PRB-WM: Physics-Regularized Beta World Models for Predictive Link Adaptation on Real Time-Varying Underwater Acoustic Channels

Shengjie Zhong; Zhongliang Zhao; Jingxuan Chen; Dianrun Huang; Zichen Zhao; Yang Liu; Dapeng O. Wu; Tony Q. S. Quek

cs.SDOct 12, 2026

PRB-WM: Physics-Regularized Beta World Models for Predictive Link Adaptation on Real Time-Varying Underwater Acoustic Channels

Authors: Shengjie Zhong, Zhongliang Zhao, Jingxuan Chen, Dianrun Huang, Zichen Zhao, Yang Liu, Dapeng O. Wu, Tony Q. S. Quek

Organizations: School of Electronic and Information Engineering, Beihang University, Beijing 100191, China · Department of Strategic and Advanced Interdisciplinary Research, Peng Cheng Laboratory · Hangzhou International Innovation Institute, Beihang University, Hangzhou · MIIT Key Lab. of Aerospace Mobile Communication, Beijing · State Key Lab. of CNS/ATM, Beijing · Department of Computer Science, City University of Hong Kong, Hong Kong, SAR, China · Hong Kong Generative AI Research and Development Center, Hong Kong, SAR, China · College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150000, China · College of Computing & Data Science, Nanyang Technological University, Singapore · Department of Computer Science, The City University of Hong Kong, Hong Kong, SAR, China · Information Systems Technology and Design Pillar, Singapore University of Technology and Design, Singapore 487372

Abstract

Adaptive modulation and coding (AMC) improves the spectral efficiency of underwater acoustic (UWA) links, but its feedback is inevitably stale: sound propagates slowly, and by the time channel state information (CSI) arrives, the fast time-varying multipath channel has moved on. Predictive link adaptation therefore needs more than a point forecast: it needs a distribution over each candidate action's consequences. We propose PRB-WM, a physics-regularized Beta world model for predictive per-subcarrier link adaptation on real time-varying UWA channels. A persistence-anchored stochastic latent-space dynamics model learns how the channel evolves; a counterfactual outcome head evaluates, for every candidate modulation and coding scheme (MCS), a Beta-binomial distribution of bit errors on shared imagined futures; and a chance-constrained receding-horizon model predictive controller maximizes expected spectral efficiency subject to a bounded probability of violating the bit error rate (BER) target. To the best of our knowledge, PRB-WM is the first world model for UWA communications. In closed-loop replay of six measured sea-trial links from the public UWA Channel Library against a 24-method pool spanning the full methodological spectrum, PRB-WM attains a mean goodput 87% above the strongest baseline, ranks first on all six time-varying links at the longest lookahead, and is the only method whose realized frame risk decreases systematically with lookahead, meeting the BER-violation contract where no baseline does. Ablations confirm that rollout sampling dispersion is essential to the chance constraint and that the physics anchor is necessary for trainability.

Figures & tables

Fig. 1 : Scenario and decision loop. Left: a single-hop UWA orthogonal frequency-division multiplexing (OFDM) link between a surface-vessel transmitter and an autonomous underwater vehicle (AUV)/mooring receiver; direct, surface-bounce, and bottom-bounce paths, internal waves, and platform Doppler make the channel fast time-varying, and the long acoustic propagation delay makes the feedback CSI stale at decision time. Top right: measured channel frequency response (CFR) magnitude and per-frame signal-to-noise ratio (SNR) trajectory of the sea-trial link red_2 from the UWA Channel Library, illustrating the fast time-frequency variation that motivates stochastic prediction. Bottom right: at the start of every epoch, the world model rolls out a distribution of futures anchored at the current observation, the chance-constrained planner scores every candidate MCS on these imagined futures, and the selected per-subcarrier allocation is transmitted on the next frame.

