Transformer Equalizer

The self-attention mechanism computes a weighted sum of all received symbols in a sequence, allowing the model to directly relate a current symbol to distant, interfering symbols. Unlike finite impulse response filters, this provides a global receptive field that can capture long delay spreads without an exponential increase in parameters. The attention weights are dynamically computed based on the received signal itself, making the equalizer context-aware and robust to varying channel conditions.

For streaming applications, a causal attention mask is applied to restrict the self-attention computation to only past and present symbols. This prevents the model from peeking at future samples, ensuring it can operate in a real-time, online fashion. The mask is typically an upper-triangular matrix of negative infinities applied before the softmax, zeroing out attention weights for future time steps.

Raw IQ samples are treated as complex-valued tokens. Instead of splitting into real and imaginary streams, specialized embeddings preserve the magnitude and phase relationships inherent in the baseband signal. This can be achieved through complex linear projections or by using Rotary Position Embedding (RoPE), which naturally encodes relative positions via rotation in the complex plane, a mathematically elegant fit for phase-coherent signals.

The equalizer uses cross-attention layers to condition its symbol estimates on known pilot symbols. The received signal sequence acts as the query, while the known pilot sequence serves as the key and value. This allows the model to explicitly learn the channel response at pilot locations and interpolate it to data symbols, effectively performing implicit channel estimation and equalization in a single unified step.

Inspired by deep unfolding, the transformer block can be applied iteratively, with the output of one pass fed as input to the next. This mimics the iterative nature of classical turbo equalization but with learned, attention-based updates. Each iteration refines the symbol estimates, progressively reducing inter-symbol interference and improving log-likelihood ratio (LLR) quality for the channel decoder.

The transformer equalizer can be extended to output soft bit estimates (LLRs) directly, bypassing the need for a separate demapping stage. The final linear layer projects the attended symbol representations to logits over the constellation points, and a softmax produces probabilities. This end-to-end differentiability allows the entire receiver chain—from IQ samples to bits—to be optimized jointly.

A fully learned neural receiver that replaces the entire traditional baseband processing chain—including channel estimation, equalization, and demapping—with a single end-to-end deep learning model. Unlike a standalone Transformer Equalizer, DeepRx jointly optimizes all receiver functions, often using a hybrid convolutional-transformer backbone to process raw IQ samples and output log-likelihood ratios directly.

• Replaces the full signal processing pipeline
• Often trained end-to-end on simulated channel data
• Demonstrates superior performance in non-linear, hardware-impaired channels

A transformer model designed to process Channel State Information (CSI) matrices, leveraging self-attention to capture spatial and frequency correlations across antenna ports and subcarriers. While a Transformer Equalizer operates on received symbols to combat ISI, a CSI Transformer focuses on compressing and reconstructing the channel response itself, enabling more accurate channel estimation for massive MIMO systems.

• Input: CSI matrices in the spatial-frequency domain
• Output: Reconstructed or compressed channel estimates
• Key mechanism: Multi-head self-attention over antenna and subcarrier dimensions

A transformer architecture adapted to process raw in-phase and quadrature (IQ) sample sequences directly. It uses specialized tokenization—often linear projections of complex-valued samples—and Rotary Position Embedding (RoPE) to encode temporal relationships in the complex baseband waveform. This forms the foundational backbone upon which a Transformer Equalizer is built, enabling the model to attend across hundreds of symbols to resolve inter-symbol interference.

• Operates natively on complex baseband samples
• Tokenization: Complex-to-real projection or complex-valued linear layers
• Positional encoding: RoPE or learned complex embeddings

An attention masking pattern that restricts the self-attention mechanism to only attend to past and present time steps, preventing information leakage from future symbols. This is critical for deploying a Transformer Equalizer in real-time, streaming communication systems where causality must be strictly enforced. The mask is typically a lower-triangular matrix applied to the attention scores.

• Enforces strict temporal causality
• Suitable for online, low-latency equalization
• Contrasts with bidirectional attention used in offline processing

An extension of the standard attention mechanism that operates natively on complex numbers, preserving the magnitude and phase relationships inherent in IQ baseband signals. Standard transformers treat real and imaginary components as separate real-valued channels, potentially losing phase coherence. Complex-valued attention uses complex multiplications and activations, providing a more expressive and physically meaningful computation for a Transformer Equalizer.

• Preserves phase information through complex operations
• Uses complex-valued weights and activations (e.g., modReLU)
• Improves representation power for physical-layer signals

A learned vector representation that encodes the delay and Doppler shift characteristics of individual multipath propagation paths. When used as input tokens for a transformer, these embeddings allow the model to process the wireless channel as a set of discrete scatterers. A Transformer Equalizer can leverage this representation to explicitly model the channel's delay-Doppler structure, improving equalization in high-mobility scenarios.

• Encodes physical propagation parameters
• Enables path-level attention over multipath components
• Particularly effective for OTFS and high-Doppler channels