Fundamental/harmonics beam control using 1-bit space time-modulated plasma DMA

This paper investigates a space-time modulated digital metamaterial array (DMA) based on reconfigurable plasma ionization. The DMA consists of 8 × 8 unit-cell elements with total dimensions of 120 × 120 × 3.2 mm3. Each unit-cell consists of a ring container filled with argon gas and is backed with a grounded dielectric substrate. The argon gas is ionized into a plasma state through metallic electrodes. The logic state of the unit cell is controlled via the changing of the plasma frequency, ωp.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\omega }_{p}.$$\end{document} The value of ωp=6×1011rad/sec\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\omega }_{p}=6\times {10}^{11}\mathrm{ rad}/\mathrm{sec}$$\end{document} represents logic “0”, and ωp=8×1011rad/sec\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\omega }_{p}=8\times {10}^{11} \mathrm{rad}/\mathrm{sec}$$\end{document} represents logic “bit 1”. The periodic time switching of the plasma ionization controls the radiation at the fundamental and harmonic frequencies. The on-time instants and on-time durations control the number of radiated beams, their directions, amplitudes, and side-lobe levels. Different time-switching sequences are investigated for beam steering, dual-sum beams, broadside beams, end-fire beams, multi-beams, and fan-shaped beams for wireless communications applications. The DMA was investigated under different switching sequences for phase-modulation and amplitude-modulation schemes. A full-wave simulation CST Microwave Studio simulator is used to analyze the proposed DMA and the results are compared with ideal point sources array excited with the same switching sequences.


Introduction
Recently, global data traffic has rapidly increased due to the advanced services introduced by modern wireless communications. Fast, secure and high transmission data rates are needed for wearable devices, broadcasting, internet of things (IOT), and emerging 5G/6G communications (Dogra et al. 2020). These systems increase the connectivity demands between transmitter and receiver points through smart, intelligent and efficient wireless networks (Zhang et al. 2019). The conventional mobile networks are controlled by user equipment or base stations. These networks suffer from propagation losses, environment conditions, large obstacles, and the non-uniform distribution of users to which they serve. These problems are partially solved using relay nodes but at the cost of high power consumption (Popli et al. 2018). Recently, reconfigurable intelligent surfaces (RISs) have been introduced to non-light of sight communications with low power consumption (Tran et al. 2022;Nguyen et al. 2021). RISs redirects the propagated electromagnetic waves (EMW) toward the desired direction. They replace conventional base stations in the mobile system which reduces costs, saves resources, and increases the coverage area. RISs consist of metamaterial unit-cells that reflect the EMW and all are backed by a control-unit. The reconfigurable response of the metamaterial unit-cells is achieved by PIN diodes, varactor diodes, liquid crystals, graphene, and plasma (Bang et al. 2018). Digital metamaterial arrays (DMAs) consist of two distinct types of unit-cells to represent the logic bit "0" and bit "1" (Bao and Cui 2020). The reflection coefficient phase difference between the two unit-cells is approximately 180° degrees (opposite phases) which is called 1-bit DMA. Different techniques are employed on the DMA unit-cell to achieve opposite reflection phase shift. In (Wang et al. 2020), a tunable multifunctional reflective digital meta-surface based on voltage tunable liquid crystals at 75 GHz is investigated. A 1-bit digital reflectarray antenna is presented in Han et al. (2018) for improving beam-scanning at Ku-band using one PIN diode with maximum aperture efficiency of 17.9% at 12.5 GHz. The digital coding introduces different facilities of the DMAs including beam shaping, beam steering, and direction of arrival applications (Venkatakrishnan et al. 2017;Lin et al. 2021). The spacetime coded DMA allows the control of EMW radiation with power distribution between fundamental and harmonic frequencies (Zhang et al. 2018). It considers periodic coding sequences to simultaneously beam steering of the harmonic frequencies. Space-time-coding digital meta-surfaces based on the time modulation of the reflection coefficient using one PIN diode are introduced in Zhang et al. (2020).
Plasma is considered as a smart material with reconfigurable electrical properties based on the applied voltage (Kumar and Bora 2010). Ionizing inert gases into plasma states increase the conductivity of the material, which is used as a replacement for conventional copper in antenna applications . Different metamaterial surfaces based on plasma reconfigurable characteristics are employed in reflectarray , transmitarray (Zainud-Deen et al. 2014), frequency selective surfaces , and artificial magnetic conductors . These surfaces are designed for beam steering, radar cross-section reduction, and polarization conversion applications. Time-modulated arrays based on reconfigurable plasma material characteristics were investigated for beam-shaping, beam-steering, and side-lobe level control (Malhat and Zainud-Deen 2022;Malhat et al. 2022aMalhat et al. , 2022b. In this paper, metamaterial unit-cells based on reconfigurable properties of plasma material are used to construct space-time-coded digital surfaces. The metamaterial properties of the unit-cell are investigated. An array of 8 × 8 unit-cells is excited using different time coding sequences. Section II introduces the effect of changing the excitation time sequence on the beam radiated at the fundamental and harmonic frequencies of the array. Finally, Section III concludes the results introduced in the paper. The unit-cell properties and the array structure were numerically simulated using the finite integral technique (CST Microwave Studio). It considers the full structure, material properties, and the environment around the structure.

