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Deep Learning-Based Communication Over the Air

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

arXiv:1707.03384v1stat.MLcs.IT

TL;DR

End-to-end neural communications had previously been validated mainly in simulations with short block transmissions, while real channels lack the gradients needed for direct training. The paper builds an over-the-air neural system, extends it to continuous transmission with neural frame synchronization, and reports BLER performance close to a practical baseline. Its central practical contribution is a two-phase procedure that trains on a stochastic model and finetunes the receiver using real-channel data.

  • Problem

    Prior end-to-end neural communications had been validated only by simulations for block-based transmissions, while actual channels present an unavailable channel gradient and hardware synchronization challenges.

  • Method

    The paper builds a complete neural transmitter-receiver system for continuous over-the-air transmission, adds neural frame synchronization, and uses stochastic-model training followed by real-channel receiver finetuning.

  • Results

    The prototype achieves BLER performance about 1 dB worse than the GNR DQPSK baseline over the tested real-channel transmissions.

  • Takeaways & Limitations

    Neural networks can implement an entire point-to-point physical layer and communicate over an actual wireless channel using the proposed training procedure.

  • Takeaways & Limitations

    The prototype remains about 1 dB behind the conventional baseline, with the authors attributing the gap to modeling and optimization choices that may be improved.

Abstract

from arXiv · show

End-to-end learning of communications systems is a fascinating novel concept that has so far only been validated by simulations for block-based transmissions. It allows learning of transmitter and receiver implementations as deep neural networks (NNs) that are optimized for an arbitrary differentiable end-to-end performance metric, e.g., block error rate (BLER). In this paper, we demonstrate that over-the-air transmissions are possible: We build, train, and run a complete communications system solely composed of NNs using unsynchronized off-the-shelf software-defined radios (SDRs) and open-source deep learning (DL) software libraries. We extend the existing ideas towards continuous data transmission which eases their current restriction to short block lengths but also entails the issue of receiver synchronization. We overcome this problem by introducing a frame synchronization module based on another NN. A comparison of the BLER performance of the "learned" system with that of a practical baseline shows competitive performance close to 1 dB, even without extensive hyperparameter tuning. We identify several practical challenges of training such a system over actual channels, in particular the missing channel gradient, and propose a two-step learning procedure based on the idea of transfer learning that circumvents this issue.

I. INTRODUCTION

Deep-learning communications systems jointly optimize transmitter and receiver without imposing conventional processing blocks. This paper demonstrates a prototype that communicates over an actual wireless channel and approaches a conventional system’s performance.

  • Deep-learning communications systems jointly optimize transmitter and receiver without an artificially introduced block structure.
  • The approach aims to learn communication over arbitrary channels without prior mathematical modeling and analysis.
  • The paper develops a prototype using two software-defined radios that learns to communicate over an actual wireless channel.
  • Continuous data transmission requires handling receiver synchronization and inter-symbol interference in the hardware implementation.
  • The prototype comes close to the performance of a well-designed conventional communications system.

A. The autoencoder concept

The communications system is formulated as an autoencoder whose neural transmitter and receiver learn a robust message representation through the channel. Unlike conventional QAM, the learned system uses non-uniform, temporally correlated transmitted symbols.

  • The autoencoder represents the transmitter and receiver as neural-network components trained to reconstruct the input message.
  • The transmitter embeds each message, maps it through a feedforward network to complex symbols, and normalizes the output to satisfy a power constraint.
  • The receiver transforms complex channel outputs into real values and uses a feedforward network with softmax output to assign message probabilities.
  • End-to-end stochastic-gradient training uses cross-entropy loss for the communication-as-classification formulation.
  • Learned constellation points are non-uniform, while correlations across the symbols representing one message provide an inherent form of channel coding.

1) Unknown channel transfer function:

Hardware deployment exposes two central constraints: the physical channel has no available gradient, and continuous transmission introduces synchronization, sampling-offset, and inter-symbol-interference problems. The paper addresses training with a stochastic model followed by receiver finetuning on real-channel data.

  • 1) Unknown channel transfer function:: Continuous transmission is needed because exhaustive autoencoder training becomes infeasible for large message sets, but it introduces timing synchronization, sampling-frequency offset, and inter-symbol interference.
  • 1) Unknown channel transfer function:: Phase I requires a stochastic channel model that approximates the expected channel closely enough to provide effective initial end-to-end training.
  • 1) Unknown channel transfer function:: The proposed two-phase strategy first trains the autoencoder on a stochastic channel model and then finetunes the receiver using labeled over-the-air samples.
  • 1) Unknown channel transfer function:: The implemented channel model includes upsampling, pulse shaping, and additive white Gaussian noise for complex-valued signals.

