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Stacked Intelligent Metasurface-Diffractive Deep Neural Networks for Onboard Terrain Classification from SAR Level-0 Raw Data

Mengbing Liu, Xin Li, Jiancheng An, Chau Yuen

arXiv:2609.34333v1eess.SP

TL;DR

Raw SAR terrain classification is constrained by noisy signals and digital-centric processing burdens. The paper proposes a multilayer SIM-D2NN that performs feature mapping in-wave, reporting around 90% accuracy in binary classification. Its linear analog design remains limited for noisy raw data in more complex classification tasks.

  • Problem

    Noisy, high-dimensional raw SAR patches and digital-centric processing impose computational and downlink burdens on onboard terrain classification.

    Source: B. Related Work · pp. 1–2

  • Method

    A multilayer SIM-D2NN uses programmable metasurface layers for in-wave feature mapping and inference on raw SAR data.

    Source: A. System Model · p. 3, §VI · p. 13

  • Results

    Around 90% accuracy is reported for binary classification directly from real raw SAR data.

    Source: §VI · p. 13

  • Takeaways & Limitations

    The framework supports onboard inference with minimal digital processing and reduced data-transmission overhead while maintaining competitive performance.

    Source: §VI · p. 14

    Linear analog architectures remain limited on noisy raw SAR data, and practical SIM implementations may face amplitude variation, parasitic mutual coupling, and temperature-dependent drift.

    Source: §VI · p. 14

Abstract

from arXiv · show

Real-time terrain classification directly from Level-0 raw Synthetic Aperture Radar (SAR) data remains restricted by traditional digital-centric paradigms, where the processing of noisy, high-dimensional patches is hindered by computationally intensive processors and significant downlink latency. To address these fundamental limitations, this work establishes a new research paradigm for autonomous on-board sensing by proposing a Stacked Intelligent Metasurface-Diffractive Deep Neural Network (SIM-D$^2$NN). This architecture leverages the physical wave-propagation medium to offload inference tasks from digital processors to a physical device. By executing in-wave feature mapping, the SIM-D$^2$NN facilitates a move toward an integrated `compute-while-transmitting' framework, providing an alternative to the traditional `digitize-then-process' sequence. The multi-layer metasurface is positioned at the forefront of the satellite communication module. The initial layer modulates the raw SAR data through both amplitude and phase adjustments, where a 90$^\circ$ phase rotation is introduced as a lightweight but effective augmentation strategy to enhance robustness against noise and Doppler distortions. Subsequent layers learn variable phase shifts, enabling advanced feature mapping for the classification task. The classification results at the terrestrial station can be directly obtained based on the signal amplitude received at each antenna. This design reduces reliance on downlink bandwidth and high-power terrestrial computing, achieving performance around 90% in the binary task directly from real raw SAR data in terms of accuracy, precision, recall, and F1 Score. Therefore, our method helps bridge the gap between next-generation remote sensing tasks and in-orbit processing needs, paving the way for computationally efficient remote sensing applications.

I. INTRODUCTION

The introduction motivates classifying raw SAR data onboard, where noise, distortion, and digital processing burdens challenge existing approaches. It proposes SIM-D2NN in-wave processing and evaluates both its raw-data performance and the limits of linear architectures.

D. Paper Organization

  • The introduction moves from SAR applications and earlier classification approaches through related work and contributions, then outlines the paper’s six-section organization.The later sections cover the system model, training and deployment, evaluation, simulation results, and conclusion.Source: A. Background · p. 1, B. Related Work · p. 2

B. Related Work

  • Digital-centric SAR pipelines treat classification as post-processing of high-level products, requiring massive raw-data transmission and adding latency and energy overheads.Raw SAR is also difficult to exploit because of sensor-specific distortions, speckle, and digital edge hardware throughput and energy bottlenecks.Source: B. Related Work · pp. 1–2

