Superdirective receive arrays, whose gain can exceed that of traditional antenna arrays, have been historically challenging to realize due to high sensitivity to white noise, strong mutual coupling, and the complexity of designing receive matching networks in conventional systems. This paper proposes and analyzes a novel superdirective receiver architecture based on an array of Rydberg atomic sensors to overcome these fundamental limitations. By leveraging the quantum properties of Rydberg atoms, the proposed receiver is inherently immune to the internal thermal noise that plagues traditional receivers. As a result, the system performance is primarily limited by external background noise and fundamental quantum noise. We develop a comprehensive signal and noise model and the-oretically derive the upper bound on the directivity gain for the proposed Rydberg-based receiver. Furthermore, we prove that for multi-user scenarios, the effective channel vectors for different users become asymptotically orthogonal as the number of sensors approaches infinity, enabling high-capacity spatial multiplexing even with deep sub-wavelength element spacing. Extensive simulations demonstrate the superior performance of the proposed system over traditional superdirective receivers and validate our theoretical findings. The results highlight Rydberg atomic arrays as a promising technology for developing ultra-sensitive, compact, and broadband superdirective receivers for next-generation communication and sensing applications.

Traditional antenna arrays with a half-wavelength spacing between elements are capable of achieving a power gain proportional to the number of antennasM. Superdirective antenna arrays, however, leverage smaller antenna spacing to approach an achievable power gain ofM2, which could provide a significant performance improvement to the spectral efficiency in wireless communication systems. In this paper, we study the power scaling law of superdirective beamforming in multi-user communication systems using a uniform linear array (ULA). First, we extend superdirective precoding from single-user to multi-user multipath scenarios. Employing the basis of Legendre polynomials, we prove that the scaling laws of both the power gain and signal-to-interference-plus-noise ratio (SINR) are betweenMandM2, whereM2is achieved in the end-fire direction. To further enhance user power gains and effectively manage interference, we formulate and solve an optimization problem that maximizes the directivity gain while nullifying interference to other users. We demonstrate that this scheme can significantly improve spectral efficiency in multi-user settings, even when antenna spacing approaches zero. Moreover, we address the narrow directivity bandwidth issue, showing that the directivity of superdirective arrays decreases sharply as the frequency moves away from the center frequency, necessitating the use of multi-carrier technology to overcome this limitation. Simulation results verify the proposed power scaling law and show significant improvements in spectral efficiency with our proposed methods compared to a traditional antenna array with half-wavelength spacing.

In traditional multiple-input multiple-output (MIMO) communication systems, the antenna spacing is often no smaller than half a wavelength. However, by exploiting the coupling between more closely-spaced antennas, a superdirective array may achieve a much higher beamforming gain than traditional MIMO. In this paper, we present a novel utilization of neural networks in the context of superdirective arrays. Specifically, a new model called MultiTransUNet-GAN is proposed, which aims to forecast the excitation coefficients to achieve “superdirectivity” or “super-gain” in the compact uniform linear or planar antenna arrays. In this model, we integrate a multi-level guided attention and a multi-scale skip connection. Furthermore, generative adversarial networks are integrated into our model. To improve the prediction accuracy and convergence speed of our model, we introduce the warm up aided cosine learning rate (LR) schedule during the model training, and the objective function is improved by incorporating the normalized mean squared error (NMSE) between the generated value and the actual value. Simulations demonstrate that the array directivity and array gain achieved by our model exhibit a strong agreement with the theoretical values. Overall, it shows the advantage of enhanced precision over the existing models, and a reduced requirement for measurement and the computation of the excitation coefficients.

Traditional multiple-input multiple-output (MIMO) systems exhibit power gains that are proportional to the number of antennas M. By contrast, a superdirective array has the potential to attain the power gain proportional to $M^{2}$, which may lead to great improvements in spectral efficiency. However, few early studies explore the superdirectivity in multi-user wireless communications. In this paper, we conduct a detailed study on the topic. Firstly, we extend the superdirective precoding from single-user scenarios to multi-user multipath scenarios. Utilizing the Legendre polynomials basis, we prove that the scaling laws of both the power gain and the signal-to-interference-plus-noise ratio (SINR) are between $\mathcal{O}(M)$ and $\mathcal{O}\left(M^{2}\right)$, where $\mathcal{O}\left(M^{2}\right)$ is achieved at the end-fire direction. We reveal that, for a fixed-aperture compact antenna array without considering ohmic loss and impedance mismatch loss, the power gain keeps growing with the increasing number of antennas. Furthermore, we propose a Multi-user Interference-Nulling Superdirective (MINS) precoding scheme to maximize user power gains while eliminating interference. Simulation results verify the proposed power scaling law and show significant improvements in spectral efficiency using our methods compared to the traditional MIMO.

The array gain of a superdirective antenna array can be proportional to the square of the number of antennas, which is much larger than the traditional array. However, the realization of the so-called superdirectivity entails accurate calculation and application of the excitations (beamforming vector). Moreover, the excitations require a large dynamic power range, especially when the number of antennas increases and the antenna spacing decreases. In this paper, we derive the closed form solution to the superdirective beamforming vector and characterize the distribution of the excitation power range for the superdirective array. We prove that as the antenna spacing tends to 0, the amplitude range of the superdirective excitations for an M-antenna array can be expressed as a list of binomial coefficients of order M-1. Moreover, to alleviate the high power range requirement, two beamforming methods are proposed to obtain the beamforming vector under a certain excitation range constraint based on Particle Swarm Optimization and convex approximation, respectively. Full-wave electromagnetic simulations validate the effectiveness of our proposed methods.

Superdirectivity has the potential to increase the array gain to the square of the number of antennas, pushing the spectral efficiency of wireless communications to a higher level. However, calculating the superdirective beamforming vector in the presence of strong coupling is a challenging task due to the lack of the coupling depiction. Another practical obstacle is the sensitivity problem—superdirective antenna arrays are susceptible to excitation errors, necessitating precise excitation controls. To address these problems, we first introduce the embedded element pattern (EEP), which describes the coupled radiation field. We propose an EEP-based beamforming (EEPB) method to achieve superdirectivity. To mitigate the sensitivity problem, we propose an EEP-aided orthogonal complement-based robust beamforming (EEP-OCRB) algorithm for computing a robust superdirective beamforming vector. Full-wave simulations and real-world experiments utilizing a prototype of a 5-dipole superdirective antenna array validate both the superdirectivity of the EEPB method and the robustness of the EEP-OCRB algorithm to excitation errors.

In most multiple-input multiple-output (MIMO) communication systems, e.g., Massive MIMO, the antenna spacing is generally no less than half a wavelength. It helps to reduce the mutual coupling and therefore facilitate the system design. The maximum array gain is the number of antennas in this settings. However, when the antenna spacing is made very small, the array gain of a compact array can be proportional to the square of the number of antennas - a value much larger than the traditional array. To achieve this so-called "superdirectivity" however, the calculation of the excitation coefficients (beamforming vector) is known to be a challenging problem. In this paper, we derive the beamforming vector of superdirective arrays based on a novel coupling matrix-enabled method. We also propose an approach to obtain the coupling matrix, which is derived by the spherical wave expansion method and active element pattern. The full-wave electromagnetic simulations are conducted to validate the effectiveness of our proposed method. Simulation results show that when the beamforming vector obtained by our method is applied, the directivity of the designed dipole antenna array has a good agreement with the theoretical values.