1) Upsampling & pulse shaping:

The stochastic channel model represents synchronization mismatches and channel distortions during end-to-end training by modeling timing offset, carrier-frequency offset, phase offset, and additive noise.

  • 1) Upsampling & pulse shaping:: The model randomly draws a sample-time offset τoff within [−τbound, τbound] to represent unsynchronized transmitter and receiver sampling.The offset is incorporated by convolving the upsampled input with a time-shifted pulse-shaping filter.
  • 1) Upsampling & pulse shaping:: Carrier-frequency mismatch produces a time-varying rotation of complex IQ samples, modeled through the CFO fcfo = frx − ftx.The model also includes an unknown phase offset and randomly samples phase-related variables for each channel input.
  • 1) Upsampling & pulse shaping:: The channel model uses an AWGN channel whose output contains complex Gaussian noise added to the transmitted waveform.Signal-strength fluctuations are represented as SNR variations, while propagation-related phase rotations are represented by the phase offset.

4) AWGN:

Continuous transmission requires sequence-aware decoding because pulse shaping creates ISI and independently trained block decoders would encounter unseen inter-message interference.

  • 4) AWGN:: Pulse shaping creates ISI between adjacent symbols, with the effective interference span determined by the filter length L.Traditional systems address this using matched filtering and timing-offset compensation, whereas the autoencoder handles the received sequence directly.
  • 4) AWGN:: Block-wise training fails for continuous sequences because inter-message interference appears without a guard interval and severely degrades performance.The receiver must therefore decode messages from slices of a longer received sequence.
  • 4) AWGN:: The sequence decoder maps a selected received-signal slice to a message and is implemented as a combination of multiple neural networks.The slice size, location, and number of padding messages are design parameters tied to filter length and receiver complexity.
  • 4) AWGN:: The model excludes channels with memory, even though such channels also create ISI.The cited implementation therefore does not evaluate multipath-memory effects in this setting.
  • 4) AWGN:: The decoder uses central samples corresponding to 2ℓ−1 messages, while neighboring messages mitigate edge effects.This sequence construction limits boundary interference in the decoded region.

2) Phase offset estimation:

A dense neural phase estimator improves continuous-transmission reception by estimating a complex correction for the phase offset, while explicit CFO estimation is omitted.

  • 2) Phase offset estimation:: The phase estimator is a dense neural network that maps a received-signal slice to a complex scalar h.The receiver multiplies detection samples by h to compensate for the constant phase offset ϕoff.
  • 2) Phase offset estimation:: The phase estimator is trained end to end without an additional loss term for the estimated correction h.Adding a weighted MSE term was tested but produced no observed gains, so its weight was set to zero.
  • 2) Phase offset estimation:: Explicit CFO compensation is omitted because the short IQ-sample sequences allow the receiver block to handle the small accumulated phase shift.A separate CFO-estimation approach was tried but did not improve performance.
  • 2) Phase offset estimation:: The receiver can use the phase-corrected observation h · yk2k1 for message detection.This places phase correction before the receiver block in the processing pipeline.

3) Feature extraction:

The receiver uses feature extraction and learned phase-offset compensation to decode continuous transmissions despite timing, phase, and interference effects. A neural offset estimator identifies frame alignment from overlapping subsequences.

  • Feature extraction: The receiver feeds a sub-slice of the observation window into the RX block and concatenates F features from a dense Feature Extractor.This reduces the direct input while retaining information from the broader received sequence.
  • Feature extraction: F = 4 features significantly improve performance in the reported experiments.
  • Feature extraction: The RX block decodes the target message from Nmsg central samples extended by γ samples on each side and the extracted features.
  • Frame synchronization: The offset estimator applies a dense NN with Nmsg softmax outputs to overlapping subsequences, averages offset probabilities, and selects the most likely frame offset.

5) Full decoding algorithm:

The decoding algorithm processes an infinite IQ-sample stream frame by frame, correcting frame offsets before sequence decoding. Overlapping frame selection preserves decodability across consecutive frames but leaves an initial boundary unresolved.

