pith. sign in

arxiv: 2604.13917 · v1 · submitted 2026-04-15 · 📡 eess.SP

Energy-Efficient Mobile Communications using an Adaptive Gearbox-PHY under Hardware Constraints

Pith reviewed 2026-05-10 12:40 UTC · model grok-4.3

classification 📡 eess.SP
keywords energy efficiencymobile communicationsphysical layer designadaptive modulationhardware impairmentsphase noisequantizationenergy per bit
0
0 comments X

The pith

The Gearbox-PHY architecture achieves energy savings up to two orders of magnitude by dynamically switching modulation schemes and analog front ends to match low data rates under hardware constraints.

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

Future mobile networks must handle growing traffic while typical operation occurs at low data rates, yet physical layer designs often prioritize peak performance. The Gearbox-PHY adapts by switching between modulation schemes and their associated analog front ends to minimize energy per bit. It jointly models front-end power consumption with hardware-aware spectral efficiency, incorporating phase noise and limited quantizer resolution as impairments that create trade-offs between complexity, non-linearities, and efficiency. This matters because low-rate regimes dominate network traffic, so hardware adaptation can reduce overall energy use without compromising peak capability. Numerical results confirm substantial savings that hold in cellular scenarios with spatially distributed users.

Core claim

The paper formulates an energy-per-bit minimization problem using a joint model of front-end power consumption and hardware-aware spectral efficiency. Non-ideal hardware effects including oscillator phase noise and limited quantizer resolution are incorporated; these impairments affect both power consumption and achievable spectral efficiency and thereby introduce trade-offs between front-end complexity, hardware non-linearities, spectral efficiency, and energy efficiency. Numerical results demonstrate that the Gearbox-PHY enables significant energy savings, particularly at low data rates, with gains of up to two orders of magnitude persisting in a cellular deployment scenario with spatially

What carries the argument

The Gearbox-PHY, an adaptive physical layer architecture that dynamically switches between modulation schemes and their associated analog front ends to adapt to varying operating requirements.

If this is right

  • Energy efficiency improves most in the low data rate regimes that dominate typical network operation.
  • Gains of up to two orders of magnitude remain achievable after including phase noise and quantization effects.
  • The approach introduces explicit trade-offs between front-end complexity and achievable spectral efficiency.
  • Savings persist across cellular deployments with spatially distributed users.

Where Pith is reading between the lines

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

  • Base stations could incorporate multiple parallel front-end chains instead of over-provisioning for peak rates alone.
  • Similar rate-adaptive hardware strategies may extend to low-duty-cycle systems such as sensor networks or satellite links.
  • If mode-switching energy is negligible, network-level power scaling could improve further as traffic patterns evolve.

Load-bearing premise

The joint model of front-end power consumption and hardware-aware spectral efficiency accurately represents real hardware without unmodeled switching overhead or implementation penalties.

What would settle it

A hardware prototype measurement that shows actual energy-per-bit savings fall below one order of magnitude at low rates due to switching overhead or unaccounted power draws would falsify the numerical claims.

Figures

Figures reproduced from arXiv: 2604.13917 by Florian Gast, Gerhard Fettweis, Meik D\"orpinghaus.

Figure 1
Figure 1. Figure 1: Energy consumption breakdown of a typical mobile operator (data from [11] and [12]). tion, mobile networks face a traffic challenge. Firstly, data traffic is expected to grow by one to two orders of magnitude in the upcoming ten years [13], [14], which will further ex￾acerbate energy demands unless mitigated by major efficiency improvements. Secondly, traffic loads vary significantly over time and space, w… view at source ↗
Figure 2
Figure 2. Figure 2: Assumed Transceiver Architectures [2] where θ(t) represents the phase noise, and η(t) is circu￾larly symmetric additive white Gaussian noise (AWGN) with variance σ 2 η = N0B. Here N0 = kΓ is the thermal noise power spectral density (PSD) with Boltzmann constant k and temperature Γ. At the receiver, the signal is filtered by hRx(t), yielding w(t) = r(t) ∗ hRx(t), and subsequently sampled at rate MRx/TNyq an… view at source ↗
Figure 3
Figure 3. Figure 3: Exemplary PSDs for σ 2 J = 0.1, K0 = −125 dBc/Hz, ADC bits bADC = 10, κ = 2, bandwidth B = 400 MHz, pilot spacing F = 10 [2] It is not intuitively clear whether (28) holds for the extreme case of 1-bit quantization. However, as shown in [58], estima￾tors using 1-bit samples [54], [59] can achieve the Bayesian Cramer-Rao lower bound, though based on a block-based ´ model with pilot and data segments. Still,… view at source ↗
Figure 4
Figure 4. Figure 4: Spectral efficiency of exemplary modulation schemes [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Results of design-time numerical energy efficiency optimization. [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Results of energy efficiency optimization for fixed front ends. [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Weighted savings of Gearbox-PHY over cell with minimum distance [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
read the original abstract

