DNN based Two-stage Compensation Algorithm for THz Hybrid Beamforming with imperfect Hardware

Chong Han; Emil Bj\"ornson; Ho-Jin Song; Wenqi Zhao

REVIEW 4 major objections 6 minor 35 references

DNN based Two-stage Compensation Algorithm for THz Hybrid Beamforming with imperfect Hardware

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A two-stage neural algorithm learns all hardware imperfections of a THz hybrid beamforming link as a black box and compensates them at baseband, cutting symbol error rate to 0.0005 at 15 dBm.

desk verdict A competent, fully simulated DNN compensation study for THz hybrid beamforming whose headline claim outruns its architecture: the stage-2 precoder is per-stream, so the general-digital-precoder claim is not established. read the letter →

arxiv 2411.14699 v1 pith:FD5GBR4D submitted 2024-11-22 cs.IT eess.SPmath.IT

Wenqi Zhao , Chong Han , Ho-Jin Song , Emil Björnson This is my paper · ORCID

classification cs.ITeess.SPmath.IT

keywords Terahertzcommunicationsultra-massiveMIMOhybridbeamforminghardwareimperfectiondeepneuralnetworksymbolerrorrateslimmingdigitalprecodercompensation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper claims that the combined hardware impairments of a THz ultra-massive MIMO hybrid-beamforming link—DAC/ADC quantization, IQ imbalance, phase noise, imperfect phase shifters, and PA nonlinearity—can be treated as a single learnable black box for compensation, so a data-driven scheme can undo their joint effect without needing separate models for each imperfection. A two-stage algorithm first trains a structured DNN to reproduce the distorted received signal from pilot transmissions, then trains a second network to design the digital precoder or combiner that undoes the learned distortion. In simulation with 256 antennas and 4-bit converters, transmitter-side compensation lowers the symbol error rate to 0.0018 at 10 dBm and 0.0005 at 15 dBm, outperforming receiver-side compensation and a generic fully connected DNN baseline. The paper also shows that pruning, parameter sharing, and conditional removal of a sub-network cut parameters by 97.2% and runtime by 39.2% with nearly unchanged SER. A reader should care because this points to a practical, low-complexity way to keep THz links usable despite hardware that is far from ideal.

What carries the argument

The load-bearing object is the stage-1 DNN, written as $\hat{y} = \mathbf{W}_{\mathrm{BB}}^H \mathcal{NN}_3(\mathbf{W}_{\mathrm{RF}}^H \mathbf{H}\, \mathcal{NN}_2(\mathbf{F}_{\mathrm{RF}}\mathbf{P}_{\mathrm{in}} \mathcal{NN}_1(\mathbf{F}_{\mathrm{BB}} \mathbf{s})))$, a chain of small sub-networks (two real inputs from the I/Q components, one hidden layer with $\mathrm{Tanh}$ activation, two outputs) arranged exactly as the signal flows through transmit RF chains, antennas, and receive RF chains. This network is trained with an MSE loss to reproduce the distorted received signal of the nonideal model, so it becomes a differentiable black-box model of the combined hardware imperfections. Stage 2 keeps that network fixed and trains a separate small NN to produce the compensating digital precoder (Tx) or combiner (Rx), reading off $\mathbf{F}_{\mathrm{BB},c}$ or $\mathbf{W}_{\mathrm{BB},c}$ from the network's input–output relation under the per-symbol power constraint. The slimming methods act on this machinery: pruning cuts hidden neurons, parameter sharing reuses one sub-network across antennas because all PAs share the same nonlinearity, and removing NN2 drops PA modeling when transmit power is low.

What would settle it

Run the two-stage algorithm on a THz hybrid beamforming testbed with real measured impairments (or on a simulator using a different PA model, such as a memory polynomial, and different phase-noise statistics) and compare the SER at 15 dBm with the reported 0.0005 for transmitter compensation; if the SER rises to a clearly higher level, the simulation-to-reality transfer claim fails.

