Rectangular Antenna Arrays Enable High Millimetre Wave Data Transmission Rates

Computational modelling of millimetre-wave communications demonstrates that asymmetric rectangular arrangements of discrete radiating sources can generate orbital angular momentum vortex waves capable of achieving high line-of-sight data transmission rates. Researchers Andjelija Ž. Ilić, Jelena Z. Trajković, Slobodan V. Savić, and Milan M. Ilić investigated the transmission capabilities of non-circular discrete antenna geometries operating at sixty gigahertz. Published in Applied Physics B, their study establishes that narrow, elongated antenna subarrays can produce usable vortex beams despite lacking the full rotational symmetry traditionally required for helical electromagnetic field generation. By applying a semi-analytical formulation based on infinitesimal Hertzian dipoles, the research team demonstrated that line-of-sight communication links can successfully recover multiplexed data channels without demanding conventional circular array form factors. Their quantitative findings show that carefully phased rectangular subarrays maintain sufficient radiation intensity, acceptable mode orthogonality, and robust per-mode bitrates, thereby confirming the feasibility of deploying non-circular radiating surfaces in compact short-range communication architectures.

Vortex waves carrying orbital angular momentum, commonly designated as OAM modes, represent a prominent physical-layer mechanism for expanding transmission capacity in emerging beyond-5G and 6G wireless networks. Mode-division multiplexing based on orbital angular momentum introduces an additional degree of freedom by utilizing orthogonal spatial phase distributions characterized by helical phase fronts. These vortex waves exhibit an azimuthal phase dependence expressed through an integer topological charge, where each distinct charge corresponds to an orthogonal transmission subchannel capable of propagating through a shared aperture. The millimetre-wave spectrum, particularly around the sixty-gigahertz band, provides extensive contiguous bandwidth essential for low-latency, high-throughput wireless links.

Uniform circular antenna arrays have historically served as the predominant physical arrangement for generating radio-frequency orbital angular momentum modes because their circular geometry mirrors the rotational symmetry of helical wave fronts. In a circular array, radiating elements reside equidistant from the propagation axis, resulting in uniform inter-element spatial spacing, identical mutual distances, and circulant channel matrices that simplify feeding and phase assignment. However, deploying large circular structures presents severe integration challenges within modern electronic devices, compact near-field communication cards, building facades, and underwater structural supports. Feeding and phasing networks for electrically large circular arrays require complex distribution hardware that becomes cumbersome at millimetre-wave frequencies. Elongated rectangular antenna subarrays offer significant practical advantages for mechanical packaging, surface mounting, and integration with planar radio-frequency modules or spatial light modulators. Nevertheless, breaking axial symmetry introduces distinct path-length differences from radiating elements to receiving points, causing severe distortions in both field magnitude and phase patterns.

To evaluate whether rectangular arrays can overcome these structural phase distortions, the researchers implemented a specialized semi-analytical model utilizing infinitesimal Hertzian dipoles customized for orbital angular momentum analysis. Rather than relying on standard far-field approximations, which fail to capture near-field divergence dynamics in short-range deployments, their model computes exact electromagnetic fields across intermediate link distances. The analytical formulation treats transmitting and receiving structures as collections of short dipoles, each possessing a physical length of one twenty-fifth of a free-space wavelength, corresponding to zero point two millimetres at sixty gigahertz. Operating under an excitation current of one milliampere, this dipole formulation determines radiated power, Poynting vectors, radiation intensity, and antenna directivity without depending on specific substrate materials or proprietary component fabrication techniques. System dimensions are defined parametrically in units of free-space wavelength, ensuring that the resulting analytical relationships remain valid across multiple operating frequencies while isolating the electromagnetic consequences of geometric array asymmetry.

The structural geometry investigated in the study comprises two narrow, parallel rectangular subarrays positioned symmetrically across the central propagation axis. Each subarray consists of sixteen antennas along its length and four rows in width, establishing a composite transmitting aperture of thirty-two by four radiating elements spanning a total aperture width of three free-space wavelengths. Sizing optimization begins by adopting a reference circular array radius of four point five wavelengths, corresponding to twenty-two point five millimetres at sixty gigahertz. The investigators introduced an adjustable lateral separation parameter, defined as twice a displacement variable, which establishes the distance between the two innermost linear subarrays. Through systematic computational sweeping of this single geometric variable, the authors established that an optimum displacement of two point five wavelengths produces stable vortex distributions, yielding an effective mean source radius of six point four six six wavelengths.

