An Introduction to Deep Learning for the Physical Layer

Timothy J. O'SheaJakob Hoydis

article2017IEEE TCCN2,684 citations

Establishes an end-to-end deep learning framework that models communication systems as autoencoders, enabling the joint optimization of transmitters and receivers directly from raw signal data.

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The article addresses the challenge of improving physical layer communications systems, where traditional designs based on mathematical models have seen diminishing performance gains amid hardware imperfections and complex channel effects. These limitations matter now because practical systems involve non-linearities and non-stationary conditions that rigid models approximate poorly, while separate optimization of components like coding and modulation often yields suboptimal end-to-end results.

The article set out to evaluate whether deep learning techniques could provide a new framework for communications design by treating transmitter, channel, and receiver as a single trainable system. It aimed to demonstrate competitive or superior performance in scenarios where optimal solutions are unknown or difficult to derive analytically.

The work relied on simulations of neural network architectures trained via stochastic gradient descent on synthetic data representing various channel conditions, including additive white Gaussian noise and multipath fading. Key elements included comparisons against established baselines such as Hamming-coded BPSK with maximum likelihood decoding, time-sharing QAM schemes, and expert-feature classifiers, using block error rate as the primary metric across ranges of signal-to-noise ratios and system parameters like (n, k) pairs.

The analysis shows that autoencoder-based systems learned joint transmitter-receiver mappings achieving block error rates matching or exceeding traditional schemes, for instance matching Hamming (7,4) performance and outperforming uncoded BPSK at rate 1 for larger block lengths. In two-user interference channels, the approach delivered gains of 0.7 to 1 dB at a 10^{-3} error rate compared to time-sharing baselines. Radio transformer networks improved results over plain autoencoders on fading channels, surpassing differential BPSK with sequence estimation. Convolutional networks applied directly to raw IQ samples outperformed boosted trees and single decision trees using expert features by about 4 dB in low-to-medium SNR regimes for modulation classification.

These findings indicate that end-to-end learned systems can better handle real-world imperfections and joint optimization tasks without relying on tractable mathematical models, potentially lowering error rates, latency, or energy use in hardware-specific deployments. The results also suggest new insights into signaling schemes for interference channels and a shift away from hand-crafted features toward learned ones, mirroring trends in other domains.

Next steps supported by the article include developing standardized benchmark datasets and impairment models for consistent comparisons, exploring complex-valued networks and transfer learning to handle real hardware, and investigating hybrid approaches that augment specific signal processing blocks rather than replacing entire systems. Scalability to large message sets remains a barrier requiring further work on compact representations and training strategies.

Limitations include reliance on simulated channels with known statistics during training, challenges in scaling to high-rate systems with message sets exceeding practical training sizes, and sensitivity of performance to training signal-to-noise ratio choices. Confidence is moderate for simulated settings but lower for immediate real-world deployment without additional validation on hardware and diverse conditions.

Bell Laboratories DeepSig Virginia Tech autoencoders classification convolutional neural networks deep learning physical layer deep unfolding

arXiv: 1702.00832

Paper: Extracting and composing robust features with denoising autoencoders, Pascal Vincent et al. (2008). Establishes the foundational autoencoder architecture and noise-reconstruction training paradigms that the source directly adapts to model physical wireless communications channels.
Paper: Gradient-based learning applied to document recognition, Yann LeCun et al. (1998). Introduces foundational gradient-based end-to-end optimization of multi-module neural architectures, providing the conceptual groundwork for the source's joint transmitter-receiver learning.
Paper: Stacked Denoising Autoencoders: Learning Useful Representations in a Deep Network with a Local Denoising Criterion, Pascal Vincent et al. (2010). Provides the essential framework for training autoencoders robust to corrupted and noisy channel representations.
Paper: Intriguing properties of neural networks, Christian Szegedy et al. (2014). Explores the sensitivity and feature representation properties of deep networks, which informs the source's analysis of neural modulation classification and radio transformer networks under channel perturbations.

Paper: Intelligent Reflecting Surface-Aided Wireless Communications: A Tutorial, Qingqing Wu et al. (2020). Provides a comprehensive tutorial on intelligent reflecting surfaces that reconfigure wireless physical propagation environments, representing a key hardware-driven evolution beyond end-to-end transceiver learning.
Paper: 1D Convolutional Neural Networks and Applications: A Survey, Serkan Kiranyaz et al. (2019). Surveys the theory and practical deployments of 1D convolutional neural networks for time-series and raw signal processing, directly extending the physical-layer raw IQ sample classification highlighted in the source.

