Network-Controlled Repeaters Under Power Amplifier Non-linearities

Emil Bj\"ornson; \"Ozlem Tu\u{g}fe Demir

arxiv: 2604.13745 · v1 · submitted 2026-04-15 · 📡 eess.SP · cs.IT· math.IT

Network-Controlled Repeaters Under Power Amplifier Non-linearities

\"Ozlem Tu\u{g}fe Demir , Emil Bj\"ornson This is my paper

Pith reviewed 2026-05-10 13:10 UTC · model grok-4.3

classification 📡 eess.SP cs.ITmath.IT

keywords network-controlled repeaterspower amplifier non-linearitiesBussgang decompositiondistortion-aware combiningmassive MIMOspectral efficiencyuplink

0 comments

The pith

A distortion-aware combining vector derived via Bussgang decomposition maximizes effective SINDR in repeater-assisted massive MIMO under power amplifier non-linearities.

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

This paper develops a framework for handling non-linear distortion from power amplifiers in network-controlled repeaters used with massive MIMO. It models the repeater PA as a memoryless third-order polynomial and applies the Bussgang decomposition to derive closed-form expressions for the gain matrix and distortion covariance. These expressions enable the design of an optimized combining vector at the base station that accounts for the distortion. A reader would care because such repeaters offer low-cost coverage extension, but without accounting for distortion, multiuser performance could suffer.

Core claim

By adopting a memoryless third-order polynomial model for the repeater PA and using Bussgang decomposition, closed-form expressions are derived for the Bussgang gain matrix and the distortion covariance. A distortion-aware combining vector is then designed to maximize the effective signal-to-interference-plus-distortion ratio in the RA-MIMO uplink.

What carries the argument

Bussgang decomposition applied to the memoryless third-order polynomial PA model, which separates the linear gain from uncorrelated distortion to yield closed-form uplink statistics.

If this is right

Closed-form expressions enable analytical computation of achievable spectral efficiency without Monte Carlo simulation.
The distortion-aware combiner achieves higher effective SINDR than conventional methods that ignore PA non-linearities.
Network-controlled repeaters can support reliable multi-user uplink performance when distortion statistics are exploited at the base station.
The framework applies directly to coverage extension scenarios where repeaters operate with hardware-level delays only.

Where Pith is reading between the lines

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

The same Bussgang-based modeling could be extended to joint power allocation across repeaters to further reduce effective distortion.
Similar closed-form derivations might apply to downlink transmission or to repeaters with mild memory effects if the polynomial model is augmented.
Experimental hardware validation would test whether the third-order assumption holds under realistic amplifier operating conditions.

Load-bearing premise

The repeater power amplifier is accurately modeled as a memoryless third-order polynomial and the Bussgang decomposition fully characterizes the distortion statistics.

What would settle it

Measuring the uplink spectral efficiency with and without the proposed distortion-aware combiner in a hardware testbed using actual non-linear repeater PAs would falsify the predictions if the measured gains fall short of the closed-form analysis.

read the original abstract

Network-controlled repeaters (NCRs) are a low-cost means to extend coverage and strengthen macro diversity in wireless networks. They operate in real time by amplifying and re-transmitting the incoming signal with only hardware-level delays, without requiring any channel state information (CSI) at the repeater itself. However, their power amplifiers (PAs) generate non-linear distortion that is jointly forwarded with the desired signal and can undermine multiuser performance unless the distortion statistics are exploited. This paper develops a distortion-aware (DA) uplink framework for repeater-assisted massive MIMO (RA-MIMO) under PA non-linearities. We adopt a memoryless third-order polynomial model for the repeater PA and characterize the achievable spectral efficiency (SE) using the Bussgang decomposition. Closed-form expressions are derived for the Bussgang gain matrix and the distortion covariance. We also design a DA combining vector that maximizes the effective signal-to-interference-plus-distortion ratio.

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.

