Indoor Non‐Line‐of‐Sight Millimeter‐Wave Coverage Enhancements by Field‐Reorganizable Passive Digital Coding Metasurfaces

Digital metasurfaces define a novel methodology for metasurface designs by adopting discrete coding meta‐atoms to engineer electromagnetic waves in programmable ways. Herein, a novel field‐reorganizable digital metasurface (FRDM) that can be used to enhance the indoor non‐line‐of‐sight (NLOS) millimeter‐wave (mmWave) signal coverage is presented. The passive binary supercells which can be reorganized with an in situ optimization characteristic to deflect the incoming mmWaves into the blind area with adjustable angles are proposed. The indoor L‐shaped corridor signal coverage simulated by the ray‐tracing technique confirms that the NLOS blind area is effectively communicated using the passive FRDM. Practical environment experiments using FRDMs with different coding sequences are conducted, indicating that the averaged signal intensity is increased by over 10 dB in the NLOS blind area in a wide operating frequency band from 26 to 30 GHz by reorganizing the passive digital metasurfaces. The results suggest that the proposed FRDM enabled by the reorganizable binary supercells is a highly flexible, low‐cost, and extensible solution for B5G and 6G mmWave wireless communications.


Introduction
Retrospection of the overview about a decade ago on 5G tells us that significant progress has been made in the new generation of wireless communication. [1]The 5 G base stations have been deploying steadily, offering a 1000Â data rate, millisecond low latency, and ubiquitous experience for end-users.However, current base stations mainly operate within the sub-6 GHz band, while the millimeter-wave (mmWave) bands for 5G are still at the early stage worldwide.As the diffraction theory implies, mmWaves could not circumvent obstacles readily, leading to poor signal coverage within the non-line-of-sight (NLOS) area.For the urban signal coverage scenarios, the parabolic reflectors were designed on the top of the dense buildings to enhance the received power in the blocked area. [2]To realize reflection beam-steering and transparency for multiband wireless signals, frequency-selective reflectarray was proposed. [3]Another scheme to enhance the coverage of the shadowed corner is the dipole scatters without additional cost. [4]When it comes to indoor scenarios, complex corridors make the signal coverage even thorny. [5]By introducing passive or active repeaters of companies with microbase stations at the corners, the L-shaped, T-shaped, and X-shaped corridors can be effectively covered.These repeaters are usually realized by a dual-antenna system, [6] which is bulky, complicated in design, and polarization sensitive.As shown, based on the mature microwave engineering technology, a huge amount of macrobase stations, microbase stations, and repeaters should be arranged to convert the NLOS scenarios into line-of-sight (LOS) scenarios. [7,8]Therefore, a low-cost, pluggable, and easy-to-deploy scheme is still urgent for mmWave communications. [9,10][26][27] The most intriguing characteristic of RIS for wireless communication is the capability of manipulating the EM wave propagation environment, providing a brand new degree of freedom over the existing architecture. [28]Recent studies suggest that RIS is also a feasible solution for the wireless-powered communication network that manages information and power simultaneously. [29]Further, the smart radio environment concept is proposed to reconcile and reunite communication and electromagnetism, leveraging RISs as the core enabler. [30,31]34] On the one hand, DMs can be applied to optimize wireless channels, which can be viewed as the middleware for existing wireless communication systems.On the other hand, the programmable metasurfaces (PMs) derived from DMs provide us with opportunities to modulate information directly, [35][36][37][38][39][40][41] which is guaranteed by the information entropy of the coding metasurface. [42,43]The reported literature on this topic demonstrates the tremendous value of DMs for wireless communications with highly flexible, highly reliable, and low-cost features.We note that the fundamental constituent of DM is the meta-atom which regulates the EM parameters at a subwavelength scale.
