Hierarchical AMC

The architecture splits classification into a coarse stage and a fine stage to mimic expert signal analysis workflows.

• Stage 1 — Family Classifier: A neural network trained to distinguish between broad modulation families such as PSK, QAM, FSK, and APSK. This classifier operates on high-level statistical features or raw I/Q samples.
• Stage 2 — Intra-Family Classifier: A specialized sub-network, selected based on the Stage 1 output, that discriminates between orders within the predicted family (e.g., BPSK vs. QPSK vs. 8-PSK).
• Gating Mechanism: The confidence score from Stage 1 determines which Stage 2 expert is activated, preventing a QAM-trained classifier from attempting to classify an FSK signal.

Higher-order cumulants provide a theoretically grounded feature set for the coarse classification stage, exploiting their Gaussian noise immunity.

• Second-Order Cumulant (C₂₁): Distinguishes between real-valued constellations (BPSK, PAM) and complex-valued constellations (QAM, PSK).
• Fourth-Order Cumulant (C₄₂): Separates PSK from QAM families by measuring the kurtosis of the signal distribution.
• Eighth-Order Cumulant (C₈₀): Resolves ambiguities between higher-order QAM constellations that share similar fourth-order statistics.
• These hand-crafted features feed a lightweight classifier such as a Support Vector Machine or a shallow neural network, minimizing Stage 1 latency.

Each Stage 2 expert is a specialized deep neural network optimized for a single modulation family, trained on a restricted output space.

• PSK Expert: A complex-valued convolutional network that exploits the constant-envelope property of PSK signals to focus on phase transitions.
• QAM Expert: A multi-scale feature extractor that analyzes both amplitude and phase variations to distinguish dense constellations like 64-QAM from 256-QAM.
• FSK Expert: A time-frequency analysis branch using Short-Time Fourier Transform front-ends to capture the distinct frequency hopping patterns.
• Training Isolation: Each expert is trained independently on its family's data, preventing the catastrophic interference that occurs when a single flat classifier must learn overlapping feature manifolds.

A critical vulnerability of hierarchical architectures is cascading errors, where a Stage 1 misclassification forces the wrong Stage 2 expert to process the signal.

• Top-K Gating: Instead of activating only the single highest-confidence expert, the system routes the signal to the top K=2 or K=3 family experts and fuses their outputs.
• Confidence Thresholding: If the Stage 1 softmax probability falls below a calibrated threshold (e.g., 0.85), the system falls back to a flat classifier or flags the signal for human-in-the-loop review.
• Joint Training with Feedback: The Stage 1 classifier receives gradient feedback from the Stage 2 experts during training, learning to minimize the end-to-end classification loss rather than just the family-level cross-entropy.

Hierarchical decomposition reduces inference latency and memory footprint compared to a monolithic classifier with an equivalent number of output classes.

• Conditional Computation: Only one lightweight family classifier and one specialized expert execute per inference, rather than a single massive network evaluating all possible modulation hypotheses.
• Model Quantization Compatibility: The smaller expert networks are more amenable to aggressive INT8 quantization without accuracy degradation, enabling deployment on FPGA and embedded SDR platforms.
• Parallelization: Multiple Stage 2 experts can be pre-loaded and executed in parallel on a GPU if latency constraints permit, trading throughput for the error mitigation benefits of Top-K gating.

Hierarchical architectures naturally support open-set recognition, where unknown modulation families must be detected and rejected rather than forcibly classified.

• Family-Level OpenMax: The Stage 1 classifier is augmented with an OpenMax layer that models the distribution of known family activations, assigning a probability to the 'unknown family' hypothesis.
• Novelty Buffer: Signals classified as unknown are buffered and clustered using unsupervised contrastive learning, enabling human analysts to label emerging modulation types for subsequent model retraining.
• Rejection Cascade: If Stage 1 identifies a known family but the Stage 2 expert's confidence is anomalously low, the system triggers a secondary rejection check, catching novel intra-family variants that were absent from training.