Watch

Extended reading notes

Core claim

The paper argues that in a THz UM-MIMO hybrid beamforming system the aggregate distortion produced by nonideal DACs and ADCs, IQ imbalance, phase noise, imperfect phase shifters, and nonlinear power amplifiers can be represented accurately by a DNN whose sub-networks follow the physical signal path: one sub-network per transmit RF chain, one per transmit antenna, and one per receive RF chain. Trained on pairs of transmitted pilots and the corresponding received signals, this network acts as a differentiable surrogate for the nonideal link. A second neural network then uses that surrogate to optimize either the digital precoder at the transmitter or the digital combiner at the receiver, minimizing mean-square error to the ideal received signal. Reported results for a 256-antenna, 4-stream, 4-bit-converter system show transmitter compensation reaching SER 0.0018 at 10 dBm and 0.0005 at 15 dBm, clearly better than receiver compensation and than a direct fully connected DNN baseline, which suggests the structured architecture and the clean training inputs at the transmitter are what make the compensation effective.

Load-bearing premise

The load-bearing premise is that the simulation models used for training faithfully represent real THz hardware imperfections, because the paper generates all training data by simulation rather than from a real hybrid beamforming testbed, and if the actual phase noise, PA behavior, or quantization differs from the Gaussian, Rapp, and AQNM models, the reported SER gains may not transfer.

Editorial extensions

If this is right

If the claimed result holds, THz hardware-imperfection compensation becomes a data-driven baseband problem: collect pilot–received pairs, learn the distortion as a black box, and optimize a low-rank digital precoder or combiner against it.
Transmitter-side compensation is the preferred design point, because its network inputs are clean 16-QAM symbols, whereas receiver-side compensation must contend with noise entering the compensation network input.
Combining pruning, parameter sharing, and conditional removal of the PA sub-network yields a 97.2% parameter reduction and a 39.2% runtime reduction with nearly unchanged SER, making the scheme plausible for resource-constrained THz transceivers.
Below 5 dBm transmit power the PA nonlinearity is weak enough that the PA sub-network can be removed entirely; above that threshold it must be kept, giving a simple transmit-power-driven complexity control.
In a coded 16-QAM system with a rate-2/3 convolutional code, the slimmed networks still reach very low SER at 15 dBm and outperform the direct fully connected DNN baseline.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: the modular, signal-flow-matched architecture is why the method beats a generic fully connected DNN at high power; if so, the same modularity should transfer to other impairment sets, such as wideband beam squint or mutual coupling, by adding corresponding sub-networks.
Editorial inference: the strongest test of the paper's practical value is a hardware-transfer experiment; because the training data are simulated, a real THz testbed with measured impairments would reveal how much of the reported SER gain survives model mismatch.
Editorial inference: the learned surrogate could be reused beyond compensation, for example to monitor hardware aging or to supply gradients for model-based precoding design, since the DNN makes the distorted link differentiable with respect to baseband inputs.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here is my take. The genuinely new thing is the joint treatment of five THz hardware impairments in one hybrid-beamforming model and a DNN whose structure follows the signal chain, plus the three slimming tricks. That is a reasonable engineering contribution, and the reported 97.2% parameter reduction at small SER cost is internally consistent, not hand-wavy. The paper also does something right that many ML-for-comms papers skip: it reports convergence, uncoded and coded SER, and compares against a direct-DNN baseline. The impairment models are cited to relevant sources, and the slimming ablation is shown rather than just claimed.

The soft spot is load-bearing. In Sec. V.B, NNct is built from Lt independent sub-networks, each with two inputs and two outputs on a single stream. Such a network produces a diagonal mapping from s to s1, so FBB,c = s1 s^{-1} is diagonal, not a general Lt x Ns digital precoder. The compensation problem in (32) allows a full precoder; the implemented network cannot realize that. The reported SER numbers therefore depend on the effective channel/beamforming product being diagonal or nearly so for the single simulated realization. The paper never specifies the channel model, the beamformer design, or the diagonal dominance of that effective channel. That is a real gap, and it makes the conclusion that the algorithm "can effectively mitigate hardware imperfections" too broad for general THz hybrid beamforming. The stress-test note is right about this.

