Design of Anomalous Reflectors by Phase Gradient Unit Cell-Based Digitally Coded Metasurface

In this letter, we propose the designs of 1-bit and 2-bit digitally coded metasurfaces, which achieve anomalous reflection-based beam steering. First, we demonstrate the systematic design flow of coded metasurface using phase gradient digital unit cells to achieve anomalous reflection in the preferred direction for a normally incident plane wave. Initially, the design procedure is analytically implemented to get the phase profiles for 1-bit and 2-bit digitally coded metasurfaces having equal sizes of <inline-formula><tex-math notation="LaTeX">$10\lambda _{0} \times 10\lambda _{0}$</tex-math></inline-formula> (where <inline-formula><tex-math notation="LaTeX">$\lambda _{0}$</tex-math></inline-formula> is the free space wavelength at 5.9 GHz) for a specific reflection angle, <inline-formula><tex-math notation="LaTeX">$(\theta _{r}=30^\circ,\phi _{r}=0^\circ)$</tex-math></inline-formula>, and subsequently, the far-field plots are generated. Furthermore, these phase profiles are used to generate 3-D-CAD models of the 1-bit and 2-bit metasurfaces using CST, and the desired far-field patterns are obtained having half-power beamwidth of <inline-formula><tex-math notation="LaTeX">$5^\circ$</tex-math></inline-formula>. It is observed that the 1-bit coded metasurface produces additional side-lobe levels, which are minimized by use of 2-bit coding. Finally, the proposed 1-bit and 2-bit coded metasurfaces are fabricated, and the anomalously reflected far-field beam is detected by the received power at desired reflection angle and comparing the results with a perfect electric conductor. The proposed design is suitable for vehicle to anything communications and can be scaled to other frequencies.


I. INTRODUCTION
I NTELLIGENT reflecting surfaces (IRS) have recently emerged as a new paradigm in wireless communications to improve energy and spectrum efficiency by controlling the channel environment dynamically [1], [2], [3], [4], [5], [6], [7], [8], [9]. One simple way to realize IRS is by using reconfigurable metasurfaces with gradient phase profiles to generate the anomalous scattering in the desired direction based on the generalized Snell's law [10], [11], [12], [13], [14]. However, IRS realization with conventional metasurfaces imposes complex Manuscript  challenges in designing and optimizing biasing networks for abrupt phase changes in adjacent unit cells [15], [24]. These problems can be solved by using digitally coded metasurfaces (DCMs), which use discretized phase maps that substantially narrow down the parameter search space. In this way, DCMs can quickly implement complex wave manipulations by simply changing the coding sequences in an intelligent manner, significantly simplifying the hardware realization [16], [17].
In [18] and [19], 1-bit DCMs are employed for beam steering through anomalous transmission. However, in those works, there is not much information about beam-steering metrics, such as half-power beamwidth (HPBW), sidelobe level (SLL), and target deviation error (TDE). While 2-bit DCMs are employed to achieve beam steering through anomalous reflection in [20] and [21], there are multiple shortcomings, such as reported inaccuracy in the desired beam-steering direction and absence of experimental results. In [22] and [23], electromagnetic (EM) surfaces comprising of 2-D array of elements using p-i-n diodes are realized, which combines the functions of phase shift and radiation together, and realizes 2-bit phase shifting for beamforming IRS application. Araghi et al. [24] realized an IRS for sub-6 GHz band using the generalized Snell's law and demonstrate real-world application of anomalous reflection by measurement campaigns. However, there is still ample scope of applied EM research to investigate the following. 1) Systematic design flow of DCM for anomalous reflectionbased beam steering to any desired reflection angle. 2) Impact of number of coding bits and reflector aperture area on HPBW and SLLs. 3) Possible minimization of TDE for such anomalous reflectors. In this letter, we present a generalized systematic design procedure for anomalous reflector design using 1-bit and 2-bit DCM for beam-steering applications in vehicle-to-anything (V2X)intelligent transportation system (ITS) scenario. To verify the proposed approach of anomalous reflector design, 1-bit and 2-bit DCMs are first conceptualized analytically using MATLAB for a specific reflection angle of (θ r = 30 • , φ r = 0 • ). The results are then compared with the same metasurfaces realized in CST-MWS. Finally, the anomalous reflection-based beam steering is demonstrated experimentally by comparing the received power from the DCM in the desired direction, with specularly reflected power from a perfect electric conductor (PEC) surface with same physical aperture.

