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Terahertz-Band Joint Ultra-Massive MIMO Radar-Communications: Model-Based and Model-Free Hybrid Beamforming
Ahmet M. Elbir, Kumar Vijay Mishra, Symeon Chatzinotas
TL;DR
THz ultra-massive MIMO joint radar-communications systems need hardware-efficient beamforming because severe attenuation requires large arrays while fully digital architectures are impractical. The paper develops GoSA hybrid beamformers, beam-split correction, and model-based and model-free designs, achieving lower hardware or computation costs while preserving radar and communications performance.
Problem
Fully digital beamforming is infeasible for ultra-massive THz MIMO, while prior THz hybrid beamforming work does not address practically feasible ultra-massive MIMO joint radar-communications systems.
Method
The paper develops GoSA and PCO GoSA hybrid beamformers using CSI or channel covariance, phase correction for beam split, manifold optimization, and deep-learning beamformer design.
Results
The proposed methods provide lower hardware complexity, approximately 500 times lower computation time for model-free methods than MO-based approaches, and spectral efficiency close to channel covariance matrix-based techniques.
Takeaways & Limitations
GoSA-based hybrid beamforming offers a hardware-efficient THz joint radar-communications architecture, while model-free learning reduces beamformer-design computation with near covariance-based spectral-efficiency performance.
Abstract
from arXiv · showhide
Wireless communications and sensing at terahertz (THz) band are increasingly investigated as promising short-range technologies because of the availability of high operational bandwidth at THz. In order to address the extremely high attenuation at THz, ultra-massive multiple-input multiple-output (MIMO) antenna systems have been proposed for THz communications to compensate propagation losses. However, the cost and power associated with fully digital beamformers of these huge antenna arrays are prohibitive. In this paper, we develop wideband hybrid beamformers based on both model-based and model-free techniques for a new group-of-subarrays (GoSA) ultra-massive MIMO structure in low-THz band. Further, driven by the recent developments to save the spectrum, we propose beamformers for a joint ultra-massive MIMO radar-communications system, wherein the base station serves multi-antenna user equipment (RX), and tracks radar targets by generating multiple beams toward both RX and the targets. We formulate the GoSA beamformer design as an optimization problem to provide a trade-off between the unconstrained communications beamformers and the desired radar beamformers. To mitigate the beam split effect at THz band arising from frequency-independent analog beamformers, we propose a phase correction technique to align the beams of multiple subcarriers toward a single physical direction. To further decrease the ultra-massive MIMO computational complexity and enhance robustness, we also implement deep learning solutions to the proposed model-based hybrid beamformers. Numerical experiments demonstrate that both techniques outperform the conventional approaches in terms of spectral efficiency and radar beampatterns, as well as exhibiting less hardware cost and computation time.
I. INTRODUCTION
THz systems offer very wide bandwidth but face severe propagation loss, beam split, and hardware constraints that complicate ultra-massive MIMO design. This paper addresses these challenges with joint radar-communications beamforming using GoSA structures, model-based optimization, beam-split correction, and deep learning.
- THz provides hundreds of GHz bandwidth for Tb/s-rate communications and improved radar range resolution.
- Severe THz path loss motivates extremely large antenna arrays, while fully digital beamforming is infeasible because of cost, area, and power.
- THz beam split is more severe than mmWave beam squint because wide bandwidth and large arrays separate the main lobes of extreme subcarriers.
- The paper develops GoSA-based ultra-massive MIMO joint radar-communications beamformers with model-based and model-free techniques, using fewer phase-shifters than fully connected and AoSA structures.
- A hardware-efficient phase-correction approach mitigates beam split without the complex time-delay network used in prior approaches.
II. SYSTEM MODEL AND PROBLEM FORMULATION
The system model considers a wideband THz ultra-massive MIMO joint radar-communications system for V2V and V2D scenarios. A GoSA-structured transmitter senses targets while communicating with a receiver.
- The transmitter probes vehicular targets and communicates with the receiver in a V2V/V2D joint radar-communications scenario.
- The transmitter and receiver use graphene-based plasmonic nano-antennas arranged in group-of-subarrays structures.
A. Communications Model
The communications model uses a wideband GoSA transmitter with subcarrier-dependent digital precoding and subcarrier-independent analog precoding. Its THz channel includes dominant LoS and weaker NLoS components, while GoSA reduces phase-shifter requirements and overlapping structures recover performance.
- The GoSA transmitter sends NS data streams using NRF RF chains, digital precoders that vary by subcarrier, and a subcarrier-independent RF precoder.
- GoSA connects each group of Q antennas to one phase-shifter, reducing phase-shifter count by a factor of Q relative to AoSA.