The second soft spot is the standard one: training and testing data both come from the paper's own simulator. The hardware models are reasonable and cited, but there is no external or measured validation. The authors are upfront about this in Sec. VII.A.2. That does not kill the paper, but it means the numbers are self-consistent rather than predictive of real hardware behavior.

Minor: training hyperparameters, the hidden-layer count, and the 5 dBm threshold for removing NN2 look post hoc. I would not call that fatal; the ablation is at least visible.

Who is this for? People building THz link-level simulators or prototyping baseband compensation schemes. It deserves a serious referee: the diagonal-vs-full precoding question needs to be settled, and the channel model needs disclosure, but the work is coherent and reproducible in principle. I would send it out and ask for those revisions. If the authors explicitly show that their setup is diagonalized, the results are useful. As it stands, I would not cite the general claim in my own work unless the scope is narrowed.

Referee Report

4 major / 6 minor

Summary. The paper studies a narrowband THz UM-MIMO hybrid-beamforming system with hardware imperfections at both the transmitter and receiver, including DAC/ADC quantization, IQ imbalance, phase noise, phase-shifter amplitude/phase errors, and PA nonlinearity. It proposes a two-stage deep-learning compensation scheme: stage 1 trains a modular DNN, built from per-RF-chain, per-antenna, and per-RF-chain sub-networks, to represent the combined impairments from pilot data; stage 2 trains either a transmitter-side NN (used in place of the digital precoder) or a receiver-side NN (used in place of the digital combiner) to minimize the MSE with respect to the ideal received signal. Three network-slimming methods are proposed and combined: reducing hidden-layer neurons, sharing parameters among the PA sub-networks, and removing the PA sub-network at low transmit power. Simulation results in uncoded and coded systems are reported to show that transmitter compensation outperforms receiver compensation and that the slimmed networks retain most of the compensation gain, with parameter reductions up to 97.2% and runtime reductions up to 39.2%.

Significance. If the central claim holds, the paper offers a practical data-driven alternative to per-imperfection calibration in THz systems: it treats the combined hardware impairments as a black box, uses a modular architecture whose parameter count is easy to analyze, and demonstrates substantial complexity reductions with explicit parameter and runtime tables. Strengths include the explicit consideration of a broad set of impairments, the coded-system evaluation, and a comparison against a direct-DNN baseline. However, the significance is conditional: the per-stream architecture of the transmitter compensation network, the absence of a specified channel and beamforming model, and the simulation-only training data all limit the generality of the demonstrated gains. The paper is a potentially useful contribution if these points are resolved or if the claims are appropriately restricted.

major comments (4)

