}\right), \tag{4}\\ \delta _{l}^{\text {inc }}&=-k(l-1) w_{d} \sin \theta ^{\text {inc }}, \tag{5}\\ \delta _{l}^{r}&=\begin{cases} \displaystyle 180^{\circ } & \text {for metal subregion} \\ \displaystyle 0^{\circ } & \text {for metamaterial subregion} \end{cases} \tag{6}\end{align*}$$ where $k$ is the wavenumber (= $2\pi / \lambda$ ), $w_{d}$ is the separation between adjacent subregions, and $N_{l}$ is the total number of divided subregions. The $l^{\mathrm {th}}$ subregion is equivalently substituted with an antenna element at its center with array antenna amplitude $A_{l}^{\mathrm {feed}}$ and phase $\delta _{l}^{\mathrm {feed}}$ . Therefore, $A_{l}^{\mathrm {feed}}$ and $\delta _{l}^{\mathrm {feed}}$ depend on the incident angle, denoted as $\theta _{l}^{\prime }$ in Fig. 4. Note that for a real situation, the magnitude of the illuminated field on each subregion also depends on the propagation distance from the transmitting antenna aperture. $L_{l}$ is the distance from the transmitting antenna to the center of the $l^{\mathrm {th}}$ subregion of the EMSS. The difference in the propagation distance ($L_{l} - L$ ) resulting from different incident angles is also taken into account in $\delta _{l}^{\mathrm {feed}}$ . $\delta _{l}^{\mathrm {inc}}$ is the phase which depends on the incident angle $\theta ^{\mathrm {inc}}\vphantom {^{\int }}$ . For all cases in this study, a transmitting antenna with high directivity is assumed, such as a horn antenna, but any type of antenna can be used if we know its complex directivity $R\left ({\theta ' }\right)$ . $D_{l}(\theta)$ for the metal subregion is the same as that of an aperture antenna having aperture size $w_{d}$ , whereas a unidirectional pattern of the patch element is used to describe $D_{l}(\theta)$ for the metamaterial subregion. ${n}$ is a coefficient that determines the shape of the directivity. To determine $n$ , the directivity from a single unit cell illuminated normally by an EM planewave at the frequency of interest is analyzed, then $n$ is determined by fitting the function ${\mathrm {sin}}^{n}\left ({\theta }\right)$ with the directivity obtained from numerical analysis. Since the metamaterial unit cell is smaller than the wavelength, $n$ is close to unity for all cases considered in this study. Note that the polarization of an incident electric field is aligned in the xz-plane, corresponding to the transverse electric (TE) case, as shown in Fig. 4. In (3)–(5), if the direction of an incident plane wave is perpendicular to the plane of the EMSS, then $\delta _{l}^{\mathrm {feed}}$ = constant, $\delta _{l}^{\mathrm {inc}}$ = 0, and $A_{l}^{\mathrm {feed}}$ = constant.

FIGURE 4.

Design methodology of metamaterial-based EM scattering sheet.

The diffusion coefficient, indicating the uniformity of a scattering pattern, is used as the figure of merit of an EMSS or the fitness in the GA optimization process. The diffusion coefficient can be calculated as

$$\begin{align*} \zeta \left ({\theta ^{\text {inc }}}\right)=\frac {\left ({\sum _{i=1}^{N_{s}}\left |{E_{\text {s}}\left ({\theta _{i}, \theta ^{\text {inc }}}\right)}\right |}\right)^{2}-\sum _{i=1}^{N_{s}}\left |{E_{\text {s}}\left ({\theta _{i}, \theta ^{\text {inc }}}\right)}\right |^{2}}{(N-1) \sum _{i=1}^{N_{s}}\left |{E_{\text {s}}\left ({\theta _{i}, \theta ^{\text {inc }}}\right)}\right |^{2}} \tag{7}\end{align*}$$ where $\theta _{i}$ is the discretized $i^{\mathrm {th}}$ angle of the scattering pattern and $N_{s}$ is the number of angle divisions over the range from −90° to 90° in the calculation of the diffusion coefficient [31], [32]. $\zeta$ = 0 indicates a perfect reflector that perfectly reflects an incoming EM wave in a specular direction and $\zeta$ = 1 represents a perfect diffuser whose scattering pattern is perfectly omnidirectional. Therefore, the diffusion coefficient indicates how close the scattering pattern is to the omnidirectional pattern. The objective of the optimization is to find the structure of the EMSS that gives the maximum value of the diffusion coefficient given by (7), which is the value determined by varying the incoming wave direction $\theta ^{\mathrm {inc}}$ . In our study, the EMSS that gives the highest average diffusion coefficient when $\theta ^{\mathrm {inc}}$ is varied from 0° to 60° is defined as the “optimum structure”.

