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DeepRx: Fully Convolutional Deep Learning Receiver

Mikko Honkala, Dani Korpi, Janne M. J. Huttunen

arXiv:2005.01494v2eess.SPcs.LGcs.NI

TL;DR

The paper addresses the challenge of jointly learning a practical receiver pipeline without an implementationally infeasible nonlinear optimum. It proposes DeepRx, a fully convolutional network that maps frequency-domain OFDM signals to soft bits while supporting 5G configurations and LDPC decoding. DeepRx outperforms traditional methods and an alternative separately structured neural receiver, with gains attributed primarily to using known data-symbol structure; computational-complexity analysis remains limited.

  • Problem

    Flexible learned receivers must handle diverse 5G reference-signal configurations, modulation schemes, and compatible downstream processing within one implementation.

  • Method

    DeepRx is a fully convolutional neural network trained to detect uncoded bits from frequency-domain received signals and output soft bits for 5G processing.

  • Results

    DeepRx outperforms traditional methods and an alternative neural network that separates channel estimation and equalization.

  • Takeaways & Limitations

    The reported gains are attributed primarily to using known constellation information and the local distribution of unknown data symbols during detection.

  • Takeaways & Limitations

    The work includes only a limited computational-complexity analysis, with a fuller analysis outside the article’s scope.

Abstract

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Deep learning has solved many problems that are out of reach of heuristic algorithms. It has also been successfully applied in wireless communications, even though the current radio systems are well-understood and optimal algorithms exist for many tasks. While some gains have been obtained by learning individual parts of a receiver, a better approach is to jointly learn the whole receiver. This, however, often results in a challenging nonlinear problem, for which the optimal solution is infeasible to implement. To this end, we propose a deep fully convolutional neural network, DeepRx, which executes the whole receiver pipeline from frequency domain signal stream to uncoded bits in a 5G-compliant fashion. We facilitate accurate channel estimation by constructing the input of the convolutional neural network in a very specific manner using both the data and pilot symbols. Also, DeepRx outputs soft bits that are compatible with the channel coding used in 5G systems. Using 3GPP-defined channel models, we demonstrate that DeepRx outperforms traditional methods. We also show that the high performance can likely be attributed to DeepRx learning to utilize the known constellation points of the unknown data symbols, together with the local symbol distribution, for improved detection accuracy.

I. INTRODUCTION

DeepRx addresses the limitations of separately optimized receiver components by jointly learning 5G-compliant physical-layer processing. The fully convolutional network uses frequency-domain received signals, pilots, and data symbols to produce soft bits, and is reported to outperform traditional receivers.

  • Motivation and approach: DeepRx jointly learns channel estimation, equalization, and soft demapping rather than optimizing receiver components separately.The approach trains a deep neural network to detect transmitted bits from a received 5G-compliant OFDM waveform.
  • Motivation and approach: The receiver treats physical-layer processing as supervised learning, using received frequency-domain waveforms as inputs and transmitted bits as labels.This avoids labeling by existing algorithms or humans.
  • DeepRx design: The network can use received data symbols and their distributions alongside pilots, with the largest gains attributed to this additional information.The reported mechanism is improved channel processing and detection through use of unknown data-symbol structure.
  • 5G compliance: DeepRx is designed to support multiple 5G reference-signal configurations, modulation schemes, and compatible downstream processing stages.Its outputs are intended for decoding by a 5G-compliant LDPC decoder.
  • DeepRx design: DeepRx is a fully convolutional architecture that maps frequency-domain signals over a transmission time interval directly to transmitted-bit LLRs.The architecture does not restrict the individual receiver-processing stages.
  • Results: The authors report that DeepRx outperforms traditional receivers and that its LLRs achieve state-of-the-art performance after 5G-compliant LDPC decoding.Performance is evaluated using BER before and after LDPC decoding on simulated uplink data.

II. SYSTEM MODEL

The system model generates 5G-compliant PUSCH uplink frames, propagates them through randomized 3GPP channels with noise and optional interference, and supplies frequency-domain samples to receiver processing. The study considers a single-transmit-antenna SIMO system and compares DeepRx with LS channel estimation and LMMSE equalization.