II. GENERALIZED DESIGN FLOW OF DIGITALLY CODED REFLECTIVE METASURFACE
This section presents the design of DCMs by considering M × N unit cells with individual lateral dimensions of Δx × Δy, to achieve desired beam steering for a normally incident plane wave. First, we estimated the necessary phase profile Φ(x, y) for the desired reflection angle based on generalized Snell's law, and then implemented it using phase gradient unit cells to accomplish anomalous reflection. Fig. 1 depicts a schematic representation of a DCM showing anomalous reflection along (θ r , φ r ) direction for an arbitrary angle of incidence (θ i , φ i ) of a free-space plane wave. Mathematically, (θ r , φ r ) and (θ i , φ i ) can be connected using the generalized Snell's law for anomalously reflective metasurface as [20] where k i and k r are the incident and reflected wave vectors, and Φ represents the phase profile of the metasurface. Assuming normal incidence (θ i = 0 • , φ i = 0 • ) without any loss of generality and keeping k i = k r = k 0 = 2π λ 0 , (1a) and (1b) can be rewritten as follows: Here, dΦ defines the phase difference between the adjacent unit cell states. Based on the number of targeted states, the number of bits is estimated to define a metasurface coding. Suppose the number of states is 2 n (here "n" defines the number of coding bits), then the phase difference between the adjacent unit cell states can be defined as dΦ = 2π 2 n . Thus, by substituting dΦ in the following, we get: where L cx and L cy represent the lateral dimensions of the required cluster along X-and Y-direction (see Fig. 1). We express the cluster size in terms of the integer multiple of metasurface unit cells by using the rounded off to nearest integer value function as follows: where C x ∈ Z and C y ∈ Z indicate the group of unit cells with the same phase states (cluster) along X-and Y-directions, respectively. Next, we generate the state matrix containing information about the state of each metasurface unit cell inside the M × N array. For this, we use the modulo operation to generate the required gradient among adjacent clusters from the information on cluster sizes and the number of states as where p and q are the indices of each unit cell along both X-and Y-directions, respectively. In the final step, we generate the required phase matrix Φ(p, q) for the desired beam-steering angle by multiplying the state matrix with the considered phase states as By using the abovementioned phase information, we develop the metasurface and observe the normalized far-field radiation pattern using the well-known array factor equation ( [20]) as follows: Fig. 2 shows the flow chart for systematic design and analysis of an n-bit-coded reflective metasurface for a desired beam-steering angle, assuming normal incidence.

III. DESIGN AND ANALYSIS OF PROPOSED DIGITALLY CODED REFLECTIVE METASURFACE
To verify the design flow in Section II, we define the operating frequency (f ), the number of bits (n) of metasurface coding, and the reflection angle (θ r , φ r ) as f = 5.9 GHz (IEEE 802.11p band for V2X-ITS), n = 1 and 2 bits, and θ r = 30 • and φ r = 0 • , respectively. Based on these stated parameters, design and analysis of the proposed DCM are carried out analytically and  numerically using MATLAB and full-wave solver CST-MWS, respectively.

A. Analytical Simulation Using MATLAB
We define a squared subwavelength dimension, a = Δx = Δy = 8.45 mm = λ 0 /6 (where λ 0 represents the free-space wavelength at 5.9 GHz operating frequency), for a single unit cell and generate the necessary phase profiles Φ(p, q) for 1-bit and 2-bit coding as shown in Fig. 3. The color variation in the phase profile in Fig. 3 represents the phase gradient between the adjacent unit cell state, where it is 180 • and 90 • for 1-bit and 2-bit coding, respectively. The reflected normalized far-field pattern based on the corresponding phase profiles for 1-bit and 2-bit coded metasurfaces are shown in Fig. 4(a) and (b), respectively. It is observed that the 1-bit coded metasurface produces a farfield beam in the desired direction i.e., θ r = 30 • and φ r = 0 • having HPBW ≈ 5 • . In addition, it produces an unwanted symmetrical beam in θ r = −30 • and φ r = 180 • direction with similar HPBW. In contrast, the 2-bit coded metasurface with better phase resolution [see Fig. 4(b)] suppresses this unwanted beam and provides radiation in the desired direction of θ r = 30 • and φ r = 0 • only, with HPBW of 5 • . The overall study is carried out on the metasurface having M × N = 60 × 60 unit cells (size of 10λ 0 × 10λ 0 ) both for 1-bit and 2-bit coding.