Future mobile networks must achieve substantial improvements in energy efficiency to offset the anticipated traffic growth. Despite this requirement, many discussions regarding physical layer design remain primarily focused on peak data rates and spectral efficiency, even though typical network operation is dominated by low-data-rate regimes. To address this mismatch, the Gearbox-PHY was proposed as an energy-efficient physical layer architecture that dynamically switches between modulation schemes and their associated analog front ends in order to adapt to varying operating requirements. This paper quantifies the achievable energy savings by jointly modeling front end power consumption and hardware-aware spectral efficiency to formulate an energy-per-bit minimization problem. To move beyond idealized assumptions, non-ideal hardware effects, including oscillator phase noise and limited quantizer resolution, are incorporated. These impairments simultaneously affect power consumption and achievable spectral efficiency, thereby introducing trade-offs between front end complexity, hardware non-linearities, spectral efficiency, and energy efficiency. Numerical results demonstrate that the Gearbox-PHY enables significant energy savings, particularly at low data rates. Evaluations with spatially distributed users confirm that gains of up to two orders of magnitude persist in a cellular deployment scenario.

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 / 1 minor

Summary. The manuscript proposes the Gearbox-PHY as an adaptive physical-layer architecture that dynamically switches between modulation schemes and associated analog front-ends to improve energy efficiency in mobile networks, especially under low-data-rate conditions. It formulates an energy-per-bit minimization problem by jointly modeling front-end power consumption with hardware-aware spectral efficiency, incorporating non-ideal effects such as oscillator phase noise and finite quantizer resolution. Numerical evaluations are presented to quantify the resulting energy savings, with claims of up to two orders of magnitude improvement in a cellular deployment scenario involving spatially distributed users.

Significance. If the underlying power and spectral-efficiency model proves accurate, the adaptive hardware-complexity approach could meaningfully advance energy-efficient PHY design for future networks where low-rate traffic dominates. The explicit treatment of hardware impairments introduces realistic trade-offs between front-end complexity, non-linearities, and efficiency that are often omitted in idealized analyses.

major comments (1)
  1. [Numerical results and cellular evaluation sections] The central energy-savings claims (up to 100x) rest on the joint front-end power and hardware-aware SE model. The formulation does not appear to include dynamic reconfiguration energy, transient settling times, or implementation penalties; if these are omitted, the reported gains at low rates become an upper bound rather than a realizable figure. This directly affects the load-bearing numerical results.
minor comments (1)
  1. [Abstract] The abstract would benefit from a brief statement of the key parameter values, simulation assumptions, or error-bar reporting used in the numerical results.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and for identifying a key modeling assumption in our analysis. We address the major comment below and describe the planned revisions.

read point-by-point responses
  1. Referee: [Numerical results and cellular evaluation sections] The central energy-savings claims (up to 100x) rest on the joint front-end power and hardware-aware SE model. The formulation does not appear to include dynamic reconfiguration energy, transient settling times, or implementation penalties; if these are omitted, the reported gains at low rates become an upper bound rather than a realizable figure. This directly affects the load-bearing numerical results.