[Sec. V.B, Eq. (51)] The transmitter-compensation network N Nct is built from Lt independent sub-NNs, each taking the real and imaginary parts of a single data stream as input and producing two outputs (Eq. (51)). Such a network implements a diagonal, memoryless, per-stream transformation and cannot represent a general digital precoder FBB,c in C^{Lt x Ns} that mixes the streams; the formula FBB,c = s1 s^{-1} is not a well-defined linear precoder when s1 is the output of a nonlinear network. Since the full-connected analog precoder FRF and the per-antenna PA nonlinearity in Eq. (24) create inter-stream coupling, this architecture cannot in general compensate the combined hardware imperfections of a hybrid-beamforming system. The reported SER gains in Figs. 7(c), 9, and 10 therefore rest on an unstated assumption that the effective ideal channel W_BB^H W_RF^H H F_RF P_in F_BB is diagonal, or nearly so, for the particular realization used. The authors should either redesign stage 2 to process all streams jointly or restrict the claim to a clearly specified diagonalized setup.
[Sec. VII.A] The simulation setup does not specify how H, FRF, WRF, FBB, and WBB are generated: no THz channel model, no beamformer design rule, and no number of channel realizations are given. The entire evaluation is performed on data produced by the authors' own simulation model (Sec. VII.A.2), with training and testing on a single fixed realization. Without the channel model and the effective-channel structure, the reader cannot determine whether the setup is representative of THz UM-MIMO or whether the per-stream compensation in Sec. V.B is adequate. The authors should report the channel model, the beamforming algorithm, the realized effective channel's off-diagonal strength, and results averaged over multiple channel realizations.
[Sec. VII.A.2] The training data are generated from the same simulation model that is used for testing, and the text explicitly notes that real THz hardware data are unavailable. The numerical results therefore demonstrate that the DNN can approximate and invert the particular simulated impairment model (AQNM quantization, Gaussian phase noise, Rapp PA, and the assumed phase-shifter error statistics), not that the method transfers to physical THz hardware if any of these models is inaccurate. The abstract and conclusion should qualify the claim to the simulated model, or the authors should add a mismatched-model robustness study, for example training under one PA or phase-noise parameter set and testing under another.
[Sec. V.A, Eqs. (45), (54), (58)] Phase noise and quantization noise are described as varying across symbols in the dataset generation (Sec. VII.A.2), but the DNNs in both stages are memoryless and have no input representing the instantaneous phase-noise or quantization realization. Under the MSE losses, such a network can only learn the conditional-mean deterministic distortion, not invert the symbol-varying random phase rotations. The paper should clarify that the compensation targets only the deterministic part of the impairments and should quantify the residual phase-noise and quantization floor; otherwise the claim that the algorithm 'can effectively mitigate the hardware imperfections' (abstract) is broader than what the architecture can achieve.

minor comments (6)

[Eq. (23b)] The term Γt2 x*2 should presumably be Γt2 x*1 or Γt2 (Pin x1)*; as written, x2 appears on the right-hand side of its own definition.
[Sec. V.A] The subscripts are inconsistent in the notation: for example, the network N N1 is described with 'lth r sub-NN' before Eq. (36), although the index should be the lth t sub-NN, and similar inconsistencies appear in the N N3 description.
[Sec. VI.A] What is called 'pruning' is actually a reduction of the number of hidden neurons before training, not pruning a trained network; renaming this to 'hidden-size reduction' or describing the pruning criterion would avoid confusion.
[Sec. VII.A.2] The training details are incomplete: learning rate, optimizer, batch size, number of epochs, initialization, and random seeds are not reported, which prevents reproduction of the convergence curves in Fig. 7(a) and of the SER results.
[Sec. VII.C.2] The signal ys is not defined in the text; the reader can infer that it is the noise-free received signal, but it should be stated explicitly.
[Table II and Abstract] The abstract's 'combined slimming methods' reduce parameters by 97.2%, but parameter sharing alone already reduces them by 96.6%; the incremental gain of the combination is small and should be described more carefully.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the DNN is trained and tested on held-out data from the same simulation model, and the compensation results follow from supervised training rather than from a self-referential derivation.

full rationale

The claimed derivation chain is not circular. Stage 1 trains a DNN to approximate the simulated imperfect end-to-end mapping of Eq. (27) using a held-out MSE objective; the fact that both training and test data are generated from the same simulation model makes the numerical study self-consistent rather than an independent hardware benchmark, but it does not make any result equivalent to its inputs by construction. The paper explicitly flags this limitation: "as it is challenging to obtain data from a real THz hybrid beamforming system with hardware imperfections, we generate the training data through simulation." Stage 2 trains a second network to minimize the MSE between the compensated received signal and the ideal received signal of Eq. (2), and the SER is then evaluated on a separate set of test symbols, not on the training symbols. The line "Since s1 = FBB,cs, the digital precoder for hardware compensation can be obtained by FBB,c = s1s−1" is an algebraic read-off from the trained network output rather than an independent prediction derived from that network; it may raise an architectural correctness concern about realizing a general digital precoder with per-stream sub-networks, but it is not a circular reduction of the central claim. The self-citations ([1], [4], [33]) support background or prior related work and are not load-bearing for the compensation result. The 5 dBm slimming threshold is selected from the curves in Fig. 9, which is model selection, not a circular prediction. Overall, the central claim is a supervised-learning/simulation claim with standard held-out evaluation, and no step reduces to its own inputs.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

