I Introduction
Analysis of detected radio signals enables classification of communication technology and modulation schemes employed by the source that emitted the signals; this information helps optimize spectrum allocation and mitigate radio interference, supports wireless environment analysis and enables improvement of communication efficiency. However, increase in the numbers of emitter types and sources of interference, as well as temporal variations in the effects of wireless environment on the transmitted signals, render the accurate inference of communication schemes and emitter types computationally challenging.
Existing methods for modulation and technology classification can be organized into two subgroups, likelihoodbased and featurebased [2]
. Likelihoodbased methods make a decision by evaluating a likelihood function of the received signal and comparing the likelihood ratio with a predefined threshold. Although the likelihoodbased classifiers are optimal in that they minimize the probability of false classification, they suffer from high computational complexity
[2]. On the other hand, featurebased approaches are relatively simple to implement and may achieve nearoptimal performance but the features and decision criteria need to be carefully designed. Such methods rely on expert features including cyclic moments
[5] and their variations [4], and spectral correlation functions of analog and digital modulated signals [7, 6]; [24] describes novel decision criteria which utilize preexisting expert features. [3]facilitates classification via a multilayer perceptron that relies on spectral correlation functions. Expert systems have been shown to achieve high accuracy on certain special tasks but may be challenging to apply in general settings since the crafted features may not fully reflect all the realworld channel effects. As an alternative, deep learning based methods that learn directly from the received signals have recently been proposed. In particular,
[16]utilizes a convolutional neural network (CNN) that operates on inphase and quadraturephase (IQ) data and outperforms expert features based methods.
[22]combines CNN and long shortterm memory (LSTM)
[11, 8] to further improve classification accuracy. [19] utilizes an LSTM on amplitude and phase data by simply transferring IQ data for modulation classification, outperforming the proposed model in [22]. [15] proposes two classification models with one adapting the Visual Geometry Group (VGG) architecture [20] principles to a 1D CNN and the other utilizing the ideas of deep residual networks (RNs) [10]. Note that while spectrum monitoring devices are capable of acquiring detailed wireless signal’s IQ components, storage of such data on distributed sensing devices or their transmission to a cloud or edge device for processing is often infeasible due to resource constraints. To this end, distributed spectrum monitoring systems such as Electrosense [18] formulate technology detection task as the classification that uses more compact Power Spectral Density (PSD) data as features. Note, however, that the aforementioned deep learning architectures are infeasible for use in distributed settings and on lowcost computational platforms. More details on practical aspects of RF acquisition can be found in [23].In this paper, we propose a new learning framework for both modulation as well as technology classification problems based on an LSTM denoising autoencoder. The framework aims to estimate posterior probabilities of the modulation or technology types using time domain amplitude and phase of a radio signal. Autoencoders in an unsupervised manner learn a lowdimensional representation of data; more specifically, they attempt to perform a dimensionality reduction while robustly capturing essential content of highdimensional data
[9]. Typically, autoencoders consist of two blocks: an encoder and a decoder. The encoder converts input data into the socalled codes while the decoder reconstructs the input from the codes. The act of copying the input data to the output would be of little interest without an important additional constraint – namely, the constraint that the dimension of codes is smaller than the dimension of the input. This enables autoencoders to extract salient features of the input data. A denoising autoencoder (DAE) [21] can help extract stable and robust features by introduction noise corruption to the input signal. In our proposed framework, the received radio signals are first partially corrupted and the framework then recovers the destroyed signals, simultaneously learning stable and robust lowdimensional signal representations and classifying the signals based on the learned features.Our main contributions are summarized as follows:

We propose a new learning framework which uses amplitude and phase data for modulation classification; the framework is based on an LSTM denoising autoencoder and achieves stateoftheart modulation classification accuracy.

We extend the proposed framework to technology classification using power spectral density data.