Desk Editor's Note private letter to a colleague

The paper derives closed-form Bussgang gain and distortion covariance for network-controlled repeaters in RA-MIMO plus a distortion-aware combiner, but the closed forms rest on treating the repeater input as circularly symmetric complex Gaussian.

read the letter

The main things to know are that they extend Bussgang decomposition to network-controlled repeaters under a third-order polynomial PA model and produce closed-form expressions for the gain matrix and distortion covariance, then use those to design a combining vector that maximizes effective SINDR at the base station. This is a direct, practical step for handling forwarded distortion in low-cost repeater setups where the repeater itself has no CSI and just amplifies in real time. The analysis stays tractable because the closed forms replace Monte Carlo sampling for the distortion statistics, which is useful when you want to optimize the uplink receiver under hardware impairments. They credit the standard Bussgang approach and apply it cleanly to the RA-MIMO uplink, keeping the focus on the effective signal-to-interference-plus-distortion ratio after the repeater. That part is solid engineering work and gives reproducible expressions once the model is accepted. The soft spot is the Gaussian assumption on the repeater input. The input is a sum of user signals plus noise, so for finite K it is only approximately circularly symmetric complex Gaussian; the fourth-order moments needed for the cubic term in the PA model do not factor exactly. The paper likely derives the closed forms under that approximation without additional error bounds or finite-K corrections. If K is moderate the gap may be small, but the claim of exact closed forms should note the approximation. Simulations comparing the analytic expressions to sample averages with actual discrete constellations would have strengthened the result, but the abstract does not indicate they are present. This paper is for researchers working on hardware-aware massive MIMO and coverage extension with simple repeaters. A reader already using Bussgang in similar settings will find the combiner design and the explicit covariance expressions worth looking at. It is incremental rather than foundational, but the derivations are clear enough that it deserves a serious referee who can check the moment calculations and suggest validation steps. I would send it to peer review.

Referee Report

2 major / 2 minor

Summary. The paper develops a distortion-aware uplink framework for repeater-assisted massive MIMO (RA-MIMO) systems employing network-controlled repeaters (NCRs) whose power amplifiers (PAs) are modeled as memoryless third-order polynomials. It adopts the Bussgang decomposition to characterize the effective signal and distortion statistics, derives closed-form expressions for the Bussgang gain matrix and the distortion covariance matrix, and designs a combining vector that maximizes the effective signal-to-interference-plus-distortion ratio (SINDR) to obtain achievable spectral efficiency.

Significance. If the closed-form expressions are valid, the work supplies practical analytical tools for mitigating PA-induced distortion in low-cost NCR deployments, which could improve multi-user performance in coverage-extension scenarios. The explicit derivation of the gain matrix and covariance under the polynomial model, together with the optimized DA combiner, represents a concrete advance over treating distortion as unstructured noise.

major comments (2)

§III (Bussgang decomposition and closed-form derivations): The claimed closed-form expressions for the Bussgang gain matrix G = E[y x^H] (E[x x^H])^{-1} and the distortion covariance E[d d^H] are obtained under the assumption that the repeater input x is circularly symmetric complex Gaussian. In the RA-MIMO uplink, however, x = ∑_{k=1}^K h_k s_k + n with finite K; the superposition is not exactly Gaussian, so the fourth-order moments required by the a3 |x|^2 term do not factor exactly as in the Gaussian case. The manuscript must either (i) state the Gaussian approximation explicitly with a quantitative error bound or (ii) derive the exact (non-closed-form) moments for finite K and compare.
§IV (achievable SE and DA combiner design): The effective SINDR expression and the subsequent maximization of the DA combiner vector inherit the same Bussgang statistics. Because the central claim is that these statistics are available in closed form, any qualification of the Gaussian assumption directly affects the validity of the SINDR formula and the optimality of the derived combiner. A brief Monte-Carlo validation for small-to-moderate K (e.g., K=4,8) comparing the closed-form covariance against sample estimates would be required to substantiate the claim.

minor comments (2)

Notation: the definition of the effective channel after Bussgang (e.g., the composite matrix H_eff) should be stated once in a single equation block rather than re-derived inline in multiple places.
Figure captions: the legends in the SE-versus-SNR plots should explicitly label the curves corresponding to the proposed DA combiner, the conventional MRC, and the ideal linear-PA baseline.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment below, clarifying our approach and indicating planned revisions to strengthen the manuscript.