    Authors: We agree with the referee that the current energy-per-bit minimization is formulated under steady-state assumptions for each Gearbox-PHY configuration. The model jointly optimizes front-end power consumption and hardware-aware spectral efficiency while incorporating phase noise and quantizer effects, but it does not account for the energy or time required to reconfigure between modulation and analog front-end states, nor for transient settling penalties. As a result, the reported gains (including the up to two orders of magnitude in the cellular scenario) represent an idealized upper bound that would be reduced by frequent switching. In the revised manuscript we will add an explicit limitations paragraph in the numerical results and cellular evaluation sections clarifying this point. We will also include a sensitivity study that quantifies the degradation in energy savings as a function of reconfiguration interval, using representative hardware settling times from the literature. This will allow readers to assess realizability for different traffic patterns without altering the core steady-state model. revision: partial

Circularity Check

0 steps flagged

No significant circularity; energy-per-bit minimization formulated from external models

full rationale

The paper formulates an energy-per-bit minimization problem by jointly modeling front-end power consumption and hardware-aware spectral efficiency, incorporating phase noise and quantizer effects as external hardware constraints. No load-bearing steps reduce by construction to self-definitions, fitted inputs renamed as predictions, or self-citation chains. The Gearbox-PHY architecture is referenced as previously proposed, but the central quantification relies on numerical evaluation of the joint model rather than tautological reduction to inputs. This is the most common honest finding for model-driven papers without explicit self-referential equations.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; the energy-per-bit minimization and hardware impairment models are referenced at a conceptual level only.

pith-pipeline@v0.9.0 · 5498 in / 1053 out tokens · 34665 ms · 2026-05-10T12:40:45.217930+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

62 extracted references · 62 canonical work pages

  1. [1]

    Energy optimization using joint modulation scheme and front end adaptation - the Gearbox-PHY,

    F. Gast, F. Roth, M. D ¨orpinghaus, P. Sen, S. Zeitz, and G. Fettweis, “Energy optimization using joint modulation scheme and front end adaptation - the Gearbox-PHY,” inProc. Int. Symp. Wireless Commun. Syst. (ISWCS), Rio de Janeiro, Brazil, Jul. 2024

  2. [2]

    The role of oscillator phase noise in maximizing transceiver en- ergy efficiency,

    ——, “The role of oscillator phase noise in maximizing transceiver en- ergy efficiency,” inProc. IEEE Wireless Commun. Netw. Conf. (WCNC), Milan, Italy, Mar. 2025

  3. [3]

    6G drivers and vision,

    NGMN Alliance, “6G drivers and vision,”NGMN, Whitepaper, 2021

  4. [4]

    The energy and carbon footprint of the global ICT and E&M sectors 2010–2015,

    J. Malmodin and D. Lund ´en, “The energy and carbon footprint of the global ICT and E&M sectors 2010–2015,”Sustainability, vol. 10, no. 9, p. 3027, 2018

  5. [5]

    2019 mobile industry impact report: Sustainable development goals

    GSMA, “2019 mobile industry impact report: Sustainable development goals.”

  6. [6]

    Umweltbezogene Technikfolgenabsch ¨atzung Mo- bilfunk in Deutschland,

    L. Stobbe et al., “Umweltbezogene Technikfolgenabsch ¨atzung Mo- bilfunk in Deutschland,” Fraunhofer-Institut f ¨ur Zuverl ¨assigkeit und Mikrointegration, IZM, Tech. Rep., 2023

  7. [7]

    The enablement effect,

    GSMA, “The enablement effect,” 2021

  8. [8]

    Radar: The sustainable telco,

    GSMAintelligence, “Radar: The sustainable telco,” 2021

  9. [9]

    The 5G guide - a reference for operators,

    GSMA, “The 5G guide - a reference for operators,” 2019

  10. [10]

    Issues and challenges in wireless sensor networks,

    S. Sharma, R. K. Bansal, and S. Bansal, “Issues and challenges in wireless sensor networks,” inProc. Int. Conf. Mach. Intell. Res. Adv., Katra, India, Oct. 2013, pp. 58–62

  11. [11]

    Going green: benchmarking the energy efficiency of mobile,

    GSMAintelligence, “Going green: benchmarking the energy efficiency of mobile,” 2021

  12. [12]

    Green future networks: Network energy efficiency,

    NGMN Alliance, “Green future networks: Network energy efficiency,” NGMN, Whitepaper, 2021

  13. [13]

    Mobility report,

    Ericsson, “Mobility report,” 2024

  14. [14]

    6G: The personal tactile internet—and open questions for information theory,

    G. P. Fettweis and H. Boche, “6G: The personal tactile internet—and open questions for information theory,”IEEE BITS Inf. Theory Mag., vol. 1, no. 1, pp. 71–82, 2021