  • Transmitter and channel: The simulator generates information bits, LDPC-encodes and rate-matches them, maps them to symbols, inserts DMRS pilots, and forms a 5G PUSCH waveform.Symbols are placed across physical resource blocks within a transmission time interval.
  • Scope: The analysis omits HARQ and restricts transmission to one antenna in a SIMO system, leaving MIMO extension for future work.The receiver architecture is transparent to higher-layer processes.
  • Transmitter and channel: The waveform is converted to OFDM using an IFFT, producing 14 OFDM symbols per transmission time interval, with a cyclic prefix added before transmission.The cyclic prefix is used to mitigate inter-symbol interference.
  • Transmitter and channel: Ten 3GPP-specified CDL and TDL channel models are randomly selected across LOS and NLOS scenarios with randomized Doppler and delay-spread parameters.Each frame receives a randomly chosen channel model and realization parameters.
  • Impairments: Received waveforms include Gaussian observation noise and, in selected experiments, inter-cell interference from another waveform with randomized timing and power.The interference signal uses similar numerology but different random information bits.
  • Receiver model: Receiver preprocessing estimates timing, removes the cyclic prefix, and applies an FFT to obtain frequency-domain samples for the 14 OFDM symbols.These samples form the input to subsequent receiver processing.
  • Receiver model: The frequency-domain signal follows y_ij = H_ijx_ij + n_ij, where received symbols combine transmitted symbols, channel effects, and noise-plus-interference across receive antennas.The baseline receiver uses least-squares channel estimation and linear MMSE equalization.

Traditional Receiver Processing

The traditional OFDM receiver estimates the channel from known pilots, interpolates it across data positions, equalizes symbols, and computes soft-bit LLRs under a noise model.

  • Channel estimation: Channel estimation begins with known pilots and forms raw estimates using the received pilot symbols and their complex conjugates.Pilot-location estimates are interpolated across the time-frequency grid to obtain channel estimates for data symbols.
  • Channel estimation: The interpolated channel estimate provides per-data-symbol channel information for subsequent equalization.The resulting estimate is defined for data-symbol and subcarrier indices in D.
  • Equalization: An LMMSE equalizer uses the channel estimate, noise-plus-interference power, and identity matrix to produce equalized symbols.The equalized-symbol expression includes the Hermitian transpose of the channel estimate.
  • Soft-bit demapping: The demapper converts equalized symbol estimates into soft bits or LLRs based on conditional bit probabilities.Each LLR corresponds to a bit position in the modulation constellation.
  • Soft-bit demapping: Under Gaussian white-noise residuals, LLRs can be approximated from constellation points grouped by each bit value.The reference implementation additionally scales final LLRs by subcarrier channel magnitude to reflect greater uncertainty under severe fading.

III. CONVOLUTIONAL NEURAL NETWORK-BASED RECEIVER

DeepRx replaces separated receiver blocks with a fully convolutional network that processes complete frequency-domain TTIs and outputs bit-level LLRs. Its design exposes received data, pilots, and pilot-based channel information while preserving symbol resolution and supporting multiple modulation schemes.

  • Network input and output: DeepRx processes Fourier-transformed frequency-domain data collected over an entire transmission time interval.The network input includes both unknown received data and known pilots, and its output is the final bit-level LLRs.
  • Design rationale: DeepRx gives the CNN unrestricted access to unknown data because local symbol distributions can help estimate LLRs away from sparse pilot locations.This avoids separate pilot-based channel-estimation and data-equalization paths.
  • Network input and output: The input combines received data and pilots, pilot references aligned to pilot positions, and raw channel estimates computed at those positions.These components are stacked as channels, with complex values split into real and imaginary channels.
  • Configuration support: A single trained network successfully handled all pilot configurations defined in the 5G standard when those configurations were presented during training.The raw-channel estimate is not strictly necessary, but including it makes learning somewhat easier and faster.
  • Architecture: The fully convolutional architecture maintains S × F resolution without pooling or striding, allowing output size to follow the input size.Dilated convolutions enlarge the receptive field while retaining detailed information for each input symbol.
  • Training and decoding: The network outputs bit LLRs and is trained with binary sigmoid cross-entropy, while the LLRs retain uncertainty information for LDPC decoding.The output has dimensions S × F × B, where B is the number of bits in the used constellation.
  • Modulation support: Hierarchical relationships among 5G QAM constellations allow one network to support multiple modulation schemes through corresponding output bits and LLRs.The same output bits or LLRs represent the same constellation regions across modulation orders, and masking is used during training and inference.