Adopting DMs to improve wireless channels is a promising and challenging solution for mmWave communications.46][47][48][49][50] Technically speaking, the RISs driven by the DMs can be divided into the active type and the passive type. [49]The active components, such as p-i-n diodes, varactors, and MEMS switches, are utilized on the meta-atoms to dynamically regulate the EM waves.Obviously, numerous active components would increase the cost and the control complexity.In contrast, the passive RISs are cost-effective but with fixed functionality, which cannot fulfill the complicated application environments.A compromise scheme that combines the flexibility of active-type RIS and low-cost passive-type RIS would be a preferred solution for indoor NLOS 5 G mmWave coverage enhancement, which is still unavailable to the best of the authors' knowledge.To that end, based on the digital coding idea, we propose the fieldreorganizable digital metasurface (FRDM).The reorganizable scheme possesses in-situ tunability while keeping the low fabrication cost. [50]Different from the conventional DM using metaatoms as the constituent, the binary supercells are proposed as a unit in the FRDM.According to a specific corridor length for signal coverage, the FRDM could reflect the EM waves from the base station into an optimum angle using the coding sequence combining supercell '0' and supercell '1'.We detail the diffraction mode analysis and the equivalent gradient method for the optimum angle by the 1-bit quantized angles.Both the simulations and experiments confirm the feasibility of our scheme.The advantages of the proposed metasurface have two aspects when compared with conventional metasurfaces based on the generalized Snell's law.First, the physical aperture size using the proposed binary supercells is scalable, which can be confirmed in situ according to a practical scenario.Second, in a practical scenario, the deflection angle is adjustable by carefully designing the coding sequences.[53] However, the proposed FRDM uses binary supercells, corresponding to nonuniform metagratings which have not been studied in this application scenario.More importantly, binary supercells are more suitable for implementing programmability compared with binary metaatoms, which could inspire more novelty designs in the future.

Field-Reorganizable Digital Metasurface
We consider an L-shaped corridor, which is the elementary junction of giant buildings as shown in Figure 1a, to detail the operation principle of the proposed FRDM.As aforementioned, when only one mmWave base station is assigned, the signal blind area (signal intensity less than À105 dBm) will appear within the NLOS domain, [1] as illustrated in Figure 1b.Using another mmWave base station in the NLOS area is a concrete but expensive solution.The conventional active or passive repeater is an alternative scheme; however, it would occupy a large corner space, which is not feasible for practical use.Deploying the proposed FRDM on the corner wall is a concise and effective method.Based on the anomalous reflection theory, the FRDM can deflect the incoming signals into the blind area, as shown in Figure 1c.Benefitting from the digital binary supercells, the reflection angle θ r , which is the critical parameter to enhance coverage, can be reorganized in situ.
Quantizing the phase shifts of a meta-atom into digital states is the main idea of DMs.By sequentially ordering the digital meta-atoms, one will obtain the desired scattered fields.In other words, only two digital states '0' and '1' are required to regulate the complicated EM fields.However, for the signal coverage enhancement application, only deflection beams within a small adjustable range are required.Thus, designing meta-atoms in the subwavelength scale is not necessary.In this article, we extend the digital idea into a coarse granularity scale, that is, super-cell '0' and super-cell '1' that operate greater than one wavelength.The supercell concept was proposed in the optical domain to design an anomalous broadband reflector; however, the digital idea is not utilized there. [44]We note that the proposed binary supercells correspond to two distinct reflection angles, θ 0 r and θ 1 r (θ 0 r < θ 1 r ), which are more suitable for the in situ reorganization than subwavelength meta-atoms.To implement a given angle θ r ∈[θ 0 r , θ 1 r ], one could rapidly determine the supercell coding sequence using our equivalent gradient method presented later.In contrast to the conventional solution that uses mature microwave technology or PMs, the scheme proposed here provides us a new insight to facilitate the commercial application of DMs.

