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Fast Deep Learning for Automatic Modulation Classification

Sharan Ramjee, Shengtai Ju, Diyu Yang, Xiaoyu Liu, Aly El Gamal, Yonina C. Eldar

arXiv:1901.05850v1eess.SPcs.AIcs.LGstat.ML

TL;DR

The paper asks whether deep learning can accurately classify modulation types from subsampled wireless-signal data while reducing costly training. It compares deep architectures and training-data reduction methods, finding high classification accuracy with substantially shorter training times and small accuracy losses.

  • Problem

    The work addresses accurate automatic modulation classification from subsampled wireless signals and the need to reduce the long training times of deep classifiers.

  • Method

    The paper evaluates five deep architectures and combines dimensionality reduction, subsampling, and representative SNR selection to reduce training data.

  • Results

    Training time can be reduced by up to 20 times with classification-accuracy losses as low as 2%.

  • Takeaways & Limitations

    CLDNN, ResNet, and LSTM provide high-performing candidates across SNR ranges, while PCA, subsampling, and SNR selection reduce training time with limited accuracy degradation.

Abstract

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In this work, we investigate the feasibility and effectiveness of employing deep learning algorithms for automatic recognition of the modulation type of received wireless communication signals from subsampled data. Recent work considered a GNU radio-based data set that mimics the imperfections in a real wireless channel and uses 10 different modulation types. A Convolutional Neural Network (CNN) architecture was then developed and shown to achieve performance that exceeds that of expert-based approaches. Here, we continue this line of work and investigate deep neural network architectures that deliver high classification accuracy. We identify three architectures - namely, a Convolutional Long Short-term Deep Neural Network (CLDNN), a Long Short-Term Memory neural network (LSTM), and a deep Residual Network (ResNet) - that lead to typical classification accuracy values around 90% at high SNR. We then study algorithms to reduce the training time by minimizing the size of the training data set, while incurring a minimal loss in classification accuracy. To this end, we demonstrate the performance of Principal Component Analysis in significantly reducing the training time, while maintaining good performance at low SNR. We also investigate subsampling techniques that further reduce the training time, and pave the way for online classification at high SNR. Finally, we identify representative SNR values for training each of the candidate architectures, and consequently, realize drastic reductions of the training time, with negligible loss in classification accuracy.

I. INTRODUCTION

The paper evaluates deep architectures for automatic modulation classification and develops ways to reduce their training time. It reports strong accuracy across SNR ranges, with up to 20-fold faster training and accuracy losses as low as 2%.

  • Architectures: The work studies five deep architectures for modulation classification, including newly designed CNN, DenseNet, and CLDNN models and optimized ResNet and LSTM variants.The architectures are evaluated on the modulation-recognition dataset from [29].
  • Architecture performance: CLDNN and optimized ResNet deliver superior performance at low SNR, while ResNet and optimized LSTM perform best at high SNR.The identified architectures cover different SNR ranges from -20 dB to 18 dB.
  • Training-time reduction: 20 times faster training is achieved with classification-accuracy losses as low as 2%.The paper targets the long training times that hinder real-time adaptation and online training.
  • Dimensionality reduction: PCA is more effective than subsampling at low SNR, whereas subsampling is more effective at high SNR.The proposed magnitude-based subsampling method produces little classification degradation at high SNR.

II. EXPERIMENTAL SETUP

The study classifies modulation types from received wireless signals using deep neural networks and evaluates the approach on a simulated, imperfect-channel dataset. Training and testing use windowed complex samples spanning ten modulation classes and SNR values from −20 to 18 dB.

  • The pure LSTM receives amplitude-and-phase polar samples, whereas other architectures use rectangular complex samples.
  • The task is to recognize modulation type i from received signal r(t) using deep neural-network classifiers.
  • The RadioML2016.10b dataset contains eight digital and two analog modulation types, with equal representation across classes.
  • Channel and device imperfections are simulated through thermal noise, multipath fading, sample-rate offset, noise, center-frequency offset, and fading models.
  • Samples are segmented into 128-sample windows with a 64-sample shift and represented as 2×128 vectors separating real and imaginary parts.
  • SNR values are uniformly distributed from −20 dB to +18 dB in 2 dB steps, and accuracy is the percentage of correctly classified test samples.

