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OFDM-Autoencoder for End-to-End Learning of Communications Systems

Alexander Felix, Sebastian Cammerer, Sebastian Dörner, Jakob Hoydis, Stephan ten Brink

arXiv:1803.05815v1cs.ITeess.SP

TL;DR

The paper addresses synchronization and multipath challenges in single-carrier neural communication systems. It embeds an end-to-end autoencoder in OFDM with a cyclic prefix and evaluates it against an OFDM baseline, finding robust multipath communication and learned compensation for nonlinear hardware effects.

  • Problem

    Single-carrier autoencoder communication faces demanding synchronization, while communication systems still need adaptable processing for complex or imperfect channels.

  • Method

    The authors extend neural transmitter–receiver autoencoders to OFDM with a cyclic prefix using differentiable layers suitable for gradient-based training.

  • Results

    The OFDM autoencoder mitigates synchronization issues, simplifies multipath equalization, and outperforms the QPSK baseline by approximately 2 dB over the whole SNR range at the same spectral efficiency.

  • Takeaways & Limitations

    The system provides a flexible communication design that can incorporate channel effects and hardware nonlinearities directly into end-to-end learning.

Abstract

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We extend the idea of end-to-end learning of communications systems through deep neural network (NN)-based autoencoders to orthogonal frequency division multiplexing (OFDM) with cyclic prefix (CP). Our implementation has the same benefits as a conventional OFDM system, namely singletap equalization and robustness against sampling synchronization errors, which turned out to be one of the major challenges in previous single-carrier implementations. This enables reliable communication over multipath channels and makes the communication scheme suitable for commodity hardware with imprecise oscillators. We show that the proposed scheme can be realized with state-of-the-art deep learning software libraries as transmitter and receiver solely consist of differentiable layers required for gradient-based training. We compare the performance of the autoencoder-based system against that of a state-of-the-art OFDM baseline over frequency-selective fading channels. Finally, the impact of a non-linear amplifier is investigated and we show that the autoencoder inherently learns how to deal with such hardware impairments.

I. INTRODUCTION

The paper extends end-to-end neural communication to OFDM, combining adaptive transmitter–receiver optimization with synchronization robustness, single-tap equalization, and hardware-imperfection resilience.

  • Motivation: End-to-end autoencoders jointly optimize transmitter and receiver for differentiable channel models rather than optimizing handcrafted processing blocks separately.This supports adaptive and flexible communication-system design.
  • Contribution: The work extends a prior single-carrier autoencoder to OFDM with CP for reliable multipath transmission and improved sampling-synchronization robustness.The OFDM system also provides single-tap equalization over multipath channels.
  • Implementation: FFT operations can be inserted as nondifferentiable-to-train intermediate computations because state-of-the-art deep-learning libraries provide the required gradients.This preserves end-to-end gradient-based training.
  • Design rationale: Fixed expert transformations such as OFDM can speed training and increase performance despite reducing the neural network’s expressive freedom.The paper compares this design choice with specialized network structures such as CNNs.
  • Contribution: The proposed design targets robustness against synchronization errors, moderate training complexity, compatibility with existing schemes, and nonlinear-amplifier impairments.These benefits are listed as design objectives for the OFDM autoencoder.

II. END-TO-END LEARNING OF A COMMUNICATIONS LINK

The communication link is formulated as an autoencoder: a neural transmitter maps messages to channel inputs, and a neural receiver reconstructs them after a noisy channel. End-to-end training learns robust message representations for deployment.

  • System formulation: A transmitter sends one of m messages over a noisy channel, while the receiver estimates the transmitted message using n channel uses.The resulting rate is R = log2(m)/n bits/channel use.
  • Training: End-to-end stochastic-gradient training teaches the receiver to recover transmitted information, after which trained transmitter and receiver weights can be deployed.The paper gives software-defined radio as an example deployment platform.
  • Architecture: The transmitter and receiver use dense layers and interpret pairs of real outputs as complex IQ symbols for communication processing.The receiver structure follows a sequence detector using a radio transformer network.
  • Learned representations: For m = 256 messages, the encoder learns robust symbol-sequence representations, with each message comprising four complex-valued IQ symbols.The constellation diagrams show symbols at corresponding message positions.

