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arxiv: 2605.01328 · v1 · submitted 2026-05-02 · 📡 eess.SP

Analysis and Compensation of Tx and Rx IQ Imbalances in AFDM System

Hongjun Liu , Liaoyuan Zeng , Junhao Tian , Qingyu Li , Fuchen Xu , Chengxiang Liu , Guanghui Liu This is my paper

Pith reviewed 2026-05-09 18:43 UTC · model grok-4.3

classification 📡 eess.SP
keywords AFDMIQ imbalancetransmitter receiver impairmentsBER analysiscompensation schemechirp modulationimproper noise
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The pith

Joint Tx and Rx IQ imbalances create an error floor in AFDM bit error rates that a cascade compensation scheme removes.

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

The paper investigates how in-phase and quadrature imbalances at the transmitter and receiver distort affine frequency division multiplexing signals. It establishes that AFDM experiences stronger effects than OFDM or OTFS because its chirp-assisted modulation turns the imbalances into improper noise and residual signal terms. The authors derive closed-form pairwise and average bit error probabilities that show these distortions cap the usable signal-to-noise ratio and achievable rates. They then introduce a cascade compensation method that first removes receiver imbalance to restore additive white Gaussian noise statistics and afterward cancels transmitter imbalance through a specific signal design. If the approach holds, AFDM can deliver its promised performance in real radio hardware without the error floors that otherwise appear at moderate to high SNR.

Core claim

Joint transmitter and receiver IQ imbalance in AFDM produces an irreducible error floor in bit error rate because the chirp-assisted modulation converts the impairments into improper Gaussian noise and inter-symbol interference that standard receivers cannot eliminate; the proposed cascade scheme first compensates receiver IQ imbalance to convert the noise back to proper additive white Gaussian noise and then applies a judicious precoding design to null the transmitter IQ imbalance, restoring the bit error rate curve to its ideal slope.

What carries the argument

The cascade compensation scheme that first corrects receiver IQ imbalance to convert improper Gaussian noise into additive white Gaussian noise and then eliminates transmitter IQ imbalance through a judicious signal design.

If this is right

  • AFDM can reach the same high-SNR bit error rates as ideal balanced hardware when the cascade scheme is used.
  • The derived pairwise error probability expressions give exact predictions of the operating SNR limits imposed by any given level of IQ imbalance.
  • The compensation steps preserve the doubly selective channel robustness that distinguishes AFDM from OFDM.
  • Data-rate targets that were previously unreachable because of the error floor become attainable.

Where Pith is reading between the lines

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

  • Designers of future multicarrier systems for high-mobility links may need to embed similar IQI-aware preprocessing as a standard block rather than an optional add-on.
  • The comparison of AFDM severity against OTFS and OFDM suggests a practical test: measure which waveform shows the lowest error floor in the same hardware before choosing one for deployment.
  • Extending the cascade idea to joint estimation of both IQ parameters and channel coefficients in one receiver stage could reduce overhead in fast-fading scenarios.

Load-bearing premise

The IQ imbalance parameters must be known exactly or estimated without error at the receiver so the cascade steps can be applied perfectly.

What would settle it

A high-SNR simulation or over-the-air test in which the bit error rate continues to fall after the cascade compensation is applied, rather than flattening into a visible floor, would confirm the claim.

Figures

Figures reproduced from arXiv: 2605.01328 by Chengxiang Liu, Fuchen Xu, Guanghui Liu, Hongjun Liu, Junhao Tian, Liaoyuan Zeng, Qingyu Li.