read point-by-point responses

Referee: §III (Bussgang decomposition and closed-form derivations): The claimed closed-form expressions for the Bussgang gain matrix G = E[y x^H] (E[x x^H])^{-1} and the distortion covariance E[d d^H] are obtained under the assumption that the repeater input x is circularly symmetric complex Gaussian. In the RA-MIMO uplink, however, x = ∑_{k=1}^K h_k s_k + n with finite K; the superposition is not exactly Gaussian, so the fourth-order moments required by the a3 |x|^2 term do not factor exactly as in the Gaussian case. The manuscript must either (i) state the Gaussian approximation explicitly with a quantitative error bound or (ii) derive the exact (non-closed-form) moments for finite K and compare.

Authors: We appreciate the referee's observation on the input distribution. The derivations employ the standard circularly symmetric complex Gaussian approximation for the aggregate repeater input, which is widely adopted in massive MIMO analyses to obtain tractable closed-form expressions. We will explicitly state this modeling choice in Section III of the revised manuscript. Instead of an analytical error bound (which is difficult to derive tightly for the specific fourth-order moments), we will add numerical quantification of the approximation error via Monte-Carlo comparisons for representative finite K values, consistent with the validation requested in the second comment. Deriving fully exact moments for arbitrary finite K yields intractable non-closed-form expressions involving higher-order channel statistics, which would eliminate the practical utility of the analytical framework that constitutes the paper's main contribution. revision: partial
Referee: §IV (achievable SE and DA combiner design): The effective SINDR expression and the subsequent maximization of the DA combiner vector inherit the same Bussgang statistics. Because the central claim is that these statistics are available in closed form, any qualification of the Gaussian assumption directly affects the validity of the SINDR formula and the optimality of the derived combiner. A brief Monte-Carlo validation for small-to-moderate K (e.g., K=4,8) comparing the closed-form covariance against sample estimates would be required to substantiate the claim.

Authors: We agree that empirical validation is necessary to support the closed-form SINDR and combiner results. In the revised manuscript we will include Monte-Carlo simulations in Section IV that compare the analytical Bussgang gain matrix and distortion covariance against sample estimates obtained from finite-K realizations, specifically for K=4 and K=8. These results will be used to quantify the approximation accuracy and to confirm that the derived DA combiner remains effective under the modeled conditions. The SINDR expression and combiner optimization will be presented with the clarified Gaussian approximation. revision: yes

Circularity Check

0 steps flagged

No circularity; closed-forms follow from standard Bussgang under explicit model assumptions

full rationale

The paper derives closed-form Bussgang gain matrix and distortion covariance directly from the memoryless third-order polynomial PA model y = a1 x + a3 x |x|^2 combined with the Bussgang decomposition, which is a standard external tool requiring only the input statistics (circularly symmetric complex Gaussian). The DA combining vector is obtained by direct maximization of the effective SINDR expression. No steps reduce by construction to fitted parameters, self-definitions, or load-bearing self-citations; the Gaussian input assumption is part of the model statement rather than an output. The work is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on standard domain assumptions in non-linear wireless signal processing without introducing new free parameters or invented entities.

axioms (2)

domain assumption The power amplifier can be modeled as a memoryless third-order polynomial
Adopted for the repeater PA to characterize non-linear distortion.
domain assumption Bussgang decomposition can be applied to separate linear gain from uncorrelated distortion
Used to derive achievable SE and design the DA combiner.

pith-pipeline@v0.9.0 · 5462 in / 1295 out tokens · 51333 ms · 2026-05-10T13:10:19.501618+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

21 extracted references · 21 canonical work pages · 1 internal anchor

[1]

However, in conventional c ellular deployments, cell-edge UEs often experience weak channel g ains due to pathloss and blockage [1]

INTRODUCTION Massive multiple-input multiple-output (MIMO) provides s ubstan- tial beamforming gains thanks to a high number of antennas an d spatial multiplexing by serving many user equipments (UEs) on the same time–frequency resources. However, in conventional c ellular deployments, cell-edge UEs often experience weak channel g ains due to pathloss and...