- The RF precoder uses unit-modulus phase-shifter constraints and the transmitted signal is formed as x[m] = FRFFBB[m]s[m].
- The THz channel is modeled as a dominant LoS path plus clustered NLoS paths with frequency-dependent gains and molecular absorption.
- Overlapping phase-shifter terms in PCO GoSA improve performance at the cost of additional phase-shifters while remaining below AoSA complexity.
- Communications beamforming maximizes mutual information by approximating the unconstrained singular-vector beamformer with a hybrid precoder.
B. Radar Model
The radar model searches for targets and then forms directional beams toward their estimated directions using orthogonal GoSA waveforms. Radar beamformer design controls the transmitted covariance under hybrid hardware constraints.
- Radar first uses omnidirectional waveforms for target search, then generates directional beams for tracking.
- Each GoSA transmits a distinct orthogonal waveform, enabling coherent processing gain across subarrays.
- The radar-only beamformer is constructed as a block-diagonal matrix whose blocks steer beams toward the target directions.
- For multiple targets, radar beampattern design is equivalent to designing the transmitted-signal covariance matrix under the hybrid architecture.
- Hybrid radar beamformers are designed by minimizing the distance between the hybrid beamformer and the radar-only beamformer, with a unitary auxiliary matrix matching their dimensions.
C. Problem Formulation
The work designs a hybrid beamformer that jointly serves communications and radar targets in an ultra-massive MIMO THz system. The formulation balances communications spectral efficiency against radar-target SNR using available instantaneous CSI or channel covariance information.
- The beamformer jointly maximizes communications spectral efficiency and SNR toward radar targets through transmit-array beampattern control.
- The optimization uses η to trade off communications and radar objectives, with η=1 yielding communications-only and η=0 radar-only design.
- CSI-based design assumes the THz channel matrix H[m] is available, either directly or through channel-estimation techniques.
- Statistical design assumes the channel covariance matrix is available at the transmitter and obtained through temporal averaging, angular-spectrum estimation, or model-based approaches.
III. MODEL-BASED HYBRID BEAMFORMER DESIGN
The paper's model-based hybrid beamformer designs use either instantaneous CSI or channel covariance information to construct beamformers for the THz joint radar-communications system.
- Model-based hybrid beamformer techniques rely on CSI and channel covariance matrix-based channel information.
A. Hybrid Beamformer Design With CSI
The CSI-based design solves the joint radar-communications hybrid beamforming problem under overlapped GoSA constraints using alternating optimization and manifold optimization. It reconstructs feasible analog beamformers, updates digital and radar-related variables, and applies beam-split correction.
- Optimization formulation: The design minimizes the distance between the unconstrained radar-communications beamformer and the feasible hybrid beamformer under analog-precoder constraints.
- Optimization formulation: The radar-communications reference beamformer combines communications and radar-only beamformers through η and 1−η.
- Optimization formulation: Alternating minimization updates the analog beamformer, broadband digital beamformers, and radar matrix one by one while fixing the others.
- Manifold optimization: For the overlapped structure, manifold optimization excludes zero analog-precoder entries and optimizes the remaining unit-modulus entries on a complex circle manifold.
- Manifold optimization: The Riemannian-gradient method iteratively updates the nonzero analog-precoder entries using conjugate-gradient descent from a random initialization.
- Algorithm: Algorithm 1 initializes the beamformers, constructs the GoSA support sets, alternates updates until convergence, and then performs beam-split correction.
- Complexity and convergence: The iterative implementation takes no more than 10 iterations, with approximately 20 manifold-optimization sub-iterations for NT=1024, Q=9, and NRF=10.
- Complexity and convergence: After solving communications-only and radar-only problems, the special-case analysis can generate the JRC beamformer as a function of η without resolving the full optimization for every η.
B. Hybrid Beamformer Design With Channel Covariance Matrix
The channel covariance matrix approach reduces channel feedback by retaining channel statistics rather than complete instantaneous channel knowledge. It then designs an unconstrained statistical beamformer and approximates it with an analog precoder through optimization.
- The unconstrained statistical beamformer is obtained from the eigenvectors associated with the largest eigenvalues of the channel covariance matrix.
- The THz channel covariance matrix is formed from path steering matrices and path-gain statistics, with independent channel gains removing cross terms.
- Because NLoS path gains are much smaller than the LoS gain, the covariance matrix can be approximated using the dominant LoS contribution.
- Channel covariance matrix beamforming uses long-term channel statistics instead of complete instantaneous channel knowledge, reducing channel feedback overhead.The retained statistics include received path-gain variance, while the covariance matrix omits complete instantaneous channel information.
- The analog precoder is optimized to approximate the unconstrained statistical beamformer, following a procedure analogous to the CSI-based design.