  15. [15]

    Spatial modeling of the traffic density in cellular networks,

    D. Lee, S. Zhou, X. Zhong, Z. Niu, X. Zhou, and H. Zhang, “Spatial modeling of the traffic density in cellular networks,”IEEE Trans. Wireless Commun., vol. 21, no. 1, pp. 80–88, Feb. 2014

  16. [16]

    A new spatio- temporal model for data rate distributions in mobile networks,

    F. Gast, M. D ¨orpinghaus, F. Roth, and G. Fettweis, “A new spatio- temporal model for data rate distributions in mobile networks,” inProc. Int. Workshop Smart Antennas (WSA), Dresden, Germany, Mar. 2024. 13

  17. [17]

    Intelligent sustainability: the role of AI in energy consumption, management and new revenues,

    E. Fersman, J. Pettersson, A. H ¨oglund, E. Sanders, and L. Eleftheri- adis, “Intelligent sustainability: the role of AI in energy consumption, management and new revenues,” Ericsson Blog, Jun. 2023, accessed: 2025-07-07

  18. [18]

    Adaptive coded modulation for fading channels,

    A. Goldsmith and S.-G. Chua, “Adaptive coded modulation for fading channels,”IEEE Trans. Commun., vol. 46, no. 5, pp. 595–602, 1998

  19. [19]

    Meller, F

    G. Meller, F. Gast, F. Protze, J. Wagner, F. Ellinger, and G. Fettweis, “Noise analysis of a 434-MHz wakeup receiver analog frontend core with−93-dBm input sensitivity and 65-pJ/bit efficiency based on a switched injection-triggered oscillator with surface acoustic wave resonator,”IEEE Trans. Microw. Theory Techn., pp. 1–16, 2024

  20. [20]

    Hardware- aware energy efficiency optimization in wireless communications using a Gearbox-PHY,

    F. Gast, M. D ¨orpinghaus, P. Sen, A. Nimr, and G. Fettweis, “Hardware- aware energy efficiency optimization in wireless communications using a Gearbox-PHY,”IEEE Commun. Lett., Apr. 2024

  21. [21]

    Empirical formula for propagation loss in land mobile radio services,

    M. Hata, “Empirical formula for propagation loss in land mobile radio services,”IEEE Trans. Veh. Technol., vol. 29, no. 3, pp. 317–325, 1980

  22. [22]

    ADC Performance Survey 1997-2023,

    B. Murmann, “ADC Performance Survey 1997-2023,” [Online]. Avail- able: https://github.com/bmurmann/ADC-survey

  23. [23]

    Zero crossing modulation for communication with temporally oversampled 1-bit quantization,

    G. Fettweis, M. D ¨orpinghaus, S. Bender, L. Landau, P. Neuhaus, and M. Schl ¨uter, “Zero crossing modulation for communication with temporally oversampled 1-bit quantization,” inProc. 53rd Asilomar Conf. Signals, Syst. Comput., Pacific Grove, CA, USA, Nov. 2019

  24. [24]

    The peak-SNR per- formances of voltage-mode versus time-mode circuits,

    S. Ziabakhsh, G. Gagnon, and G. W. Roberts, “The peak-SNR per- formances of voltage-mode versus time-mode circuits,”IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 65, no. 12, pp. 1869–1873, 2018

  25. [25]

    Zero-crossing modula- tion for wideband systems employing 1-bit quantization and temporal oversampling: Transceiver design and performance evaluation,

    P. Neuhaus, M. D ¨orpinghaus, and G. Fettweis, “Zero-crossing modula- tion for wideband systems employing 1-bit quantization and temporal oversampling: Transceiver design and performance evaluation,”IEEE Open J. Commun. Soc., vol. 2, pp. 1915–1934, 2021

  26. [26]

    Why to use the phase in time-encoding modulation and its effect on the spectral efficiency,

    F. Roth, M. D ¨orpinghaus, S. Zeitz, F. Gast, and G. Fettweis, “Why to use the phase in time-encoding modulation and its effect on the spectral efficiency,” inProc. IEEE Int. Symp. Pers., Indoor Mobile Radio Commun. (PIMRC), Valencia, Spain, Sep. 2024