Cover for An Introduction to Deep Learning for the Physical Layer

Abstract

We present and discuss several novel applications of deep learning for the physical layer. By interpreting a communications system as an autoencoder, we develop a fundamental new way to think about communications system design as an end-to-end reconstruction task that seeks to jointly optimize transmitter and receiver components in a single process. We show how this idea can be extended to networks of multiple transmitters and receivers and present the concept of radio transformer networks as a means to incorporate expert domain knowledge in the machine learning model. Lastly, we demonstrate the application of convolutional neural networks on raw IQ samples for modulation classification which achieves competitive accuracy with respect to traditional schemes relying on expert features. The paper is concluded with a discussion of open challenges and areas for future investigation.

Topics

autoencoders classification convolutional neural networks domain knowledge encoder-decoder physical layers radio reconstruction systems design transceivers

Keywords

deep learning physical layer deep unfolding modulation classification Spatial Transformer Networks plain autoencoder channel model backpropagation algorithm

I Introduction
I-A Potential of for the physical layer
I-B Historical context and related work
II Deep learning basics
II-A Convolutional layers
II-B Machine learning libraries
II-C Network dimensions and training
III Examples of machine learning applications for the physical layer
III-A Autoencoders for end-to-end communications systems
III-B Autoencoders for multiple transmitters and receivers
III-C Radio transformer networks for augmented signal processing algorithms
III-D CNNs for classification tasks
IV Discussion and open research challenges
IV-A Data sets and challenges
IV-B Data representation, loss functions, and training SNR
IV-C Complex-valued neural networks
IV-D ML-augmented signal processing
IV-E System identification for end-to-end learning
IV-F Learning from CSI and beyond
V Conclusion
References

Knowls

Knowl 1 — End-to-End Communications System as a Channel Autoencoder
model/method
A point-to-point communications system can be formulated as an autoencoder neural network where the transmitter, channel, and receiver form a continuous feedforward architecture trained end-to-end.

The transmitter aims to communicate one message $s \in \mathcal{M} = \{1, 2, \dots, M\}$ using $n$ channel uses (communication rate $R = k/n$ bits per channel use, where $k = \log_2(M)$ ). The input message $s$ is represented as an $M$ -dimensional one-hot vector $\mathbf{1}_s \in \mathbb{R}^M$ . The transmitter is implemented as a neural network $f: \mathcal{M} \to \mathbb{R}^n$ that produces a transmitted vector $\mathbf{x} = f(s) \in \mathbb{R}^n$ , terminated with a normalization layer ensuring physical hardware constraints such as:
- Fixed energy constraint: $\|\mathbf{x}\|_2^2 = n$
- Amplitude constraint: $|x_i| \le 1, \; \forall i \in \{1, \dots, n\}$
- Average power constraint: $\mathbb{E}[|x_i|^2] \le 1, \; \forall i \in \{1, \dots, n\}$
The channel is modeled as a stochastic layer with transition density $p(\mathbf{y}|\mathbf{x})$ , such as an additive white Gaussian noise (AWGN) layer outputting $\mathbf{y} = \mathbf{x} + \mathbf{n}$ , where $\mathbf{n} \sim \mathcal{N}(\mathbf{0}, \beta \mathbf{I}_n)$ and noise variance $\beta = (2 R E_b/N_0)^{-1}$ ( $E_b/N_0$ is the energy per bit to noise power spectral density ratio).

The receiver is a neural network $g: \mathbb{R}^n \to (0, 1)^M$ with a softmax final activation that generates a posterior probability distribution $\mathbf{p} = g(\mathbf{y}) \in (0, 1)^M$ over all candidate messages. The decoded message is estimated as $\hat{s} = \arg\max_i p_i$ .

The end-to-end system is trained using stochastic gradient descent (SGD) to minimize the categorical cross-entropy loss:

$l(\mathbf{1}_s, \mathbf{p}) = -\sum_{j=1}^M [\mathbf{1}_s]_j \log(p_j) = -\log(p_s)$

Knowl 2 — Layer Layout and Parameter Count of Single-User Channel Autoencoder

data/table

The single-user channel autoencoder maps an $M$ -dimensional one-hot input message through dense feedforward layers to an $n$ -dimensional channel representation, adds channel noise, and decodes back to an $M$ -dimensional softmax probability distribution.

The total number of trainable parameters in this architecture is $(2M + 1)(M + n) + 2M$ . For specific configurations $(n, k)$ where $M = 2^k$ :

$(n=2, k=2)$ : $M=4$ , yielding $62$ trainable parameters.
$(n=7, k=4)$ : $M=16$ , yielding $791$ trainable parameters.
$(n=8, k=8)$ : $M=256$ , yielding $135{,}944$ trainable parameters.

