Terahertz-Band Direction Finding With Beam-Split and Mutual Coupling Calibration

Terahertz (THz) band is currently envisioned as the key building block to achieving the future sixth generation (6G) wireless systems. The ultra-wide bandwidth and very narrow beamwidth of THz systems offer the next order of magnitude in user densities and multi-functional behavior. However, wide bandwidth results in a frequency-dependent beampattern causing the beams generated at different subcarriers split and point to different directions. Furthermore, mutual coupling degrades the system's performance. This paper studies the compensation of both beam-split and mutual coupling for direction-of-arrival (DoA) estimation by modeling the beam-split and mutual coupling as an array imperfection. We propose a subspace-based approach using multiple signal classification with CalibRated for bEAam-split and Mutual coupling (CREAM-MUSIC) algorithm for this purpose. Via numerical simulations, we show the proposed CREAM-MUSIC approach accurately estimates the DoAs in the presence of beam-split and mutual coupling.

Sparse Array Design for Direction Finding using Deep Learning

In the past few years, deep learning (DL) techniques have been introduced for designing sparse arrays. These methods offer the advantages of feature engineering and low prediction-stage complexity, which is helpful in tackling the combinatorial search inherent to finding a sparse array. In this chapter, we provide a synopsis of several direction finding applications of DL-based sparse arrays. We begin by examining supervised and transfer learning techniques that have applications in selecting sparse arrays for a cognitive radar application. Here, we also discuss the use of meta-heuristic learning algorithms such as simulated annealing for the case of designing two-dimensional sparse arrays. Next, we consider DL-based antenna selection for wireless communications, wherein sparse array problem may also be combined with channel estimation, beamforming, or localization. Finally, we provide an example of deep sparse array technique for integrated sensing and communications (ISAC) application, wherein a trade-off of radar and communications performance makes ISAC sparse array problem very challenging. For each setting, we illustrate the performance of model-based optimization and DL techniques through several numerical experiments. We discuss additional considerations required to ensure robustness of DL-based algorithms against various imperfections in array data.

Antenna Selection With Beam Squint Compensation for Integrated Sensing and Communications

Next-generation wireless networks strive for higher communication rates, ultra-low latency, seamless connectivity, and high-resolution sensing capabilities. To meet these demands, terahertz (THz)-band signal processing is envisioned as a key technology offering wide bandwidth and sub-millimeter wavelength. Furthermore, THz integrated sensing and communications (ISAC) paradigm has emerged jointly access spectrum and reduced hardware costs through a unified platform. To address the challenges in THz propagation, THz-ISAC systems employ extremely large antenna arrays to improve the beamforming gain for communications with high data rates and sensing with high resolution. However, the cost and power consumption of implementing fully digital beamformers are prohibitive. While hybrid analog/digital beamforming can be a potential solution, the use of subcarrier-independent analog beamformers leads to the beam-squint phenomenon where different subcarriers observe distinct directions because of adopting the same analog beamformer across all subcarriers. In this paper, we develop a sparse array architecture for THz-ISAC with hybrid beamforming to provide a cost-effective solution. We analyze the antenna selection problem under beam-squint influence and introduce a manifold optimization approach for hybrid beamforming design. To reduce computational and memory costs, we propose novel algorithms leveraging grouped subarrays, quantized performance metrics, and sequential optimization. These approaches yield a significant reduction in the number of possible subarray configurations, which enables us to devise a neural network with classification model to accurately perform antenna selection.

Spatial Path Index Modulation in mmWave/THz-Band Integrated Sensing and Communications

As the demand for wireless connectivity continues to soar, the fifth generation and beyond wireless networks are exploring new ways to efficiently utilize the wireless spectrum and reduce hardware costs. One such approach is the integration of sensing and communications (ISAC) paradigms to jointly access the spectrum. Recent ISAC studies have focused on upper millimeter-wave and low terahertz bands to exploit ultrawide bandwidths. At these frequencies, hybrid beamformers that employ fewer radio-frequency chains are employed to offset expensive hardware but at the cost of lower multiplexing gains. Wideband hybrid beamforming also suffers from the beam-split effect arising from the subcarrier-independent (SI) analog beamformers. To overcome these limitations, this paper introduces a spatial path index modulation (SPIM) ISAC architecture, which transmits additional information bits via modulating the spatial paths between the base station and communications users. We design the SPIM-ISAC beamformers by first estimating both radar and communications parameters by developing beam-split-aware algorithms. Then, we propose to employ a family of hybrid beamforming techniques such as hybrid, SI, and subcarrier-dependent analog-only, and beam-split-aware beamformers. Numerical experiments demonstrate that the proposed SPIM-ISAC approach exhibits significantly improved spectral efficiency performance in the presence of beam-split than that of even fully digital non-SPIM beamformers.