From Meta-Atom to Binary Supercells
We construct the binary supercells from the conventional metaatom.Directly building the supercells is also applicable; however, considering the combination of two different supercells, starting from the meta-atom that constitutes the proposed binary supercells is more suitable for this work.We used a framed Jerusalem cross as the meta-atom which has a wide working frequency band, [54] as illustrated in Figure 2a.By varying L2, we obtain the reflection phase and amplitude responses at 26, 28, and 30 GHz when the meta-atom is immersed within an infinite  uniform environment, as shown in Figure 2b.The central operating frequency is selected at 28 GHz where the total phase shift exceeds 360°.All reflection amplitudes for different L2 lengths at each frequency point nearly approach unity, indicating a good candidate for supercell design.We note that this meta-atom is full polarized, showing identical responses for arbitrarily polarized incident waves.In this work, for brevity, we consider a fixed normal incident angle and an adjustable reflection angle θ r .Meanwhile, we confine the incident and outgoing waves within the xoz-plane.Thus, the gradient of the FRDM only exists along the x-axis and remains uniform along the y-axis.Under such assumptions, the supercell should contain an integer number of meta-atoms as a period to realize our reorganizable scheme.Here, we group four meta-atoms as supercell '0' with a period of D 0 x = 16 mm and group three meta-atoms as supercell '1' with a period of D 1 x = 12 mm.According to the relationship [42] one could easily find that the reflection angles corresponding to the binary supercells are θ 0 r = 42°and θ 1 r = 63.2°at28 GHz, as shown in Figure 2c,d.Next, within the periods D 0 x and D 1 x , the detail phase shifts should be determined according to the generalized law of reflection, which follows where k 0 is the wave number in free space and x is the coordinate in each period.Then, we could calculate the structural parameters L2 for the supercell '0' are 1.0, 1.67, 1.95, and 2.19 mm, while L2 for the supercell '1' are 1.0, 1.77, and 2.11 mm, respectively.We mention that other reflection angles for the binary supercells are also applicable based on the digital idea.An alternative method that eliminates undesired parasitic reflection by the "active-lossy" design is not adopted to design the phase shift in each digital supercell. [42]The reason is that in the signal coverage application, the loss should be avoided for the proposed passive structure.We note that the D 0 x and D 1 x are about 1.49 λ and 1.12 λ, respectively, where λ is the wavelength at 28 GHz.As shown, the binary supercells based on periods that are larger than one working wavelength gain flexible beam deflection functionality without using active components at the expense of sacrificing all directional coverage.Within the specific coverage sector, one could accurately control the reflection angle by combining the binary supercells.

Field-Reorganizable Anomalous Reflection Based on Binary Supercells
Based on the binary supercells, we further investigate the anomalous reflection angles using the digital coding theory. [32]We observe the beam reflection tunability in near field by different coding sequences.The detailed simulation configuration is available in Experimental Section.Here, we present three simulated results that use "0001…/0001…", "01…/01…", and "0111…/ 0111…" coding sequences, as reported in Figure 3a-c.We emphasize that these coding sequences are based on the constructed periods of binary supercells which are distinct from the conventional coding sequences based on the meta-atoms.Thus, the period of the coding sequence is related to the numbers and periods of D 0 x and D 1 x .From the real parts of the scattered electric field over the incident field in each case, one could clearly recognize a quasiplan wave with an oblique propagation direction, demonstrating that one could manipulate the reflection waves by coding the binary super-cells.According to the passivity condition, the amplitude of reflected waves should be greater than the incident waves; [42] therefore, all the maximum amplitudes are normalized to 1.9 V m À1 for better observation.Considering the unity incident amplitude in the simulation, obvious spatial phase shifts are imposed on the scattered electric fields for the presented three cases.Meanwhile, we should also find that the reflected plane waves are not perfect ones due to the additional periods of combining binary supercells rather than the conventional meta-atoms.