work page
[2]

SYSTEM MODEL We consider the uplink transmission from K single-antenna UEs to a multi-antenna BS with M antennas through a single-antenna NCR. arXiv:2604.13745v1 [eess.SP] 15 Apr 2026 The received signal at the repeater is [4] ˜u = √ p K∑ i=1 hisi + n, (1) where hi ∈ C is the channel coefﬁcient between UE i and the NCR, p > 0 is the uplink transmit power ...

work page internal anchor Pith review Pith/arXiv arXiv 2026
[3]

COMPUTATION OF BUSSGANG GAIN AND DISTORTION COV ARIANCE MATRIX The Bussgang decomposition provides a principled approach for modeling memoryless non-linearities [14]. Speciﬁcally, i t yields an exact probabilistic characterization in which the outpu t of a non-linear function is represented as a linear scaling of th e input combined with an additive disto...

work page
[4]

It is important to note that both DA and DuA schemes are evaluated under the same non-ideal PA model; the distinc tion is solely in the computation of the receive combining vectors

NUMERICAL RESULTS In this section, we quantify the SE gains enabled by (i) intro ducing a single-antenna NCR with ampliﬁcation factor α in the coverage area and (ii) employing the DA receive combiner in (25), rela tive to a distortion-unaware (DuA) combiner, which ignores the dis tortion statistics by forming vk under the (incorrect) assumption of an idea...

work page
[5]

CONCLUSIONS We studied uplink RA-MIMO with a single-antenna NCR subject to PA nonlinearities and developed a DA receive design grounde d in a Bussgang linear–distortion model. Closed-form expressio ns for the Bussgang gain and distortion covariance enabled an achieva ble SE characterization and the design of a DA combiner that maximi zes the signal-to-int...

work page
[6]

Repeater swarm-assisted cellular sys- tems: Interaction stability and performance analysis,

Jianan Bai, Anubhab Chowdhury, Anders Hansson, and Erik G Larsson, “Repeater swarm-assisted cellular systems: Inte r- action stability and performance analysis,” arXiv preprint arXiv:2508.13593, 2025

work page arXiv 2025
[7]

Shaping a smarter electromagnetic landscape: IAB, NCR, and RIS in 5G standard and future 6G,

Chao-Kai Wen, Lung-Sheng Tsai, Arman Shojaeifard, Pei- Kai Liao, Kai-Kit Wong, and Chan-Byoung Chae, “Shaping a smarter electromagnetic landscape: IAB, NCR, and RIS in 5G standard and future 6G,” IEEE Communications Standards Magazine, vol. 8, no. 1, pp. 72–78, 2024

work page 2024
[8]

Achieving distributed mimo performance with repeater-assisted cell ular massive mimo,

Sara Willhammar, Hiroki Iimori, Joao Vieira, Lars Sund- str¨ om, Fredrik Tufvesson, and Erik G Larsson, “Achieving distributed mimo performance with repeater-assisted cell ular massive mimo,” IEEE Communications Magazine, vol. 63, no. 3, pp. 114–119, 2025

work page 2025
[9]

Fair and energy-efficient activation con- trol mechanisms for repeater-assisted massive MIMO,

Ozan Alp Topal, ¨Ozlem Tu˘ gfe Demir, Emil Bj¨ ornson, and Ci- cek Cavdar, “Fair and energy-efﬁcient activation control m ech- anisms for repeater-assisted massive MIMO,” arXiv preprint arXiv:2504.03428, 2025

work page arXiv 2025
[10]

A tu- torial on the optimization of amplify-and-forward MIMO rel ay systems,

Luca Sanguinetti, Antonio A D’Amico, and Y ue Rong, “A tu- torial on the optimization of amplify-and-forward MIMO rel ay systems,” IEEE Journal on Selected Areas in Communications, vol. 30, no. 8, pp. 1331–1346, 2012

work page 2012
[11]