C. Technical Contribution

  • The proposed framework performs progressive linear feature mapping in the electromagnetic domain, shifting inference from digital processors to a compute-while-transmitting pipeline.The SIM acts as a physical computational medium during signal propagation.Source: C. Technical Contribution · p. 2
  • A lightweight 90° phase-rotation strategy addresses raw SAR’s speckle and Doppler distortions, raising binary-task accuracy from a 50% random-guess baseline to 90%.The authors describe it as an in-wave alternative to traditional digital preprocessing pipelines.Source: C. Technical Contribution · p. 2
  • The SIM-D2NN improves accuracy over single-layer counterparts but declines from 89.5% in binary tasks to 63.2% in complex four-class scenarios, while reaching 93% on a 14-class high-level SAR dataset.The authors identify this pattern as evidence of linear processing’s limits on complex raw data, while it remains effective on thoroughly pre-processed data.Source: C. Technical Contribution · p. 2

II. SIM-AIDED SATELLITE COMMUNICATION SYSTEM

The system uses a multilayer SIM to transform raw SAR inputs through wave propagation and map received antenna intensities to terrain classes. A labeled coastal dataset workflow supports training and evaluation.

A. System Model

  • The initial metasurface layer modulates each patch’s augmented input, while subsequent layers apply learned phase shifts to map features.The initial layer is controlled to align with augmented patch features; later layers use programmable diagonal operators.Source: A. System Model · p. 3
  • The SIM-D2NN cascades programmable phase-shift layers and diffraction to perform spatial feature extraction through in-wave matrix-vector operations.The metasurface layers synthesize a complex spatial impulse response that correlates raw SAR echoes with learned terrain signatures.Source: A. System Model · p. 3
  • The labeling workflow uses processed imagery of the Sao Paulo–Santos region to sample ocean and land patches while excluding mixed-terrain boundaries.Figure 2 identifies ocean in blue, land in grey, and excluded areas in red.Source: Figure 2 · p. 4
  • Terrain class is read from the receive antenna with the greatest signal intensity, with the number of physical antennas matched to the number of categories.Square-law intensity detection serves as a physical-domain activation, and the receiver obtains the classification outcome rather than requiring a full data payload.Source: A. System Model · p. 4

B. Space-to-Ground Channel Modeling

The space-to-ground link is modeled with Rician fading and satellite-to-ground path loss. The receiver’s controlled analog transformation lets its antennas directly extract category likelihoods, reducing subsequent computation.

B. Space-to-Ground Channel Modeling

  • The space-to-ground channel uses Rician fading with line-of-sight and non-line-of-sight components, alongside a satellite-to-ground path-loss model.The passage identifies carrier frequency and distance, atmospheric absorption, and interactions with near-surface urban structures as path-loss factors.Source: B. Space-to-Ground Channel Modeling · p. 4
  • The receiver antenna array directly extracts category likelihoods from the controlled analog transformation, simplifying signal processing and reducing computational overhead.The passage also associates this approach with lower energy consumption.Source: B. Space-to-Ground Channel Modeling · p. 4

C. Raw SAR Data Labeling

The study creates a Level-0 raw SAR dataset with terrain labels because the raw patches are difficult to interpret directly. It focuses data into reference imagery for labeling, using range and azimuth processing.

C. Raw SAR Data Labeling

  • The dataset pairs raw SAR data with corresponding ground-truth terrain labels to support near-real-time classification research.The authors contrast their raw-data focus with typical datasets based on SLC and other advanced formats.Source: C. Raw SAR Data Labeling · p. 4
  • Noise and Doppler distortions obscure raw SAR terrain features, so an open-source Sentinel-1 Level-0 decoder is used to generate reference imagery for labeling.Raw SAR preserves phase and amplitude but lacks radiometric and geometric corrections.Source: C. Raw SAR Data Labeling · p. 4
  • Range compression uses a matched filter, followed by range-cell migration correction to compensate for motion-induced range walk.The processing pipeline first transforms the raw data into the frequency domain using an FFT.Source: C. Raw SAR Data Labeling · p. 5
  • Azimuth compression focuses the data, and a final inverse FFT returns it to the spatial domain for clearer terrain labeling.The resulting imagery has reduced noise and enhanced clarity.Source: C. Raw SAR Data Labeling · p. 5

III. PROBLEM FORMULATION AND PROPOSED SIM-D2NN FRAMEWORK

The SIM-D2NN treats terrain classification as physical phase optimization, processing Level-0 raw SAR through metasurface layers rather than relying on ground-side digital inference. Its objective and constraints reflect the cascaded physical propagation and intensity-based detection.