Using two dense transmitter layers instead of a single linear mapping provides an expanded parameter search space, which reduces the probability of stochastic gradient descent converging to suboptimal local minima by making them emerge as saddle points during optimization.

Knowl 3 — Error Rate and Constellation Packing of Channel Autoencoders
empirical result
When trained on an AWGN channel with the Adam optimizer at a fixed $E_b/N_0 = 7\text{ dB}$ :
- A $(n=7, k=4)$ autoencoder operating at rate $R = 4/7$ achieves a block error rate (BLER) identical to a classical Hamming $(7,4)$ code decoded via Maximum Likelihood Decoding (MLD), without receiving any prior knowledge of coding or modulation theory.
- A $(n=8, k=8)$ autoencoder operating at rate $R = 1$ outperforms uncoded BPSK across the entire $E_b/N_0$ range (from $-2\text{ dB}$ to $10\text{ dB}$ ), demonstrating that the autoencoder autonomously learns a joint coding and modulation scheme with coding gain.
- For $(n=2, k=2)$ , the learned constellation converges to a rotated quadrature phase-shift keying (QPSK) constellation.
- For $(n=4, k=2)$ under an energy constraint, the learned constellation converges to a rotated 16-PSK constellation.
- For $(n=4, k=2)$ under an average power constraint, the constellation converges to a mixed pentagonal/hexagonal grid with a central point at the origin surrounded by five equidistant neighbors, each surrounded by six equidistant outer neighbors, achieving BLER performance indistinguishable from 16-QAM.
Knowl 4 — Two-User Interference Channel Autoencoder Model
model/method
The autoencoder framework extends to multi-user scenarios where two transmitter-receiver pairs communicate concurrently across a shared interference channel. Transmitter 1 encodes message $s_1 \in \mathcal{M} = \{1, \dots, M\}$ into $\mathbf{x}_1 \in \mathbb{C}^n$ , and Transmitter 2 encodes $s_2 \in \mathcal{M}$ into $\mathbf{x}_2 \in \mathbb{C}^n$ , where each message of $k = \log_2(M)$ bits is transmitted over $n$ complex channel uses.

The received complex signals at Receiver 1 and Receiver 2 are given by:

$\mathbf{y}_1 = \mathbf{x}_1 + \mathbf{x}_2 + \mathbf{n}_1$

$\mathbf{y}_2 = \mathbf{x}_2 + \mathbf{x}_1 + \mathbf{n}_2$

where $\mathbf{n}_1, \mathbf{n}_2 \sim \mathcal{CN}(\mathbf{0}, \beta \mathbf{I}_n)$ are additive complex white Gaussian noise vectors with $\beta = (2 R E_b/N_0)^{-1}$ and rate $R = k/n$ .

Each receiver $i \in \{1, 2\}$ maps its received signal $\mathbf{y}_i$ through a neural network to produce an estimated posterior distribution $\hat{\mathbf{s}}_i \in (0, 1)^M$ with associated individual cross-entropy losses:

$l_1 = -\log([\hat{\mathbf{s}}_1]_{s_1}), \quad l_2 = -\log([\hat{\mathbf{s}}_2]_{s_2})$
Knowl 5 — Dynamic Loss Weighting Algorithm for Multi-User Autoencoder Training
algorithm
When training coupled multi-user autoencoders with conflicting objectives, static weights (such as $\alpha = 0.5$ ) often lead to unfair or degenerate solutions where one transmitter dominates. Dynamic loss weighting continuously balances the training loss between both links.
Input: Training mini-batches of messages $s_1, s_2 \in \mathcal{M}$ , initial weight $\alpha_0 = 0.5$ , learning rate $\eta > 0$
Output: Optimized parameter vector $\theta$
for each mini-batch iteration $t = 0, 1, 2, \dots$ do
    Compute mini-batch average cross-entropy losses $\tilde{L}_1(\theta_t)$ and $\tilde{L}_2(\theta_t)$
    if $t = 0$ then
         $\alpha_t = \alpha_0$
    else
         $\alpha_t = \frac{\tilde{L}_1(\theta_{t-1})}{\tilde{L}_1(\theta_{t-1}) + \tilde{L}_2(\theta_{t-1})}$
    end if
    Compute combined weighted loss $\tilde{L}(\theta_t) = \alpha_t \tilde{L}_1(\theta_t) + (1 - \alpha_t) \tilde{L}_2(\theta_t)$
    Update network parameters $\theta_{t+1} = \theta_t - \eta \nabla_{\theta} \tilde{L}(\theta_t)$
end for
Under this update rule, if Receiver 1 achieves a lower loss than Receiver 2 ( $\tilde{L}_1 < \tilde{L}_2$ ), its weight $\alpha_{t+1}$ decreases for the subsequent mini-batch, allocating more gradient effort to improving Receiver 2 and ensuring equal BLER across both communication pairs.
Knowl 6 — Interference Channel Autoencoder Performance and Learned Signaling
empirical result
In a two-user Gaussian interference channel with $(n, k)$ parameters representing $k$ bits sent over $n$ complex channel uses:
- For $(1,1)$ and $(2,2)$ , the learned autoencoders achieve BLER identical to conventional $2^{2k/n}$ -QAM with time-sharing (TS).
- For $(4,4)$ and $(4,8)$ , the autoencoder outperforms time-sharing with 4-QAM and 16-QAM by approximately $0.7\text{ dB}$ and $1.0\text{ dB}$ at $\text{BLER} = 10^{-3}$ , respectively.
- Learned constellation geometries reveal non-trivial signaling schemes:
  - For $(n=1, k=1)$ , the two transmitters learn orthogonal BPSK-like constellations rotated relative to each other.
  - For $(n=2, k=2)$ , the networks learn asymmetric superposition coding: Transmitter 1 uses high transmit power on the first complex symbol and low power on the second, while Transmitter 2 allocates low power to the first symbol and high power to the second.
  - For $(n=4, k=4)$ and $(n=4, k=8)$ , the learned constellations form orthogonal ellipses with varying focal distances across channel uses.
Knowl 7 — Radio Transformer Networks (RTN)
model/method
A Radio Transformer Network (RTN) integrates physical domain knowledge into a deep learning model by embedding a differentiable parametric transformation directly into the network architecture.