Figure 2
Figure 2. Figure 2: Spectra illustration of the joint effect of TX and Rx IQ imbalance for view at source ↗
Figure 1
Figure 1. Figure 1: BER performance of QPSK modulated AFDM with MMSE detector view at source ↗
Figure 3
Figure 3. Figure 3: Analytical and numerical BER performance with ML detector in terms view at source ↗
Figure 4
Figure 4. Figure 4: The BER performance of the designed compensation method com view at source ↗
read the original abstract

Affine frequency division multiplexing (AFDM) is a recently proposed multicarrier waveform whose bit error rate (BER) performance in doubly selective channels is comparable to that of orthogonal time-frequency space (OTFS) and superior to that of orthogonal frequency division multiplexing (OFDM). In this paper, the impacts of joint transmitter (Tx) and receiver (Rx) in-phase and quadrature imbalance (IQI) on AFDM signals are investigated, where we show that AFDM suffers more severe IQI than OFDM and OTFS due to the inherent feature of complicated chirp-assisted modulation. We further derive analytical expressions for the pairwise and average bit error probability as a function of the IQI parameters. These indicate that such distortions significantly limit the achievable operating signal-to-noise ratio at the receiver side and data rates. To this end, we propose a cascade compensation scheme to mitigate these effects. Specifically, we first compensate for Rx IQI to convert the improper Gaussian noise into additive white Gaussian noise, and then apply a judicious design to eliminate the Tx IQI. Both analytical and simulation results reveal that joint Tx and Rx IQI introduce an error floor in the BER performance of AFDM systems, whereas the proposed approach effectively compensates such impairments.

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

3 major / 3 minor

Summary. The manuscript analyzes the impact of joint transmitter (Tx) and receiver (Rx) in-phase/quadrature imbalance (IQI) on affine frequency division multiplexing (AFDM) systems. It claims that AFDM suffers more severe IQI than OFDM or OTFS due to its chirp-assisted modulation, derives closed-form expressions for pairwise and average bit error probability (BEP) as functions of the IQI parameters (showing an error floor), and proposes a cascade compensation scheme: first correct Rx IQI to restore proper Gaussian noise, then eliminate Tx IQI via a judicious design. Analytical and simulation results are presented to support that the proposed approach removes the error floor.

Significance. If the derivations hold and the compensation is robust, the work would offer useful analytical tools and a practical mitigation strategy for IQI in AFDM, a waveform positioned as competitive with OTFS in doubly selective channels. The explicit derivation of BEP expressions in terms of IQI parameters (rather than empirical fits) and the direct comparison to OFDM/OTFS are strengths that could inform hardware-aware waveform design.

major comments (3)
  1. [Abstract and compensation scheme] Abstract and compensation scheme description: the cascade approach (Rx IQI correction followed by Tx IQI elimination) is derived and simulated under the assumption of perfect knowledge of the IQI parameters at the receiver. No estimation algorithm, pilot design, or sensitivity analysis to parameter mismatch is provided. Because AFDM uses chirp-assisted DAFT modulation, even small residuals can recouple into the affine-frequency domain and recreate the claimed error floor; this assumption is load-bearing for the practical effectiveness claim.
  2. [BEP derivation sections] BEP derivation sections: the analytical pairwise and average BEP expressions treat the post-Rx-compensation noise as additive white Gaussian after improper-to-proper conversion. However, the specific interaction of the chirp modulation with residual IQI and the resulting noise statistics in the affine-frequency domain are not explicitly verified, leaving open the possibility that the error-floor removal is overstated.
  3. [Simulation results] Simulation results (comparison to OFDM/OTFS): the claim that AFDM suffers more severe IQI is supported by BER curves, but the quantitative difference (e.g., the SNR at which the error floor appears or the floor level itself) is not tabulated or statistically tested against the other waveforms under identical IQI parameters, weakening the comparative severity assertion.
minor comments (3)
  1. [Signal model] Notation for the discrete affine Fourier transform (DAFT) matrix and chirp parameters should be introduced with explicit definitions early in the signal model section to aid readability.
  2. [Figures] Figure captions for the BER plots could include the exact IQI parameter values used (e.g., amplitude and phase mismatches) rather than referring only to the text.
  3. [Throughout] A few minor typographical inconsistencies appear in the equation numbering and variable subscripts between the analytical derivations and the simulation setup.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough and constructive review. We address each major comment point by point below, indicating the revisions we will make to strengthen the manuscript while preserving its core analytical contributions.

read point-by-point responses

  1. Referee: [Abstract and compensation scheme] Abstract and compensation scheme description: the cascade approach (Rx IQI correction followed by Tx IQI elimination) is derived and simulated under the assumption of perfect knowledge of the IQI parameters at the receiver. No estimation algorithm, pilot design, or sensitivity analysis to parameter mismatch is provided. Because AFDM uses chirp-assisted DAFT modulation, even small residuals can recouple into the affine-frequency domain and recreate the claimed error floor; this assumption is load-bearing for the practical effectiveness claim.

