Integrated Sensing and Communication Autoencoder

The loss function is a weighted multi-objective combination of communication and sensing metrics. Rather than designing separate waveforms, the autoencoder minimizes a composite loss:

• Communication Loss: Typically binary cross-entropy or mean squared error between transmitted and decoded bits.
• Sensing Loss: Often a mean squared error between the true target parameter (range, velocity, angle) and the neural network's estimate.
• Trade-off Parameter: A scalar weight λ balances the two tasks, allowing the system to prioritize throughput or radar accuracy based on operational context.

The bottleneck of the autoencoder learns a unified latent code that encodes both information bits and sensing illumination patterns. This shared representation is the core innovation:

• The transmitter maps input bits to a complex baseband waveform that is simultaneously information-rich and radar-optimal.
• The receiver splits into two heads: a communication decoder that recovers bits and a sensing decoder that estimates target parameters.
• The latent space forces the waveform to possess high auto-correlation for radar while maintaining distinct decision regions for communication symbols.

End-to-end training requires gradients to flow from the receiver back to the transmitter through the physical channel. This necessitates a differentiable surrogate of the wireless environment:

• The channel model must capture both communication propagation (multipath fading, noise) and radar target interaction (delay, Doppler shift, radar cross-section).
• A typical model applies a learnable tapped delay line with complex Gaussian coefficients, where the delay and Doppler parameters are functions of the target state.
• The reparameterization trick is used to maintain differentiability through stochastic channel realizations.

The autoencoder implicitly learns to shape the ambiguity function of the transmitted waveform without explicit template matching. This is a departure from classical pulse-Doppler radar design:

• The network discovers waveforms that achieve thumbtack-like ambiguity functions (narrow main lobe, low sidelobes) for high resolution in both delay and Doppler.
• Unlike fixed chirp or phase-coded sequences, the learned waveform adapts its time-frequency structure to the specific target scene and channel conditions.
• The sensing decoder learns to perform matched filtering implicitly, with the network weights acting as a learned filter bank.

ISAC autoencoders can be trained to be inherently robust to real-world RF front-end non-linearities that degrade both sensing and communication:

• Power amplifier non-linearity: The transmitter learns pre-distorted waveforms that remain effective after clipping and compression.
• I/Q imbalance: The joint optimization compensates for gain and phase mismatches in the quadrature mixer.
• Phase noise: The receiver learns to track and correct for oscillator phase drift across the coherent processing interval.
• This is achieved by including hardware impairment models in the differentiable channel during training.

The architecture naturally scales to multi-target sensing and multi-user communication scenarios through learned resource allocation:

• Multi-target sensing: The receiver head outputs a set of parameter estimates with a learned association mechanism, avoiding the data association problem of classical tracking.
• Multi-user communication: The transmitter learns a superposition of waveforms, and each user's receiver learns to decode its intended stream while treating others as interference.
• Joint multi-user precoding and beamforming: The autoencoder implicitly learns spatial multiplexing that simultaneously focuses energy on communication users and illuminates sensing targets.