A. Synchronization Challenges

Single-carrier autoencoders face difficult synchronization from sampling and carrier-frequency offsets. OFDM with a cyclic prefix addresses these issues and supplies sampled symbols to the receiver while retaining per-subcarrier processing.

  • Synchronization Challenges: Unsynchronized oscillators create sampling- and carrier-frequency offsets, while the receiver must also locate message boundaries in measured IQ streams.Dynamic sampling-frequency offset previously required an additional offset-estimation neural network.
  • Synchronization Challenges: OFDM combined with a cyclic prefix solves the synchronization issues encountered in the prior single-carrier autoencoder.The CP provides almost perfectly sampled IQ symbols to the receiver.
  • OFDM Extensions: The OFDM extension assigns independent autoencoder messages to subcarriers after applying an inverse DFT.The resulting subchannels are processed as a multi-carrier representation.
  • OFDM Extensions: A cyclic prefix is added to improve synchronization robustness and avoid inter-symbol interference before multipath transmission.The transmitted OFDM symbol length is wFFT + ℓCP.
  • OFDM Extensions: At the receiver, CP autocorrelation supports frame synchronization, and a DFT recovers inputs for the independent subcarrier receivers.The RTN equalizer operates per subcarrier, with an optional fixed pilot tone.

A. Channel model

The simulations use a WiFi-inspired, variable multipath channel based on a five-coefficient Proakis type C model, with additional experiments for offsets and nonlinear amplification.

  • Channel model: The stochastic channel model derives from a Proakis type C five-coefficient tap-delay-line model and uses its coefficients as variances of normally distributed channel taps.Changing channel conditions are used to avoid training the network for only fixed channel coefficients.
  • Channel model: The model includes a constant phase offset and incrementally increasing carrier-frequency offset in the experiment focused on those effects.These impairments are specified only for Section IV-D.
  • Channel model: The nonlinear-amplifier experiment incorporates AM-AM distortion, while the OFDM-with-CP setup avoids sample-time synchronization handling.The comparison with prior work uses five-tap multipath propagation.
  • Piloting constraint: Without additional piloting, message symbols cannot simply be distributed within one OFDM symbol because unknown per-subcarrier phase rotation would destroy the message.This constrains how symbols are arranged across the OFDM frame.
  • Channel model: Carrier-frequency offset produces a time-varying rotation between complex IQ samples because transmitter and receiver oscillators differ.The FFT itself implies rectangular pulse shaping per subcarrier.

B. Baseline

The baseline uses per-subcarrier MMSE channel equalization from pilot symbols, with conventional CFO compensation for CFO-affected channels.

  • B. Baseline: The QPSK baseline performs MMSE channel equalization independently on each subcarrier.This avoids requiring channel and noise covariance matrices across subcarriers.
  • B. Baseline: Channel estimates use received frequency-domain symbols and pilot symbols transmitted within the message blocks.The baseline uses one pilot symbol per 2 · n/2 symbols of two messages.
  • B. Baseline: For CFO-affected channels, the baseline compensates phase shifts obtained from the cyclic prefix.BLER is computed over blocks of n/2 symbols for fair comparison.

IV. SIMULATION RESULTS AND INTERPRETATION

The simulation section describes the experimental setup, including a nontrivial autoencoder analysis, short transmitted blocks, and manually configured training parameters.

  • IV. SIMULATION RESULTS AND INTERPRETATION: The autoencoder is analyzed through targeted experiments because its jointly learned effects do not map cleanly onto distinct processing blocks.The experiments aim to identify what the system learns and how it behaves.
  • IV. SIMULATION RESULTS AND INTERPRETATION: Each transmission contains two consecutive blocks of four complex-valued symbols, with an optional additional pilot at the beginning.This corresponds to n = 8 channel uses.
  • IV. SIMULATION RESULTS AND INTERPRETATION: The setup parameters are summarized in Table I.The supplied passage identifies the table but does not provide its parameter values.
  • IV. SIMULATION RESULTS AND INTERPRETATION: The simulations assume a 2.35 GHz carrier, 20 MHz sampling frequency, 20 ppm oscillator accuracy, and 1.69°/sample maximum CFO.These values are listed as CFO-related system parameters.
  • IV. SIMULATION RESULTS AND INTERPRETATION: Training is end-to-end, manually tuned for suitable performance, and takes about half a day on one NVIDIA TITAN X (Pascal).The authors did not perform exhaustive hyperparameter optimization.