III. DEEP NEURAL NETWORK ARCHITECTURES

The study compares five deep neural-network architectures for modulation classification: CNN, DenseNet, CLDNN, LSTM, and ResNet.

  • Five architectures are evaluated: CNN, DenseNet, CLDNN, LSTM, and ResNet.

A. CNN and DenseNet Architectures

The evaluated architectures progressively combine convolutional, shortcut, and recurrent structures to classify modulation signals. Accuracy reaches 92% at high SNR for LSTM, while recurrent models train more slowly and degrade under subsampling or dimensionality reduction.

  • CNN and DenseNet Architectures: 83.8% high-SNR accuracy is achieved by a four-convolutional-layer CNN, compared with 75% for the referenced CNN2 architecture.
  • CNN and DenseNet Architectures: Adding shortcut connections between non-consecutive layers yields 86.6% classification accuracy at high SNR for DenseNet.
  • CLDNN Architecture: CLDNN inserts a 50-cell LSTM layer between CNN and dense layers, achieving 88.5% accuracy above 2 dB.
  • LSTM Architecture: The pure LSTM uses amplitude-and-phase inputs, two 128-cell LSTM layers, and a Softmax output over modulation classes.
  • LSTM Architecture: 92% high-SNR classification accuracy is reported for the LSTM network, supporting recurrent architectures for modulation classification.
  • LSTM Architecture: 222 seconds per epoch makes LSTM training about four times slower than the four-convolutional-layer CNN.
  • LSTM Architecture: Subsampling or dimensionality reduction causes CLDNN and LSTM accuracy to drop rapidly at high SNR, whereas ResNet performs best in these cases.

D. ResNet Architecture

The proposed ResNet uses residual connections and a three-stack design to avoid accuracy degradation while delivering strong modulation-classification performance. It reaches 92% accuracy at high SNR with 58-second-per-epoch training.

  • Architecture: The proposed ResNet uses three residual stacks instead of six, a choice found to increase classification accuracy.Each stack contains a convolutional layer, two residual units, and a max-pooling layer.
  • Architecture: Residual units add their input to the output of the second convolutional layer, creating shortcut connections.The convolutional layers use 1x5 filters and batch normalization.
  • Motivation: The reduced complexity of each layer allows ResNet to become deeper without accuracy degradation issues.The architecture addresses degradation associated with deeper neural networks.
  • Results: 92% classification accuracy and 58 seconds per epoch characterize the ResNet's high-SNR performance and training speed.This is reported as the best result among the evaluated models.
  • Results: ResNet performs best at low SNR, while ResNet and LSTM achieve similar classification accuracies at high SNR.The overall accuracy-versus-SNR comparison identifies CLDNN, LSTM, and ResNet as strong architectures.

IV. DIMENSIONALITY REDUCTION AND SUBSAMPLING

The paper reduces classifier input dimensionality with PCA and evaluates its effect on accuracy and training time. PCA produces approximately linear training-time reductions, but its accuracy effects depend on architecture and SNR.

  • Principal Component Analysis: PCA projects test vectors onto a reduced-dimensional subspace learned from all training vectors across the 10 modulation types.The study evaluates dimensionality-reduction factors of 2^k for 1 ≤ k ≤ 5 on originally 256-dimensional inputs.
  • Training-time reduction: Training time drops approximately linearly with PCA dimensionality reduction; halving dimensions approximately halves training time.The input waveform is sampled at around six times the Nyquist rate, so factors of 8, 16, and 32 reach sub-Nyquist levels.
  • Accuracy effects: LSTM accuracy drops significantly under input-dimension reduction, whereas factors of 2 and 4 produce almost identical results across all three architectures.Dimensionality reduction can also reduce overfitting by removing task-irrelevant information.
  • Accuracy effects: The ResNet is most robust to PCA reduction, achieving approximately 70% accuracy at 2 dB with an eightfold dimension reduction.This result is reported for the ResNet PCA experiment.
  • Accuracy effects: PCA accuracy curves can become nonmonotonic with SNR, most notably for CLDNN with an eightfold reduction, whose accuracy drops above 0 dB.The passage attributes the high-SNR behavior to PCA potentially losing structural information preserved by subsampling.

