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arxiv: 2605.12557 · v1 · pith:YUULR4ZLnew · submitted 2026-05-11 · 📡 eess.SP

Localization in OFDM Passive Distributed Antenna Systems with Pilots and Unknown Data Payloads: A Marginal Maximum Likelihood Approach

Mathieu Reniers , Martin Willame , J\'er\^ome Louveaux , Luc Vandendorpe This is my paper

Pith reviewed 2026-05-14 21:18 UTC · model grok-4.3

classification 📡 eess.SP
keywords localizationOFDMmarginal maximum likelihooddistributed antenna systemspilotsdata payloadsISAC
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The pith

A marginal maximum likelihood estimator localizes OFDM signals by using both pilots and unknown data symbols without decoding.

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

The paper establishes a Marginal Maximum Likelihood estimator for localizing a transmitting user equipment captured by a distributed receiver array in an OFDM system. This estimator incorporates position information from the entire frame by averaging the likelihood over all possible unknown data symbol values according to their constellation probabilities. A reader would care because data payloads make up most of each frame, so ignoring them limits accuracy, while methods that decode data first tie localization quality to the communication link performance. The approach avoids decoding and works with high-order constellations even in low signal-to-noise conditions.

Core claim

The central claim is that the derived Marginal Maximum Likelihood estimator jointly processes known pilot symbols and unknown data payloads by marginalizing the likelihood function over the data symbols, thereby achieving localization performance that approaches the genie-aided bound (perfect data knowledge) at lower SNR than decision-directed methods and remains effective for large constellation sizes.

What carries the argument

The Marginal Maximum Likelihood estimator that computes the position by maximizing the marginal probability of the received signals after integrating out the unknown data symbols weighted by their discrete uniform prior from the constellation.

If this is right

  • The MML method achieves superior localization accuracy compared to pilot-only and decision-directed baselines in numerical simulations.
  • It converges to the genie bound at a lower SNR than any decision-directed approach.
  • The performance stays robust as the modulation order increases, unlike decision-directed methods which degrade.
  • A computational complexity analysis shows how system parameters affect the cost of the proposed estimator relative to baselines.

Where Pith is reading between the lines

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

  • This suggests that communication signals in ISAC systems can be more fully exploited for sensing without additional overhead.
  • Similar marginalization techniques could apply to other waveform-based localization problems where part of the signal is unknown.
  • The method may extend to scenarios with multiple users or imperfect channel knowledge if the marginalization is adjusted accordingly.

Load-bearing premise

The data symbols are independent and follow a known discrete distribution from the constellation, with the noise and channel model allowing exact computation of the marginal likelihood.

What would settle it

Monte Carlo simulations in which the MML estimator's root-mean-square localization error fails to approach the genie-aided error as SNR increases would disprove that it fully utilizes the data information without decoding.

Figures

Figures reproduced from arXiv: 2605.12557 by J\'er\^ome Louveaux, Luc Vandendorpe, Martin Willame, Mathieu Reniers.

Figure 1
Figure 1. Figure 1: Illustration of the considered scenario. The UE (i.e., the TX) transmits [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of the considered resource grid. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: 16-QAM constellation decomposed into BPSK-like amplitude levels along the real and imaginary axes (indicated by dashed arrows). Finally, it is worth emphasizing that this reformulation is purely analytical: MMLfast (18) is guaranteed to yield identical position estimates to MMLa (16), i.e., xbMMLfast s = xbMMLa s , while achieving significant computational savings, especially for large constellations. Note… view at source ↗
Figure 4
Figure 4. Figure 4: RMSE as a function of SNR for different data constellations. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: SER as a function of the SNR, for different data constellations. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: RMSE as a function of D for different SNR values. Parameters: N = 8, Q = 64, ∆f = 120 kHz (yielding the same bandwidth as in Table I), Nmc = 2000; all other parameters are left at their default values. 4 8 16 32 N 10−1 100 101 102 RMSE { bxs)} (λs) Genie HDDLMMSE distr HDDLMMSE centr MMLfast SNR = 0 dB SNR = 20 dB SNR = 40 dB [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: RMSE as a function of N for different SNR values. Parameters: Q = 64, ∆f = 120 kHz (yielding the same bandwidth as in Table I), Nmc = 2000; all other parameters are left at their default values. 3) Number of subcarriers [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: RMSE as a function of Q for different SNR values. Parameters: N = 8, ∆f = 120 kHz, Nmc = 2000; all other parameters are left at their default values. The effect of the bandwidth coherent gain is illustrated in [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Normalized coherent and non-coherent AF, [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
read the original abstract