Before we look into the accurate modeling of the far-field patterns, we discuss the diffraction modes of the proposed coding sequence that uses supercells.We assume that in a given coding sequence, there are N 0 '0' coding and N 1 '1' coding.Therefore, the tangential electric field of a coding sequence to realize anomalous reflection can be expressed as a periodic function E p (x). Expanding the above period function as a Fourier series, we have Since a m is the amplitude coefficient, we could calculate the propagation angle of each diffraction mode by the phase term, that is All propagating modes that can be recognized in the far field should be a real angle.For the conventional design using meta-atoms by generalized law of reflection, which corresponds to the N 0 = 0 and N 1 = 1 case or the N 0 = 1 and N 1 = 0 case here, the propagating modes are first-order mode (m = À1), normal reflection mode (m = 0), and anomalous reflection mode (m = þ1). [44]In other words, when we investigate the radiations in the far field, only the above three modes can be measured.If κ m exceeds k 0 , θ m will result in a complex angle, indicating a nonpropagating mode.Due to the digital coding of binary super-cells proposed in this work, additional propagating modes will be excited.We calculate the propagating angles of different diffraction modes for different coding states, as reported in Table 1.Refer Figure S1, Supporting Information for the validation of the diffraction modes of FRDM by full-wave simulations.We note that other modes (|m| > 6) are all nonpropagating modes for the listed five cases.Compared with the uniform coding using all '0' or all '1' supercell, the coding states combining '0' supercell and '1' supercell possess extra propagating modes, which means that peaks will appear at these calculated angles in the far-field radiation patterns.We also note that for a practical FRDM the simulated or measured peak angles would show slight deviations from the theoretical angles by Equation (3) due to the finite periodic array.
To rapidly and accurately model the proposed FRDM, we developed a modified planewave angular spectrum (MPWAS) approach.The conventional planewave angular spectrum (CPWAS) approach has been applied to effectively analyze the PMs in our previous work, [39] which is derived from the scalar diffraction theory in the optic domain.However, the CPWAS approach could only model the anomalous reflection mode (m = þ1) precisely.Therefore, we propose the MPWAS approach for the FRDM by considering all the propagation modes in the tangential electric fields for the binary supercells.Refer to S2, Supporting Information for a detailed deduction of the MPWAS approach and comparisons of the far-field radiation patterns between the CPWAS approach, the MWPAS approach, and the full-wave simulation.Comparisons of far-field patterns of the simulated results and the MPWAS approach results for d) "0001…/0001…", e) "01…/01…", and f ) "0111…/0111…" coding sequences.The shaded region indicates the available coverage range using the binary supercells.Full-space far-field patterns of the MPWAS approach result for g) "0001…/0001…", h) "01…/01…", and i) "0111…/0111…" coding sequences.The white cross symbol indicates the direction of the incident wave.
Using the MPWAS approach, we calculate the far-field patterns in the xoz-plane of the aforementioned three coding sequences ("0001…/0001…", "01…/01…", and "0111…/ 0111…") and report the results in Figure 3d-f respectively.The full-wave simulated results are also plotted.The array sizes of these three coding sequences for MPWAS and simulation are 180 Â 180, 168 Â 168, and 208 Â 208 mm 2 , ensuring an integer number of periods for each case.As shown, the results calculated by MPWAS agree well with the simulated ones.The main lobes of "0001…/0001…", "01…/01…", and "0111…/0111…" coding sequences point at 45.4°, 49.9°, and 55.4°, which are coincident with the propagating angles of m = þ4, m = þ2, and m = þ4 respectively, as listed in Table 1.All the reorganized reflection angles are within a coverage range greater than 42°and less than 63.2°.We also report the 3D radiation patterns of each case in the uv-plane, as shown in Figure 3g-i.From the results, one could observe that the proposed FRDM significantly deflects the normal incident waves into the desired direction with a field reorganizable feature.