IV. MODEL-FREE HYBRID BEAMFORMING
The model-free method uses DeepMUSIC to estimate radar directions and DeepBF to predict hybrid beamformer weights. This decomposes the difficult joint learning problem into direction estimation followed by beamformer prediction.
- The joint learning problem is challenging because it contains multiple large matrix variables associated with channels, analog and digital beamformers, radar weights, and power allocation.
- DeepMUSIC estimates radar target directions from the sample covariance matrix, after which peak-finding produces target locations and constructs the radar beamformer.
- DeepBF uses the radar beamformer together with the channel matrix as input to predict hybrid beamformer weights for radar and communications tasks.
V. NUMERICAL EXPERIMENTS
The experiments evaluate spectral efficiency, radar beampatterns, hardware complexity, task trade-offs, and model-based versus model-free designs across GoSA and AoSA structures. The proposed GoSA and PCO configurations provide radar-communications trade-offs with substantially reduced phase-shifter complexity, while performance depends on η, array spacing, channel information, and operating assumptions.
- Evaluation setup: The experiments assess spectral efficiency, radar beampatterns, task trade-offs, and array structures including fully-connected, partially-connected, and PCO configurations.
- Evaluation setup: The baseline simulation uses a 300 GHz carrier, 15 GHz bandwidth, 1024 transmit antennas, 81 receive antennas, and nine GoSA subarrays.
- Hardware complexity: GoSA uses fewer phase-shifters than AoSA, with the reduction reaching a factor of Q for the corresponding architecture connections.
- Spectral efficiency: For CSI-based beamforming at η = 0.5, GoSA has slightly lower spectral efficiency than AoSA while using Q = 9 times fewer phase-shifters.
- Task trade-off: Increasing η moves spectral efficiency toward the unconstrained beamformer, whereas η approaching zero directs the RF precoder toward radar targets and reduces communications spectral efficiency.
- Radar performance: At η = 0.5, the proposed GoSA PCO approach generates beams toward both radar targets and the RX in one- and two-dimensional angular spaces.
- Array design: Increasing GoSA subarray spacing parameter d̄ makes AoSA performance approach GoSA performance, while d̄ = 2 is retained as the lower limit to avoid spatial aliasing.
- Radar-communications performance: Radar direction RMSE and spectral efficiency both improve with SNR, while GoSA PCO maintains satisfactory performance despite partially-connected arrays performing worse than fully-connected arrays.
VI. SUMMARY
The paper develops model-based and model-free hybrid beamforming for a THz ultra-massive MIMO joint radar-communications architecture. The proposed GoSA and learning-based methods reduce hardware or computation costs while maintaining spectral-efficiency and radar-beampattern performance.
- Contributions: The proposed architecture combines GoSA ultra-massive MIMO with model-based and model-free hybrid beamforming for THz joint radar-communications.The design targets communications and radar beampattern objectives while reducing implementation burden.
- Hardware complexity: GoSA provides lower hardware complexity than full-array and AoSA structures.The architecture is evaluated using spectral efficiency and radar beampattern metrics.
- Computational complexity: The model-free method achieves approximately 500 times lower computation time than MO-based approaches while maintaining spectral efficiency close to the channel-covariance-matrix technique.This comparison concerns computational complexity and spectral-efficiency performance.
- Beamforming trade-offs: Channel-covariance-matrix-based beamforming has slightly lower performance than CSI-based beamforming but requires less channel overhead.The paper also introduces phase correction to mitigate beam split using a hardware-efficient approach.
APPENDIX A BEAM SPLIT CORRECTION
The appendix explains how frequency-independent analog beamformers misalign subcarrier beams in wideband THz systems. It proposes frequency-dependent phase correction and shifts the correction into baseband beamformers to avoid duplicating large phase-shifter networks.
- Beam split effect: In wideband hybrid beamforming, frequency-independent analog beamformers can point in different directions across subcarriers because of ultra-wide bandwidth and large arrays.The analog beamformers are typically designed at the central frequency while baseband beamformers vary with frequency.
- Beam split effect: The generated beam aligns with a frequency-dependent physical direction vector rather than a single fixed direction.The appendix relates the beamforming vector to the spatial direction represented by Ω_l.
- Phase correction: Phase correction multiplies the phase values of the hybrid analog beamformer by the relative frequency factor Δ_m so every subcarrier points toward the intended direction.The relative frequency is defined using the subcarrier and central frequencies.
- Implementation: Implementing separate corrected RF beamformers for all subcarriers is inefficient because it requires M phase-shifter networks of size N_TN_RF.The proposed alternative conveys the correction to frequency-dependent baseband beamformers.