End-to-End Learned PHY

The fundamental structure treats the transmitter as an encoder neural network and the receiver as a decoder neural network, with the physical channel acting as a non-trainable bottleneck layer. During training, backpropagation passes through a differentiable channel model, allowing both ends to learn optimal representations jointly. This eliminates the need for separate algorithms for source coding, channel coding, modulation, and equalization—the network discovers the most efficient scheme for the given channel statistics and task objective.

Unlike classical PHY designs optimized for generic bit-error rate (BER), learned PHY systems are trained end-to-end for the actual application objective. Examples include:

• Image transmission: Maximizing peak signal-to-noise ratio (PSNR) or structural similarity (SSIM) at the receiver, not bit accuracy
• Semantic communication: Preserving only the meaning relevant to a downstream classifier, discarding irrelevant pixel-level detail
• Low-latency control: Minimizing age of information (AoI) for industrial automation packets This task-aware optimization can achieve significant gains in application-level performance while using less bandwidth than bit-centric designs.

The transmitter network learns an optimal constellation geometry directly in the I/Q plane through gradient descent, rather than using fixed schemes like QPSK or 64-QAM. The resulting constellation points are irregularly spaced to maximize mutual information for the specific signal-to-noise ratio (SNR) and channel impairment profile. This geometric shaping can approach the Shannon capacity more closely than traditional probabilistic shaping alone, particularly in non-AWGN channels with non-linearities or phase noise.

A critical limitation is the requirement for a differentiable channel model during training. The stochastic gradient must flow from the receiver loss back through the channel to the transmitter. Solutions include:

• Generative adversarial networks (GANs) trained on real channel measurements to create differentiable surrogates
• Reinforcement learning approaches that estimate policy gradients without explicit channel differentiation
• Alternating training where transmitter and receiver are updated separately using feedback channels In deployment, the trained transmitter generalizes to the real physical channel without requiring differentiability.

Learned PHY systems inherently compensate for non-linear hardware impairments that classical models struggle to address. The autoencoder can learn to pre-distort signals to counteract:

• Power amplifier non-linearity near saturation
• I/Q imbalance from imperfect quadrature mixing
• Phase noise from low-cost oscillators
• Quantization errors from low-resolution digital-to-analog converters (DACs) This allows operation closer to hardware limits, improving power efficiency and enabling cheaper radio front-ends without sacrificing link quality.

Despite promising results in simulations, several barriers prevent widespread deployment:

• Training overhead: Requires massive datasets of channel realizations and may need periodic retraining as environments change
• Interpretability: The learned representations are opaque, making debugging and certification difficult for safety-critical systems
• Standardization: No framework exists for interoperability between different vendors' learned transmitters and receivers
• Computational complexity: Real-time inference on embedded radio hardware with strict latency budgets remains challenging Active research focuses on model-driven unfolding and meta-learning to address these gaps.

The core architectural blueprint for end-to-end learned PHY, where the transmitter acts as the encoder mapping source bits to channel symbols, the wireless channel serves as a non-trainable stochastic bottleneck layer, and the receiver functions as the decoder reconstructing the original message. Training minimizes a loss function—typically categorical cross-entropy for bit recovery or mutual information maximization—via backpropagation through the channel model. This joint optimization eliminates the information bottlenecks inherent in modular designs where channel estimation, equalization, and decoding are optimized independently.

A critical enabler for end-to-end training: the wireless channel must be represented as a differentiable stochastic transformation to allow gradient flow from receiver loss back to transmitter weights. Approaches include:

• Generative channel models (e.g., Channel GANs) that learn a differentiable surrogate from real measurements
• Probabilistic channel models with known parametric distributions (AWGN, Rayleigh fading) that support reparameterization tricks
• Alternating training where transmitter and receiver are updated in separate phases when a true differentiable channel is unavailable Without differentiability, the transmitter cannot learn optimal constellation shaping or coding strategies.

A direct application of end-to-end learning where the physical positions of constellation points in the I/Q complex plane are treated as trainable parameters. Unlike traditional QAM with fixed grid positions, learned constellations optimize point locations via gradient descent to maximize mutual information or minimize bit-error rate for a specific signal-to-noise ratio and channel model. The resulting constellations often exhibit non-uniform, Gaussian-like distributions that approach the Shannon capacity bound, particularly in non-linear fiber optic and satellite channels where geometric shaping provides significant shaping gain over probabilistic shaping alone.

An extension of the end-to-end paradigm that shifts the optimization objective from bit-level fidelity to task-level semantic meaning. Rather than reconstructing exact transmitted bits, the receiver is trained to perform a specific task—such as image classification or text comprehension—directly from the received signal. This enables joint source-channel coding where the transmitter learns to extract and encode only the semantically relevant features, dramatically reducing bandwidth requirements. Key distinction: while standard end-to-end PHY optimizes for symbol or bit accuracy, semantic communication optimizes for downstream task performance, trading reconstruction fidelity for transmission efficiency.

A hybrid methodology that bridges classical signal processing with end-to-end learning by unrolling iterative algorithms (like ISTA, ADMM, or belief propagation) into neural network layers. Each unrolled iteration becomes a network layer where hand-crafted parameters—such as step sizes, thresholds, or damping factors—are replaced with learnable parameters optimized via backpropagation. This approach preserves the structural inductive bias of the original algorithm while leveraging data-driven adaptation. In the context of end-to-end PHY, unfolded detectors and decoders can be integrated into the receiver portion of the autoencoder, combining the interpretability of model-based methods with the performance of learned systems.

A technique that exploits the superposition property of the wireless multiple-access channel to compute mathematical functions (sum, average, maximum) of distributed sensor readings directly during simultaneous analog transmission. When integrated with end-to-end learned PHY, the transmitter and receiver are jointly trained to pre-process and post-process signals such that the channel's natural summation computes a target function—critical for federated learning model aggregation. This eliminates the need for orthogonal resource allocation and individual decoding, achieving communication efficiency that scales with the function's complexity rather than the number of devices.