B. Numerical Simulation Using CST Full-Wave Solver
Using the same input parameters as that used in the analytical simulation, both 1-bit and 2-bit coded metasurfaces are realized in CST-MWS using conductor-backed 2.4 mm thick FR4 substrate ( r = 4.4 and tanδ = 0.025).
Here, the phase gradient between the adjacent unit cell stages is realized by varying the physical dimension of unit cells [25]. For 1-bit coding, metasurface exhibits 2 1 = 2 phase stages having phase gradient of Φ = 2π 2 n = π rad = 180 • between the adjacent states. Therefore, the dimensions    Fig. 5)] such that the phase difference between them is 180 • at 5.9 GHz [see Fig. 6(a)]. Similarly, the dimensions for the 2-bit metasurface unit cells at 5.9 GHz are chosen as W 00 = 8.45 mm, W 01 = 6.6 mm, W 10 = 7.3 mm, and W 11 = 7.75 mm (see Fig.  5) to achieve a phase gradient of 90 • (for n = 2, Φ = 2π 2 n = π/2 rad= 90 • ) between the adjacent unit cells [see Fig. 6(b)]. Further, we use the phase profile generated from analytical predictions (see Fig. 3) and design the complete 1-bit and 2-bit coded metasurfaces in CST-MWS. The corresponding far-field scattering radiation patterns for plane-wave illuminations on the 1-bit and 2-bit coded metasurfaces are shown in Fig. 7. It is observed that the 1-bit coded metasurface produces two identical beams in θ r = 30 • and φ r = 0 • (desired) and θ r = −30 • and φ r = 180 • directions whereas the 2-bit coded metasurface produces an anomalously reflected beam only in θ r = 30 • and φ r = 0 • (desired) having 5 • HPBW in each. These beam patterns are exactly identical to that of the analytical results having 0% TDE  (difference between the targeted and achieved angles [20]). In addition, it is observed that the 2-bit coded metasurface has a lower SLL of −12.18 dB along θ r = 0 • and φ r = 0 • direction (see Fig. 7), compared with the SLL of −7.6 dB for 1-bit coded metasurface. In summary, the 2-bit coded metasurface performs better than the 1-bit due to its improved phase resolution. The proposed work shows better performance compared with other state-of-the-art designs in terms of TDE and suppression of side lobes (see Table I). Some observations on the coded metasurface design are as follows.
1) Increase in the number of coding bits (i.e., > 2) causes the phase profile of the metasurface to match closely with that of the continuous phase distribution, but the improvement in terms of SLL suppression is marginal as compared with the 2-bit coded design. 2) The proposed metasurface achieves a zero-TDE with an acceptable SLL of below −10 dB over a bandwidth of 150 MHz (5.85 − 6 GHz), which satisfies the V2X-ITS application requirements [26], [27], [28]. 3) We have verified that the HPBW mainly depends on the aperture area of the metasurface (e.g. increasing the aperture area to 15λ 0 × 15λ 0 from 10λ 0 × 10λ 0 reduces HPBW to 3 • from 5 • ).

IV. FABRICATION AND EXPERIMENTAL VALIDATION
The fabricated prototypes of the proposed 1-bit and 2-bit coded metasurface are shown in Fig. 8. The experimental setup for reflected power measurement using anomalous reflection characteristics of the proposed metasurfaces is shown in Fig. 9(a). The measurement setup consists of two standard high-gain horn antennas for transmission and reception of the plane waves and the metasurface under test (MUT). To validate the functionality of the fabricated metasurface prototypes, initially, a PEC is mounted in the place of MUT, and the reflected power is measured at θ = 30 • position for the normal incident plane wave from the Tx-horn. Further, a similar procedure is repeated for 1-bit and 2-bit coded MUTs. Fig. 9(b) shows the measured received power for PEC, 1-bit, and 2-bit MUTs at θ = 30 • . It is clearly observed that the 2-bit coded MUT provides maximum received power at the desired anomalous reflection angle (θ = 30 • ) followed by 1-bit MUT. However, the PEC provided the least reflected power at θ = 30 • due to its specular reflection property for a normally incident plane wave. The experimental results validate the behavior of the proposed coded metasurfaces as an anomalous reflector, which is consistent with the analytical and numerical simulation results.

V. CONCLUSION
In this letter, the systematic design flow and development of 1-bit and 2-bit digitally coded beam-steering metasurfaces using the concept of anomalous reflection are presented for V2X-ITS application. Both analytical and EM simulation results verify that at operating frequency of 5.9 GHz, the designed metasurfaces produce a desired reflective beam direction of (θ r = 30 • , φ r = 0 • ) for a normally incident plane wave. Both 1-bit and 2-bit coded metasurfaces of size 10λ 0 × 10λ 0 , provide the desired main beam (zero-TDE) with an HPBW of 5 • . However, the 2-bit coded metasurface provides a lower SLL of −12.18 dB than the 1-bit coded metasurface. Finally, measured results on the prototypes for both 1-bit and 2-bit coded metasurfaces conform with the analytical and numerical predictions. The proposed design flow is very general and can be used for any other set of beam-steering angle and incidence angle. The proposed coded metasurfaces can be used as passive fixed beam reflectors to the blind-spot location to establish comm-links in scatter-rich urban environment, and also can be extended to IRS-based 6G communication systems [29].