An RTN consists of three connected modules:
1. Parameter Estimator $g_{\boldsymbol{\omega}}: \mathbb{R}^n \to \mathbb{R}^p$ : A neural network that estimates a parameter vector $\boldsymbol{\omega} \in \mathbb{R}^p$ from the received signal $\mathbf{y} \in \mathbb{R}^n$ .
2. Parametric Transform $t: \mathbb{R}^n \times \mathbb{R}^p \to \mathbb{R}^{n'}$ : A deterministic and differentiable function parameterized by $\boldsymbol{\omega}$ that canonicalizes the input signal $\mathbf{y}$ into $\bar{\mathbf{y}} = t(\mathbf{y}, \boldsymbol{\omega})$ . For example, for phase offset compensation on IQ input $\mathbf{y} = [\operatorname{Re}\{\mathbf{y}_c\}^T, \operatorname{Im}\{\mathbf{y}_c\}^T]^T$ with estimated phase $\hat{\phi} = g_{\boldsymbol{\omega}}(\mathbf{y})$ :
$\bar{\mathbf{y}} = t(\hat{\phi}, \mathbf{y}) = \begin{bmatrix} \cos(\hat{\phi})\operatorname{Re}\{\mathbf{y}_c\} + \sin(\hat{\phi})\operatorname{Im}\{\mathbf{y}_c\} \\ \cos(\hat{\phi})\operatorname{Im}\{\mathbf{y}_c\} - \sin(\hat{\phi})\operatorname{Re}\{\mathbf{y}_c\} \end{bmatrix}$
1. Discriminative Network $g: \mathbb{R}^{n'} \to \mathcal{M}$ : A neural network that predicts the transmitted message $\hat{s}$ from the canonicalized representation $\bar{\mathbf{y}}$ .
The parameter estimator $g_{\boldsymbol{\omega}}$ is trained end-to-end through backpropagation to minimize the final task loss (e.g., categorical cross-entropy of message detection) rather than an explicit parameter estimation error.
Knowl 8 — RTN Multipath Fading Equalization and Convergence
empirical result
In an $(8,4)$ complex communications autoencoder operating over an $L = 3$ tap Rayleigh fading channel:

$\mathbf{y}_{c, i} = \sum_{\ell=1}^L h_{c, \ell} x_{c, i - \ell + 1} + n_{c, i}$

where $\mathbf{h}_c \sim \mathcal{CN}(\mathbf{0}, L^{-1}\mathbf{I}_L)$ and $\mathbf{n}_c \sim \mathcal{CN}(\mathbf{0}, (R E_b/N_0)^{-1}\mathbf{I}_n)$ :
- The parameter estimation network predicts an inverse filter $\boldsymbol{\omega}_c \in \mathbb{C}^L$ ( $2L$ real outputs) using two dense layers with $\tanh$ activations followed by a linear dense layer, and the transformation layer computes the complex convolution of $\mathbf{y}_c$ with $\boldsymbol{\omega}_c$ .
- The RTN-augmented autoencoder outperforms a baseline consisting of Differential BPSK (DBPSK) with Maximum Likelihood Sequence Estimation (MLSE) and a Hamming $(7,4)$ code across the entire $E_b/N_0$ range ( $0\text{ dB}$ to $20\text{ dB}$ ).
- A plain autoencoder without an RTN fails to achieve the baseline's performance and exhibits significantly slower training convergence, requiring more epochs to reach a higher asymptotic validation loss.