  27. [27]

    A survey of high-speed high-resolution current steering DACs,

    X. Li and L. Zhou, “A survey of high-speed high-resolution current steering DACs,”J. Semicond., vol. 41, no. 11, p. 111404, 2020

  28. [28]

    Energy-constrained modulation optimization,

    S. Cui, A. J. Goldsmith, and A. Bahai, “Energy-constrained modulation optimization,”IEEE Trans. Wireless Commun., vol. 4, no. 5, pp. 2349– 2360, 2005

  29. [29]

    Enabling energy-efficient Tbit/s communications by 1-bit quantization and oversampling,

    P. Neuhaus, M. Schl ¨uter, C. Jans, M. D ¨orpinghaus, and G. Fettweis, “Enabling energy-efficient Tbit/s communications by 1-bit quantization and oversampling,” inProc. 2021 Joint Eur. Conf. on Networks and Commun. & 6G Summit (EuCNC/6G Summit), Porto, Portugal, Jul. 2021

  30. [30]

    Optimal design of CMOS mixer: A research review,

    H. Zhang, S. Tang, M. Cai, and Y . Jiang, “Optimal design of CMOS mixer: A research review,”Int. J. RF Microw. Comput.-Aided Eng., vol. 32, no. 12, 2022

  31. [31]

    Low noise figure 2.4 GHz down conversion CMOS mixer for wireless sensor network application,

    S. A. Z. Murad, S. N. Mohyar, A. Harun, M. N. M. Yasin, I. S. Ishak, and R. Sapawi, “Low noise figure 2.4 GHz down conversion CMOS mixer for wireless sensor network application,” inProc. IEEE Student Conf. Res. Develop. (SCOReD), Kuala Lumpur, Malaysia, Dec. 2016

  32. [32]

    8 GHz, 1V, high linearity, low power CMOS active mixer,

    F. Mahmoudi and C. A. T. Salama, “8 GHz, 1V, high linearity, low power CMOS active mixer,” inProc. IEE Radio Freq. Integr. Circuits Syst., Dig. Papers, Fort Worth, TX, USA, Aug. 2004, pp. 401–404

  33. [33]

    A 28-GHz bidirectional active Gilbert-cell mixer in 90-nm CMOS,

    Y .-T. Chang and K.-Y . Lin, “A 28-GHz bidirectional active Gilbert-cell mixer in 90-nm CMOS,”IEEE Microw. Wireless Compon. Lett., vol. 31, no. 5, pp. 473–476, 2021

  34. [34]

    60 GHz CMOS downconversion mixer with 15.46 dB gain and 64.7 dB LO-RF isolation,

    J. Lee and Y . Lin, “60 GHz CMOS downconversion mixer with 15.46 dB gain and 64.7 dB LO-RF isolation,”Electron. Lett., vol. 49, no. 4, 2013

  35. [35]

    Wang and K

    H. Wang and K. Sengupta,RF and mm-wave Power Generation in Silicon. Academic Press, 2015

  36. [36]

    Power amplifiers performance survey 2000–present

    H. Wang, T.-Y . Huang, N. S. Mannem, J. Lee, E. Garay, D. Munzer, E. Liu, Y . Liu, B. Lin, M. Eleraky, H. Jalili, J. Park, S. Li, F. Wang, A. S. Ahmed, C. Snyder, S. Lee, H. T. Nguyen, and M. E. D. Smith, “Power amplifiers performance survey 2000–present.”

  37. [37]

    Improving power amplifier efficiency of zero-crossing modulation at sub-THz frequen- cies,

    F. Gast, K. Xu, M. D ¨orpinghaus, and G. Fettweis, “Improving power amplifier efficiency of zero-crossing modulation at sub-THz frequen- cies,” inProc. Ger. Microw. Conf. (GeMiC), Dresden, Germany, Mar. 2025

  38. [38]

    Root-raised cosine filter influences on PAPR distribution of single carrier signals,

    S. Daumont, B. Rihawi, and Y . Lout, “Root-raised cosine filter influences on PAPR distribution of single carrier signals,” inProc. 3rd Int. Symp. Commun., Control Signal Process. (ISCCSP), Saint Julian’s, Malta, Mar. 2008, pp. 841–845

  39. [39]

