Autocorrelation Embedding

Autocorrelation embedding explicitly encodes cyclostationary signatures—statistical properties that vary periodically with time—which are fundamental to distinguishing modulated signals. By computing the autocorrelation function at multiple lag values, the embedding captures the symbol rate, carrier frequency offset, and pulse shaping characteristics that remain invariant to random data content. This transforms a raw time-series into a compact, discriminative representation that highlights the signal's underlying periodic structure.

The autocorrelation function is sampled at discrete lag intervals to produce a fixed-length vector, which is then projected through a learned linear layer or small MLP to create a dense embedding token. This token serves as a single input to a transformer encoder, representing the entire signal segment's temporal correlation structure. Unlike raw IQ samples that require long sequences, a single autocorrelation embedding token can summarize hundreds of samples, dramatically reducing sequence length and computational complexity.

Autocorrelation naturally suppresses uncorrelated additive white Gaussian noise (AWGN) because noise samples at different time lags have zero expected correlation. This property makes autocorrelation embeddings inherently more robust to low signal-to-noise ratio (SNR) conditions compared to raw waveform embeddings. The signal's deterministic periodic components accumulate constructively in the autocorrelation domain, while random noise contributions diminish, providing a cleaner representation for downstream classification.

The autocorrelation function discards absolute phase information while preserving relative phase relationships between time-shifted copies of the signal. This provides a degree of invariance to arbitrary carrier phase rotations and constant time delays, which are common channel impairments. The embedding focuses on the signal's second-order statistics—the correlation structure—rather than its exact waveform shape, improving generalization across varying channel conditions without requiring explicit phase synchronization.

By computing autocorrelation values across a range of discrete lags, the embedding captures temporal dependencies at multiple timescales simultaneously. Short lags encode fine-grained pulse shaping and rapid variations, while longer lags reveal symbol-period periodicity and frame-level structure. This multi-resolution representation allows a single embedding vector to encode both micro-level signal characteristics and macro-level protocol patterns, providing rich input to the transformer's attention mechanism.

Autocorrelation embeddings serve as a feature extraction frontend within end-to-end learned receiver architectures like DeepRx. The embedding module replaces traditional synchronization and matched filtering blocks, providing a differentiable transformation from raw IQ samples to a compact statistical representation. This allows the entire receiver—from feature extraction through classification—to be trained jointly via backpropagation, optimizing the autocorrelation lag selection and embedding projection for the specific classification task.

The process of isolating periodic statistical parameters from a signal's autocorrelation function. Unlike stationary noise, modulated signals exhibit cyclostationarity at symbol rates, chip rates, and carrier frequency offsets. The autocorrelation embedding is a learned, compressed representation of these features, capturing the cyclic spectral density that distinguishes different modulation formats and emitter hardware imperfections.

A preprocessing module that converts a raw time-series signal into a sequence of tokens representing localized time-frequency patches. Before an autocorrelation embedding is generated, the signal often passes through this tokenizer to create a spectrogram-like representation. The autocorrelation is then computed on these patches to capture periodicities, producing tokens that a standard transformer backbone can process efficiently.

The application of Rotary Position Embedding (RoPE) to RF signal tokens, encoding relative temporal or frequency offsets through rotation in the complex plane. This is particularly synergistic with autocorrelation embeddings, as RoPE naturally captures the phase relationships inherent in the complex-valued autocorrelation function, providing a strong inductive bias for modeling periodic signal structures.

An attention masking pattern that restricts a transformer model to only attend to past and present time steps. When processing a sequence of autocorrelation embeddings for real-time signal classification, causal attention ensures the model does not peek into the future, making it suitable for streaming, low-latency applications like cognitive radio and electronic warfare where decisions must be made on live signal captures.

A neural network architecture that applies the self-attention mechanism directly to sequences of spectral data. Autocorrelation embeddings serve as a powerful input token for this architecture, as they provide a noise-robust, translation-invariant representation of a signal's periodic structure. The spectrum transformer can then model long-range dependencies between these cyclical features for superior modulation classification.

The use of deep learning for specific emitter identification (SEI) by analyzing unique hardware impairments. Autocorrelation embeddings are a critical feature for this task, as they capture subtle, device-specific periodicities caused by non-linear power amplifiers, oscillator phase noise, and I/Q imbalance. These embeddings provide a stable, identifying signature that persists across different transmitted data payloads.