Theory of space-time digital metamaterial
Consider a space-time metamaterial array consists of N × N elements. The reflection coefficient phase from each element is switched between the two cases, "0" and "1" according to the coding matrix. The switching frequency (modulation speed) of the element is chosen to be much smaller than that of the EMW. The scattered far-field pattern from the DMA under normal incident plane-wave is expressed by Zhang et al. (2018); where E pq ( , ) is the far-field patterned of the (p, q)th element calculated at the fundamental frequency, f o , as a function of azimuth and elevation angles, and , respectively. The complex reflection coefficient of each element with amplitude, A n pq and phase, n pq . is expressed as The phase φ pq is a periodic function of time, whose values are either 0° or 180° for phase modulation (PM) scheme; and it takes the value 0 or 1 for amplitude modulation (AM) scheme. By Applying Fourier series on periodic pulse function U pq (t) result in with Fourier series coefficients given by Thus, the Fourier series coefficients a pq of the periodic function Γ pq (t) can be represented as where pq = t on pq /T o and pq = t i pq /T o stand for normalized values of on-time duration ( t on pq ) and on-time instant ( t i pq ) , respectively of the pulse U pq (t) . Thus, the far-field scattering pattern of the DMA at the m th harmonic frequency f o ± mf m is given by, Throughout the paper, ( E pq = 1 ) is assumed. By controlling the time-coding sequences of the individual elements, a set of complex reflection coefficients A pq is synthesized to control their scattering properties. More specifically, via Eq. (6), the equivalent amplitude and phase excitations of all elements at a specific harmonic frequency are synthesized.

