arxiv: 2604.18391 · v1 · submitted 2026-04-20 · 💻 cs.IT · eess.SP· math.IT

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Feedforward Phase Noise Compensation for Intersymbol Interference Channels

Alex J\"ager , Gerhard Kramer

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Pith reviewed 2026-05-10 03:30 UTC · model grok-4.3

classification 💻 cs.IT eess.SPmath.IT

keywords phase noisesum-product algorithmintersymbol interferenceinformation rateISI channelvon Misesmismatched decodingfeedforward compensation

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The pith

The sum-product algorithm enables non-iterative phase noise compensation on intersymbol interference channels, delivering higher information rates than linear MMSE filtering at similar complexity.

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

This paper introduces a feedforward phase noise compensation technique using the sum-product algorithm for channels affected by intersymbol interference. The method models outputs as independent Gaussians and employs mismatched von Mises processing at the receiver. When tested on ISI-free channels, standard single-mode fiber, and multipath OFDM channels, the SPA approach achieves better information rates than linear minimum-mean-square-error filtering. Readers interested in communication systems would care because it offers a way to mitigate phase noise without iterative processing, potentially improving throughput in practical links.

Core claim

A non-iterative phase noise compensation method based on the sum-product algorithm is applied to the outputs of intersymbol interference channels modeled as independent Gaussian random variables with the receiver using mismatched von Mises statistics. This SPA method achieves higher information rates at similar complexity compared to linear minimum-mean-square-error filtering for ISI-free, standard single-mode fiber, and multipath channels with orthogonal frequency-division multiplexing.

What carries the argument

The sum-product algorithm applied to a factor graph representation for estimating and compensating phase noise using von Mises distributions in a mismatched decoding setup.

If this is right

The method works across multiple channel types including fiber and wireless OFDM.
Higher achievable rates are obtained without increasing computational complexity significantly.
Feedforward operation avoids the need for iterative decoding loops.
Performance gains hold under the Gaussian output assumption for the tested channels.

Where Pith is reading between the lines

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

If the phase noise is slowly varying, the SPA could be combined with pilot symbols for better estimation.
The approach might extend to channels with nonlinear impairments beyond simple phase noise.
Implementation in hardware could reduce latency in high-speed optical links.

Load-bearing premise

The received signals can be treated as independent Gaussian random variables even in the presence of phase noise and intersymbol interference.

What would settle it

An experiment or simulation computing the mutual information or achievable rates for the SPA receiver and the LMMSE receiver on a standard single-mode fiber channel showing no rate advantage for the SPA at equivalent complexity.

Figures

Figures reproduced from arXiv: 2604.18391 by Alex J\"ager, Gerhard Kramer.

**Figure 1.** Figure 1: System model. The side information S is based on either pilot symbols or symbols decoded in a previous stage of a successive decoding strategy. A. Contributions and Organization We extend the SPA-based algorithms in [10]–[16] to ISI channels by modeling the Z1, . . . , Zn as independent Gaussians. We study a feedforward structure without turbo iterations to avoid excessive latency. We also show that the … view at source ↗

**Figure 2.** Figure 2: Factor graph of the PN compensation. Circle nodes represent variables [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: Rates for ISI-free channels with (SNR, ν∆) = (13 dB, 5 · 10−3 ) (upper curves) and (SNR, ν∆) = (5 dB, 10−6 ) (lower curves). 10−6 10−5 10−4 10−3 0 1 2 3 4 SNR 13 dB SNR 5 dB ν∆ AIR [bpcu] I(Z;Y |S) I(Z;Y |S) I(Zi ;Y |S) SPA LMMSE, 25 LMMSE, ∞ [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: Rates for ISI-free channels and optimized [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

**Figure 5.** Figure 5: Rates for SSMF with SNR 13 dB, ν∆ = 5 · 10−3 , and 16-QAM (solid) and 64-QAM (dashed). −20 −15 −10 −5 0 0 0.5 1 1.5 2 10 log10 ρ [dB] AIR [bpcu] SPA, interleaved SPA, superposed LMMSE, 25 LMMSE, ∞ SPA, no ISI Ccoh [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 8.** Figure 8: Rates for a multipath channel with SNR 5 dB, [PITH_FULL_IMAGE:figures/full_fig_p005_8.png] view at source ↗

read the original abstract

A non-iterative phase noise compensation method based on the sum-product algorithm (SPA) is applied to the outputs of intersymbol interference (ISI) channels. The outputs are modeled as independent Gaussian random variables, and the receiver applies mismatched processing with von Mises statistics. The performance is compared with that of linear minimum-mean-square-error filtering. The SPA achieves higher information rates at similar complexity for three channel types: ISI-free, standard single-mode fiber, and multipath channels with orthogonal frequency-division multiplexing.