Compensating for the absence of axial symmetry required a targeted phase correction strategy applied directly to the driving currents of the discrete radiating elements. In symmetric circular arrays, antenna phasing progresses linearly around the azimuth in direct proportion to the intended mode index and element angle. For planar rectangular arrangements, the geometric path difference between each radiator and the observation plane varies nonlinearly across the aperture. The researchers resolved this challenge by calibrating the excitation phase of every individual dipole relative to a single axial singularity point located at the receiver plane on the propagation axis. By matching the electromagnetic phase of each element to the phase that would be produced by an equivalent element on the reference circular boundary, the central vortex core remains completely stabilized. While this calibration leaves residual phase variations across peripheral receiving zones, it prevents the vortex singularity from tearing, thereby ensuring that azimuthal phase progression remains continuous and monotonic across the specific annular regions where signal reception occurs.

Quantitative validation of the resulting field distributions was performed using spiral spectrum analysis and stream separation convolution integrals across four consecutive orbital angular momentum modes. Calculating the Fourier transform of the complex phase pattern along receiving contours yielded the relative energy distribution across discernible mode indices ranging from zero to fourteen. The baseline uniform circular array concentrated virtually all radiated energy into the intended target mode, displaying exceptional purity. In contrast, the uniform rectangular array and an alternative non-uniform linear arrangement exhibited slight spectral leakage, with spurious energy concentrating predominantly in immediately adjacent azimuthal modes. Nevertheless, convolving the simulated received electric field with ideal orthogonal phase patterns confirmed that the desired communication modes remain fully resolvable. The mathematical orthogonality of the vortex states enables matched receiving networks to separate multiplexed signals cleanly, demonstrating that moderate phase imperfections do not prevent reliable multi-channel demodulation.

Radiation performance was evaluated across physical footprint parameters, antenna array gain, spatial field coherence, and directivity stability over varied receiving apertures. Both the uniform rectangular array and non-uniform linear arrangement exhibited radiating areas closely comparable to the reference circular array, with the rectangular configuration demonstrating a slightly higher element filling factor per square wavelength. Transmitting gain was calculated by integrating the axial Poynting vector across sixty-four equidistant observation points arranged along circles corresponding to optimal reception radii. For operating modes one through four, the optimal reception radii were established at twenty-eight, thirty-eight, fifty, and sixty millimetres. Directivity variations across a radial tolerance band of plus or minus six millimetres remained modest across all configurations, confirming mechanical tolerance against slight alignment offsets. However, geometric asymmetry exerted a marked influence on field coherence: while the circular array maintained spatial cross-correlation levels near ninety-nine percent, the rectangular source fields exhibited coherence values of approximately seventy percent along the reception trajectory.

Achievable line-of-sight data transmission rates were estimated by coupling the calculated antenna gains with an indoor link budget equation at sixty gigahertz across a link range of five hundred eight point nine four millimetres. The link budget incorporated realistic operational parameters, including ten milliwatts of transmitted power, a signal bandwidth of two point one six gigahertz, a receiver noise figure of seven decibels, six decibels of implementation loss, and a ten-decibel link margin. Receiving arrays consisted of matched sixteen-element uniform circular arrays aligned with each mode reception radius. The resulting signal-to-noise ratio directly determined channel capacity and achievable data bitrates under Shannon channel formulations. Because transmitting gains for rectangular arrays remained within close margins of circular array gains, single-mode data transmission rates achieved comparable magnitudes.

While computational modelling confirms that discrete rectangular antenna arrays represent viable sources for short-range orbital angular momentum communication links, several operational constraints define the boundaries of the present findings. The semi-analytical dipole framework did not incorporate electromagnetic mutual coupling between closely packed radiators, dielectric substrate losses, feedline attenuation, or realistic transceiver circuitry. Furthermore, the reported transmission rates represent theoretical capacity estimates derived from idealized line-of-sight propagation rather than direct empirical measurements gathered from fabricated hardware prototypes. Future experimental investigations must construct prototype rectangular arrays operating alongside matched circular or partial receivers to confirm laboratory transmission rates. Nonetheless, this study provides an actionable theoretical foundation proving that circular symmetry is not indispensable for orbital angular momentum communications, clearing a practical path toward embedding high-capacity vortex antennas within real-world planar technologies.

Subject of Research: Data transmission rate estimates for orbital angular momentum millimetre waves generated by rectangular discrete antenna arrays

Article Title: Data transmission rate estimates for OAM-carrying millimetre waves generated by rectangular arrangements of discrete radiating sources

Article References: Ilić, A. Ž., Trajković, J. Z., Savić, S. V., & Ilić, M. M. (2026). Data transmission rate estimates for OAM-carrying millimetre waves generated by rectangular arrangements of discrete radiating sources. Applied Physics B, 132(6), Article 75. https://doi.org/10.1007/s00340-026-08689-y

Image Credits: AI Generated

DOI: 10.1007/s00340-026-08689-y

Keywords: orbital angular momentum, millimetre-wave communications, antenna arrays, 6G networks, mode-division multiplexing, uniform rectangular arrays, uniform circular arrays, vortex waves, line-of-sight transmission, spiral spectrum, Hertzian dipoles, channel capacity, phase calibration, spatial coherence, radio frequency, short-range communications