The central claim rests on imported hardware impairment models from the literature (AQNM, Gaussian phase noise, IQ imbalance matrices, phase shifter error model, Rapp PA), on the unstated THz channel model, and on the architectural hypothesis that a single-hidden-layer MLP can represent the combined impairments. No new physical entities are introduced.

free parameters (3)

Hidden layer neuron count Nh = 10 (baseline); 8, 6, 4, 2 (pruned)
Chosen by hand as the default sub-NN width; pruning reduces it to trade parameter count against SER.
Transmit power threshold for NN2 removal = 5 dBm (SNR 7.95 dB)
Selected based on observed simulation behavior in Fig. 9; below this power the PA nonlinearity is treated as negligible and NN2 is removed.
Training data size per stage = 8000 symbols
Arbitrary but symmetric choice; no sensitivity analysis is provided.

assumptions (7)

domain assumption AQNM models DAC/ADC quantization as linear gain plus Gaussian noise (Eq. 5).
Imported from [9]; if real converters deviate, the learned compensation will be mismatched.
domain assumption Phase noise follows a Gaussian distribution with given variance (Sec. III-C).
Imported from [14]; used for both Tx and Rx oscillators.
domain assumption IQ imbalance is captured by diagonal gain/phase matrices (Eqs. 8-11).
Imported from [11], [12]; assumes frequency-independent imbalance per RF chain.
domain assumption Imperfect phase shifters introduce per-element amplitude and phase errors (Eqs. 14-15).
Imported from [35]; errors are fixed per manufacturing instance.
domain assumption PA nonlinearity follows the Rapp model with published parameters (Eqs. 18-19).
Imported from [18]; all PAs share the same characteristic.
domain assumption The THz channel is narrowband, known perfectly, and has few paths (Secs. II and VII).
The channel matrix H is assumed known for training and equalization, but its generation is not specified.
ad hoc to paper A single-hidden-layer MLP with Tanh can represent the combined hardware imperfections accurately (Sec. V-A).
This architectural hypothesis is validated only by fitting to the paper's own simulation data.

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Cite this review

Pith. "Pith review of DNN based Two-stage Compensation Algorithm for THz Hybrid Beamforming with imperfect Hardware." pith.science (2026). https://pith.science/paper/FD5GBR4D

@misc{pith2026241114699,
  author       = {Pith},
  title        = {Pith review of: DNN based Two-stage Compensation Algorithm for THz Hybrid Beamforming with imperfect Hardware},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FD5GBR4D}},
  note         = {Machine review of arXiv:2411.14699}
}

read the original abstract

Terahertz (THz) communication is envisioned as a key technology for 6G and beyond wireless systems owing to its multi-GHz bandwidth. To maintain the same aperture area and the same link budget as the lower frequencies, ultra-massive multi-input and multi-output (UM-MIMO) with hybrid beamforming is promising. Nevertheless, the hardware imperfections particularly at THz frequencies, can degrade spectral efficiency and lead to a high symbol error rate (SER), which is often overlooked yet imperative to address in practical THz communication systems. In this paper, the hybrid beamforming is investigated for THz UM-MIMO systems accounting for comprehensive hardware imperfections, including DAC and ADC quantization errors, in-phase and quadrature imbalance (IQ imbalance), phase noise, amplitude and phase error of imperfect phase shifters and power amplifier (PA) nonlinearity. Then, a two-stage hardware imperfection compensation algorithm is proposed. A deep neural network (DNN) is developed in the first stage to represent the combined hardware imperfections, while in the second stage, the digital precoder in the transmitter (Tx) or the combiner in the receiver (Rx) is designed using NN to effectively compensate for these imperfections. Furthermore, to balance the performance and network complexity, three slimming methods including pruning, parameter sharing, and removing parts of the network are proposed and combined to slim the DNN in the first stage. Numerical results show that the Tx compensation can perform better than the Rx compensation. Additionally, using the combined slimming methods can reduce parameters by 97.2% and running time by 39.2% while maintaining nearly the same performance in both uncoded and coded systems.

