Neural Network Demapper

The core function of a neural network demapper is to output a log-likelihood ratio (LLR) for each transmitted bit. Unlike a hard decision that outputs a 0 or 1, the LLR quantifies the confidence of the decision.

• Positive LLR: Indicates a logical '0' is more probable.
• Negative LLR: Indicates a logical '1' is more probable.
• Magnitude: The absolute value represents the confidence level; a larger magnitude means higher certainty. This soft information is critical for downstream channel decoders (like LDPC or Turbo decoders) to achieve near-Shannon-limit performance.

Classical maximum-likelihood demapping assumes additive white Gaussian noise (AWGN) and computes Euclidean distances to fixed constellation points. A neural network demapper learns a complex, non-linear decision boundary directly from data.

• Handles Impairments: It naturally adapts to non-Gaussian noise, phase noise, and I/Q imbalance without explicit modeling.
• Arbitrary Geometry: The learned boundary can warp to separate symbols in ways impossible for rigid Voronoi regions, effectively learning to de-noise the received signal constellation.

A key advantage is robustness to hardware impairments that devastate model-based receivers. The neural network demapper learns to implicitly invert these distortions during training.

• Power Amplifier Non-Linearity: Compensates for saturation and memory effects without a separate pre-distortion step.
• Phase Noise: Tracks and corrects for common oscillator phase errors.
• I/Q Imbalance: Learns to separate the cross-talk between in-phase and quadrature components. This single-network approach simplifies the receiver chain by absorbing multiple correction blocks into one learned function.

Neural network demappers operate directly on complex baseband symbols (I/Q samples), preserving the phase and amplitude relationship. Architectures are designed to handle complex arithmetic:

• Complex-Valued Neural Networks (CVNNs): Use complex weights and activation functions to maintain the algebraic structure of the signal.
• Dual-Input Real Networks: A common alternative is to split the complex sample into two real-valued channels (I and Q) and process them with a standard real-valued network. Direct I/Q processing allows the network to learn features in the phase domain that are lost in magnitude-only representations.

The demapper is typically trained using binary cross-entropy (BCE) loss between the predicted LLRs and the true transmitted bits. This loss function directly optimizes the quality of the soft information.

• End-to-End Training: The demapper can be trained in isolation with known transmitted bits, or jointly with the channel decoder.
• Gradient Path: For joint training, gradients must flow through the channel decoder back to the demapper, requiring a differentiable decoder or a proxy loss. BCE loss penalizes confident wrong predictions heavily, ensuring well-calibrated LLR outputs.

While a neural network demapper replaces the algorithmic complexity of maximum-likelihood detection, it introduces a fixed computational graph that executes in constant time.

• Inference Latency: A forward pass through a small multi-layer perceptron is deterministic and often faster than an exhaustive search over a high-order constellation.
• Memory Footprint: The model weights require storage, but this is typically negligible compared to large lookup tables.
• Edge Deployment: Optimized models can be quantized and deployed on FPGA or embedded ARM processors for real-time, low-power symbol detection.

The classical statistical baseline that neural demappers aim to outperform. A maximum-likelihood (ML) demapper computes log-likelihood ratios by exhaustively evaluating the Euclidean distance between a received I/Q symbol and every ideal constellation point, assuming additive white Gaussian noise. This approach is optimal under ideal linear channel conditions but degrades catastrophically in the presence of hardware impairments such as phase noise, I/Q imbalance, or non-linear amplifier distortion. The computational complexity scales exponentially with the modulation order, making it prohibitive for high-order QAM schemes like 4096-QAM. Neural demappers bypass this by learning a direct, non-linear mapping from received symbols to soft bits, implicitly modeling the impairment distribution without explicit mathematical characterization.

The fundamental output of any soft demapper, representing the confidence that a received bit is a 0 or 1. An LLR is defined as the natural logarithm of the ratio of probabilities: L(b) = ln[P(b=0|y)/P(b=1|y)], where y is the received symbol. A large positive LLR indicates high confidence in a 0, while a large negative value indicates high confidence in a 1. LLRs near zero signal uncertainty. Neural network demappers are trained to output well-calibrated LLRs directly, often using a binary cross-entropy loss function. The quality of these soft estimates critically determines the performance of the subsequent channel decoder, such as an LDPC or Polar decoder, which relies on accurate soft information for iterative belief propagation.

The primary advantage of neural demappers over classical methods. Real-world transceivers suffer from power amplifier non-linearity, phase noise from local oscillators, I/Q imbalance from imperfect mixers, and quantization errors from analog-to-digital converters. These impairments distort the received constellation in ways that cannot be modeled by simple additive Gaussian noise. A neural demapper learns the empirical conditional distribution P(b|y) directly from labeled training data captured on the target hardware, effectively learning a complex, non-linear decision boundary that accounts for all impairment sources simultaneously. This data-driven approach eliminates the need for explicit impairment modeling and separate compensation algorithms.

A hybrid approach that embeds classical signal processing structure within the neural network to improve data efficiency and interpretability. A model-based neural demapper might first apply a conventional linear minimum mean square error equalizer, then feed the equalized symbols into a lightweight neural network that only learns the residual non-linear correction. This contrasts with purely black-box approaches by incorporating domain knowledge as inductive bias. The result is a demapper that requires fewer training samples, generalizes better to unseen channel conditions, and provides a degree of algorithmic transparency. This architecture is particularly valuable in mission-critical applications where purely learned components require rigorous verification and validation.