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arxiv: 2606.06110 · v1 · pith:EKLPCISKnew · submitted 2026-06-04 · 📡 eess.SP

Subarray based Wideband Beamforming and Variational Sparse CSI Estimation for Low-Resolution MU THz MIMO Systems

Abhisha Garg , Suraj Srivastava , Akash Kumar , Aditya K. Jagannatham This is my paper

Pith reviewed 2026-06-28 00:15 UTC · model grok-4.3

classification 📡 eess.SP
keywords THz MIMOchannel estimationvariational Bayesian inferencebeamforminglow-resolution ADCsbeam squinttrue time delaysparse CSI
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The pith

A variational Bayesian framework jointly estimates sparse channels and designs beamformers for low-resolution wideband THz MIMO systems while compensating beam squint via true time delays.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a unified variational Bayesian inference approach for channel estimation and beamforming in multi-user THz MIMO systems constrained by low-resolution ADCs and partially connected subarray architectures. It introduces a dual-wideband channel model that incorporates root-raised-cosine pulse shaping to capture band-limited frequency dependence and applies Bussgang decomposition to linearize the nonlinear quantization effects. The method handles both on-grid and off-grid angular sparsity for improved resolution and derives the multi-user Bayesian Cramér-Rao lower bound as a performance benchmark. A true-time-delay hybrid transceiver architecture is embedded to eliminate the frequency-dependent beam-squint deviation that arises with conventional phase-shifter beamformers.

Core claim

The paper claims that the variational Bayesian inference-based estimator combined with the TTD-enabled hybrid transceiver provides accurate directional alignment and robust sparse CSI recovery across all subcarriers in practical wideband THz conditions, with the estimator accommodating on-grid and off-grid domains and its performance benchmarked against the derived multi-user Bayesian CRLB.

What carries the argument

Variational Bayesian inference applied to a dual-wideband channel model linearized via Bussgang decomposition, integrated with a true time delay (TTD) hybrid beamforming architecture in subarray-based transceivers.

If this is right

  • The TTD-based design ensures frequency-independent beam alignment across the entire bandwidth.
  • The estimator recovers sparse CSI with higher resolution than grid-restricted methods by handling off-grid angles.
  • Performance remains robust under the combined effects of wideband propagation and low-resolution quantization.
  • The multi-user Bayesian CRLB serves as a tight benchmark for any competing estimator in the same setting.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The subarray-plus-TTD architecture could lower the number of RF chains needed in future THz deployments.
  • The off-grid variational formulation might transfer to sparse recovery tasks outside THz communications.
  • Combining the linearized Bussgang model with other inference methods could further reduce computational cost.

Load-bearing premise

The dual-wideband channel model with root-raised-cosine pulse shape accurately captures band-limited propagation effects, and Bussgang decomposition yields a tractable linear model for the distortions caused by low-resolution ADCs.

What would settle it

A measurement campaign or simulation in which the proposed estimator's mean-squared error fails to approach the derived multi-user Bayesian Cramér-Rao lower bound under the modeled THz channel and ADC conditions would falsify the performance claims.

Figures

Figures reproduced from arXiv: 2606.06110 by Abhisha Garg, Aditya K. Jagannatham, Akash Kumar, Suraj Srivastava.

Figure 1
Figure 1. Figure 1: (a) Schematic diagram of SC-FDE based MU THz MIMO system (b) Normalized array gain with spatial direction at fc = 650 GHz, B = 5 GHz and K = 128. y˜m(p) = Q  WH RF,mX U u=1 Hp,u⊗K [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Subarray-based combining with ADCs and TD elements V. TTD BASED HYBRID TRANSCEIVER DESIGN In this section, we develop a beam-squint mitigation strategy in which frequency-dependent TTD elements perform coarse delay compensation across the signal bandwidth, followed by a bank of frequency-flat phase shifters (PS) that refine the residual steering error. Accordingly, the overall beamformer design is structur… view at source ↗
Figure 3
Figure 3. Figure 3: (a) NMSE vs SNR comparison for the proposed and existing state-of-the-art approaches (b) BER vs SNR comparison for the proposed and existing state￾of-the-art approaches (c) Effect of low-resolution ADCs on proposed Bayesian inference (d) NMSE vs SNR comparison by varying pilot blocks M. minimum separation constraint of | ˜θu − ˜θv| ≥ dmin ∀ u ̸= v. To generate angles corresponding to distinct users, the me… view at source ↗
Figure 4
Figure 4. Figure 4: (a) NMSE vs SNR comparison for the uniform and Taylor based off-grid dictionary (b) NMSE vs SNR comparison by varying the offset angles △θ (c) ∥ Γ (ι) k,U − Γ (ι−1) k,U ∥ 2 F vs number of iterations by varying the users at SNR = [30, −30]dB (d) Run time comparison for the considered sparse frameworks. -5 0 5 10 15 20 25 30 SNR (dB) 10 -1 10 0 N M S E Original " f=-a " f2[-a,a] " f=a 5 10 1.2 1.4 1.6 1.8 (a… view at source ↗
Figure 5
Figure 5. Figure 5: (a) NMSE vs SNR comparison by varying CFO values (b) NMSE vs SNR comparison for true and mismatched channel (c) Normalized array gain vs physical direction corresponding to all the users -10 -5 0 5 10 10 20 30 40 Optimal DPP+SOMP DPP-[25] SOMP-[23] IC-[54] Proposed (a) Insertion Loss (dB) 0 0.5 1 1.5 S p e ctral E f icie n c y (G b p s) 0 20 40 60 80 100 Rect-PSF RRC-PSF (b) SNR (dB) -15 -10 -5 0 5 10 15 S… view at source ↗
Figure 6
Figure 6. Figure 6: (a) Spectral efficiency vs SNR for the proposed and existing state-of-the-art approaches (b) SE vs insertion loss for Rect-PSF and RRC-PSF based dual￾wideband channels (c) SE vs SNR for exact and quantized delay (d) Spectral efficiency comparison for the Rect-PSF and RRC-PSF based dual-wideband channels. on-grid approach for both the M-FOCUSS [10] and Bayesian inference, primarily because it can effectivel… view at source ↗
read the original abstract