III. PROBLEM FORMULATION AND PROPOSED SIM-D2NN FRAMEWORK

  • The SIM-D2NN maps Level-0 raw echoes onto an initial metasurface and transmits semantic classification results, unlike digital workflows that send raw data for ground processing.The authors state that this design reduces onboard computational overhead, latency, and communication burden relative to the conventional pipeline.Source: §III · p. 5

A. Problem Formulation

  • The task optimizes metasurface phase shifts to minimize the discrepancy between network outputs and one-hot labels, thereby maximizing classification accuracy.The dataset is defined as raw SAR patches paired with their corresponding category labels.Source: A. Problem Formulation · p. 5
  • The objective minimizes cross-entropy loss by adjusting each layer’s learnable phases, with received-signal modulus used for intensity-based classification.The transmission constraints model cascaded complex-valued linear propagation, while unit modulus is imposed on each meta-atom.Source: A. Problem Formulation · p. 6
  • The forward model represents inter-layer propagation as a cascaded complex-valued linear operator, subject to unit-modulus phase constraints on meta-atoms.These physical constraints make the optimization non-trivial and motivate a specialized training and deployment procedure.Source: A. Problem Formulation · p. 6
  • Offline phase updates use the complex-valued chain rule because forward propagation through the diffractive layers is differentiable with respect to phase shifts.The gradient is computed for a real-valued loss with respect to real phase parameters.Source: A. Problem Formulation · p. 6
  • The physical phase configurations are optimized to approximate a task-specific matched-filtering response,.The incident field component is defined at each meta-atom from the preceding layer.Source: A. Problem Formulation · p. 6

B. Procedures of the SIM-D2NN

The procedure augments spatially aggregated Level-0 SAR patches with phase-rotated components, then trains phase shifts offline and fixes them for analog inference. The model’s antenna with the highest received intensity supplies the predicted terrain class.

1) Phase-rotation Augmentation:

  • Each 128 × 128 raw SAR patch is magnitude-normalized while preserving phase, then coherently averaged over non-overlapping 4 × 4 regions before phase augmentation.The aggregated representation is 32 × 32, with 1,024 complex coefficients.Source: 1) Phase-rotation Augmentation · p. 6
  • The augmentation concatenates original coefficients with fixed 90° phase-rotated coefficients to enrich the complex-valued input representation.The two components are assigned to spatially distinct groups of input apertures.Source: 1) Phase-rotation Augmentation · p. 6
  • Distinct propagation coefficients for the spatially separated components let their relative phase alter interference in the received intensity used for classification.The paper presents this as a way to exploit phase information in complex Level-0 SAR data.Source: 1) Phase-rotation Augmentation · pp. 6–7
  • Offline training updates metasurface phases by backpropagation while injecting independent Gaussian channel noise across forward passes to promote robustness.Training uses a spatially isolated subset and a predetermined channel realization fixed during training and testing.Source: 2) Training and Deployment of the… · p. 7

B. Procedures of the SIM-D2NN

  • After training, optimized phases are fixed in the metasurface, and inference selects the terrain class associated with the antenna receiving the highest intensity.The feedforward inference process is analog and requires no additional onboard computation.Source: 2) Training and Deployment of the… · p. 7
  • Channel acquisition and coherence-interval variations are handled separately through communication-layer mechanisms, rather than by the in-wave inference model.The paper names SIM-specific channel estimation, channel equalization, and transfer learning as possible mechanisms.Source: 2) Training and Deployment of the… · p. 7

IV. DESIGN EVALUATION AND PARAMETER SENSITIVITY

The evaluation examines how network configurations, training strategies, and optimization techniques affect SIM-D2NN performance. Its ablations cover binary, three-class, and four-class terrain classification tasks.

IV. DESIGN EVALUATION AND PARAMETER SENSITIVITY

  • Ablations compare network configurations, training strategies, and optimization techniques for the proposed SIM-D2NN.The section evaluates their influence on performance.Source: §IV · p. 7
  • The experiments span a binary task within one geographic zone and three-class and four-class tasks across diverse regions.Source: §IV · p. 7
  • Table I groups precision, recall, F1 score, and overall accuracy by task, with each row representing an ablation setting.Source: §IV · p. 7

A. Dataset Construction and Setup

The evaluation uses spatially isolated Level-0 SAR patches to construct binary and geographically diverse multiclass datasets. Precision, recall, F1 score, and accuracy provide the evaluation basis across tasks.

