Semi-Blind Channel Estimation and Hybrid Receiver Beamforming in the Tera-Hertz Multi-User Massive MIMO Uplink

We develop a pragmatic multi-user (MU) massive multiple-input multiple-output (MIMO) channel model tailored to the THz band, encompassing factors such as molecular absorption, reflection losses and multipath diffused ray components. Next, we propose a novel semi-blind based channel state information (CSI) acquisition technique i.e. MU whitening decorrelation semi-blind (MU-WD-SB) that exploits the second order statistics corresponding to the unknown data symbols along with pilot vectors. A constrained Cramer-Rao Lower Bound (C-CRLB) is derived to bound the normalized mean square error (NMSE) performance of the proposed semi-blind learning technique. Our proposed scheme efficiently reduces the training overheads while enhancing the overall accuracy of the channel learning process. Furthermore, a novel hybrid receiver combiner framework is devised for MU THz massive MIMO systems, leveraging multiple measurement vector based sparse Bayesian learning (MMV-SBL) that relies on the estimated CSI acquired through our proposed semi-blind technique relying on low resolution analog-to-digital converters (ADCs). Finally, we propose an optimal hybrid combiner based on MMV-SBL, which directly reduces the MU interference. Extensive simulations are conducted to evaluate the performance gain of the proposed MU-WD-SB scheme over conventional training-based and other semi-blind learning techniques for a practical THz channel obtained from the high-resolution transmission (HITRAN) database. The metrics considered for quantifying the improvements include the NMSE, bit error rate (BER) and spectral-efficiency (SE).

Terahertz Beamforming and Group Sparse Channel Estimation Relying on Low-Resolution ADCs in MU Hybrid MIMO systems

A unified beamforming and channel estimation framework relying on Bayesian learning is conceived. Recognizing the limitations imposed by low-resolution analog-to-digital converter (ADCs) and frequency-dependent propagation effects occurring in the Terahertz (THz) band, we formulate a dual-wideband channel model incorporating root raised cosine (RRC) pulse shaping. To address the non-linear distortions introduced by low-resolution ADCs, Bussgang decomposition is employed, leading to a tractable linearized inference process. By leveraging the shared sparsity inherent in a multi-user (MU) scenario of THz systems, we propose a Hierarchical Bayesian Group-sparse Regression (HBG-SR) based channel learning technique that exploits the group-sparse structure of THz band channels. The estimated dominant angle-of-arrival/ angle-of-departure (AoA/AoD) indices are then exploited for appropriately configuring the true-time-delay (TTD) elements in the hybrid transceiver, enabling precise beam alignment across subcarriers and the effective compensation of the beam-squint effect occurring in wideband THz systems. Extensive simulation results validate the efficiency of the proposed channel estimator and the TTD-aided beamforming architecture, highlighting their robustness and performance gains under practical wideband THz system constraints.

Two-Stage Hybrid Transceiver Design Relying on Low-Resolution ADCs in Partially Connected MU Terahertz (THz) MIMO Systems

A two-stage hybrid transceiver is designed by considering a partially connected architecture at the base station (BS) for a low-resolution multi-user (MU) THz massive multiple input multiple output (MIMO) system. Due to its high bandwidth coupled with a high number of antennas, the THz band suffers from the deleterious spatial-wideband and frequency-wideband effects jointly termed as the dual-wideband effect. To address this undesired phenomenon, we rigorously model the THz MIMO channel at each subarray corresponding to each user by incorporating the absorption, reflection, and free-space losses. Subsequently, a novel beamforming technique is proposed that employs only a few true time delay (TTD) lines for eliminating the beam-split effect, which is the manifestation of the spatial-wideband effect in the frequency domain. Our simulation results demonstrate a performance improvement of around 13% in terms of spectral efficiency over the existing state-of-the-art techniques.

Bayesian Learning Aided Simultaneous Sparse Estimation of Dual-Wideband THz Channels in Multi-User Hybrid MIMO Systems

This work conceives the Bayesian Group-Sparse Regression (BGSR) for the estimation of a spatial and frequency wideband, i.e., a dual wideband channel in Multi-User (MU) THz hybrid MIMO scenarios. We develop a practical dual wideband THz channel model that incorporates absorption losses, reflection losses, diffused ray modeling and angles of arrival/departure (AoAs/AoDs) using a Gaussian Mixture Model (GMM). Furthermore, a low-resolution analog-to-digital converter (ADC) is employed at each RF chain, which is crucial for wideband THz massive MIMO systems to reduce power consumption and hardware complexity, given the high sampling rates and large number of antennas involved. The quantized MU THz MIMO model is linearized using the popular Bussgang decomposition followed by BGSR based channel learning framework that results in sparsity across different subcarriers, where each subcarrier has its unique dictionary matrix. Next, the Bayesian Cramér Rao Bound (BCRB) is devised for bounding the normalized mean square error (NMSE) performance. Extensive simulations were performed to assess the performance improvements achieved by the proposed BGSR method compared to other sparse estimation techniques. The metrics considered for quantifying the performance improvements include the NMSE and bit error rate (BER).

Angularly Sparse Channel Estimation in Dual-Wideband Tera-Hertz (THz) Hybrid MIMO Systems Relying on Bayesian Learning

Bayesian learning aided massive antenna array based THz MIMO systems are designed for spatial-wideband and frequency-wideband scenarios, collectively termed as the dual-wideband channels. Essentially, numerous antenna modules of the THz system result in a significant delay in the transmission/ reception of signals in the time-domain across the antennas, which leads to spatial-selectivity. As a further phenomenon, the wide bandwidth of THz communication results in substantial variation of the effective angle of arrival/ departure (AoA/ AoD) with respect to the subcarrier frequency. This is termed as the beam squint effect, which renders the channel state information (CSI) estimation challenging in such systems. To address this problem, initially, a pilot-aided (PA) Bayesian learning (PA-BL) framework is derived for the estimation of the Terahertz (THz) MIMO channel that relies exclusively on the pilot beams transmitted. Since the framework designed can successfully operate in an ill-posed model, it can verifiably lead to reduced pilot transmissions in comparison to conventional methodologies. The above paradigm is subsequently extended to additionally incorporate data symbols to derive a Data-Aided (DA) BL approach that performs joint data detection and CSI estimation. We will demonstrate that it is capable of improving the dual-wideband channels estimate, despite further reducing the training overhead. The Bayesian Cramer-Rao bounds (BCRLBs) are also obtained for explicitly characterizing the lower bounds on the mean squared error (MSE) of the PA-BL and DA-BL frameworks. Our simulation results show the improved normalized MSE (NMSE) and bit-error rate (BER) performance of the proposed estimation schemes and confirm that they approach their respective BCRLB benchmarks.