    On the maximum efficiency of power amplifiers in OFDM broadcast systems with envelope following,

    R. Wolf, F. Ellinger, and R. Eickhoff, “On the maximum efficiency of power amplifiers in OFDM broadcast systems with envelope following,” inProc. Int. ICST Conf. Mobile Lightw. Wireless Syst. (MOBILIGHT). Barcelona, Spain: Springer, May. 2010, pp. 160–170

  40. [40]

    Chapter 6 - 6G energy-efficient physical layer,

    F. Gast et al., “Chapter 6 - 6G energy-efficient physical layer,” in6G- life, F. H. Fitzek, H. Boche, W. Kellerer, and P. Seeling, Eds. Academic Press, 2026, pp. 89–118

  41. [41]

    Figures of merit for CMOS low-noise amplifiers and estimates for their theoretical limits,

    L. Belostotski and E. A. M. Klumperink, “Figures of merit for CMOS low-noise amplifiers and estimates for their theoretical limits,”IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 69, no. 3, pp. 734–738, 2022

  42. [42]

    Modeling and minimization of transceiver power consumption in wireless networks,

    A. Mezghani and J. A. Nossek, “Modeling and minimization of transceiver power consumption in wireless networks,” inProc. Int. ITG Workshop Smart Antennas (WSA), Aachen, Germany, Feb. 2011

  43. [43]

    Down with noise: An introduction to a low-noise amplifier survey,

    L. Belostotski and S. Jagtap, “Down with noise: An introduction to a low-noise amplifier survey,”IEEE Solid-State Circuits Mag., vol. 12, no. 2, pp. 23–29, 2020

  44. [44]

    Flexible, brain-inspired communication in massive wireless networks,

    B. Bossy, P. Kryszkiewicz, and H. Bogucka, “Flexible, brain-inspired communication in massive wireless networks,”Sensors, vol. 20, no. 6, p. 1587, 2020

  45. [45]

    Energy limits in A/D converters,

    B. Murmann, “Energy limits in A/D converters,” inProc. IEEE Faible Tension Faible Consomm. (FTFC), Paris, France, Jun. 2013, pp. 1–4

  46. [46]

    A power efficient 60 GHz 90nm CMOS OOK receiver with an on-chip antenna,

    K. Kang, P. D. Dong, J. Brinkhoff, C.-H. Heng, F. Lin, and X. Yuan, “A power efficient 60 GHz 90nm CMOS OOK receiver with an on-chip antenna,” inProc. IEEE Int. Symp. Radio-Freq. Integr. Technol. (RFIT), Singapore, Jan. 2009

  47. [47]

    Calculation of the performance of communication systems from measured oscillator phase noise,

    M. R. Khanzadi, D. Kuylenstierna, A. Panahi, T. Eriksson, and H. Zi- rath, “Calculation of the performance of communication systems from measured oscillator phase noise,”IEEE Trans. Circuits Syst. I, Regul. Pap., vol. 61, no. 5, pp. 1553–1565, 2014

  48. [48]

    Jitter-power trade-offs in PLLs,

    B. Razavi, “Jitter-power trade-offs in PLLs,”IEEE Trans. Circuits and Syst. I: Regul. Pap., vol. 68, no. 4, pp. 1381–1387, 2021

  49. [49]

    21.4 a 42mW 230fs-jitter sub-sampling 60GHz PLL in 40nm CMOS,

    V . Szortyka, Q. Shi, K. Raczkowski, B. Parvais, M. Kuijk, and P. Wambacq, “21.4 a 42mW 230fs-jitter sub-sampling 60GHz PLL in 40nm CMOS,” inProc. IEEE Int. Solid-State Circuits Conf. - Dig. Tech. Papers (ISSCC), San Francisco, CA, USA, Feb. 2014, pp. 366–367

  50. [50]

    A fast startup CMOS crystal oscillator using two-step injection,

    K. M. Megawer, N. Pal, A. Elkholy, M. G. Ahmed, A. Khashaba, D. Griffith, and P. K. Hanumolu, “A fast startup CMOS crystal oscillator using two-step injection,”IEEE J. Solid-State Circuits, vol. 54, no. 12, 2019

  51. [51]

    A 200-GHz sub-harmonic injection-locked oscillator with 0-dBm output power and 3.5% DC-to- RF-efficiency,