Fig. 2 : PRB-WM framework. A causal observation window (CFR history plus the recorded noise floor) is compressed by a CNN encoder into the belief of a recurrent state-space world model with a Beta-distributed stochastic latent (posterior during training, prior at rollout). A persistence physics anchor $\bar{H}_{t+1}{=}H_{t}$ is injected into the anchored decoder, which reconstructs future CFRs as anchor plus learned residual. Prior sampling of the latent dynamics yields $S$ stochastic rollouts $\{\hat{H}^{(s)}_{t+1:t+h}\}$ ; the counterfactual outcome heads evaluate every candidate MCS (off, BPSK, QPSK, 8PSK, 16QAM) on each rollout; and the chance-constrained MPC selects the per-subcarrier allocation whose predicted probability of respecting the $10^{-3}$ BER target is at least $1{-}\delta$ , which is then executed on the OFDM link. The channel is a measured replay from the UWA Channel Library; the feedback path carries observations only (no future CSI), and the physical causality constraint—MCS $\nrightarrow$ channel—is enforced structurally.

Fig. 3 : Measured-channel exploration on the six time-varying UWA Channel Library links. Top: per-frame SNR trajectories. Bottom: CFR magnitude heat maps over subcarriers and time. The links cover distinct dynamical regimes, from the severely fluctuating red_2 to the slowly decaying yellow_4.

Symbol	Meaning
$H_{t,f}\in\mathbb{C}$	CFR of subcarrier $f$ at symbol $t$
$N_{f}$ , $N_{f}^{\mathrm{act}}$	total / active (data) subcarriers, $256$ / $240$
$\gamma_{t,f}$ , $\gamma_{t}$	per-subcarrier SNR (linear) / link SNR (dB)
$o_{t}$	observation at $t$ : $[\Re H_{t},\Im H_{t},\sigma^{2}_{t},\gamma_{t}]$
$e_{t}$	CNN encoding of the observation window ending at $t$
$W$	history window length, $64$ symbols

TABLE I : Notation

Fig. 4 : Observe-and-rollout detail of PRB-WM, illustrated at

h{=}5

. Left (observe): at observed steps, the posterior infers the latent

z_{t}

from the encoded observation, and the resulting belief is carried into the rollout; the horizon weights

\eta_{\tau}{=}2\tau/h

form a linear ramp. Right (rollout): future steps receive zero input (no future observation exists) and sample the prior; the persistence anchor

\bar{H}_{t+\tau}{=}H_{t}

is held fixed, and the decoder emits per-step Beta parameters

(\alpha_{\tau},\beta_{\tau})

that induce a Beta–binomial error distribution per candidate MCS. The planner scores and filters the candidate MCSs by the empirical violation rate

\hat{q}\leq\delta

and loads the highest feasible MCS per subcarrier.

Parameter	Value
OFDM subcarriers	$256$ ( $240$ data $+16$ null, active $[8,248)$ )
Bandwidth / subcarrier spacing	$6$ kHz / $23.4$ Hz
Symbol / CP duration	$42.7$ ms / $20$ ms
MCS set $\mathcal{M}$	off, BPSK, QPSK, 8PSK, 16QAM
Bits per subcarrier $b_{m}$	$\{0,1,2,3,4\}$
BER target $P_{b}^{\mathrm{tar}}$	$10^{-3}$

TABLE II : Scenario Parameters

Method (pool rank order)	Goodput
PRB-WM (ours)	506
DLinear / NLinear	270 / 241
N-BEATS / PatchCSI-T	173 / 155
DeepAR / BiGRU	150 / 150
MTL-LSTM / TimeGrad / iTransformer	145 / 144 / 144
RLS / CNN1d-LSTM / TimesNet	133 / 126 / 122

TABLE III : Mean Closed-Loop Goodput (bps) Averaged over Seven Links (Including the Static Black Link) and

h\in\{8,16,32\}

, Full 24-Method Pool (22 Baselines, PRB-WM, and a Genie Reference)

Fig. 6 : Goodput at the endpoint horizons

h{=}1

and

h{=}32

, with the Perfect-CSI genie shown as a reference series (a greedy one-step reference, not an upper bound). At

h{=}32

PRB-WM ranks first on all six links; at

h{=}1

the field is mixed.