IV. GENERATION OF TRAINING AND VALIDATION DATA

Training and validation data are generated with a link-level 5G simulator using randomized operating conditions, pilot configurations, and channel models. The split includes both realistic 3GPP channels and a synthetic correlated Rayleigh model to test generalization.

  • Training and validation data are generated with a Matlab 5G Toolbox link-level simulator modeling a 5G PUSCH link.
  • HARQ is omitted because it affects processing after LLR calculation, leaving the DeepRx architecture transparent to HARQ.
  • SNR, SIR, and other simulation parameters are randomized per 10-TTI frame, with logarithmic SNR sampled uniformly to improve training efficiency.
  • Four DMRS configurations are randomly selected per 10-TTI frame and summarized as one-pilot or two-pilot cases.
  • Ten 3GPP channel models are used, with six for training and four held out for validation in a 60%/40% split.
  • A synthetic seven-tap Rayleigh model changes each OFDM symbol while retaining 90% of the previous channel variance to impose temporal correlation.

V. RESULTS

The evaluation compares DeepRx with practical and full-channel-knowledge LMMSE receivers using uncoded and coded BER. Coded BER tests whether DeepRx’s soft outputs preserve uncertainty sufficiently for 5G LDPC decoding.

  • DeepRx is compared with practical LMMSE and full-channel-knowledge LMMSE receivers.
  • Uncoded BER uses hard decisions on LLRs, while coded BER compares LDPC-decoded bits with the original sequence.
  • Coded BER evaluates whether DeepRx’s LLRs capture detected-bit uncertainty sufficiently for LDPC decoding.
  • Direct LLR evaluation is difficult because the utilized channel models lack an explicit formula for ideal LLRs.
  • Models are trained on simulated link-level data using LAMB optimization, large batches, learning-rate warmup, and decay.
  • Overfitting was not observed with the described datasets, including memorization of training samples that would compromise performance.

A. Primary Validation Results

DeepRx outperforms practical LMMSE benchmarks across pilot and interference conditions, while its coded BER can match or exceed full-channel-knowledge LMMSE. Its advantage is especially pronounced with one pilot and inter-cell interference.

  • DeepRx clearly outperforms practical LMMSE under inter-cell interference, even surpassing the full-channel-knowledge benchmark.
  • At higher SINRs, one-pilot DeepRx outperforms two-pilot practical LMMSE by a factor of 10.
  • DeepRx’s coded BER matches full-channel-knowledge LMMSE and gains roughly 2 dB over practical two-pilot LMMSE.
  • Reducing DeepRx from two pilots to one causes only a marginal performance reduction.
  • The interference gap could be reduced if LMMSE receivers used interference rejection combining.
  • DeepRx avoids the traditional demapper’s Gaussian-white-noise assumption and learns from noise-plus-interference distributions in training data.
  • 2 dB: DeepRx’s inter-cell-interference gain over full-channel-knowledge LMMSE, while practical LMMSE remains outside the code waterfall region.

B. Exploring the Reasons Behind DeepRx’s Performance

Additional experiments attribute DeepRx’s performance to temporal channel tracking and use of received data-symbol distributions, while probing generalization beyond 3GPP training channels. Restricted access to data symbols substantially weakens performance.

  • Temporal Tracking of the Channel: At 500 Hz Doppler, one-pilot DeepRx matches full-channel-knowledge LMMSE, corresponding to roughly 135 km/h UE velocity.
  • DeepRx Does Not Cheat by Learning Channel Models: Training on a synthetic channel yields somewhat worse performance than 3GPP training but remains an order of magnitude better than practical LMMSE with one pilot.
  • DeepRx Does Not Cheat by Learning Channel Models: These synthetic-channel results indicate that DeepRx learns a generic bit-detection solution transferable across different channel models.
  • Blind Utilization of the Unknown Data During the Detection Process: The restricted CNN has only symbol-by-symbol equalization and demapping, preventing spatial or temporal correlations from improving bit estimates.
  • Blind Utilization of the Unknown Data During the Detection Process: Full access to data subcarriers is identified as crucial, consistent with jointly learning receiver tasks rather than imposing a traditional processing flow.
  • Blind Utilization of the Unknown Data During the Detection Process: A restricted CNN unable to use multiple received symbols outperforms unrestricted DeepRx under the manipulated distribution.
  • Temporal Tracking of the Channel: DeepRx and iterative receivers can use unknown data symbols for near-perfect channel estimation, unlike practical LMMSE with a single noisy pilot.