A. Dataset Construction and Setup

  • Training and evaluation swaths are separated along azimuth, with a 288-pixel guard band preventing pixel-sharing between the distributions.Patches are 128 × 128 pixels with a stride of 32; samples are drawn after block isolation.Source: A. Dataset Construction and Setup · p. 7
  • The binary Santos–São Paulo dataset contains 285,680 land and ocean patches, evenly split between the two categories.Labels are assigned using reference imagery.Source: A. Dataset Construction and Setup · p. 7
  • The three-class subset has 34,436 desert, forest, and ocean patches; the four-class subset has 45,915 desert, ocean, urban, and forest patches from distinct regions.The tasks increase in geographic diversity and terrain complexity.Source: A. Dataset Construction and Setup · p. 7

B. Performance Metrics

  • Evaluation uses class-wise TP, TN, FP, and FN counts to define precision, recall, F1 score, and accuracy across classification scenarios.The metrics are intended to provide a comprehensive basis for evaluating varying task complexity.Source: B. Performance Metrics · p. 8

C. Performance Analysis

A 90° phase rotation and four-layer design support learning from noisy raw SAR data, while data volume, optimizer, and loss choices also affect performance. Results indicate diminishing gains from additional training data and depth.

C. Performance Analysis

  • 89.51% to 91.56% binary ∆Acc is reported when sampling increases from 10% to the full dataset; four-class accuracy gains only 3.92%.Performance improves with increased sampling across tasks, but the reported gains diminish with larger datasets.Source: C. Performance Analysis · p. 8
  • Approximately 32% and 42% ∆F1 gains are reported for 90° phase rotation over duplicated 0° input in the binary and four-class tasks, respectively.The 0° setting achieves 53.90% binary accuracy; nonzero rotations improve performance, with 90° best among tested settings.Source: C. Performance Analysis · pp. 8–9
  • 64.71% versus 87.33% four-class ∆Acc is reported at η = 1 × 10−4 versus η = 1 × 10−2; SGD and RMSprop trail AdamW by 5%–10%.The passage attributes the lower-learning-rate result to underfitting and the alternative-optimizer gap to weaker handling of phase-only parameters.Source: C. Performance Analysis · p. 9
  • Focal loss and label smoothing remain within 1–2% of the baseline; standard complex CE loss consistently achieves the best performance.Focal loss slightly improves recall and label smoothing marginally improves precision in the four-class task.Source: C. Performance Analysis · p. 9

V. NUMERICAL RESULTS

The numerical evaluation configures a multilayer metasurface for direct terrain-class output and compares it with analog and digital model variants. It also examines binary-task performance as transmit power varies.

A. Parameter Configurations and Benchmark Description

  • The SIM-D2NN uses 2,048 meta-atoms across four layers, with receive antenna count matched to the number of terrain classes.Experiments use a 5 GHz carrier, 150 km space-to-ground distance, and a 0.05 m SIM thickness unless otherwise noted.Source: A. Parameter Configurations and… · p. 9
  • Phase-only modulation is the primary SIM-D2NN model; the phase-and-amplitude variant offers greater expressiveness but adds hardware complexity.The phase-only design is described as fully analog and hardware-friendly.Source: A. Parameter Configurations and… · pp. 9–10
  • Fig. 4 relates transmit power Pt to performance for the binary terrain-classification task.The passage identifies the plotted relationship but does not specify its outcome.Source: Figure 4 · p. 10
  • The reference models include a linear classifier, a two-layer complex-valued MLP, a three-layer CNN, and a single-layer, single-head ViT.The ViT uses 4 × 4 input patches and 64 tokens.Source: A. Parameter Configurations and… · p. 10

B. Performance Evaluation

SIM-D2NN trades some accuracy against digital computation, with performance also varying across transmit power, training settings, and layer depth. The visualization results show coherent binary-task segmentation with phase rotation, while deeper models offer diminishing gains beyond four layers.