    S. Li, D. Fritsche, C. Carta, and F. Ellinger, “A 200-GHz sub-harmonic injection-locked oscillator with 0-dBm output power and 3.5% DC-to- RF-efficiency,” inProc. IEEE Radio Freq. Integr. Circuits Symp. (RFIC), Philadelphia, PA, USA, Jun. 2018, pp. 212–215

  52. [52]

    A fully integrated 120-GHz six-port receiver front-end in a 130-nm SiGe BiCMOS technology,

    B. Laemmle, K. Schmalz, J. Borngraeber, J. C. Scheytt, R. Weigel, A. Koelpin, and D. Kissinger, “A fully integrated 120-GHz six-port receiver front-end in a 130-nm SiGe BiCMOS technology,” inProc. IEEE Topical Meet. Silicon Monolithic Integr. Circuits RF Syst. (SiRF), Austin, TX, USA, Jan. 2013, pp. 129–131

  53. [53]

    Phase noise estimation via adapted interpolation,

    V . Simon, A. Senst, M. Speth, and H. Meyr, “Phase noise estimation via adapted interpolation,” inProc. IEEE Glob. Telecommun. Conf. (GLOBECOM), vol. 6, San Antonio, TX, USA, Nov. 2001

  54. [54]

    Comparing iterative and least-squares based phase noise tracking in receivers with 1-bit quantization and oversampling,

    F. Gast, S. Zeitz, M. D ¨orpinghaus, and G. Fettweis, “Comparing iterative and least-squares based phase noise tracking in receivers with 1-bit quantization and oversampling,” inProc. IEEE Stat. Signal Process. Workshop (SSP), Hanoi, Vietnam, Jul. 2023

  55. [55]

    H. Meyr, M. Moeneclaey, and S. A. Fechtel,Digital communication receivers: synchronization, channel estimation and signal processing. Wiley, 1998

  56. [56]

    On the gain of joint processing of pilot and data symbols in stationary Rayleigh fading channels,

    M. D ¨orpinghaus, A. Ispas, and H. Meyr, “On the gain of joint processing of pilot and data symbols in stationary Rayleigh fading channels,”IEEE Trans. Inf. Theory, vol. 58, no. 5, 2012

  57. [57]

    Dithered quantizers,

    R. M. Gray and T. G. Stockham, “Dithered quantizers,”IEEE Trans. Inf. Theory, vol. 39, no. 3, pp. 805–812, 1993

  58. [58]

    On the Bayesian Cram´er-Rao bound for phase noise estimation based on 1-bit quantized samples,

    S. Zeitz, F. Gast, M. D ¨orpinghaus, and G. Fettweis, “On the Bayesian Cram´er-Rao bound for phase noise estimation based on 1-bit quantized samples,” inProc. IEEE Glob. Commun. Conf. (GLOBECOM), Rio de Janeiro, Brazil, Dec. 2022

  59. [59]

    Phase noise tracking for receivers with 1-bit quantization and oversam- pling,

    F. Gast, M. Schl ¨uter, M. D ¨orpinghaus, H. Halbauer, and G. Fettweis, “Phase noise tracking for receivers with 1-bit quantization and oversam- pling,” inProc. IEEE Int. Conf. Commun. (ICC), Seoul, Korea (South), May. 2022

  60. [60]

    Simulation-based computation of information rates for channels with memory,

    D. M. Arnold, H.-A. Loeliger, P. V ontobel, A. Kavcic, and W. Zeng, “Simulation-based computation of information rates for channels with memory,”IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3498–3508, 2006

  61. [61]

    Timing synchronization and detection for systems with 1-bit quantization and runlength coding,

    S. Zeitz, F. Roth, F. Gast, M. D ¨orpinghaus, and G. Fettweis, “Timing synchronization and detection for systems with 1-bit quantization and runlength coding,” inProc. IEEE Int. Workshop Signal Process. Adv. Wireless Commun. (SPAWC), Lucca, Italy, Sep. 2024

  62. [62]

    Optimal decoding of linear codes for minimizing symbol error rate (corresp.),

    L. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate (corresp.),”IEEE Trans. Inf. Theory, vol. 20, no. 2, pp. 284–287, 1974