Finally, we discuss how to figure out a coding sequence that points to the angle of θ r within the available coverage range [θ 0 r , θ 1 r ].Because the proposed FRDM is constructed by the binary supercells, not the conventional meta-atoms, one cannot directly determine the propagating direction by the generalized law of reflection.Here, an equivalent gradient method is proposed to calculate the main lobe direction for an arbitrary coding sequence.Similarly, we suppose that a coding period has N 0 '0' coding and N 1 '1' coding, where N 0 and N 1 are integer numbers.From the previous analyses, we know that one specific coding sequence must relate to one main lobe angle.Therefore, we calculate the equivalent gradient of a coding period and equate it to the gradient of an equivalent angle calculated by the generalized law of reflection, yielding Thus, the corresponding equivalent reflection angle can be expressed as We illustrate the phase shifts of the actual discrete gradient and the equivalent gradient of 49.9°calculated by Equation ( 5) for the "01…/01…" coding sequence, as shown in Figure 4a.We also plot the phase shifts of the gradient θ 0 r and θ 1 r as references.In Figure 3e, the simulated and calculated results demonstrate that the scattered beam point at 49.9°is the same as the angle calculated by the equivalent gradient method.If we compare Equation ( 3) and ( 5), we will find that the equivalent reflection angle should equal one of the diffraction modes with the condition of m = N 0 þ N 1 .Actually, on the other hand, since the diffraction mode defines all the possible propagating directions by Equation ( 3), the main lobe angle must appear in one of these directions.We emphasize that the proposed equivalent gradient method can be used to exactly find this main lobe angle.Further, based on Equation ( 5), we investigate the main lobe angle distribution of different combinations of N 0 and N 1 in a period, as shown in Figure 4b.As shown, the proposed DM utilizing binary supercells can cover the range [θ 0 r , θ 1 r ], quasicontinuously.The more precise coverage required, the larger period should be designed.We also report the total propagating modes of different combinations of N 0 and N 1 in a period, as shown in Figure 4c.It can be seen that as a coding period becomes larger, the total propagating modes increase accordingly, giving rise to multiple side lobes and therefore reducing the performance compared with the conventional gradient metasurfaces.It is also worth noting that the order of '0' and '1' in a specific coding sequence only affects the side lobe levels in far-field patterns, which is obvious by comparing Equation ( 3) and ( 5).The reflection efficiency of the proposed FRDM is further examined.The detailed simulation configuration is available in Experimental Section.The calculated power reflection efficiencies from Floquet mode 0 to Floquet mode N 0 þ N 1 of "0001…/0001…", "01…/01…", and "0111…/0111…" coding sequences are 95%, 92.6%, and 89.6% at 28 GHz respectively.Two special cases 0…/0… and 1…/1… are also simulated with reflection efficiencies of 97.7% and 87.4%.The simulated efficiencies are comparable to the existing works of anomalous reflections which are dedicated to a specific deflection angle. [42,47]e have elaborated the field-reorganizable anomalous reflection based on the binary supercells, including radiation pattern calculation by MPWAS, diffraction mode analysis of coding sequence, and the equivalent gradient method for finding the main lobe direction.In the next section, the proposed FRDM will be placed in a corridor to examine its coverage enhancement capability.

Corridor Environment Simulations
We consider a practical corridor environment available for measurement and simulation, as shown in Figure 5a.The model can be viewed as an L-shaped corridor with an additional space that is constructed according to the practical indoor scenario.The simulation process is detailed in Experimental Section.The basic mechanism of the developed cosimulation method is based on effective isotropic radiated power (EIRP) and 3D standard ray-tracing (SRT) technique.The EIRP combines the power and gain of the proposed metasurface, which is required in the Altair WinProp 2021.The SRT technique accurately computes the wave propagation in the corridor using a deterministic model.From the results shown in Figure 5a, we find that when only one mmWave base station is deployed in this scenario, a blind area inevitably appears behind the corner.We label the middle line of the corridor that is directly covered by the mmWave base station as Path 1 and label the middle line of the blind corridor as Path 2. We also define Region 1 and Region 2, which contain Path 1 and Path 2, respectively.Lengths of Path 1 and Path 2 are 8 m and 30 m, respectively, which are identical in the simulations and the following experiments.For the case shown in Figure 5a, only a distance less than 4 m can be covered in Path 2. The corridor width is 2.5 m.