Design of plasma metamaterial unit-cell
A three-dimensional schematic view of the ring-shaped plasma metamaterial unit-cell is shown in Fig. 1. It consists of a dielectric ring-shaped cover connected to a central cylinder The detailed construction of the ring plasma metamaterial unit-cell element through two rectangular arms of thickness t c , along their diagonal. The cover has thickness H c , dielectric constant ε rc = 3.4 and is placed on grounded FR4 substrate with thickness H s and ε rd = 4.6 and tanδ = 0.036. The cover is filled by argon noble gas occupying a total height H p . The gas is ionized into the plasma state by applying a voltage source between a metallic electrode and a shorted via pin. Table 1 lists the detailed dimensions of the unitcell construction. The dispersive electrical properties of the plasma material are modeled by Drude model given by Malhat and Zainud-Deen (2020), where o is the free space permittivity, is the angular operating frequency, v p is the collision frequency, and p is the plasma angular frequency which is related to the electron density n e as where e and m e are the electron charge and mass. The electron density of the ionized plasma medium is controlled by the applied voltage as given by Zainud-Deen et al. (2020) where K is Boltzmann constant, and T e is the electron temperature. By increasing the plasma frequency, the electron density and then the plasma conductivity are increased at fixed operating frequency. The electromagnetic responses of the ring-shaped plasma metamaterial unit-cell were numerically simulated with unit-cell boundary conditions in commercially available software CST Microwave Studio. The waveguide simulator was used to investigate the reflection coefficient spectra of the proposed unit-cell. The perfect electric conductor (PEC) boundary is applied along x-axis, while the perfect magnetic conductor (PMC) boundary is applied along the y-axis. A plane-wave is incident normally on the unit-cell surface. Unit-cell characteristics were investigated in the frequency band from 7 to 11 GHz with v p = 2GHz and T = 300 K. The plasma material complex permitivity against frequency is plotted in Fig. 2a. Increasing the plasma frequency, p , reduces the real part of relative permitivity, εʹ, and increases the imaginary part of relative permitivity, εʺ. At p = 6 × 10 11 rad∕sec, the plasma material has = −152.2 + j5.42 and at p = 8 × 10 11 rad∕sec, the plasma material has = −199 + j7.08 at 9 GHz. The change in material properties is used to control the reflection coefficient from the unit-cell element. Figure 2b shows the reflection coefficient, magnitude and phase, versus frequency for case (1) with p = 6 × 10 11 rad∕sec and case (2) with p = 8 × 10 11 rad∕sec . The phase difference between the unit-cell response in the two cases was 180° degrees with a reflection magnitude of − 4.5 dB at 9 GHz. The unit-cell phase response is used in 1-bit coding, where case (1) with p = 6 × 10 11 rad∕sec represents bit "0", and case (2) with p = 8 × 10 11 rad∕sec represents bit "1". The simulated S-parameters of the ring plasma unit-cell element are used to calculate the impedance, z, and refractive index, n, as introduced in Malhat and Zainud-Deen (2022), and where where d is the substrate thickness and k o is the wave number in free space. The relative electric permittivity, ε r , and the relative magnetic permeability, μ r , are calculated from: The frequency responses of the ring plasma metamaterial unit-cell element are shown in Fig. 3. The unit-cell has negative ε r , μ r, and refractive index, n, around 9 GHz.
The layout of the 8 × 8 ring plasma metamaterial array is designed for space-time modulation as shown in Fig. 4. The DMA occupies a total dimension of 120 × 120 × 3.2 mm 3 . The unit-cell elements are spaced by L c = 15 mm. All the plasma unit-cell elements in each column share the same plasma ionization voltage to meet the designed code arrangement. The magnitudes and phases of the reflection coefficients are controlled by changing the ionization voltage of the plasma inside the unit-cell elements. The unit-cells are 1-bit coded according to the coding matrix designed for beam control at the fundamental and harmonic frequencies. The amplitude distribution is assumed uniform with periodic phase of 0° or 180° degrees according to the bit digit 0 or 1. Figure 5a shows the ontime durations for uniform array excitations. All the array elements are switched on at the same instant and stay on for the whole periodic time duration. The DMA performance is compared with isotropic arrays excited using the same time sequences. The DMA radiates the ordinary uniform-array with SLL = -13.2 dB for the fundamental component without radiating any harmonics. The field patterns in x-z plane at 9 GHz for the isotropic array and the DMA are compared in Fig. 5b. The mutual coupling between the DMA elements causes slight differences in the side-lobes minima and maxima. The 3D field pattern and the corresponding contour field pattern are shown in Fig. 5c, d. A broadside beam with HPBW = 25° degrees is obtained.