A. BLER-Results

The autoencoder-based OFDM system outperforms the QPSK baseline by approximately 2 dB across the SNR range at equal spectral efficiency.

  • A. BLER-Results: Approximately 2 dB: the autoencoder outperforms the QPSK baseline over the whole SNR range at the same spectral efficiency.The comparison concerns BLER performance.

B. Equalizing

The experiments show that the neural network can perform equalization without an explicit equalizer or pilot, while learning a constellation structure consistent with superimposed piloting.

  • B. Equalizing: The design evaluates how well the neural network can emulate single-tap equalization while retaining broad transmitter and receiver freedom.The goal is to include as few explicit components as possible.
  • B. Equalizing: The learned constellations cover all m = 256 messages under average power normalization, with four messages highlighted separately.Each message contributes symbols shown in the scatter plot.
  • B. Equalizing: The experiments compare explicit-pilot and no-pilot systems across three equalization configurations.The analysis reports results in Fig. 5 and includes an explicit-pilot, explicit-MMSE-equalizer proof-of-concept.
  • B. Equalizing: Without a pilot or explicit equalizer, the system shows a slight improvement over the baseline despite operating at a different rate.This configuration does not require a dedicated pilot.
  • B. Equalizing: The autoencoder therefore learns to equalize a single-tap channel without explicit pilots or explicit equalization.This is the authors’ stated conclusion from the configuration comparisons.
  • B. Equalizing: Without explicit piloting, the encoder shifts constellation centers, producing a form of superimposed piloting across symbols.The comparison uses constellation diagrams from systems trained with and without explicit pilots.
  • B. Equalizing: When pilot rate loss is included, the autoencoder without explicit pilots performs comparably to the explicit-pilot autoencoder.The SNR calculation otherwise neglects pilot-related rate loss because the pilot fraction is arbitrary.

D. CFO Compensation

The autoencoder adapts to carrier-frequency offset (CFO) with less performance degradation than the baseline, while the experiments also introduce nonlinear amplifier and clipping effects. Direct training on the new channel model substantially improves performance without additional compensation algorithms.

  • CFO Compensation: The autoencoder adapts to CFO with smaller performance degradation than the baseline.Both systems use an explicit pilot; the baseline applies conventional time-domain CFO compensation, while the autoencoder estimates the phase offset with an RTN.
  • Effects of Non-Linearities: The channel model introduces AM-AM distortion through a third-order nonlinear function with normalized input.The experiment evaluates the autoencoder's flexibility in accounting for nonlinear amplifiers and clipping.
  • Effects of Non-Linearities: When directly trained on the new channel model, the autoencoder improves significantly without further compensation algorithms.The baseline shows degraded performance under the nonlinear amplifier and clipping model.

V. CONCLUSIONS AND OUTLOOK

Embedding the autoencoder in an OFDM system with cyclic prefix mitigates synchronization issues and simplifies equalization over multipath channels. The system retains practical training and inference complexity while supporting pilots, MMSE-quality equalization, and time-domain CFO handling.

  • Conclusions and Outlook: Embedding the autoencoder into OFDM with cyclic prefix mitigates synchronization issues and simplifies equalization over multipath channels.The resulting system is described as practical, with feasible training and inference complexity.
  • Conclusions and Outlook: The system learns to use pilots when required and performs equalization equally well as a conventional MMSE equalizer.The paper notes that the system is difficult to analyze, despite these observed capabilities.
  • Conclusions and Outlook: An additional RTN handles CFO directly in the time domain.This provides a learned approach to CFO handling within the OFDM autoencoder system.
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