Fig. 7 : Realized frame risk

R(h)=\Pr(\mathrm{BER}>P_{b}^{\mathrm{tar}})

versus horizon; the dashed line marks the contract

\delta{=}0.1

. No baseline meets the contract at any point; baseline risk is close to

1.0

at short lookahead and stays at or above

0.5

even at

h{=}32

. PRB-WM’s risk decreases monotonically with lookahead, reaching

0

h{=}32

on blue_1, yellow_4, and red_4;

0.2

on red_2;

0.42

on red_1; and

0.6

on red_3.

Fig. 8 : Mechanism ablations. (a) Sampling ablation: closed-loop goodput with stochastic versus determinized rollout at identical validation NMSE; determinization costs

25.3\%

goodput, showing that rollout dispersion is essential for the chance constraint. (b) Anchor ablation: exposing the persistence anchor to the decoder improves validation NMSE by

64/77/74\%

h=1/4/16

Fig. 9 : Waveform-level validation on blue_1: measured BER of OFDM waveforms replayed through the recorded channel versus the per-subcarrier analytic model. The analytic trend is correct but systematically optimistic by about

5\times

(deep fades dominate); a

2

–

4

dB implementation margin absorbs the offset, and method rankings are unchanged under this margin. In the figure, ideal-CSI ZF denotes zero-forcing equalization with perfect channel knowledge.

Fig. 10 : Chance-constraint tolerance sensitivity: goodput versus

\delta\in\{0.05,0.1,0.2\}

h{=}8

for eight methods on six links. PRB-WM leads or co-leads at every

\delta

on every link, and

\delta{=}0.1

is optimal or near-optimal for all methods: the tolerance is not tuned to favor the proposed method.

Fig. 11 : Noise stress test on four links: goodput retention under

+6

and

+12

dB injected noise, Gaussian (solid) and impulsive

\alpha

-stable (dashed), at fixed horizons. PRB-WM attains the best retention throughout (

0.393

versus

0.239

for PatchCSI-T and

0.152

for Markov at

+12

dB impulsive); at long horizons baselines collapse toward zero while PRB-WM retains several hundred bps.

Fig. 12 : Multi-link aggregation: net goodput summed over

K{=}3

non-interfering links under a shared world model. At

h{=}8

PRB-WM reaches

\approx\!1984

bps, versus

\approx\!610

bps (PatchCSI-T),

\approx\!660

bps (Perfect-CSI genie),

\approx\!450

bps (Markov), and

\approx\!250

bps (persistence).

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 16 — Fig. 13 : Full-spectrum results for all 20 predictors on the six time-varying links. Left: NMSE versus horizon, where PatchCSI-T and several forecasters rank deeper (better) than PRB-WM. Right: goodput versus horizon, where PRB-WM’s top row improves visibly from $h\geq 16$ . The reversed orderings support that predictive accuracy is not decision value.

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Underwater Optical Wireless Communication (UOWC) has emerged as a promising technology for high-speed underwater data transmission, offering significantly higher bandwidth and lower latency compared to acoustic and Radio Frequency (RF) technologies. However, the underwater medium introduces severe impairments that degrade link performance and limit communication range. The growing complexity of these challenges has increased research interest in Machine Learning (ML) and Deep Learning (DL) approaches, which offer powerful tools for channel modeling, signal processing, and system adaptation in ways that conventional analytical methods struggle to achieve. This survey provides a comprehensive review of ML methods applied across the full UOWC system pipeline, covering channel modeling, transmitter design, receiver detection and equalization, link alignment, and emerging applications, including wireless power transfer, semantic communication, object detection, optical sensing, and localization. Finally, we discuss open challenges and future research directions to motivate further work in this rapidly growing field.

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