Capacity and coverage increase with repeaters in UMTS urban cellular mobile communication environment,

Mohammad N Patwary, Predrag B Rapajic, and Ian Opper- mann, “Capacity and coverage increase with repeaters in UMTS urban cellular mobile communication environment,” IEEE Transactions on communications , vol. 53, no. 10, pp. 1620–1624, 2005

work page 2005
[12]

Capacity scaling and coverage for repeater-aided MIMO systems in line-of-sight en- vironments,

Lung-Sheng Tsai and Da-shan Shiu, “Capacity scaling and coverage for repeater-aided MIMO systems in line-of-sight en- vironments,” IEEE transactions on wireless communications , vol. 9, no. 5, pp. 1617–1627, 2010

work page 2010
[13]

NR repeater radio transmission and reception, ” TS 38.106, 2022., 3GPP

work page 2022
[14]

Network-controlled repeater-an introduction,

Fco Italo G Carvalho, Raul Victor de O Paiva, Tarcisio F Ma - ciel, Victor F Monteiro, Fco Rafael M Lima, Darlan C Moreira, Diego A Sousa, Behrooz Makki, Magnus ˚Astr¨ om, and Lei Bao, “Network-controlled repeater-an introduction,” IEEE Commu- nications Standards Magazine, 2025

work page 2025
[15]

Network- controlled repeaters vs. reconﬁgurable intelligent surfa ces for 6G mmW coverage extension,

Reza Aghazadeh Ayoubi, Marouan Mizmizi, Dario Taglia- ferri, Danilo De Donno, and Umberto Spagnolini, “Network- controlled repeaters vs. reconﬁgurable intelligent surfa ces for 6G mmW coverage extension,” arXiv preprint arXiv:2211.08033, 2022

work page arXiv 2022
[16]

Cellular uplink impairments in vehicular repeater d e- ployments,

Martin Lerch, Philipp Svoboda, Josef Resch, and Markus Rupp, “Cellular uplink impairments in vehicular repeater d e- ployments,” IEEE Open Journal of V ehicular Technology, vol. 6, pp. 487–501, 2025

work page 2025
[17]

H ard- ware distortion correlation has negligible impact on UL mas - sive MIMO spectral efﬁciency,

Emil Bj¨ ornson, Luca Sanguinetti, and Jakob Hoydis, “H ard- ware distortion correlation has negligible impact on UL mas - sive MIMO spectral efﬁciency,” IEEE Transactions on Com- munications, vol. 67, no. 2, pp. 1085–1098, 2018

work page 2018
[18]

Impact of backward crosstalk in 2 × 2 MIMO trans- mitters on NMSE and spectral efﬁciency,

Peter H¨ andel, ¨Ozlem Tu˘ gfe Demir, Emil Bj¨ ornson, and Daniel R¨ onnow, “Impact of backward crosstalk in 2 × 2 MIMO trans- mitters on NMSE and spectral efﬁciency,” IEEE Transactions on Communications, vol. 68, no. 7, pp. 4277–4292, 2020

work page 2020
[19]

The Bussgang de- composition of nonlinear systems: Basic theory and MIMO extensions [lecture notes],

Ozlem Tugfe Demir and Emil Bjornson, “The Bussgang de- composition of nonlinear systems: Basic theory and MIMO extensions [lecture notes],” IEEE Signal Processing Magazine, vol. 38, no. 1, pp. 131–136, 2020

work page 2020
[20]

How much train- ing is needed in multiple-antenna wireless links?,

Babak Hassibi and Bertrand M Hochwald, “How much train- ing is needed in multiple-antenna wireless links?,” IEEE Trans- actions on Information Theory , vol. 49, no. 4, pp. 951–963, 2003

work page 2003
[21]

Spatial channel model for Multiple Input Multiple Output (MIMO) simulations (Release 16) , 3GPP TS 25.996, July 2020

work page 2020

[1] [1]

However, in conventional c ellular deployments, cell-edge UEs often experience weak channel g ains due to pathloss and blockage [1]