To maintain consistency, we adopt the above-analyzed coding sequences of "0001…/ 0001…", "01…/01…", and "0111…/0111…" to enhance the signal coverage in Region 2 along Path 2, as reported in Figure 5b-d.These three FRDMs have the same aperture size of 320 mm Â 320 mm, which is also the prototype size in the following experiments.As can be observed from the results, the original blind area is significantly covered by the deflected wireless powers when the FRDM is applied.The wireless signal from Path 1 is reflected into Path 2 and bounced between the walls in Region 2 to enhance the coverage.Using different coding sequences, we could clearly recognize the ray trajectory in Region 2 with varying angles of reflection.Therefore, the "0111…/0111…" coding sequence shows the longest ray trajectory, over 10 m.However, we cannot conclude that the larger reflection angle gives rise to better coverage.In fact, for fixed aperture size, the larger reflection angle is also accompanied by an obvious gain reduction.Compared with the "0001…/0001…" coding sequence, the gain reductions of the "01…/01…" and "0111…/0111…" coding sequences are 0.75 and 2.76 dB, respectively.Refer to Figure S3, Supporting Information for the scan loss of the FRDM.Thus, the metasurfaces that realize signal coverage enhancement should be adjustable according to practical scenario parameters, for example, corridor type, length, width, etc.Our field-reorganizable scheme achieves that goal while featuring low cost and high reliability.
The signal intensity distribution along Path 1 is reported in Figure 5e.We also compare the power distributions along Path 2 between the above three coding sequences and the case without FRDM, as plotted in Figure 5f.As shown, using the proposed FRDM, the blind area is communicated effectively.When we compare the three results using different coding sequences, the larger reflection angle ("01…/01…" and "0111…/0111…") could extend the signal peaks further along Path 2. However, after multiple bouncing propagations, the average signal intensities at the end of Path 2 are related to the gains of the coding sequences.To obtain an optimized signal coverage in the blind area through the proposed FRDM, one should perform detailed simulations and end-user experiments comprehensively to determine the final coding sequence.

Configuration
To examine the performance of the FRDM and validate the simulation model, we conducted the experiments in a practical environment.As mentioned before, considering that the proposed FRDM distributes uniformly along the y-direction and the ease of use for the supercells, we arranged 20 identical supercells along the y-direction.The fabricated supercell '0' and supercell '1' are shown in Figure 6a.Further, the "01…/01…" and "0111…/ 0111…" FRDMs were constructed by reorganizing the fabricated binary supercells following the coding sequences, respectively, as shown in Figure 6b,c.The "0001…/0001…" case is dropped due to the similar performance as the "01…/01…" case according to the above simulations.We note that a 320 mm Â 320 mm metallic plane that holds all the super-cells for each coding sequence is adopted.
The practical measurement that emulates the mmWave signal coverage scenario includes three parts: a signal generator connected to a transmitter (Tx) as the mmWave base station, the fabricated FRDM, and a spectrum analyzer connected to a receiver (Rx) as the end-user.Both the Tx and Rx are a y-polarized horn antenna operating from 22 to 33 GHz, which is identical to the simulations.Detail configuration of the measurement system is illustrated in Figure 6d and elaborated as follows.First, at a specific frequency, the signal generator produces the EM waves which are radiated into the corridor by the Tx.We mention that the output power is calibrated as À15 dBm, the same as the simulations.The distance between the Tx and the FRDM is 7.5 m, assuring a plane incident wave.Then, we recorded the signal intensities along Path 2 of the corridor with 0.8 m sampling intervals.The height of the whole system is 1.5 m from the floor to emulate a practical end-user.Finally, the measurement frequency was changed to test the spectrum performance of the two FRDMs.Note that before measuring the two FRDMs we measured the background power distribution along Path 2, which corresponds to the without FRDM case.Due to the apparatus limitation, the spectrum analyzer could only detect the power level at À110 dBm.