SECTION IV. Optimized EMSS Structure and Fabrication

First, the metamaterial structure having a reflection phase of 0° is determined from the equivalent circuit model described in Appendix. Our design frequency is 28 GHz for all EMSS structures in this study. Although low-loss substrate materials such as low-temperature co-fired ceramic (LTCC) are often used for mmWave frequencies, we use an FR-4 substrate, which is a low-cost and commercially available material in the printed circuit board industry. Whereas typical substrates used for mmWave applications are LTCCs and low-loss dielectrics such as Megtron 7 (Panasonic Co.), they are costly and involve many fabirication processes. The reason for using an FR-4 substrate is that FR-4 is a low-cost material and the fabrication is already a mature technology used in the printed circuit board industry. The relative permittivity, conductivity, and thickness of the FR-4 substrate are 4.3, 0.13 S/m, and 0.8 mm, respectively. Note that all the metals in our simulation are perfect electric conductors without loss. The periodicity of the metamaterial unit cell is chosen to be 1.2 mm or $0.1164\lambda$ at 28 GHz. Fig. 5 shows the reflection magnitude and phase calculated using the equivalent circuit model with respect to frequency when varying the side length ($w$ ) of the patch. As $w$ increases, the reflection phase crosses 0° at a lower frequency. The reflection coefficient becomes smaller owing to loss in the substrate at frequencies having a reflection phase close to 0°. The loss due to a difference in the magnitude of reflection coefficients is so small that it can be disregarded in the calculation of the scattering pattern using array antenna theory. When $w$ = 0.985 mm, the reflection phase is almost 0° (0.0095°). Then, the unit cell structure with $p$ = 1.2 mm and $w$ = 0.985 mm is used in the next optimization process.

FIGURE 5.

Magnitude and phase of reflection coefficients for different side lengths of the patch-type unit cell.

We use the determined unit-cell structure in this optimization process. Each metamaterial subregion comprises 10 unit cells ($w_{d} = 10p$ ) so as to consider mutual interactions between patches and to ensure a reflection phase of 0° at the designed subregion. The number of subregions ($N_{l}$ ) is set to 15; thus, the total side length of the EMSS is equal to $N_{l} \times w_{d} = 15\times12$ = 180 mm. The parameters used in the optimization process are listed in Table 1.

TABLE 1 Parameters Used in Optimization Procedure

As the first step in the optimization, code sequences are randomly generated and evaluated using the diffusion coefficients in (7). The candidate code sequences are selected by the roulette method, in which the probability of being selected as a candidate for crossover is calculated and ranked on the basis of fitness. The selected code sequences and their elite, that is, the code sequence with the highest fitness or the highest diffusion coefficient in the same generation, are then utilized in the crossover process. A two-point crossover is conducted for each selected pair of code sequences. The mutation rate is 75%, the number of samples for each generation is $N_{s}$ = 24, and the number of generations is 40. The total number of randomly generated codes and those produced by a genetic process (crossover, mutation) is thus equal to $N_{s} \times N_{l}$ = 960, which is the number of structures to be evaluated on the basis of the diffusion coefficient. Meanwhile, the total number of code sequences for all combinations is 2¹⁵ = 32,768. Consequently, we can reduce the computation cost by 97% compared with the brute-force approach when searching for the optimum structure of the EMSS.