Integrated Sensing and Communications (ISAC) is emerging as a key paradigm for future Sixth-Generation (6G) networks, with communication-centric designs favored for their compatibility with existing standards. Communication signals contain both known deterministic pilot symbols and unknown random data payloads. Most localization approaches rely solely on pilots, discarding the position information contained in the data symbols, which constitute the majority of each transmitted frame. Alternatively, Decision-Directed (DD) approaches exploit data decisions, thereby inherently limiting positioning performance to that of the communication system. In this paper, we derive a Marginal Maximum Likelihood (MML) estimator that jointly leverages pilot and data payloads without requiring data decoding, enabling operation with high-order constellations and under challenging noise conditions. We consider an opportunistic scenario in which an Orthogonal Frequency-Division Multiplexing (OFDM) signal transmitted by a User Equipment (UE) is captured by a distributed receiver array. Through numerical simulations, we demonstrate that the proposed method achieves superior localization performance compared to existing approaches and consistently converges to the genie bound (where data symbols are assumed perfectly known) at a lower Signal-to-Noise Ratio (SNR) than any DD method. Furthermore, the proposed method remains robust to constellation size, unlike DD approaches, whose performance degrades with increasing modulation order. Finally, we provide a computational complexity analysis of the proposed method and the considered baselines, highlighting the impact of system parameters on their respective computational costs.

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

0 major / 2 minor

Summary. The paper derives a Marginal Maximum Likelihood (MML) estimator for UE localization in an OFDM passive distributed antenna system. The estimator jointly processes known pilot symbols and unknown data payloads by marginalizing the likelihood over the data symbols (modeled as i.i.d. draws from the known constellation) without performing data decoding. Simulations show the method converges to the genie-aided bound at lower SNR than decision-directed baselines and remains robust as constellation order increases.

Significance. If the central derivation holds, the result would meaningfully advance ISAC localization by exploiting the data portion of the frame (the majority of transmitted symbols) in a communication-compatible manner. The reported robustness to high-order constellations and lower-SNR convergence to the genie bound are practically relevant; the accompanying complexity analysis further strengthens the contribution.

minor comments (2)
  1. The abstract and simulation section should explicitly list the key parameters (number of receive antennas, subcarriers, frame length, exact SNR grid, and number of Monte-Carlo trials) to allow direct reproduction of the reported convergence curves.
  2. In the complexity analysis, a compact table comparing asymptotic costs of the MML estimator versus the DD and pilot-only baselines as functions of constellation size M and number of subcarriers would improve readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive review, accurate summary of our contributions, and recommendation for minor revision. The assessment of the practical relevance of the MML estimator and its robustness properties is encouraging.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper derives its Marginal Maximum Likelihood estimator directly from the joint likelihood of the OFDM received signal model by treating unknown data symbols as i.i.d. draws from the known finite constellation and marginalizing them out exactly. OFDM subcarrier independence reduces the marginalization to a product of finite sums (one per subcarrier), which follows immediately from the signal model assumptions without any fitted parameters, self-citations, or redefinitions. The resulting estimator is then applied to position parameters; performance is assessed via simulation against a genie bound (perfect data knowledge) and decision-directed baselines. No step in the derivation chain reduces to its own inputs by construction, and the central claim rests on standard marginalization principles applied to the stated model rather than on any load-bearing self-reference or ansatz smuggled from prior work.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach relies on standard domain assumptions for OFDM signal models and statistical treatment of data symbols to enable marginalization; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (2)
  • domain assumption Transmitted data symbols are independent and identically distributed according to the known constellation
    Required to compute the marginal likelihood by averaging over possible data values.
  • domain assumption Additive white Gaussian noise and standard OFDM channel model
    Typical assumption enabling closed-form or tractable marginalization in wireless localization.

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Reference graph

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