Knowl 9 — CNN Architecture for Raw IQ Modulation Classification

data/table

A convolutional neural network (CNN) can perform modulation classification directly on raw complex-valued baseband IQ time-series data without handcrafted expert features.

Layer	Output dimensions
Input	$2 \times 128$
Convolution ( $128$ filters, size $2 \times 8$ ) + ReLU	$128 \times 121$
Max Pooling (size 2, strides 2)	$128 \times 60$
Convolution ( $64$ filters, size $1 \times 16$ ) + ReLU	$64 \times 45$
Max Pooling (size 2, strides 2)	$64 \times 22$
Flatten	$1408$
Dense + ReLU	$128$
Dense + ReLU	$64$
Dense + ReLU	$32$
Dense + softmax	$10$

The architecture contains $324{,}330$ trainable parameters and operates on an input tensor of size $2 \times 128$ representing the in-phase (I) and quadrature (Q) components across 128 time samples.

Knowl 10 — Empirical Modulation Classification Performance on Raw Baseband IQ Samples
empirical result
Evaluated on the RadioML 2016.10b benchmark dataset ( $1.2\times 10^6$ sequences of 128 baseband IQ samples across 10 digital/analog modulations: 8PSK, AM-DSB, BPSK, CPFSK, GFSK, PAM4, QAM16, QAM64, QPSK, WBFM, under fading, sample rate offset, and carrier frequency offset from $\text{SNR} = -20\text{ dB}$ to $18\text{ dB}$ ):
- The CNN on raw IQ samples outperforms an extreme gradient boosting model (1000 estimators) trained on 16 expert cumulant and analog features by approximately $4\text{ dB}$ in the low-to-medium SNR regime, reaching identical asymptotic classification accuracy ( $\approx 85\%$ ) at high SNR.
- A single decision tree baseline performs approximately $6\text{ dB}$ worse than the CNN at medium SNR and $3.5\%$ worse at high SNR.
- Primary confusion modes at high SNR ( $\text{SNR} = 10\text{ dB}$ ) occur between QAM16 and QAM64 (due to shared constellation points in short 128-sample bursts) and between AM-DSB and WBFM (during voice pauses with low information content).
Knowl 11 — Fundamental Limitations of Deep Learning in the Physical Layer
limitation
End-to-end deep learning for communications physical layer designs faces several key open challenges:
1. Curse of Dimensionality: Formulating message transmission as an $M$ -ary classification problem scales exponentially with bit length $k = \log_2(M)$ . For practical block lengths (e.g., $k = 100$ bits, requiring $M = 2^{100}$ classes), training autoencoders becomes intractable because the model must observe all possible messages during training.
2. Differentiable Channel Requirement (Black-Box Problem): End-to-end backpropagation requires an exact, differentiable analytic model of the channel transfer function $p(\mathbf{y}|\mathbf{x})$ to compute $\nabla_{\mathbf{x}} l$ . Over real hardware and unknown radio propagation channels, analytical gradients are unavailable, requiring surrogate system identification, transfer learning, or reinforcement learning approaches.
3. Training SNR Sensitivity: Learned communications systems do not generalize uniformly across all SNRs; training at low SNR fails to learn high-SNR constellation structures, while training over wide SNR ranges significantly impedes training speed and convergence.

Coverage note — None omitted; all core contributions, network architectures, mathematical models, algorithms, empirical findings, and limitations from the paper are fully covered.