Results and Discussion
We report the measurement results of FRDMs using "01…/01…" and "0111…/0111…" coding sequences at 26, 28, and 30 GHz, as plotted in Figure 7a,c.The background signal intensity at 28 GHz along Path 2 is also plotted for comparison.It can be seen from the results that the coverage of the original area with signal intensity less than À105 dBm is significantly enhanced over -105 dBm utilizing the proposed FRDMs.For the "01…/01…" coding sequence, the averaged signal intensities are enhanced by 19.9, 17.4, and 12.5 dB at 26, 28, and 30 GHz, respectively.For the "0111…/0111…" coding sequence, the averaged signal intensities are enhanced by 18.9, 17.0, and 14.7 dB at 26, 28, and 30 GHz, respectively.A closer inspection of the spectrum performance for both cases shows that a lower frequency gives rise to a higher coverage enhancement.This result may be explained by the fact that the metasurface which realizes the perfect anomalous reflection is a dispersive device. [44]According to Equation ( 5), the main lobes point to 55.4°, 49.9°, and 45.5°at 26, 28, and 30 GHz, respectively, for the "01…/01…" coding sequence, while for the "0111…/0111…" coding sequence the angles are 62.5°, 55.5°, and 50.3°.These results suggest that the beam deflection angle of the FRDM at the central frequency should be dedicated to operating a wide frequency range.In this work, the presented coding sequences can improve the signal quality by over 10 dB from 26 to 30 GHz.
Further, we compare the measured results and the aforementioned simulated ones at 28 GHz for both coding sequences, as plotted in Figure 7b,d.As shown, the measured results in the presented two cases are in accordance with the simulated ones.The multiple bouncing propagation effects can be clearly recognized.However, apparent fluctuations in the latter half part of Path 2 are observed in the measured results.Two factors may explain this result.First, the measured data recorded from the spectrum analyzer are unstable at lower signal intensities.Second, the testers and the moving part that hold the spectrum analyzer and the Rx would slightly affect the signal distribution.However, the measured results prove that the proposed coding sequence reorganizable scheme can effectively enhance the signal coverage and further optimize the wireless channels.
Additionally, we also compare our results with previous works on mmWave signal coverage enhancement.In ref. [55], the authors reported an outdoor experiment of phase-gradient metasurface reflectors for mmWave enhancement at 26 GHz, improving the received signal strength by more than 10 dB.In ref. [56], outdoor open space measurements in an NLOS show that the received power improves by about 15 dB at 28 GHz.In ref. [8], passive metallic reflectors were examined for NLOS mmWave coverage enhancement.The measured results showed that the coverage enhancement of reflectors with different sizes and shapes possesses about 20 dB enhancement effects.However, the adopted passive reflectors must be oriented at a specific angle with respect to the incident antenna.As shown, even though the experimental scenarios and methods are different in the aforementioned works, satisfied coverage enhancements are verified in this work.Compared with the previous works, this work offers an in situ adjustable metasurface while keeping low fabrication cost and no tunable components, which have not been reported.We remark that existing works on signal coverage enhancement for 5 G mmWave using metasurface or reflectors mainly focused on path loss modeling, [57] estimation of throughput improvement, [58] and functional verifications reported earlier.

Conclusion
We have elaborated on the design, radiation characteristics, and practical environment experiments of the proposed FRDM constructed by only two passive supercells.This study has indicated that the digital idea can be utilized to guide an application design to solve the ubiquitous NLOS coverage blindness at the mmWave band.The presented work also confirms, for the first time, that regulating EM waves through DM in a coarse granularity scale is feasible.Both the simulated and measured results provide an intuitive working mechanism and the effects of the proposed scheme.Another implication of this study is the proof of concept for the supercell level operation, which would inspire the design of a programmable supercell.Note that realizing programmability on a supercell level will remarkably reduce the active components compared with that on a meta-atom level.Returning to the application background of B5G and 6G mmWave communication, it is now possible to claim that RISs that leverage DMs as the fundamental hardware show their incomparable advantage over existing techniques.

Experimental Section
Modeling of Near-Field Distributions using Binary Supercells Coding: For a given coding sequence using binary supercells, we simulated the near-field distribution through ANSYS Electromagnetic Suite 2021.Assuming that the coding period has N 0 '0' coding and N 1 '1' coding, where N 0 and N 1 are integer numbers, the total model length N 0 D 0 x þ N 1 D 1 x along the x-axis should be larger than 10 λ, where λ is the wavelength at 28 GHz.The model length along the y-axis is the meta-atom period of L = 4 mm.We assigned the Jerusalem patches at z = 0 plane and the ground plane at z = À1.524mm plane.The periodic boundary condition was applied to enclose the model to emulate an infinite surface.A y-polarized plane wave with an amplitude of 1 V m À1 was assigned to excite the model.An observation window that was 9 λ wide along the x-axis and 3.7 λ high along the z-axis at the xoz-plane was set in the simulator.The real parts of the scattered fields are recorded and reported in Figure 3.