  • Full decoding algorithm: The first and last ℓ−1 messages in each frame cannot be decoded because the sequence decoder requires Nseq = (2ℓ−1)Nmsg samples per message.
  • Full decoding algorithm: Subsequent frame starts are chosen so that the last ℓ−1 messages of one frame become the first decodable messages of the next.The first ℓ−1 messages are therefore never decoded.
  • Full decoding algorithm: For later frames, the design limits the sample offset to {−1, 0, 1} and adjusts it by skipping or repeating one sample.The stated example uses 50 ppm SFO at a 1 MHz sample frequency.
  • Full decoding algorithm: Training uses τbound = Ts so the sequence decoder tolerates a wider timing-offset range than the minimum τbound,min = Ts/2.
  • Full decoding algorithm: The algorithm takes infinite IQ samples, frame length N, SD input length Nseq, and message length Nmsg, and outputs a sequence of decoded frames.

IV. RESULTS

The system is evaluated in simulation and over-the-air measurements using a common parameter set and neural-network architecture. Receiver finetuning uses selected measured sequences, while performance is compared with a GNU Radio DQPSK baseline.

  • IV. RESULTS: Simulation and measurement evaluations use the same system parameters and specify neural-network layouts for TX, RX, FE, PE, and OE.PE, FE, and OE process 11 messages; Nmsg = 16 and Nseq = 176 complex samples.
  • IV. RESULTS: The autoencoder is trained over a stochastic channel model with Adam at learning rate 0.001 and constant Eb/N0 = 9 dB.Training runs for 60 epochs with increasing batch sizes and without extensive hyperparameter optimization.
  • IV. RESULTS: Receiver finetuning uses measured IQ sequences selected for initial BLER between 10^-2 and 10^-4.Sequences with worse than about 10^-2 can improve low-SNR performance but produce a high-SNR error floor; finetuning can also overfit.
  • IV. RESULTS: The comparison baseline is a GNU Radio DQPSK transceiver using polyphase filterbank clock recovery with 32 phase filters and 1408 RRC taps per filter.

A. Learned Constellations

The learned transmitter develops non-uniform IQ constellations for 256 messages, using symbol structure to support energy efficiency and phase-offset estimation. Generated sequences are less periodic than DQPSK and remain decodable after realistic over-the-air impairments.

  • Learned constellations: The autoencoder learns IQ constellations for M = 256 messages, with most symbols on the unit circle or near zero.The distribution indicates efficient use of available energy and possible time sharing between symbols.
  • Learned constellations: The first symbols cluster in the second quadrant, indicating implicit use for phase offset estimation.
  • Signal sequences: Autoencoder sequences show less periodicity than random DQPSK because their learned constellation is non-uniform.
  • Signal sequences: Received autoencoder sequences include random phase offset, random timing offset, and added noise while serving as inputs for message decoding.The illustrated receiver input sequence has length Nseq = 176.

B. Performance over simulated channels

Over a GNR channel model incorporating realistic radio impairments, the autoencoder performs close to the DQPSK baseline across a broad Eb/N0 range. Fine-tuning provides little additional benefit because the stochastic and GNR channel models are closely matched.

  • Evaluation procedure: The simulated evaluation uses separate channel-model sequences for receiver fine-tuning and BLER measurement.The first five output sequences are used for fine-tuning, while the remaining ten evaluate BLER.
  • Simulated-channel performance: About 1 dB separates the autoencoder from the GNR DQPSK baseline in BLER across the full Eb/N0 range.The autoencoder was trained at a fixed Eb/N0 = 9 dB yet generalized across different Eb/N0 values.
  • Simulated-channel performance: Fine-tuning yields very little gain because the mismatch between the stochastic and GNR channel models is small.

C. Performance over real channels

The NN-based system is evaluated over an SDR wireless link and coaxial cable, where fine-tuning narrows its BLER gap to the practical DQPSK baseline. Real-channel deployment exposes stronger mismatch between training and actual channels than simulated evaluation.

  • Over-the-air setup: The SDR testbed uses USRP B200 and B210 radios separated by 46 m indoors with an unobstructed line-of-sight path.
  • Over-the-air performance: At BLER 10^-4, fine-tuning reduces the over-the-air autoencoder gap to the DQPSK baseline from 2 dB to 1 dB.
  • Over-the-air performance: The increased value of fine-tuning over the real channel reflects greater mismatch between the stochastic training model and the actual channel.
  • Conclusions and outlook: The prototype demonstrates point-to-point communication with the entire physical layer implemented by neural networks, while synchronization and channel mismatch remain practical challenges.
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