References

1.T. S. Rappaport, Wireless communications: Principles and practice, 2nd ed. Prentice Hall, 2002.
2.R. M. Gagliardi and S. Karp, Optical communications, 2nd ed. Wiley, 1995.
3.H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital communication receivers: Synchronization, channel estimation, and signal processing. John Wiley & Sons, Inc., 1998.
4.T. Schenk, RF imperfections in high-rate wireless systems: Impact and digital compensation. Springer Science & Business Media, 2008.
5.J. Proakis and M. Salehi, Digital Communications, 5th ed. McGraw-Hill Education, 2007.
6.Y. LeCun et al., "Generalization and network design strategies," Connectionism in perspective, pp. 143–155, 1989.
7.K. He, X. Zhang, S. Ren, and J. Sun, "Delving deep into rectifiers: Surpassing human-level performance on imagenet classification," in Proc. IEEE Int. Conf. Computer Vision, 2015, pp. 1026–1034.
8.D. G. Lowe, "Object recognition from local scale-invariant features," in Proc. IEEE Int. Conf. Computer Vision, 1999, pp. 1150–1157.
9.Z. S. Harris, "Distributional structure," Word, vol. 10, no. 2-3, pp. 146–162, 1954.
10.A. Goldsmith, "Joint source/channel coding for wireless channels," in Proc. IEEE Vehicular Technol. Conf., vol. 2, 1995, pp. 614–618.
11.E. Zehavi, "8-PSK trellis codes for a Rayleigh channel," IEEE Trans. Commun., vol. 40, no. 5, pp. 873–884, 1992.
12.H. Wymeersch, Iterative receiver design. Cambridge University Press, 2007, vol. 234.
13.K. Hornik, M. Stinchcombe, and H. White, "Multilayer feedforward networks are universal approximators," Neural networks, vol. 2, no. 5, pp. 359–366, 1989.
14.S. Reed and N. de Freitas, "Neural programmer-interpreters," arXiv preprint arXiv:1511.06279, 2015.
15.H. T. Siegelmann and E. D. Sontag, "On the computational power of neural nets," in Proc. 5th Annu. Workshop Computational Learning Theory. ACM, 1992, pp. 440–449.
16.V. Vanhoucke, A. Senior, and M. Z. Mao, "Improving the speed of neural networks on CPUs," in Proc. Deep Learning and Unsupervised Feature Learning NIPS Workshop, 2011.
17.Y.-H. Chen, T. Krishna, J. S. Emer, and V. Sze, "Eyeriss: An energy-efficient reconfigurable accelerator for deep convolutional neural networks," IEEE J. Solid-State Circuits, vol. 52, no. 1, pp. 127–138, 2017.
18.R. Raina, A. Madhavan, and A. Y. Ng, "Large-scale deep unsupervised learning using graphics processors," in Proc. Int. Conf. Mach. Learn. (ICML). ACM, 2009, pp. 873–880.
19.M. Ibnkahla, "Applications of neural networks to digital communications–A survey," Elsevier Signal Processing, vol. 80, no. 7, pp. 1185–1215, 2000.
20.M. Bkassiny, Y. Li, and S. K. Jayaweera, "A survey on machine-learning techniques in cognitive radios," IEEE Commun. Surveys Tuts., vol. 15, no. 3, pp. 1136–1159, 2013.
21.J. Qadir, K.-L. A. Yau, M. A. Imran, Q. Ni, and A. V. Vasilakos, "IEEE Access Special Section Editorial: Artificial Intelligence Enabled Networking," IEEE Access, vol. 3, pp. 3079–3082, 2015.
22.E. Nachmani, Y. Be’ery, and D. Burshtein, "Learning to decode linear codes using deep learning," in Proc. IEEE Annu. Allerton Conf. Commun., Control, and Computing (Allerton), 2016, pp. 341–346.
23.E. Nachmani, E. Marciano, D. Burshtein, and Y. Be’ery, "RNN decoding of linear block codes," arXiv preprint arXiv:1702.07560, 2017.
24.N. Samuel, T. Diskin, and A. Wiesel, "Deep MIMO detection," arXiv preprint arXiv:1706.01151, 2017.
25.J. R. Hershey, J. L. Roux, and F. Weninger, "Deep unfolding: Model-based inspiration of novel deep architectures," arXiv preprint arXiv:1409.2574, 2014.
26.M. Borgerding and P. Schniter, "Onsager-corrected deep learning for sparse linear inverse problems," arXiv preprint arXiv:1607.05966, 2016.
27.Y.-S. Jeon, S.-N. Hong, and N. Lee, "Blind detection for MIMO systems with low-resolution ADCs using supervised learning," arXiv preprint arXiv:1610.07693, 2016.
28.N. Farsad and A. Goldsmith, "Detection algorithms for communication systems using deep learning," arXiv preprint arXiv:1705.08044, 2017.
29.H. Sun, X. Chen, Q. Shi, M. Hong, X. Fu, and N. D. Sidiropoulos, "Learning to optimize: Training deep neural networks for wireless resource management," arXiv preprint arXiv:1705.09412, 2017.
30.T. J. O’Shea, K. Karra, and T. C. Clancy, "Learning to communicate: Channel auto-encoders, domain specific regularizers, and attention," in Proc. IEEE Int. Symp. Signal Process. and Inf. Technol. (ISSPIT), 2016, pp. 223–228.
31.T. J. O’Shea, J. Corgan, and T. C. Clancy, "Convolutional radio modulation recognition networks," in Proc. Int. Conf. Eng. Applications of Neural Networks. Springer, 2016, pp. 213–226.
32.T. J. O’Shea, J. Corgan, and T. C. Clancy, "Unsupervised representation learning of structured radio communication signals," in Proc. IEEE Int. Workshop Sensing, Processing and Learning for Intelligent Machines (SPLINE), 2016, pp. 1–5.
33.T. Gruber, S. Cammerer, J. Hoydis, and S. ten Brink, "On deep learning-based channel decoding," in Proc. IEEE 51st Annu. Conf. Inf. Sciences Syst. (CISS), 2017, pp. 1–6.
34.S. Cammerer, T. Gruber, J. Hoydis, and S. t. Brink, "Scaling deep learning-based decoding of polar codes via partitioning," arXiv preprint arXiv:1702.06901, 2017.