Figures

Figures reproduced from arXiv: 2411.14699 by the authors.

**Figure 2.** Constellations for different situations. (The red arrows indicate the distortion in the constellation points, illustrating the effects of expansion, [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** The structure of the proposed DNN in the first stage. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: The structure of the proposed NN in the second stage. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 6.** Figure 6: The SER performance of the system with ideal hardware, each [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 5.** Figure 5: Three methods of network slimming. A. Pruning Firstly, we calculate the number of the parameters in the sub-NN. From the input layer to the hidden layer, the numbers of the weight and bias parameters are 2Nh and Nh, respectively. From the hidden layer to the output la…

**Figure 7.** Figure 7: The performance of hardware imperfection compensation algorithm. [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 8.** Figure 8: The constellation of hardware imperfection compensation algorithm. [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

**Figure 9.** Figure 9: The performance of hardware imperfection compensation algorithm with different slimming methods. [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

**Figure 10.** Figure 10: The SER performance of the coded system with combined slimming [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Hardware Distortion Correlation Has Negligible Impact on UL Massive MIMO Spectral Efficiency,

E. Bj ¨ornson, L. Sanguinetti, and J. Hoydis, “Hardware Distortion Correlation Has Negligible Impact on UL Massive MIMO Spectral Efficiency,” IEEE Trans. Commun. , vol. 67, no. 2, pp. 1085–1098, Feb. 2019

2019
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Multiple Antenna Systems With Hardware Impairments: New Performance Limits,

S. Javed, O. Amin, S. S. Ikki, and M.-S. Alouini, “Multiple Antenna Systems With Hardware Impairments: New Performance Limits,” IEEE Trans. V eh. Technol., vol. 68, no. 2, pp. 1593–1606, Feb. 2019

2019
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Cell-Free Massive MIMO Systems With Non-Ideal Hardware: Phase Drifts and Distortion Noise,

Y . Zhang et al. , “Cell-Free Massive MIMO Systems With Non-Ideal Hardware: Phase Drifts and Distortion Noise,” IEEE Trans. V eh. Tech- nol., vol. 70, no. 11, pp. 11 604–11 618, Nov. 2021

2021
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On the MIMO capacity with residual transceiver hardware impairments,

X. Zhang et al. , “On the MIMO capacity with residual transceiver hardware impairments,” in Proc. of IEEE ICC , Jun. 2014, pp. 5299– 5305. 14

2014
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Joint Model and Data-Driven Receiver Design for Data- Dependent Superimposed Training Scheme With Imperfect Hardware,

C. Qing et al., “Joint Model and Data-Driven Receiver Design for Data- Dependent Superimposed Training Scheme With Imperfect Hardware,” IEEE Trans. Wirel. Commun. , vol. 21, no. 6, pp. 3779–3791, Jun. 2022

2022
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Composite Neural Network Digital Predistortion Model for Joint Mitigation of Crosstalk, I/Q Imbalance, Nonlinearity in MIMO Transmitters,

P. Jaraut, M. Rawat, and F. M. Ghannouchi, “Composite Neural Network Digital Predistortion Model for Joint Mitigation of Crosstalk, I/Q Imbalance, Nonlinearity in MIMO Transmitters,” IEEE Trans. Microw. Theory Techn., vol. 66, no. 11, pp. 5011–5020, Nov. 2018

2018
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Augmented Real-Valued Time-Delay Neural Network for Compensation of Distor- tions and Impairments in Wireless Transmitters,

D. Wang, M. Aziz, M. Helaoui, and F. M. Ghannouchi, “Augmented Real-Valued Time-Delay Neural Network for Compensation of Distor- tions and Impairments in Wireless Transmitters,” IEEE Trans. Neural Networks Learn. Syst. , vol. 30, no. 1, pp. 242–254, Jan. 2019

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Signal Detection in MIMO Systems With Hardware Imperfections: Message Passing on Neural Networks,