NBA-OMP: Near-field Beam-Split-Aware Orthogonal Matching Pursuit for Wideband THz Channel Estimation

The sixth-generation networks envision the terahertz (THz) band as one of the key enabling technologies because of its ultrawide bandwidth. To combat the severe attenuation, the THz wireless systems employ large arrays, wherein the near-field beam-split (NB) severely degrades the accuracy of channel acquisition. Contrary to prior works that examine only either narrowband beamforming or far-field models, we estimate the wideband THz channel via an NB-aware orthogonal matching pursuit (NBA-OMP) approach. We design an NBA dictionary of near-field steering vectors by exploiting the corresponding angular and range deviation. Our OMP algorithm accounts for this deviation thereby ipso facto mitigating the effect of NB. Numerical experiments demonstrate the effectiveness of the proposed channel estimation technique for wideband THz systems.

Near-Field Terahertz Communications: Model-Based and Model-Free Channel Estimation

Terahertz (THz) band is expected to be one of the key enabling technologies of the sixth generation (6G) wireless networks because of its abundant available bandwidth and very narrow beam width. Due to high frequency operations, electrically small array apertures are employed, and the signal wavefront becomes spherical in the near-field. Therefore, near-field signal model should be considered for channel acquisition in THz systems. Unlike prior works which mostly ignore the impact of near-field beam-split (NB) and consider either narrowband scenario or far-field models, this paper introduces both a model-based and a model-free techniques for wideband THz channel estimation in the presence of NB. The model-based approach is based on orthogonal matching pursuit (OMP) algorithm, for which we design an NB-aware dictionary. The key idea is to exploit the angular and range deviations due to the NB. We then employ the OMP algorithm, which accounts for the deviations thereby ipso facto mitigating the effect of NB. We further introduce a federated learning (FL)-based approach as a model-free solution for channel estimation in a multi-user scenario to achieve reduced complexity and training overhead. Through numerical simulations, we demonstrate the effectiveness of the proposed channel estimation techniques for wideband THz systems in comparison with the existing state-of-the-art techniques.

BSA-OMP: Beam-Split-Aware Orthogonal Matching Pursuit for THz Channel Estimation

Terahertz (THz)-band has been envisioned for the sixth generation wireless networks thanks to its ultra-wide bandwidth and very narrow beamwidth. Nevertheless, THz-band transmission faces several unique challenges, one of which is beam-split which occurs due to the usage of subcarrier-independent analog beamformers and causes the generated beams at different subcarriers split, and point to different directions. Unlike the prior works dealing with beam-split by employing additional complex hardware components, e.g., time-delayer networks, a beam-split-aware orthogonal matching pursuit (BSA-OMP) approach is introduced to efficiently estimate the THz channel and beamformer design without any additional hardware. Specifically, we design a BSA dictionary comprised of beam-split-corrected steering vectors which inherently include the effect of beam-split so that the proposed BSA-OMP solution automatically yields the beam-split-corrected physical channel directions. Numerical results demonstrate the superior performance of BSA-OMP approach against the existing state-of-the-art techniques.

Millimeter-Wave Radar Beamforming with Spatial Path Index Modulation Communications

To efficiently utilize the wireless spectrum and save hardware costs, the fifth generation and beyond (B5G) wireless networks envisage integrated sensing and communications (ISAC) paradigms to jointly access the spectrum. In B5G systems, the expensive hardware is usually avoided by employing hybrid beamformers that employ fewer radio-frequency chains but at the cost of the multiplexing gain. Recently, it has been proposed to overcome this shortcoming of millimeter wave (mmWave) hybrid beamformers through spatial path index modulation (SPIM), which modulates the spatial paths between the base station and users and improves spectral efficiency. In this paper, we propose an SPIM-ISAC approach for hybrid beamforming to simultaneously generate beams toward both radar targets and communications users. We introduce a low complexity approach for the design of hybrid beamformers, which include radar-only and communications-only beamformers. Numerical experiments demonstrate that our SPIM-ISAC approach exhibits a significant performance improvement over the conventional mmWave-ISAC design in terms of spectral efficiency and the generated beampattern.

Twenty-Five Years of Advances in Beamforming: From Convex and Nonconvex Optimization to Learning Techniques

Beamforming is a signal processing technique to steer, shape, and focus an electromagnetic wave using an array of sensors toward a desired direction. It has been used in several engineering applications such as radar, sonar, acoustics, astronomy, seismology, medical imaging, and communications. With the advances in multi-antenna technologies largely for radar and communications, there has been a great interest on beamformer design mostly relying on convex/nonconvex optimization. Recently, machine learning is being leveraged for obtaining attractive solutions to more complex beamforming problems. This article captures the evolution of beamforming in the last twenty-five years from convex-to-nonconvex optimization and optimization-to-learning approaches. It provides a glimpse of this important signal processing technique into a variety of transmit-receive architectures, propagation zones, paths, and conventional/emerging applications.