    Authors: We acknowledge that the compensation analysis and simulations assume perfect knowledge of the IQI parameters at the receiver. This is a standard modeling choice in analytical impairment studies to isolate the effectiveness of the cascade scheme itself. The manuscript's primary contribution is the demonstration that joint Tx-Rx IQI produces an error floor in AFDM due to chirp-assisted modulation and that the proposed cascade removes it under known parameters. In the revised version we will (i) explicitly state the perfect-knowledge assumption in the abstract, (ii) add a dedicated paragraph in the conclusions discussing the necessity of IQI estimation algorithms and pilot designs for practical deployment, and (iii) include a brief sensitivity analysis showing BER degradation under small parameter mismatches. These additions will address the concern about residual errors without requiring a full estimation scheme, which lies outside the current scope. revision: partial

  2. Referee: [BEP derivation sections] BEP derivation sections: the analytical pairwise and average BEP expressions treat the post-Rx-compensation noise as additive white Gaussian after improper-to-proper conversion. However, the specific interaction of the chirp modulation with residual IQI and the resulting noise statistics in the affine-frequency domain are not explicitly verified, leaving open the possibility that the error-floor removal is overstated.

    Authors: The BEP expressions are derived after the Rx IQI compensator restores proper complex Gaussian noise; the subsequent DAFT (a unitary transform) preserves the whiteness and Gaussianity of this noise in the affine-frequency domain. Consequently, the pairwise error probability integrals remain valid and the error floor is eliminated. We will insert a short clarifying remark immediately after the noise model in the BEP derivation section, explicitly noting that the post-compensation noise covariance matrix is a scaled identity in the DAFT domain. This verification step directly addresses the interaction concern and confirms that the analytical removal of the error floor is not overstated. revision: yes

  3. Referee: [Simulation results] Simulation results (comparison to OFDM/OTFS): the claim that AFDM suffers more severe IQI is supported by BER curves, but the quantitative difference (e.g., the SNR at which the error floor appears or the floor level itself) is not tabulated or statistically tested against the other waveforms under identical IQI parameters, weakening the comparative severity assertion.

    Authors: We agree that a tabulated quantitative comparison would make the severity claim more precise. In the revised manuscript we will add a table in the numerical-results section that lists, for identical IQI parameters, the observed error-floor levels and the approximate SNR values at which the floors appear for AFDM, OFDM, and OTFS. This will provide a clear, side-by-side quantitative basis for the comparative statement. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives closed-form pairwise and average BEP expressions directly as functions of the IQI parameters from the AFDM signal model and improper Gaussian noise statistics. The cascade compensation (Rx IQI correction followed by Tx IQI elimination) follows from standard linear signal-processing steps applied to the received vector without any fitted parameters renamed as predictions or self-referential definitions. No load-bearing step reduces to a self-citation, ansatz smuggled via prior work, or uniqueness theorem imported from the same authors. The chain remains self-contained against the stated assumptions of known IQI coefficients and the affine-frequency domain model.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard communication-theory models for IQ imbalance and noise; no new entities are postulated and no parameters are fitted to produce the target result.

axioms (2)
  • domain assumption IQ imbalance can be modeled as linear amplitude and phase mismatches at Tx and Rx
    Invoked when deriving the distorted signal model and the cascade compensation steps.
  • domain assumption After Rx IQI compensation the residual noise is additive white Gaussian
    Stated as the first step of the proposed scheme that converts improper noise to AWGN.

pith-pipeline@v0.9.0 · 5535 in / 1440 out tokens · 72467 ms · 2026-05-09T18:43:38.387353+00:00 · methodology

discussion (0)

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Reference graph

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