Modeling of Reflection Efficiency of the Proposed FRDM: To evaluate the reflection efficiency of the proposed FRDM, one period of a specific coding sequence that contains N 0 '0' coding supercell and N 1 '1' coding supercell was modeled by ANSYS Electromagnetic Suite 2021.This period was simulated within a periodic boundary condition, which was excited by a single Floquet port with different Floquet modes.Distance from the FRDM to the Floquet port was about one working wavelength to eliminate the influence of evanescent waves.According to our analyses, the FRDM would deflect the Floquet mode 0 (normal incidence) into the Floquet mode N 0 þ N 1 ; therefore, the reflection efficiency could be calculated by the S-parameter jS 0!N 0 þN 1 11 j 2 , which indicated the power deflection efficiency from Floquet mode 0 to Floquet mode N 0 þ N 1 . [47]imulation of Indoor Signal Coverage: The indoor signal coverage enhanced by the proposed FRDM was simulated in the Altair WinProp 2021.The L-shaped corridor according to a practical scenario was constructed first.The wall of the model was set as concrete which almost could not be penetrated by the mmWaves.Then, a standard gain horn antenna working from 22 to 33 GHz was set to emulate the mmWave base station.The gain of this antenna at 28 GHz was 21.5 dBi.The 3D raytracing technique was selected in the simulator for higher reliability.The transmitted power of the horn antenna was set as À15 dBm.The wireless signal distribution was recorded.We also recorded the average power at the corner which was about À45 dBm.Further, far-field patterns of the FRDMs with different coding sequences were calculated by the proposed MPWAS.The calculated patterns were converted to a ".ffe" format for the simulator.We set the power of the FRDMs as À45 dBm, resimulated the model, and recorded the wireless signal distribution while the horn antenna was not excited.Finally, we added the two power distributions together to complete the simulations.The results are plotted in Figure 5.We noted that the height of the system under investigation for both simulations and experiments was 1.5 m from the floor.The background power intensity was set as À115 dBm.

Figure 1 .
Figure 1.Conceptual illustration of the signal intensity enhancement in an L-shaped corridor.a) Typical indoor L-shaped corridor for a giant building.b) Signal intensity distribution using only one mmWave base station.c) Enhanced coverage signal intensity distribution using one mmWave base station and an FRDM at the corner.The incident wave will be deflected into the blind area with an angle of θ r .

Figure 3 .
Figure3.Anomalous reflections using different binary supercell coding sequences.Simulated near-field distributions of the real part of the scattered electric field over the incident electric field for a) "0001…/0001…", b) "01…/01…", and c) "0111…/0111…" coding sequences.The observation region is 9 λ along the x-axis and 3.7 λ along the z-axis where λ is the wavelength at 28 GHz.The white arrows indicate the reflection directions.Comparisons of far-field patterns of the simulated results and the MPWAS approach results for d) "0001…/0001…", e) "01…/01…", and f ) "0111…/0111…" coding sequences.The shaded region indicates the available coverage range using the binary supercells.Full-space far-field patterns of the MPWAS approach result for g) "0001…/0001…", h) "01…/01…", and i) "0111…/0111…" coding sequences.The white cross symbol indicates the direction of the incident wave.

Figure 4 .
Figure 4. a) Illustration of the equivalent gradient method for the "01…/01…" coding sequence.The ticks of the horizontal axis are the distance from the previous one.b) The main lobe angle distribution of a coding period with different N 0 and N 1 combinations.c) Total propagating mode distribution of a coding period with different N 0 and N 1 combinations.The data for N 0 = 0 case and N 1 = 0 case is meaningless and suppressed.

Table 1 .
Propagation angles (°) of different diffraction modes for different coding states.