Beam steering of harmonic frequencies
The time-modulated array is characterized by harmonic radiation patterns associated with fundamental radiation patterns. Multi-beam radiations are controlled for beam steering through the design of the excitation time sequences. Due to the time switching sequences, a progressive phase-shift is generated at the harmonic frequencies f o ± mf p where m ≠ 0. Figure 6a shows the time coding sequence (2). Each element is energized for 1/16 of the normalized modulation period with sequential normalized time delay of 1/8 of the normalized modulation period. The contour plot of field distribution on the radiated harmonic beams is plotted in Fig. 6b. The normalized radiated beam patterns generated at m = 0, ± 1, ± 2, and ± 3 for PM and AM modulation schemes are plotted in Fig. 6c. The beams are directed toward θ = ± 16° degrees for m = ± 1, θ = ± 32° degrees for m = ± 2, and θ = ± 54° degrees for m = ± 3 with maximum SLL = -17 dB. The power levels of different harmonics are constant at 8 dBi and the fundamental component is at 16 dBi for the PM case. All the harmonics and the fundamental components have the same power level for the AM case. Figure 7a shows the time coding sequence (3), where each element is energized for 1/8 of the normalized periodic time and delayed by 1/8 of the normalized modulation period. The harmonic beams are steered every θ = ± 17° degrees at m = ± 1, ± 2, and ± 3 for PM and AM modulation schemes as shown in Fig. 7b. For the PM case, the power level in the harmonics is reduced gradually as its index is increased. The power level is 8.5 dBi for m = ± 1, 8 dBi for m = ± 2, and 6 dBi for m = ± 3. The power levels of all harmonics are maintained constant for the AM case. The time coding sequence (4), with on-time duration of 2/8 of the normalized periodic time and delayed by 1/8 of the normalized periodic time is shown in Fig. 8a. The 3D gains patterns for DMA excited for beam steering using sequence (4) at m = 0, ± 1, ± 2, and ± 3 are plotted in Fig. 8b. The beam is centered at θ = 15° degrees for m = ± 1; centered at θ = 30° degrees for m = ± 2, and centered at θ = 45° degrees for m = ± 3. Figure 8c shows the PM and AM modulation schemes. The power level drops off as the harmonic index is increased for the PM scheme, while they are kept the same for the Fig. 3 The ring plasma metamaterial unit-cell properties at different plasma frequencies AM scheme. The power levels are 6.5 dBi, 4 dBi, and − 1.2 dBi for m = ± 1, ± 2, and ± 3, respectively for PM scheme.

Double sum multi-beam pattern
Multi-beam antennas are used to transmit or receive multiple signals from different directions. By properly controlling the time coding sequence of the DMA, multi-beam radiation is generated at different frequencies. Figure 9a shows the time coding sequence (5) in which half of the array elements are energized for 1/8 of the normalized modulation period and the other half is energized on after time delay of 3/8 of the normalized modulation period. Both the fundamental frequency and the even harmonics beams are directed at θ = 0° (broadside direction). The odd harmonics have dual-beams directed at θ = ± 10° degrees, as appeared from Fig. 9b. The maximum SLL = − 13.2 dB and HPBW = 15° degrees for the m = 0, and maximum SLL = − 10.2 dB and HPBW = 10° degrees for m = 1. Due to the closer angles between the radiated beams at fo + fp, results in high power level of − 6.5 dB at θ = 0° as shown in Fig. 9c. Sequence (6) is designed to radiate multi-beams directed toward θ = ± 32° degrees. The elements are sequentially energized on for 1/2 of the normalized modulation period in two columns followed by the next two columns energized after time delay of 1/2 of the normalized modulation period as plotted in Fig. 10a. The field patterns in Fig. 10b, c show a single broadside beam radiated at fo and dual beams in θ = ± 32° degrees at fo + fp for both PM and AM schemes. The maximum SLL is below − 15 dB with HPBW = 14° degrees for the radiated beams.

Broadside/endfire multi-beam pattern
An array with broadside beam and/or endfire beam radiation is a challenge problem in many applications. The space-time modulated DMA is excited with a timing sequence The DMA radiation charactertics excited by time coding sequence (4) for harmonic beam steering. a. The time coding sequence (4). b. 3D field patterns at different harmonics. c. The Field pattern in x-z plane at (fo ± mfp, m = 0, 1, 2, 3) to radiate broadside beams at the fundamental and even harmonic frequencies while radiating end-fire beams at the odd harmonic frequencies. In sequence (7), the elements are sequentially switched on (plasma energization) for a time duration of 1/8 of the normalized modulation period with time delay of 1/2 of the normalized modulation Fig. 9 The DMA radiation charactertics excited by time coding sequence (5) for harmonic beam steering. a. The time coding sequence (5). b. 3D field patterns at different harmonics. c. The Field pattern in x-z plane at fo and fo + fp period as shown in Fig. 11a. A pencil broadside beam at θ = 0° is radiated at m = 0 and m = 2 with maximum SLL = − 12.7 dB and HPBW = 15° degrees. Figure 11b shows the end-fire beam at θ = ± 90° degrees are radiated at m = 1 and m = 3 with maximum SLL = − 14 dB and HPBW = 120° degrees. To suppress the radiated even harmonics, the DMA plasma unit-cell elements were alternately energized using sequence (8) as plotted in Fig. 12a. The elements have alternately on-time duration is 1/2 of the Fig. 10 The DMA radiation charactertics excited by time coding sequence (6) for multi-beam radiation. a. The time coding sequence (6). b. 3D field patterns at fo + fp c. The Field pattern in x-z plane at fo and fo + fp 192 Page 16 of 21 normalized modulation period and the on-time instant is 1/2 of the normalized modulation period. The even-harmonics are suppressed and the odd-harmonics have end-fire radiation at θ = ± 90° degrees as seen in Fig. 12b.