This work conceives a unified channel estimation and beamforming framework, formulated within the principles of variational Bayesian inference. Recognizing the limitations imposed by hardware constraints, frequency-dependent propagation effects, and the structural restrictions of partially connected architectures in the Terahertz (THz) band, we formulate a dual-wideband channel model incorporating root raised cosine (RRC) pulse shape to account its band-limited nature. To further address the nonlinear distortions introduced by low-resolution ADCs, Bussgang decomposition is employed, enabling a tractable linearized inference process. Unlike conventional techniques, the proposed method accommodates both on-grid and off-grid angular domains, capturing spatial sparsity with improved resolution and robustness. The multi-user (MU) Bayesian Cram\'er-Rao lower bound is also derived to benchmark the performance of the proposed estimator. Moreover, the framework incorporates a true time delay (TTD)-based hybrid transceiver design that inherently compensates for the beam-squint effect; a frequency-dependent angular deviation that arises due to the fixedphase nature of the conventional beamformer in wideband systems, thereby ensuring accurate directional alignment across all subcarriers. Extensive simulation results validate the effectiveness of the proposed variational Bayesian inference-based estimator and the TTD-enabled beamforming architecture, highlighting their robustness and performance gains under practical wideband THz system.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript proposes a unified variational Bayesian inference framework for joint channel estimation and beamforming in low-resolution multi-user THz MIMO systems. It introduces a dual-wideband channel model that incorporates root-raised-cosine pulse shaping to capture band-limited effects, employs Bussgang decomposition to linearize the effect of low-resolution ADCs, accommodates both on-grid and off-grid angular sparsity, derives the multi-user Bayesian Cramér-Rao lower bound, and integrates a true-time-delay (TTD) hybrid transceiver architecture to mitigate beam squint. Extensive simulations are claimed to demonstrate robustness and performance gains under practical wideband THz conditions.

Significance. If the variational updates and TTD design deliver the reported gains while remaining stable under realistic propagation and quantization mismatch, the work would provide a concrete, implementable approach to two central practical obstacles in THz MIMO—frequency-dependent beam squint and low-resolution ADC distortion—thereby strengthening the case for partially connected hybrid architectures in the THz band.

major comments (1)
  1. [Abstract / simulation section] Abstract and § on simulation results: the central claim that the estimator and TTD architecture exhibit 'robustness … under practical wideband THz system' rests on simulations that, by the abstract’s own description, employ the identical dual-wideband RRC model and Bussgang-linearized observation model used to derive the inference algorithm. No evidence is presented that performance remains stable when these modeling assumptions are violated (e.g., different pulse shapes, non-Gaussian quantization noise, or measured THz channels). This directly undermines the robustness assertion.
minor comments (2)
  1. [System model] Notation for the dual-wideband channel model and the precise definition of the RRC pulse in the frequency-domain formulation should be stated explicitly before the variational update equations are derived.
  2. [Estimation algorithm] The manuscript should clarify whether the off-grid angular refinement is performed jointly with the variational updates or in a separate post-processing step.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for the constructive comment on the robustness claims. We address the concern point-by-point below and indicate planned revisions.

read point-by-point responses

  1. Referee: [Abstract / simulation section] Abstract and § on simulation results: the central claim that the estimator and TTD architecture exhibit 'robustness … under practical wideband THz system' rests on simulations that, by the abstract’s own description, employ the identical dual-wideband RRC model and Bussgang-linearized observation model used to derive the inference algorithm. No evidence is presented that performance remains stable when these modeling assumptions are violated (e.g., different pulse shapes, non-Gaussian quantization noise, or measured THz channels). This directly undermines the robustness assertion.

    Authors: We acknowledge that all reported simulations employ the dual-wideband RRC model and Bussgang-linearized observation model derived in the paper. These elements are included precisely to reflect key practical THz impairments (band-limited pulse shaping and low-resolution ADC distortion). The robustness claim is therefore scoped to performance under this realistic modeling framework rather than arbitrary model mismatches. To address the concern, we will revise the abstract and simulation section to explicitly qualify the scope of the robustness results. We will also add a short discussion (and, space permitting, one or two additional simulation curves) examining sensitivity to alternative pulse shapes and a Gaussian approximation to quantization noise. Results on measured THz channels cannot be added, as the work is simulation-based and no such datasets were available. revision: partial

standing simulated objections not resolved
  • Results on measured THz channels cannot be provided without access to real-world measurement data, which is outside the scope of this simulation study.

Circularity Check

0 steps flagged

No circularity in derivation chain; self-contained variational estimator and BCRLB benchmark

full rationale

The abstract and available text describe a variational Bayesian estimator derived from the dual-wideband RRC model and Bussgang linearization, with an independent MU Bayesian CRLB derived as benchmark and TTD architecture for beam-squint compensation. No quoted equations reduce a claimed prediction or uniqueness result to a fitted input or self-citation by construction. Simulations are presented as validation under the stated model rather than as load-bearing derivations. The central claims rest on explicit modeling choices and standard variational inference techniques, not on self-referential reductions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No explicit free parameters, axioms, or invented entities are identifiable from the abstract alone.

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discussion (0)

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