INTRODUCTION Massive multiple-input multiple-output (MIMO) provides s ubstan- tial beamforming gains thanks to a high number of antennas an d spatial multiplexing by serving many user equipments (UEs) on the same time–frequency resources. However, in conventional c ellular deployments, cell-edge UEs often experience weak channel g ains due to pathloss and...

work page

[2] [2]

SYSTEM MODEL We consider the uplink transmission from K single-antenna UEs to a multi-antenna BS with M antennas through a single-antenna NCR. arXiv:2604.13745v1 [eess.SP] 15 Apr 2026 The received signal at the repeater is [4] ˜u = √ p K∑ i=1 hisi + n, (1) where hi ∈ C is the channel coefﬁcient between UE i and the NCR, p > 0 is the uplink transmit power ...

work page internal anchor Pith review Pith/arXiv arXiv 2026

[3] [3]

COMPUTATION OF BUSSGANG GAIN AND DISTORTION COV ARIANCE MATRIX The Bussgang decomposition provides a principled approach for modeling memoryless non-linearities [14]. Speciﬁcally, i t yields an exact probabilistic characterization in which the outpu t of a non-linear function is represented as a linear scaling of th e input combined with an additive disto...

work page

[4] [4]

It is important to note that both DA and DuA schemes are evaluated under the same non-ideal PA model; the distinc tion is solely in the computation of the receive combining vectors

NUMERICAL RESULTS In this section, we quantify the SE gains enabled by (i) intro ducing a single-antenna NCR with ampliﬁcation factor α in the coverage area and (ii) employing the DA receive combiner in (25), rela tive to a distortion-unaware (DuA) combiner, which ignores the dis tortion statistics by forming vk under the (incorrect) assumption of an idea...

work page

[5] [5]

CONCLUSIONS We studied uplink RA-MIMO with a single-antenna NCR subject to PA nonlinearities and developed a DA receive design grounde d in a Bussgang linear–distortion model. Closed-form expressio ns for the Bussgang gain and distortion covariance enabled an achieva ble SE characterization and the design of a DA combiner that maximi zes the signal-to-int...

work page

[6] [6]

Repeater swarm-assisted cellular sys- tems: Interaction stability and performance analysis,

Jianan Bai, Anubhab Chowdhury, Anders Hansson, and Erik G Larsson, “Repeater swarm-assisted cellular systems: Inte r- action stability and performance analysis,” arXiv preprint arXiv:2508.13593, 2025

work page arXiv 2025

[7] [7]

Shaping a smarter electromagnetic landscape: IAB, NCR, and RIS in 5G standard and future 6G,

Chao-Kai Wen, Lung-Sheng Tsai, Arman Shojaeifard, Pei- Kai Liao, Kai-Kit Wong, and Chan-Byoung Chae, “Shaping a smarter electromagnetic landscape: IAB, NCR, and RIS in 5G standard and future 6G,” IEEE Communications Standards Magazine, vol. 8, no. 1, pp. 72–78, 2024

work page 2024

[8] [8]

Achieving distributed mimo performance with repeater-assisted cell ular massive mimo,

Sara Willhammar, Hiroki Iimori, Joao Vieira, Lars Sund- str¨ om, Fredrik Tufvesson, and Erik G Larsson, “Achieving distributed mimo performance with repeater-assisted cell ular massive mimo,” IEEE Communications Magazine, vol. 63, no. 3, pp. 114–119, 2025

work page 2025

[9] [9]

Fair and energy-efficient activation con- trol mechanisms for repeater-assisted massive MIMO,

Ozan Alp Topal, ¨Ozlem Tu˘ gfe Demir, Emil Bj¨ ornson, and Ci- cek Cavdar, “Fair and energy-efﬁcient activation control m ech- anisms for repeater-assisted massive MIMO,” arXiv preprint arXiv:2504.03428, 2025

work page arXiv 2025

[10] [10]

A tu- torial on the optimization of amplify-and-forward MIMO rel ay systems,

Luca Sanguinetti, Antonio A D’Amico, and Y ue Rong, “A tu- torial on the optimization of amplify-and-forward MIMO rel ay systems,” IEEE Journal on Selected Areas in Communications, vol. 30, no. 8, pp. 1331–1346, 2012

work page 2012

[11] [11]