Fig. 6 shows the distribution of the diffusion coefficients of the EMSS structures that are generated and evolved by GA in our optimization process. As shown in Fig. 6, the diffusion coefficients increase as the number of generations. It should be emphasized again that the diffusion coefficient is calculated as an average value for the cases in which the incident angle varies from 0° to 60° in 5° steps. The largest diffusion coefficient at 28 GHz is 0.534 at the $40^{th}$ generation, for which the code sequence is “000110010010101”, where “1” and “0” represent the metamaterial and metal subregions, respectively. For a metal plate of the same size as the EMSS, the diffusion coefficient at 28 GHz obtained by array antenna theory is 0.195, whereas the value derived by a hybrid simulation using physical optics and the method of moments (MoM) for modeling the metal plate and horn antenna is 0.202, respectively. For reference, we also randomly generated the code sequences and obtained the largest diffusion coefficient value of 0.519. Since all the sequences are randomized, we may not achieve as large a diffusion coefficient as that obtained from GA.

FIGURE 6.

Distribution of diffusion coefficients of EMSS structures generated and evolved by GA.

Fig. 7 shows our optimized EMSS fabricated using laser-processing technology. The dimensions of the metamaterial unit cell are chosen to be $p$ = 1.2 mm and $w$ = 1.0 mm (the initial design value was 0.985 mm). Therefore, the minimum gap between patches is 0.2 mm, whereas the fabrication accuracy using the laser-processing technology is $\pm 20 \mu \text{m}$ . For $w$ = 1.0 mm, the magnitude and phase of the reflection coefficient are −0.256 dB and −8.98°, respectively, which are slightly different from our design values of 0 dB and 0°.

FIGURE 7.

Optimized EMSS fabricated using laser-processing technology.

SECTION V. Experimental Validation and Demonstration of Improved Coverage

In this section, we discuss the measurements of the scattering patterns of the fabricated EMSSs and use them to demonstrate the expansion of the coverage area.

A. Scattering Patterns

Fig. 8 shows the experiment setup for the measurement of the scattering pattern using a network analyzer (Agilent Technologies E8363B) and two horn antennas (A. H. Systems, Model no. SAS-574) for transmitting (Tx) and receiving (Rx), respectively. The measured frequency is between 24 and 32 GHz with a frequency step of 0.1 GHz and an intermediate frequency filter bandwidth of 100 Hz. Time-domain gating is applied to cut off multiple reflections between the fabricated EMSS and the antennas using a gating time from −11.7 to −11.5 ns. The transmitting antenna is fixed at three incident angles: $\theta _{\mathrm {inc}}$ = 0°, 20°, and 40°. The receiving antenna is moved along the hemispherical guide rail with an angle step of 1°. The Tx antenna is placed 6 cm above the Rx antenna in the vertical direction to avoid collision when the measurement angle between the two antennas is close to 0°.

FIGURE 8.

Setup for measuring scattering pattern of EMSS.

Figs. 9(a)-​9(c) show the measured scattering patterns of our designed EMSS at 28 GHz for $\theta _{\mathrm {inc}}$ = 0°, 20°, and 40°, respectively. The structure of the EMSS was optimized using our methodology proposed in Section III. The scattering pattern from a metal plate with the same side length of 0.18 m when $\theta _{\mathrm {inc}}$ = 0° is also shown in Fig. 9(d) for reference. As shown in Figs. 9(a)-​9(c), the scattering patterns obtained from array antenna theory match those calculated using MoM except when the scattering angle is close to the broadside angle or ±90°, confirming the validity of using array antenna theory in the design. A difference in the scattering pattern appears at around ±90° since array antenna theory cannot consider the edge effect of the substrate. Therefore, the diffusion coefficients obtained from MoM results are larger than those obtained using array antenna theory. Note that the results obtained using both MoM and array antenna theory are far-field values, whereas measurement results were obtained using the measurement system shown in Fig. 8, in which the distance from the EMSS surface to the Rx antenna was only 0.66 m, much smaller than $2D^{2} / \lambda$ or 6.05 m at 28 GHz. Therefore, the measurement results indicate broader directivity than the numerical results of MoM and array antenna theory, resulting in higher diffusion coefficients.

FIGURE 9.