Fan-shaped beam pattern
Fan-shaped beams are employed in radar for search and detection applications. To generate fan-shaped beams at different harmonic frequencies, sequence (9) is employed. Figure 13a  The DMA radiation charactertics excited by time coding sequence (7) for harmonic beam steering. a. The time coding sequence (7). b. 3D field patterns at different harmonics shows that the elements are energized with reverse periodicity for 1/4 normalized periodic time with progressive delay of 1/4 of the normalized modulation period. The radiated beams are plotted in Fig. 13b. Broadside beam is radiated at m = 0 with SLL = − 12.7 dB and HPBW = 15° degrees. At m = 1, fan-shaped beam with maximum SLL = − 14 dB and covering radial angle of 90° degrees. For m = 2 and m = 3, wide fan-beams are radiated with two nulls appearing at θ = ± 17° degrees which produce three beams directed toward θ = ± 56° degrees and θ = 0°. Finally, sequence (10) depicted in Fig. 14a that is employed for radiated single/multi-beams. Half of the array elements are periodically energized for 1/4 of the Fig. 12 The DMA radiation charactertics excited by time coding sequence (8) for broadside/endfire beams. a. The time coding sequence (8). b. Field distrbution at 1st and 3rd -harmonics normalized modulation period and incremental delay of 1/4 of the normalized modulation period and this sequence is repeated for the other half of the array. Figure 14b shows the radiated field distribution at different frequencies. Single broadside beam is radiated at m = 0. At m = 1 and m = 3, single beam is radiated at θ = 30° degrees and θ = − 30° degrees, respectively, while multi-beams are radiated at θ = 90°, 30°, 0°, − 30°, and − 90 o degrees.

Conclusion
This paper investigates a ring plasma array for space-time digital metamaterial arrays for x-band communications. The electrical properties of the unit-cell metamaterial are investigated at 9 GHz at different plasma frequencies. A reflection coefficient with 180° degrees phase shift is obtained to represent logic "0" and "1" at p = 6 × 10 11 rad∕secand p = 8 × 10 11 rad∕sec , respectively. An array consists of 8 × 8 Fig. 13 The DMA radiation charactertics excited by time coding sequence (9) for Fan-beam. a The time coding sequence (9). b. 3D field patterns at different harmonics unit-cells is arranged and excited using different time sequences. Sequence (1) is used to generate uniform array with maximum SLL of − 13.2 dB. Beam steering harmonics are radiated using time excitation sequences (2), (3), and (4) with different decaying levels of Fig. 14 The DMA radiation charactertics excited by time coding sequence (10) for single/multibeam radiation. a. The time coding sequence (10). b. 3D field patterns at different harmonics sideband harmonics. Double-sum beams radiated at ± 10° degrees and ± 32° degrees at the 1st-harmonics are obtained using sequence (5) and sequence (6), respectively. Broadside beams are radiated at the fundamental frequency and even harmonics while end-fire beams at the odd-harmonics are radiated using sequence (7). In sequence (8), the even-harmonics are suppressed while endfire beam is radiated at the odd-harmonics only. Fan-shaped beams for radar applications are excited using the timing sequence (9). Finally, sequence (10) is used to radiate single or multi-beams at different directions for different harmonics. The reconfigurable characteristics of the plasma metamaterial-coded array allow the control of beam direction and its shape at different harmonic frequencies according to the proper excitation time sequence.