Frequency-Domain Positional Encoding

Assigns a unique, learnable vector to each discrete frequency bin or subcarrier index in the spectral sequence. This is the direct frequency-domain analog of standard sinusoidal positional encoding. The model learns a distinct embedding for the 1st, 2nd, and Nth subcarrier, allowing the self-attention mechanism to understand that a signal at bin 50 is structurally different from a signal at bin 500, even if their magnitudes are identical. This is critical for tasks like automatic modulation classification where the spectral shape's location matters.

Applies Rotary Position Embedding to encode relative frequency offsets between spectral tokens. Instead of learning an absolute index, RoPE rotates the query and key vectors in the complex plane by an angle proportional to their frequency separation. This is exceptionally well-suited for complex-valued IQ signals because:

• It naturally preserves magnitude and phase relationships
• The dot-product attention score depends only on the relative distance between bins
• It allows the model to generalize to sequence lengths unseen during training, a vital property for flexible spectrum analysis

Replaces hand-crafted sinusoidal encodings with a small neural network that learns a continuous frequency embedding function. A multi-layer perceptron (MLP) maps a scalar frequency value (e.g., 2.4 GHz) directly to a high-dimensional vector. This is essential for irregularly sampled spectra or non-uniform channel spacing where discrete index-based methods fail. The learned function can interpolate smoothly between known frequencies, providing a semantically meaningful representation for any arbitrary point in the spectrum.

Combines two independent positional encodings—one for the time axis and one for the frequency axis—to tokenize a full spectrogram. Each patch in a patchified spectrogram receives a composite embedding that sums a temporal position vector and a frequency position vector. This allows a Spectrogram Vision Transformer to simultaneously learn:

• When a signal occurs (temporal onset, duration)
• Where in the spectrum it resides (center frequency, bandwidth) This dual encoding is fundamental for separating overlapping emitters in dense electromagnetic environments.

Directly injects positional information into the real and imaginary components of complex-valued tokens. Instead of adding a real-valued vector, the encoding modulates the phase of the IQ sample based on its frequency index. A frequency offset is encoded as a phase rotation in the complex plane, mathematically aligning with the physical property that a frequency shift corresponds to a time-domain phase ramp. This preserves the algebraic structure of the signal and is used in Complex-Valued Attention mechanisms for superior physical-layer processing.

Adds a learned scalar bias to the attention logits based on the distance between frequency bins. This is a lightweight alternative to full positional encoding. For every pair of tokens, a bias term is looked up from a table indexed by their frequency separation. This explicitly encourages or discourages attention between nearby vs. distant subcarriers. It is particularly effective in Channel State Information (CSI) transformers, where the correlation between subcarriers decays predictably with frequency separation due to the channel's delay spread.

Standard attention operates on real numbers, but RF signals are inherently complex (IQ samples). This mechanism extends self-attention to operate natively on magnitude and phase.

• Preserves the phase relationships critical for coherent signal processing
• Uses complex-valued matrix multiplications and softmax variants
• Avoids the information loss from splitting IQ into separate real channels
• Essential for tasks like beamforming and channel estimation

The preprocessing module that converts a raw waveform into a sequence of tokens a transformer can ingest. It bridges the gap between continuous signals and discrete attention.

• Applies Short-Time Fourier Transform (STFT) to create spectrogram patches
• Each token represents a localized time-frequency bin
• The frequency index of each token becomes the basis for positional encoding
• Enables standard transformer backbones to process spectral content efficiently

An adaptation of the Vision Transformer that treats a spectrogram as an image. The model learns spatial and temporal features by applying self-attention to flattened 2D patches.

• Divides the spectrogram into a grid of non-overlapping patches
• Each patch is linearly projected into a token embedding
• Positional encoding must capture both time and frequency axes
• Effective for emitter identification and modulation classification

A masking pattern that restricts the attention mechanism to only past and present time steps. This is critical for real-time, streaming signal processing where future samples are unavailable.

• Implements a lower-triangular attention mask
• Prevents information leakage from future tokens
• Enables online inference for streaming RF applications
• Often combined with frequency-domain positional encoding for causal spectral processing

A spectrogram divided into a grid of 2D patches, each flattened into a token vector. This patchification step is the critical bridge between spectral imagery and transformer sequence models.

• Non-overlapping or overlapping patches capture local time-frequency structure
• Patch size determines the granularity of spectral analysis
• Smaller patches capture fine-grained signal features
• Larger patches provide broader context at the cost of resolution