Scattering pattern of EMSS at 28 GHz. (a) $\theta _{\mathbf {inc}}$ = 0°, (b) $\theta _{\mathbf {inc}}$ = 20°, (c) $\theta _{\mathbf {inc}}$ = 40°, and (d) $\theta _{\mathbf {inc}}$ = 0° for metal plate.

Fig. 10 shows the diffusion coefficients of the EMSS and metal from 24 to 32 GHz. It can be seen that the diffusion coefficients of the metal are almost constant over this frequency range, whereas those of the EMSS tend to decrease with increasing frequency. The measured diffusion coefficients of our designed EMSS and the metal plate are 0.531 and 0.303, respectively. Therefore, the diffusion coefficients of the EMSS are higher than those of the metal plate with the same area over this band, indicating that it is possible to use the EMSS to improve the coverage area of communication. In addition, the experimental results always give higher coefficient values. This is due to the insufficient measurement distance between the EMSS and the antennas as described earlier.

FIGURE 10.

Frequency characteristics of diffusion coefficient of designed EMSS when $\theta _{\mathbf {inc}} = 0^{\mathbf {o}}$ .

B. Demonstration of Improved Coverage

To demonstrate the usefulness of the EMSS in improving the coverage area in an indoor environment, we constructed an office room inside a shielded room for experiments, as illustrated in Fig. 11(a). Fig. 11(b) shows details of the room in a perspective view. The size of the room is $4\times 3\times2.4\,\,\text{m}^{3}$ . There is no ceiling due to a restriction stipulated in Japanese construction law, which prohibits a ceiling without a fire detector installed. However, in our experiment, an EM wave diffracted at the upper edge of the room wall is small and, thus, has a negligible effect on our measurement results.

FIGURE 11.

Floor plan and perspective view of an office room for measurement of coverage area.

There are three desks occupying a volume of $0.9\times 0.7\times0.7\,\,\text{m}^{3}$ each and one metal cabinet ($0.9\times 0.45\times1.81\,\,\text{m}^{3}$ ) inside the room. Two cabinets are placed outside the room as obstructions to prevent a direct wave from reaching part of the room, creating an NLOS area. The door of the room has a size of $1.188\times2.023\,\,\text{m}^{2}$ and is made of wood, whereas the walls on the four sides of the room are made of plasterboards of 12 mm thickness, which are fixed to wall studs made of aluminum on both sides. As shown in Fig. 11(b), the spacing between the wall studs is 0.303 m in the framework of the room and, hence, part of the EM waves can pass through the wall through the spacing. The size of the measurement regions inside the room is $1.9\times3.2\,\,\text{m}^{2}$ .

Figs. 12(a)-​12(d) show photographs of the setup for the coverage area measurements with the EMSS installed outside the room. The Tx antenna (MI Technologies, Model no. 12A-18) is fixed on a tripod at a height of 1.5 m and connected to a signal generator (Agilent Technologies, E8267D) via a coaxial cable with 2.92 mm connectors. The designed EMSSs, each of $0.18\times0.18\,\,\text{m}^{2}$ size, are arranged in a $3\times3$ array to make a large reflector of $0.54\times0.54\,\,\text{m}^{2}$ size. The incident angle of the Tx antenna to the EMSS is 21°. The array of EMSSs or a metal plate made of aluminum with a size of $0.6\times0.6\,\,\text{m}^{2}$ is installed near the wall of the shielded room at a height of 1.5 m, as shown in Fig. 12(c). An omnidirectional antenna (Eravant, Model no. SAO-2734030345-KF-S1) is used as a receiving antenna and connected to a 43 dB broadband mmWave amplifier (Eravant, SBB-0524034318-KFKF-E8) and then to a signal analyzer (Keysight Technologies, Model no. UXA N9040B with “IQ Analyzer and Swept SA Measurement Application” Option) to demodulate the signal and calculate the bit-error rate (BER), as shown in Fig. 12(d). The Rx antenna, amplifier, and signal analyzer are all placed on a slide positioner automatically controlled by a PC via a general-purpose interface bus (GPIB) protocol. The setup parameters of the signal generator and signal analyzer are tabulated in Table 2. The carrier frequency is 28 GHz and the modulation type used in the signal is 16-QAM.