C. Ablation Studies and Notes on Complexity

The ablation studies examine architecture depth, receptive field, parameter count, convolution type, and access to unknown data symbols, while complexity analysis compares scaling with LMMSE. CNN receivers generally outperform LMMSE baselines, but DeepRx has higher practical computational cost and multi-antenna scaling remains unresolved.

  • Evaluation checks: A second test set with a different random seed showed no significant difference from the validation-set results.The no-interference results were treated as a separate test set.
  • Performance across architectures: With interference, almost all tested CNN architectures outperform the LMMSE baselines.Without interference, the margin is smaller, although gains remain considerable for one-pilot cases.
  • Depth and receptive field: 11 ResNet blocks provide good performance across scenarios while allowing narrower layers for more efficient inference.Dilated networks can perform relatively well with 3 or 5 blocks, but one-pilot interference BER worsens from 6.23 × 10−4 to 1.63 × 10−3 with fewer blocks.
  • Depth and receptive field: A receptive field of sufficient size is needed for good performance, although deep 11-block networks work well without dilations.For 11 blocks, BER is 6.91×10−4 without dilations versus 6.23 × 10−4 with dilations.
  • Input access and convolution type: Restricting channel estimation from using unknown data symbols reduces performance to the LMMSE-baseline level, while normal convolutions cause a slight drop.The restricted model and convolution variants were evaluated within the 11-block architecture study.
  • Complexity: DeepRx and LMMSE both have asymptotic complexity O(SF) in subcarrier and time dimensions when pilot density remains roughly constant.DeepRx has a larger constant multiplier and is therefore expected to cost more in practice, despite superior radio performance; antenna scaling is left for future work.

VI. CONCLUSION

The paper proposes DeepRx as a supervised, fully convolutional receiver that directly maps frequency-domain antenna signals to uncoded bits. Simulations show significant gains over traditional methods and indicate that using unknown data symbols and local symbol distributions supports accurate channel estimation and equalization, while complexity and MIMO extension remain open issues.

  • DeepRx receiver: DeepRx maps the complete receiver task from frequency-domain signals to uncoded bits in a 5G-compliant implementation.The output is designed for a single network supporting the relevant receiver processing chain.
  • Design rationale: DeepRx jointly optimizes receiver processing for the end task of recovering transmitted bits.The paper contrasts this with training multiple smaller receiver components separately.
  • Design rationale: The minimally restricted architecture can learn improved receiver schemes and implicitly address radio-channel and hardware impairments.This potential follows from allowing the network to learn beyond a narrowly specified receiver decomposition.
  • DeepRx receiver: DeepRx detects uncoded bits directly from frequency-domain antenna signals and supports different 5G-specific pilot configurations and modulation schemes.Its input arranges unknown data and known pilot symbols as convolutional channels for joint channel estimation.
  • Results: In simulated 5G uplink transmission, DeepRx significantly outperforms traditional methods and an alternative network separating channel estimation and equalization.The comparison supports jointly learning the receiver pipeline rather than splitting these stages.
  • Results: The reported success is primarily attributed to using known constellation points and local symbol distributions to estimate and equalize the channel accurately.Experiments also indicate that DeepRx’s internal processing somewhat resembles iterative receivers.
  • Results: DeepRx learns to deal efficiently with non-Gaussian interference and noise.The conclusion specifically identifies this behavior as part of the observed receiver performance.
  • Limitations and future work: The work provides only limited computational-complexity analysis because its primary focus is radio-performance gains.A comprehensive comparison with conventional receivers and adaptation to inference-time neural-network chips are identified as future work.
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