D. Gao, Q. Guo, G. Liao, Y . C. Eldar, Y . Li, Y . Yu, and B. Vucetic, “Signal Detection in MIMO Systems With Hardware Imperfections: Message Passing on Neural Networks,” IEEE Trans. Wireless Commun., vol. 23, no. 1, pp. 820–834, Jan. 2024

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Terahertz Wireless Channels: A Holistic Survey on Measurement, Modeling, and Analysis,

C. Han et al. , “Terahertz Wireless Channels: A Holistic Survey on Measurement, Modeling, and Analysis,” IEEE Commun. Surv. Tutorials, vol. 24, no. 3, pp. 1670–1707, Jun. 2022

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245-GHz LNA, Mixer, and Subharmonic Receiver in SiGe Technology,

Y . Mao et al. , “245-GHz LNA, Mixer, and Subharmonic Receiver in SiGe Technology,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 12, pp. 3823–3833, Dec. 2012

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A 220–320-GHz Vector-Sum Phase Shifter Using Single Gilbert-Cell Structure With Lossy Output Matching,

Y . Kim et al. , “A 220–320-GHz Vector-Sum Phase Shifter Using Single Gilbert-Cell Structure With Lossy Output Matching,”IEEE Trans. Microw. Theory Techn., vol. 63, no. 1, pp. 256–265, Dec. 2015

2015

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

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Dynamic Hybrid Beamforming for Terahertz Multi-User Ultra-Massive MIMO Systems with Imperfect Hardware,

W. Zhao, C. Han, H. Liu, and T. Yang, “Dynamic Hybrid Beamforming for Terahertz Multi-User Ultra-Massive MIMO Systems with Imperfect Hardware,” in Proc. of IEEE ICC , Jun. 2024, pp. 1819–1824

work page 2024

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Terahertz band: Next frontier for wireless commu- nications,

I. F. Akyildiz et al., “Terahertz band: Next frontier for wireless commu- nications,” Phys. Commun. , vol. 12, pp. 16–32, Sep. 2014

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Hybrid Precoding for Physical Layer Multi- casting,

M. Dai and B. Clerckx, “Hybrid Precoding for Physical Layer Multi- casting,” IEEE Commun. Lett. , vol. 20, no. 2, pp. 228–231, Feb. 2016

work page 2016

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A Dynamic Array-of-Subarrays Ar- chitecture and Hybrid Precoding Algorithms for Terahertz Wireless Communications,

L. Yan, C. Han, and J. Yuan, “A Dynamic Array-of-Subarrays Ar- chitecture and Hybrid Precoding Algorithms for Terahertz Wireless Communications,” IEEE J. Sel. Areas Commun. , vol. 38, no. 99, pp. 2041–2056, Sep. 2020

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Hybrid Digital and Analog Beamforming Design for Large-Scale Antenna Arrays,

F. Sohrabi and W. Yu, “Hybrid Digital and Analog Beamforming Design for Large-Scale Antenna Arrays,” IEEE J. Sel. Topics Signal Process. , vol. 10, no. 3, pp. 501–513, Apr. 2016

2016

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Terahertz Communications: Challenges in the Next Decade,

H.-J. Song and N. Lee, “Terahertz Communications: Challenges in the Next Decade,” IEEE Trans. Terahertz Sci. Technol. , vol. 12, no. 2, pp. 105–117, Mar. 2022

work page 2022

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Received Signal Modelling for Millimeter Wave and Terahertz Systems with Practical Impairments,

X. Huang, H. Zhang, A. T. Le, J. Andrew Zhang, and Y . Jay Guo, “Received Signal Modelling for Millimeter Wave and Terahertz Systems with Practical Impairments,” IEEE Trans. Commun., pp. 1–1, May 2024

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On the Spectral Efficiency of Massive MIMO Systems With Low-Resolution ADCs,

J. Zhang, L. Dai, S. Sun, and Z. Wang, “On the Spectral Efficiency of Massive MIMO Systems With Low-Resolution ADCs,” IEEE Commun. Lett., vol. 20, no. 5, pp. 842–845, May 2016

work page 2016