TABLE 2 Parameters of Signal at Signal Generator and Signal Analyzer

FIGURE 12.

Experimental configuration: (a) transmitting antenna and room, (b) space inside room, (c) transmitting antenna and EMSS, and (d) receiving antenna on one-dimensional positioner.

Figs. 13(a) and 13(b) show the received signal strength indicator (RSSI) distribution inside the room when the metal plate and EMSS are used as a reflector, respectively, at the location shown in Fig. 10(a). As shown in Fig. 13(a), the reflection from the metal plate can pass through the plaster boards and has a strong RSSI value in and near the line of the specular direction. However, owing to the barriers generated by the vertical wall studs, parts of the EM waves are blocked, resulting in a stripe-like distribution in the $y$ -direction. When our designed EMSS is used instead of the metal plate as the reflector, the RSSI at the locations in the specular direction is smaller than or comparable to those of the metal plate, but the RSSI increases at the positions far from the specular line, where the RSSI is very small and the received signal information is lost. Therefore, without increasing the transmission power or amplification using a low-noise amplifier at the receiving antenna, the demodulation of signals in these regions is almost impossible. It can be clearly seen that the RSSI in the corner of the room on average increases to a level larger than −60 dBm, enlarging the coverage area. Consequently, it has been demonstrated that using the EMSS as a reflector can efficiently improve the coverage area without using an active device.

FIGURE 13.

Measurement results of RSSI distribution inside office room for (a) metal plate and (b) EMSS (black regions are the regions obstructed by a cabinet, where RSSI cannot be measured).

Figs. 14(a)-​14(d) show constellation diagrams of the 16-QAM-modulated signal at the signal analyzer for the metal reflector at locations A and B and for the EMSS at the same locations (see Fig. 13), respectively. As indicated in Fig. 14(a), at location A, a strong reflection from the metal reflector is observed, and the receiving signal strength is as high as −39.37 dBm, whereas at location B, which is on a deflected course far from the specular direction of the metal reflector, demodulation is impossible because the signal strength is too small and the constellation diagram collapses, as clearly shown in Fig. 14(b). The BER at location B is thus 0.5, which is the worst-case value. When we replaced the metal reflector with the designed EMSS, the signal strength at location A decreased by approximately 12 dB to −51.30 dBm, and a BER of 0.05 was obtained owing to the decrease in the scattering cross section of EMSS in the observed direction. However, an increase in the signal strength of approximately 7 dB from −60.97 to −53.58 dBm was observed at location B, and it was found that demodulation could still be performed with a BER of 0.11 at location B.

FIGURE 14.

Constellation of receiving 16-QAM-modulated signals for (a) metal reflector at location A, (b) metal reflector at location B, (c) EMSS at location A, and (d) EMSS at location B. (Values in the figures indicate RSSI and BER for each case).

Meanwhile, if a correction scheme is applied to the received signal at location B, we can expect a BER even better than 0.11. However, at this location, demodulation is impossible for the metal reflector. Our results demonstrate the effectiveness of using the EMSS as a reflector or diffuser of incoming EM fields to expand the coverage area of communication in the 28 GHz band.

Finally, in Table 3, we indicate the performance of our designed EMSS and similar structures in the literature, which have been used as EM reflectors or diffusers. The diffusion coefficient defined in (7) is also derived for each structure using the data provided in these papers. The diffusion coefficient of a cement wall at 28 GHz is also provided for reference [4]. Most of the designed surfaces use metamaterials or an artificial magnetic conductor (AMC) structure to realize the broad-angle scattering characteristics of an EM diffuser [33] or to achieve strong scattering in a specifically designed direction as an EM reflector by controlling the phase at each scattering element [34], [35], [36]. These designed surfaces were used as functional surfaces to decrease or increase the scattering cross section in a specific direction, not to expand the coverage area as described in our paper. Most of the EM diffusers employed a checkerboard pattern, but we have demonstrated that this pattern may not provide the best solution for improving the coverage area when the incident angle of an incoming EM field is unknown [37]. As shown in Table 3, the diffusion coefficient of our designed EMSS is higher than those in the literature. In addition, our designed EMSS provides a high diffusion coefficient over a wide angle of incidence from 0° to 60°, demonstrating its high potential for expanding the coverage area of wireless communication.