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 shows SPA phase noise compensation beating MMSE on rates for fiber and OFDM channels under a mismatched model, but the independent Gaussian outputs assumption is a real concern for ISI cases.

read the letter

The main point is that they apply the sum-product algorithm in a non-iterative way to handle phase noise on ISI channels. Outputs are treated as independent Gaussians with mismatched von Mises statistics at the receiver, and this setup produces higher information rates than linear MMSE filtering at similar complexity. The tests cover ISI-free channels, standard single-mode fiber, and multipath OFDM setups. This is a straightforward extension of message passing to these practical channels, and the non-iterative aspect could matter for implementation speed. The comparisons on fiber and wireless channels are the useful part, as they tie the method to real systems where phase noise and memory both appear. The paper earns credit for running those specific cases and reporting the rate gains. The soft spot is the independence assumption on the outputs. ISI and multipath create dependence between samples, so forcing independence can inflate the mutual information numbers and make the SPA look stronger than it would against a joint model. The abstract states the modeling choice but gives no sign they measured the approximation error or checked it against the true statistics. If the full paper skips that quantification, the rate advantage partly reflects the modeling shortcut rather than the algorithm itself. For the ISI-free case this is not a problem, but it matters for the other two. This work is aimed at people designing receivers for phase noise in optical or wireless links with memory. Someone already using factor graphs or mismatched decoding would get the most from the concrete comparisons. It has enough simulation evidence and a clear practical angle to deserve peer review, though referees should press on the independence validation. I would send it out.

Referee Report

1 major / 1 minor

Summary. The manuscript presents a non-iterative phase noise compensation technique for intersymbol interference (ISI) channels that applies the sum-product algorithm (SPA) to channel outputs modeled as independent Gaussian random variables. The receiver uses mismatched von Mises statistics. Achievable information rates are compared to those obtained with linear minimum-mean-square-error (MMSE) filtering, with the claim that SPA yields higher rates at comparable complexity for ISI-free channels, standard single-mode fiber, and OFDM-multipath channels.

Significance. If the modeling assumptions and rate comparisons hold under scrutiny, the work offers a low-complexity feedforward alternative for phase-noise mitigation in memory channels, with potential relevance to optical and wireless systems where both phase noise and ISI are present.

major comments (1)

[Abstract and System Model] Abstract and System Model: the central rate comparisons rest on treating channel outputs as independent Gaussians while applying mismatched von Mises processing. For any channel with memory (ISI or multipath), the outputs are statistically dependent; the manuscript must quantify the resulting approximation error in the mutual-information estimates or validate them against the true joint distribution, because this directly determines whether the reported SPA advantage over MMSE is reliable.

minor comments (1)

[Abstract] The abstract states performance gains without accompanying details on simulation parameters, number of Monte-Carlo realizations, or error-bar reporting; adding these would improve reproducibility of the empirical claims.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and the constructive comment on our modeling assumptions. We address the point below and will revise the manuscript to strengthen the presentation of the rate comparisons.

read point-by-point responses

Referee: [Abstract and System Model] Abstract and System Model: the central rate comparisons rest on treating channel outputs as independent Gaussians while applying mismatched von Mises processing. For any channel with memory (ISI or multipath), the outputs are statistically dependent; the manuscript must quantify the resulting approximation error in the mutual-information estimates or validate them against the true joint distribution, because this directly determines whether the reported SPA advantage over MMSE is reliable.

Authors: We agree that outputs of channels with memory are statistically dependent. The independence assumption is an explicit modeling choice that allows the sum-product algorithm to be applied on a cycle-free factor graph of per-symbol observation nodes, preserving the feedforward and non-iterative character of the compensator. The achievable rates are evaluated under the resulting mismatched decoding metric (von Mises likelihoods), which yields a valid lower bound on mutual information that is attainable with the proposed receiver. The same simulation framework is used for the linear MMSE benchmark, so the relative advantage is measured consistently. To address the referee's concern, we will revise the System Model section to discuss the approximation explicitly, including a short analytical argument on the expected impact for the three channel classes considered and a note that the reported rates remain achievable even under the mismatch. revision: yes

Circularity Check

0 steps flagged

No circularity detected in derivation or claims

full rationale

The provided abstract and context describe a modeling assumption (channel outputs treated as independent Gaussians with mismatched von Mises receiver processing) followed by a direct performance comparison of information rates against linear MMSE filtering. No equations, parameter fitting steps, self-citations, or derivation chains are shown that reduce a claimed result to its inputs by construction. The independence modeling choice for ISI channels is an explicit approximation whose validity can be assessed externally; it does not constitute self-definitional, fitted-input, or self-citation circularity. The central claim therefore remains self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities.

pith-pipeline@v0.9.0 · 5368 in / 974 out tokens · 39553 ms · 2026-05-10T03:30:56.015502+00:00 · methodology

discussion (0)

Reference graph

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