B. Uniform Subsampling

Uniform subsampling reduces input dimensions by sampling at regular intervals and generally lowers training time linearly. Its accuracy depends on architecture, SNR, and sampling rate, with different behavior above and below Nyquist.

  • Method: Uniform subsampling samples the input vector at regular intervals and trains the architectures on the resulting subsampled vectors.The method is evaluated for CLDNN, ResNet, and LSTM using the corresponding experiments in Figs. 13–15.
  • Training-time reduction: Training time drops linearly as the number of input dimensions decreases under uniform subsampling.The same linear relationship is observed in the PCA experiments.
  • Comparison with PCA: Uniform subsampling outperforms PCA for high-SNR LSTM and ResNet, whereas PCA performs better for low-SNR CLDNN and ResNet.The comparison is reported for the best-performing architectures in the respective SNR ranges.
  • Accuracy effects: ResNet and LSTM improve at high SNR when using half the samples, and LSTM exceeds its full-sample accuracy with one quarter of the samples.The paper attributes this behavior to reduced overfitting caused by oversampling the training input.
  • Accuracy effects: ResNet and LSTM perform better with half the samples only from 2 dB to 10 dB, but worse from -20 dB to 0 dB.The low-SNR advantage of oversampling also holds across the dimensionality-reduction and subsampling techniques considered.
  • Comparison of sampling strategies: Uniform sampling outperforms random sampling at 1/8, 1/4, and 1/2 subsampling, while random sampling performs better at 1/16 and 1/32.The paper relates the below-Nyquist result to the superiority of effectively non-uniform sub-Nyquist strategies.

D. Magnitude Rank Subsampling

Magnitude rank subsampling keeps the highest-magnitude samples and restores their original order. It performs best well below Nyquist for most architectures, but LSTM is disadvantaged by lost temporal correlations.

  • Method: Magnitude rank subsampling selects samples by descending magnitude, then restores the selected samples to their original sequence order.Magnitudes are calculated from the real and imaginary parts of the samples.
  • Results: At 1/8, 1/4, and 1/2 subsampling, magnitude rank performs worse than uniform but better than random subsampling for all three architectures.These rates are close to or above the Nyquist rate.
  • Results: At 1/16 and 1/32 subsampling, magnitude rank performs significantly better than uniform and random sampling except for LSTM.These operating points are well below Nyquist.
  • Results: LSTM performs relatively poorly with magnitude rank subsampling because temporal correlations relevant to classification may be lost.Those correlations could depend on samples with lower magnitudes.
  • Results: Accuracy degradation under lower sampling rates is closer to linear than under PCA and uniform subsampling, and is considerably mild at high SNR.The comparison concerns the three dimensionality-reduction approaches.
  • Training-time reduction: The reported training-time behavior does not apply to LSTM, even at a 1/2 dimensionality reduction or subsampling rate.The paper attributes this to the LSTM input layer comprising a higher proportion of total neurons.

V. SNR SELECTION

The section evaluates training with one representative SNR instead of all 20 values, reducing training time while preserving classification accuracy under suitable SNR choices. High-SNR training gives the best overall performance, whereas mismatched or very-low-SNR training can degrade accuracy.

  • Representative SNR training: Training on one or two representative SNR values significantly reduces training time while incurring negligible classification-accuracy loss.The approach replaces training data spanning all 20 SNR values with smaller representative subsets.
  • Single-SNR selection: 3 seconds per epoch was achieved for CLDNN training with 10 dB data, compared with 58 seconds per epoch using the original setup.The 10 dB training set also produced the best CLDNN performance in that experiment.
  • Single-SNR selection: 2 seconds per epoch was achieved for ResNet training with 8 dB data, compared with 38 seconds per epoch using all three GPUs.The 8 dB training set yielded the highest overall ResNet classification accuracy.
  • SNR-dependent performance: High-SNR training produced the highest average testing accuracy, while training below -10 dB was not beneficial overall.Training between -10 dB and 0 dB performed best on testing data in the corresponding SNR range, but not at higher SNR.
  • Representative SNR training: Representative-SNR selection outperformed uniform sampling when the operating SNR range was known, whereas uniform selection was preferred under substantial train-test SNR mismatch.The mismatch case is illustrated at low SNR in Figs. 25–27.
  • Training-data reduction: 3.125% of the full training data retained accuracy above 70% at high SNR across all three networks.CLDNN and LSTM were more resilient than ResNet to aggressive reductions, and training time decreased linearly with dataset size.