1) Computational complexity and performance evaluation on different models:

  • 87.58%±0.7% and 86.32%±1.2% accuracy at phase-perturbation standard deviations of 0.05 and 0.1 indicate stable performance in those trials.Each accuracy is averaged over 50 independent Monte Carlo trials; the reported energy and latency characterize in-wave computation, not the complete end-to-end pipeline.Source: 1) Computational complexity and… · p. 10
  • 97.34% accuracy for CNN and 96.26% for ViT exceed SIM-D2NN's 89.51%, while SIM-D2NN uses near-zero digital FLOPs.The comparison describes a performance–complexity trade-off: nonlinear digital architectures achieve higher accuracy, while SIM-D2NN substantially reduces digital computational burden.Source: 1) Computational complexity and… · p. 11
  • 52.98% to 89.51% accuracy as transmit power rises from −20 to 20 dBm supports phase-only SIM-D2NN; phase-plus-amplitude modulation adds only 0.19% at 15 dBm.The phase-plus-amplitude configuration doubles learnable parameters, reducing its cost-effectiveness.Source: 2) The transmit power Pt versus four… · p. 11
  • 3-bit phase quantization reaches 86.48% accuracy and 92.84% F1 at 20 dBm, while 2-bit quantization remains above 83% accuracy at high SNR.Noise-aware training gives a stable performance region within 0–15 dBm; the model trained at 20 dBm generalizes better overall than the one trained at −5 dBm, particularly for recall and accuracy under high-SNR conditions.Source: 2) The transmit power Pt versus four… · p. 11

3) The visualization results on the whole binary classification dataset:

  • With 90° rotation, SIM-D2NN produces coherent binary segmentation with boundaries close to ground truth; without rotation, its predictions are spatially incoherent.The digital linear classifier also produces sharp transitions with minor boundary errors, and SIM-D2NN achieves comparable spatial accuracy under high-SNR conditions.Source: 3) The visualization results on the… · pp. 11–12, Figure 5 · p. 11
  • Depth gains rise from 5.0% for binary to 14.2% for three-class and 25.1% for four-class accuracy, but four-class accuracy moves only 63.22% to 63.61% from four to six layers.Gains in precision, recall, and F1 also become negligible beyond four layers; the four-layer model is presented as balancing performance and hardware complexity.Source: Table III · p. 12, 4) The number of layers L · p. 12, 3) The visualization results on the… · p. 12

5) Convergence analysis:

The SIM-D2NN combines phase-rotated raw-SAR inputs with multilayer in-wave processing, improving performance on binary tasks while retaining limits on complex multiclass raw data. Results also show strong depth-related gains on preprocessed AIRSAR data and identify practical hardware validation and nonlinear processing as future needs.

5) Convergence analysis:

  • Phase rotation yielded relative accuracy gains of 55.68%, 43.65%, and 46.37% for binary, three-class, and four-class tasks, while aperture-wide interference physically filters phase fluctuations.The reported gains compare models trained with and without phase rotation; the multilayer architecture is described as a spatial integrator.Source: 5) Convergence analysis · p. 12

7) Benchmark Testing on L-band AIRSAR Flevoland Dataset

5) Convergence analysis:

  • In four-class classification, SIM-D2NN accuracy was 61.9% for forest, 60.5% for desert, and 66.7% for urban, versus MLP accuracy above 81.7% across classes.The passage attributes this gap to the linear model’s limits on overlapping features and notes forest patches misclassified as desert.Source: 6) Confusion matrix comparison on… · p. 13
  • Final intensity detection’s square-law nonlinearity remains insufficient for highly overlapping multiclass raw-SAR features without intermediate hidden-layer nonlinearities.The passage identifies this as a boundary of the linear architecture for complex, multi-region raw SAR data.Source: 7) Benchmark Testing on L-band AIRSAR… · p. 13

VI. CONCLUSION

  • Around 90% classification accuracy was achieved under binary tasks directly from raw SAR data.The conclusion reports this result for the proposed method.Source: §VI · p. 13
  • The framework enables onboard inference with minimal digital processing and substantially reduces data-transmission overhead while maintaining competitive performance.Source: §VI · p. 14
  • Practical SIM implementations may face amplitude variations, parasitic mutual coupling, temperature-dependent drift, fabrication tolerances, and material losses; prototype hardware-in-the-loop validation is planned.The passage describes these as practical effects not yet characterized through prototype validation.Source: §VI · p. 14
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