TABLE 3 Comparison of Designed EMSS and Similar Structures for Use as EM Reflector or Diffuser

SECTION VI. Conclusion

We proposed a metamaterial-based EMSS and a fast design method using the equivalent circuit model, antenna array theory, and GA. The structure of the designed EMSS was thin and flat. Its thickness was less than $0.1\lambda$ , making it suitable for fabrication by an additive process such as coating or covering with wallpaper to improve the appearance of the landscape. The diffusion coefficient was calculated and evaluated for all structures produced and evolved by GA in the optimization process. The advantage of our proposed method is that there is no need to perform a full-wave simulation in the design process, making the method suitable for the rapid design of EMSSs for many different situations. The design method also includes information on the transmitting antenna, EMSS size, number of region divisions, range of incident angle, and distance from the Tx antenna to the EMSS. By inputting these data into our program, optimized structures are rapidly obtained in a few minutes by our design method. We also fabricated an optimized EMSS and evaluated its scattering characteristics. The measured scattering patterns were shown to be in reasonable agreement with those derived numerically using array antenna theory and MoM, demonstrating the validity of our design method. We clarified that the proposed EMSS has a higher diffusion coefficient or broader directivity than a metal plate of the same size. Finally, we experimentally verified its improved coverage by using the fabricated EMSS in a small office room built for experiments. The coverage area inside the room increased at the expense of decreased receiving signal strength owing to the decreased scattering cross section of the EMSS compared with that of the metal reflector in the specular direction. However, at a location on a deflected course from the specular direction, the signal strength was increased when using the EMSS, whereas we did not receive any signal when using the metal reflector. Consequently, we demonstrated that our designed EMSS is useful for improving the coverage area.

ACKNOWLEDGMENT

The authors would like to express their gratitude to Takehiro Tsuruta of Takenaka Corporation for his guidance on the construction of an office room for the experiments.

Appendix

Strip gratings can be represented as the LC equivalent circuit shown in Fig. 15. Its surface impedance $Z$ for normal incidence can be obtained as [27] and [28]

$$\begin{equation*} Z=j\omega L+\frac {1}{j\omega C}, \tag{8}\end{equation*}$$ where $$\begin{align*} \omega L&=\frac {w}{\lambda }\left [{ \ln {\left ({\csc \frac {\pi w}{2p} }\right)+G\left ({p,w,\lambda }\right)} }\right], \tag{9}\\ \omega C&=\frac {4w\varepsilon _{e}}{\lambda }\left [{ \ln {\left ({\csc \frac {\pi w}{2p} }\right)+G\left ({p,w,\lambda }\right)} }\right], \tag{10}\end{align*}$$ $\varepsilon _{e}=(1+\varepsilon _{r})/2$ is the effective permittivity, and $\varepsilon _{r}$ is the relative permittivity of the substrate. $p$ and $w$ are the periodicity and strip width, respectively. $G\left ({p,w,\lambda }\right)$ is the first-order correction term for the quasi-static term of the reactance of the strip. The detailed expression for $G\left ({p,w,\lambda }\right)$ can be found in [23]. Next, since the overall structure of the patch-type metamaterial can be considered as the transmission line, as shown in Fig. A, the reflection coefficient $R$ of the metamaterial can be expressed as $$\begin{align*} R&=\frac {Z_{\mathrm {in}}-Z_{0}}{Z_{\mathrm {in}}+Z_{0}}, \\ Z_{\mathrm {in}}&=\frac {jZ_{0}}{-B^{\prime }+\sqrt \varepsilon _{r} \cot {\beta h}}, \tag{11}\end{align*}$$ where $Z_{0}$ and $Z_{\mathrm {in}}$ are the wave impedances of the free space and metamaterial, respectively, and $B^{\prime }$ is the susceptance of the surface impedance ($B^{\prime }$ = Im(1/$Z$ )), which can be obtained from (8).

FIGURE 15.

Equivalent circuit of patch-type metamaterial. Left: LC circuit of patch-type surface. Right: transmission line representation of patch-type metamaterial.