35.I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning. MIT Press, 2016.
36.N. Srivastava, G. E. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, "Dropout: A simple way to prevent neural networks from overfitting." J. Mach. Learn. Res., vol. 15, no. 1, pp. 1929–1958, 2014.
37.V. Nair and G. E. Hinton, "Rectified linear units improve restricted boltzmann machines," in Proc. Int. Conf. Mach. Learn. (ICML), 2010, pp. 807–814.
38.Y. Jia, E. Shelhamer, J. Donahue, S. Karayev, J. Long, R. Girshick, S. Guadarrama, and T. Darrell, "Caffe: Convolutional architecture for fast feature embedding," arXiv preprint arXiv:1408.5093, 2014.
39.T. Chen, M. Li, Y. Li, M. Lin, N. Wang, M. Wang, T. Xiao, B. Xu, C. Zhang, and Z. Zhang, "MXNet: A flexible and efficient machine learning library for heterogeneous distributed systems," arXiv preprint arXiv:1512.01274, 2015.
40.M. Abadi et al., "TensorFlow: Large-scale machine learning on heterogeneous systems," 2015, software available from tensorflow.org. [Online]. Available: http://tensorflow.org/
41.R. Al-Rfou, G. Alain, A. Almahairi et al., "Theano: A Python framework for fast computation of mathematical expressions," arXiv preprint arXiv:1605.02688, 2016.
42.R. Collobert, K. Kavukcuoglu, and C. Farabet, "Torch7: A matlab-like environment for machine learning," in BigLearn, NIPS Workshop, 2011.
43.F. Chollet, "keras," https://github.com/fchollet/keras, 2015.
44.T. O’Shea and J. Hoydis, "Source code," https://github.com/-available-after-review, 2017.
45.G. E. Hinton, S. Osindero, and Y.-W. Teh, "A fast learning algorithm for deep belief nets," Neural computation, vol. 18, no. 7, pp. 1527–1554, 2006.
46.D. Kingma and J. Ba, "Adam: A method for stochastic optimization," arXiv preprint arXiv:1412.6980, 2014.
47.Y. N. Dauphin, R. Pascanu, C. Gulcehre, K. Cho, S. Ganguli, and Y. Bengio, "Identifying and attacking the saddle point problem in high-dimensional non-convex optimization," in Advances in Neural Information Processing Systems (NIPS), 2014, pp. 2933–2941.
48.L. v. d. Maaten and G. Hinton, "Visualizing data using t-SNE," J. Mach. Learn. Res., vol. 9, no. Nov, pp. 2579–2605, 2008.
49.I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, "Generative adversarial nets," in Advances in Neural Information Processing Systems (NIPS), 2014, pp. 2672–2680.
50.M. Abadi and D. G. Andersen, "Learning to protect communications with adversarial neural cryptography," arXiv preprint arXiv:1610.06918, 2016.
51.M. Jaderberg, K. Simonyan, A. Zisserman et al., "Spatial transformer networks," in Advances in Neural Information Processing Systems (NIPS), 2015, pp. 2017–2025.
52.J. Estaran et al., "Artificial neural networks for linear and non-linear impairment mitigation in high-baudrate IM/DD systems," in Proc. 42nd European Conf. Optical Commun. (ECOC). VDE, 2016, pp. 1–3.
53.A. K. Nandi and E. E. Azzouz, "Algorithms for automatic modulation recognition of communication signals," IEEE Trans. Commun., vol. 46, no. 4, pp. 431–436, 1998.
54.A. Fehske, J. Gaeddert, and J. H. Reed, "A new approach to signal classification using spectral correlation and neural networks," in IEEE Int. Symp. New Frontiers in Dynamic Spectrum Access Networks (DYSPAN), 2005, pp. 144–150.
55.K. Simonyan and A. Zisserman, "Very deep convolutional networks for large-scale image recognition," arXiv preprint arXiv:1409.1556, 2014.
56.F. Pedregosa et al., "Scikit-learn: Machine learning in Python," J. Mach. Learn. Res., vol. 12, pp. 2825–2830, 2011.
57.A. Abdelmutalab, K. Assaleh, and M. El-Tarhuni, "Automatic modulation classification based on high order cumulants and hierarchical polynomial classifiers," Physical Communication, vol. 21, pp. 10–18, 2016.
58.D. George and E. Huerta, "Deep neural networks to enable real-time multimessenger astrophysics," arXiv preprint arXiv:1701.00008, 2016.
59.D. Maclaurin, D. Duvenaud, and R. P. Adams, "Gradient-based hyper-parameter optimization through reversible learning," in Proc. 32nd Int. Conf. Mach. Learn. (ICML), 2015.
60.J. Bergstra and Y. Bengio, "Random search for hyper-parameter optimization," J. Mach. Learn. Res., vol. 13, pp. 281–305, Feb. 2012.
61.A. Hirose, Complex-valued neural networks. Springer Science & Business Media, 2006.
62.M. F. Amin, M. I. Amin, A. Al-Nuaimi, and K. Murase, "Wirtinger calculus based gradient descent and Levenberg-Marquardt learning algorithms in complex-valued neural networks," in Int. Conf. on Neural Information Processing. Springer, 2011, pp. 550–559.
63.G. C. Goodwin and R. L. Payne, Dynamic system identification: experiment design and data analysis. Academic press, 1977.
64.S. J. Pan and Q. Yang, "A survey on transfer learning," IEEE Trans. Knowl. Data Eng., vol. 22, no. 10, pp. 1345–1359, 2010.
65.F. Adib, C.-Y. Hsu, H. Mao, D. Katabi, and F. Durand, "Capturing the human figure through a wall," ACM Trans. Graphics (TOG), vol. 34, no. 6, p. 219, 2015.
66.M. Zhao, F. Adib, and D. Katabi, "Emotion recognition using wireless signals," in Proc. ACM Annu. Int. Conf. Mobile Computing and Networking, 2016, pp. 95–108.