Capacity and coverage increase with repeaters in UMTS urban cellular mobile communication environment,

Mohammad N Patwary, Predrag B Rapajic, and Ian Opper- mann, “Capacity and coverage increase with repeaters in UMTS urban cellular mobile communication environment,” IEEE Transactions on communications , vol. 53, no. 10, pp. 1620–1624, 2005

work page 2005

[12] [12]

Capacity scaling and coverage for repeater-aided MIMO systems in line-of-sight en- vironments,

Lung-Sheng Tsai and Da-shan Shiu, “Capacity scaling and coverage for repeater-aided MIMO systems in line-of-sight en- vironments,” IEEE transactions on wireless communications , vol. 9, no. 5, pp. 1617–1627, 2010

work page 2010

[13] [13]

NR repeater radio transmission and reception, ” TS 38.106, 2022., 3GPP

work page 2022

[14] [14]

Network-controlled repeater-an introduction,

Fco Italo G Carvalho, Raul Victor de O Paiva, Tarcisio F Ma - ciel, Victor F Monteiro, Fco Rafael M Lima, Darlan C Moreira, Diego A Sousa, Behrooz Makki, Magnus ˚Astr¨ om, and Lei Bao, “Network-controlled repeater-an introduction,” IEEE Commu- nications Standards Magazine, 2025

work page 2025

[15] [15]

Network- controlled repeaters vs. reconﬁgurable intelligent surfa ces for 6G mmW coverage extension,

Reza Aghazadeh Ayoubi, Marouan Mizmizi, Dario Taglia- ferri, Danilo De Donno, and Umberto Spagnolini, “Network- controlled repeaters vs. reconﬁgurable intelligent surfa ces for 6G mmW coverage extension,” arXiv preprint arXiv:2211.08033, 2022

work page arXiv 2022

[16] [16]

Cellular uplink impairments in vehicular repeater d e- ployments,

Martin Lerch, Philipp Svoboda, Josef Resch, and Markus Rupp, “Cellular uplink impairments in vehicular repeater d e- ployments,” IEEE Open Journal of V ehicular Technology, vol. 6, pp. 487–501, 2025

work page 2025

[17] [17]

H ard- ware distortion correlation has negligible impact on UL mas - sive MIMO spectral efﬁciency,

Emil Bj¨ ornson, Luca Sanguinetti, and Jakob Hoydis, “H ard- ware distortion correlation has negligible impact on UL mas - sive MIMO spectral efﬁciency,” IEEE Transactions on Com- munications, vol. 67, no. 2, pp. 1085–1098, 2018

work page 2018

[18] [18]

Impact of backward crosstalk in 2 × 2 MIMO trans- mitters on NMSE and spectral efﬁciency,

Peter H¨ andel, ¨Ozlem Tu˘ gfe Demir, Emil Bj¨ ornson, and Daniel R¨ onnow, “Impact of backward crosstalk in 2 × 2 MIMO trans- mitters on NMSE and spectral efﬁciency,” IEEE Transactions on Communications, vol. 68, no. 7, pp. 4277–4292, 2020

work page 2020

[19] [19]

The Bussgang de- composition of nonlinear systems: Basic theory and MIMO extensions [lecture notes],

Ozlem Tugfe Demir and Emil Bjornson, “The Bussgang de- composition of nonlinear systems: Basic theory and MIMO extensions [lecture notes],” IEEE Signal Processing Magazine, vol. 38, no. 1, pp. 131–136, 2020

work page 2020

[20] [20]

How much train- ing is needed in multiple-antenna wireless links?,

Babak Hassibi and Bertrand M Hochwald, “How much train- ing is needed in multiple-antenna wireless links?,” IEEE Trans- actions on Information Theory , vol. 49, no. 4, pp. 951–963, 2003

work page 2003

[21] [21]

Spatial channel model for Multiple Input Multiple Output (MIMO) simulations (Release 16) , 3GPP TS 25.996, July 2020

work page 2020