C. Pairs of SNR Selection

The section studies pairs of training SNR values as a compromise between broad SNR coverage and reduced training cost. Selecting one high-SNR and one low-SNR value generally provides strong accuracy across the tested range, with architecture-specific choices.

  • Pair-selection strategy: Two SNR values, one high and one low, produced high classification accuracy across a wide portion of the -20 to 18 dB testing range.The results support selecting representative values from the two observed SNR ranges.
  • ResNet: 18 dB and 0 dB gave ResNet the best overall accuracy, while low-SNR-only training yielded accuracy of only around 10%.The low-SNR pair contained too much noise for the model to identify modulation patterns.
  • CLDNN: 18 dB and 0 dB achieved CLDNN accuracy comparable to using 50% of the data while reducing training time by approximately 90%.The 10 dB and 8 dB pair performed best for high-SNR testing, whereas 18 dB and 0 dB improved low-SNR accuracy.
  • LSTM: 18 dB and 0 dB yielded the highest average LSTM accuracy across all tested SNR values.For LSTM, the 12 dB and 4 dB pair also provided high high-SNR accuracy, with less than 2% loss there and reduced training time.

VI. DISCUSSION

The discussion identifies architecture-, SNR-, and representation-dependent behavior in modulation classification. It also highlights PCA and magnitude-based subsampling as practical routes to faster training, while noting sensitivity to input representation and architectural depth.

  • Architecture selection: CLDNN and ResNet perform best at low SNR, whereas LSTM and ResNet perform best at high SNR.These architecture-specific patterns guide model selection across operating conditions.
  • Dimensionality reduction: PCA is suggested for reducing input dimensions at low SNR, while magnitude-based subsampling is suggested at high SNR.Selecting samples with the largest magnitudes gives the highest classification accuracy at high SNR.
  • Online implementation: Magnitude rank subsampling can be implemented online by dynamically adjusting a threshold and ignoring samples below it.The discussion contrasts this implementation path with online PCA, which has also been studied in prior work.
  • Input representation: Rectangular input representation works better for all studied networks except pure LSTM, for which polar representation is better.LSTM is particularly effective at distinguishing different QAM constellations.
  • Architectural mechanisms: Capturing long-term dependencies can help identify repeating symbol-to-symbol transitions, while shortcut connections mitigate vanishing gradients and add architectural flexibility.The discussion links these design choices to CLDNN, LSTM, DenseNet, and ResNet architectures.
  • Architectural mechanisms: Deeper networks may overfit simpler tasks, which may require shallower architectures.The paper presents this as a scope boundary for architectural depth.

D. Why Dimensionality Reduction leads to Fast Deep Learning

The paper connects fast training to compressing inputs and retaining task-relevant information through dimensionality reduction, subsampling, and SNR selection. These methods reduce training time substantially while preserving accuracy, supporting investigation of online wireless classification.

  • Compression and training time: Minimal accuracy loss under aggressive data reduction is attributed to preserving relevant information needed for learning.The paper relates this result to the possibility that much training time is spent compressing input data.
  • Future directions: The paper proposes investigating hidden-layer representations of autoencoders for input-data compression.This is presented as future work rather than a demonstrated result in the current study.
  • Future directions: Denoising autoencoders are expected to improve low-SNR accuracy even when training data contains only high-SNR samples.This expectation motivates future work rather than establishing a current experimental finding.
  • Compression and training time: Training time was reduced by almost 20 times with accuracy loss as low as 2% at high SNR.The reduction was achieved through methods that minimize training-data size while preserving relevant information.
  • Overall conclusion: The paper reports high accuracy over a wide SNR range for 10 modulation types using CLDNN, LSTM, and ResNet architectures.It identifies architecture-specific strengths, PCA or magnitude-based reduction, and two-value SNR training as the main supported strategies.
  • Overall conclusion: Using only two SNR values, one high and one low, produced high accuracy over a wide portion of the -20 to 18 dB range.The paper presents this as a representative-training result and plans to investigate combinations with other methods.
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