Citation

MLA

O'Shea, T., and J. Hoydis. “An Introduction to Deep Learning for the Physical Layer”. IEEE Transactions on Cognitive Communications and Networking, vol. 3, no. 4, 2017, pp. 563–75, https://doi.org/10.1109/TCCN.2017.2758370.

APA

O'Shea, T., & Hoydis, J. (2017). An Introduction to Deep Learning for the Physical Layer. IEEE Transactions on Cognitive Communications and Networking, 3(4), 563–575. https://doi.org/10.1109/TCCN.2017.2758370

Chicago

O'Shea, T., and J. Hoydis. 2017. “An Introduction to Deep Learning for the Physical Layer”. IEEE Transactions on Cognitive Communications and Networking 3 (4): 563–75. https://doi.org/10.1109/TCCN.2017.2758370.

Harvard

O'Shea, T. and Hoydis, J. (2017) “An Introduction to Deep Learning for the Physical Layer”, IEEE Transactions on Cognitive Communications and Networking, 3(4), pp. 563–575. Available at: https://doi.org/10.1109/TCCN.2017.2758370.

Vancouver

1. O'Shea T, Hoydis J (2017) An Introduction to Deep Learning for the Physical Layer. IEEE Transactions on Cognitive Communications and Networking 3:563–575

BibTeX

@article{O_Shea_2017, title={An Introduction to Deep Learning for the Physical Layer}, volume={3}, ISSN={2332-7731}, url={http://dx.doi.org/10.1109/TCCN.2017.2758370}, DOI={10.1109/tccn.2017.2758370}, number={4}, journal={IEEE Transactions on Cognitive Communications and Networking}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={O’Shea, Timothy and Hoydis, Jakob}, year={2017}, month=Dec, pages={563–575} }

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An Introduction to Deep Learning for the Physical Layer

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Knowls

Knowl 1 — End-to-End Communications System as a Channel Autoencoder

Knowl 2 — Layer Layout and Parameter Count of Single-User Channel Autoencoder

Knowl 3 — Error Rate and Constellation Packing of Channel Autoencoders

Knowl 4 — Two-User Interference Channel Autoencoder Model

Knowl 5 — Dynamic Loss Weighting Algorithm for Multi-User Autoencoder Training

Knowl 6 — Interference Channel Autoencoder Performance and Learned Signaling

Knowl 7 — Radio Transformer Networks (RTN)

Knowl 8 — RTN Multipath Fading Equalization and Convergence

Knowl 9 — CNN Architecture for Raw IQ Modulation Classification

Knowl 10 — Empirical Modulation Classification Performance on Raw Baseband IQ Samples

Knowl 11 — Fundamental Limitations of Deep Learning in the Physical Layer

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