The proposed framework achieves significantly higher top1 classification accuracy while having much simpler structure than the existing models. This enables realtime modulation and/or technology classification on compact and affordable computational devices, as we demonstrate using Raspberry PI platforms.
Ii Methods
Iia Problem Formulation
Let denote a sequence of dimensional features characterizing samples of the received radio signal sampled starting at time . The goal of modulation (technology) classification is to identify the modulation (technology) type of the radio signal among classes by estimating where denotes the class and is the true class of the signal.
For modulation classification, the features are the IQ components of the sampled signal (i.e., ). Figure 1
shows examples of the IQ components for 11 different modulation types found in RadioML2016.10A dataset for signaltonoise ratio (SNR) of
dB. Although there are differences between the IQ components, it is challenging even for a domain expert to distinguish between them due to pulse shaping, distortion and other channel effects [16].For technology classification, the spectrum of interest is scanned by selecting a candidate carrier frequency
in discrete increments, and for each such frequency a fast Fourier transform (FFT) of the received signal demodulated into baseband is computed. Average values of the FFT coefficients computed for each
are then concatenated to form a sequence of features used to perform the classification task. For the Electrosense data that we analyze in this paper, and the scanning resolution is MHz. Figure 2 shows an example of wireless magnitude spectrum data from one of the Electrosense sensors.To characterize the performance of modulation and technology classification methods, we rely on top1 classification accuracy over SNR, confusion matrix, time and space complexity in terms of the number of trainable parameters and model size, and testing time on Raspberry Pi.
IiB An LSTM Denoising AutoEncoder
In this section, we describe the design of our proposed classifier based on a denoising autoencoder and recurrent neural networks. Instead of using IQ components, for modulation classification we rely on L2normalized amplitude and normalized phase (falling between 1 and 1, in radians); such normalization benefits learning temporal dependencies
[19].A sampled radio signal results in a time series, and an LSTM is utilized to efficiently capture temporal structure of such a series. Figure 3 shows the structure of an LSTM cell with a forget gate. The input gate, output gate and forget gate can be expressed respectively as
(1) 
(2) 
and
(3) 
while the cell state vector and hidden state vector are defined as
(4) 
and
(5) 
respectively, where
denotes the sigmoid function (i.e.,
), denotes a weight matrix for the input time series, is a weight matrix for the hidden state vector, andrepresents a bias vector.
The denoising autoencoder corrupts the signal by randomly setting a portion of samples of to , thus obtaining a partially destroyed signal . The partially destroyed signal is fed to the autoencoder for training while the original signal is utilized for testing.
Motivated by [21], [1] and [12], we propose a novel LSTM denoising autoencoder for modulation/technology classification where the autoencoder and classifier are trained simultaneously.
Figure 4 shows the LSTM denoising autoencoder classifier. The classifier is connected to the last hidden state vector and it consists of 3 fully connected layers followed by a softmax function, i.e.,
(6) 
(7) 
(8) 
(9) 
where denotes the weight matrix, is the bias vector, denotes the output of a fully connected layer for classification ( represents its entry), denotes the probability of predicting as the class and
denotes the rectified linear unit (ReLU). The 2layer LSTM operates as an encoder that converts the corrupted input
into hidden state vectors while a shared fully connected layer operate as a decoder, i.e.,(10) 
where is the recovered sample, denotes the weight matrix of the decoder and is the bias vector for the fully connected layer. Note that we break the symmetry of the architecture by using a shared fully connected layer for the decoder since doing so reduces computational complexity.
Therefore, the loss function of the network consists of the reconstruction loss,
, and the classification loss, . The final loss function is a weighted combination of these two terms, i.e.,(11) 
where
is a hyperparameter balancing
and . It is worth pointing out that a small eliminates the effects of classification layers while a large distorts the learned representation of data. We set the value of to 0.1 to promote extraction of reliable lowdimensional representations of the original signals and thus enable efficient classification with reduced dimensionality of the hidden state of an LSTM cell. This allows the proposed model to achieve higher classification accuracy at a significantly reduced computational complexity. The reconstruction loss is defined to be the meansquared error (MSE) and can be expressed as(12) 
while the classification loss is defined to be the categorical cross entropy
(13) 
where if belongs to the class and otherwise.
IiC Model Parameters
For both tasks, we rely on Adam optimizer [13]
since it helps avoid local optima. The dimensionality of the hidden states of the LSTM in our denoising autoencoder is set to
. Please note that prior LSTMbased methods require more than 128 hidden states to achieve desired level of accuracy; otherwise, the classification accuracy deteriorates significantly as shown in [19]. The number of nodes in the dense layer of decoder is set to and the number of nodes in the fully connected layers of the classifier are set to , and , respectively. The learning rate is set toand the number of epochs is set to
. Dropout rate is chosen to be for the LSTMs and fully connected layers; randomly selected 10% of the entries of the input signal in the training data are masked by . The models are implemented on a computer with 3.70GHz Intel i78700K processor, 2 NVIDIA GeForce GTX 1080Ti computer graphics cards and 32GB of RAM. The minibatch size of 128 is utilized. The parameter controlling how the reconstruction loss and classification loss are combined is set to .Iii Results
Iiia Performance Comparison on RadioML2016.10A
We first evaluate performance of the proposed model for modulation classification on a realistic RadioML2016.10A dataset. RadioML data^{1}^{1}1https://www.deepsig.io/datasets includes a series of synthetic and overtheair modulation classification sets created by DeepSig Inc. Among them, RadioML2016.10A has in particular been widely used for benchmark testing [17, 22, 19]. Radio channel effects including timedelay, timescaling, phase rotation, frequency offset and additive thermal noise are accounted for to emulate practical radio communications (details can be found in [14]). The set contains data for 11 modulation schemes (8PSK, AMDSB, AMSSB, BPSK, CPFSK, GFSK, PAM4, QAM16, QAM64, QPSK and WBFM). The SNR ranges from 20dB to 18dB with 2dB step size; there are samples for each SNR resulting in the total of 220k samples. The sample length is 128. We used 50%, 25% and 25% of the dataset for training, validation and testing, respectively.
Model  20dB  18dB  16dB  14dB  12dB  10dB  8dB  
DAE  Mean  9.30  9.35  9.92  12.27  15.75  23.70  35.29 
Std  0.09  0.17  0.43  0.98  1.32  1.25  1.13  
LSTM  Mean  9.22  9.51  9.67  11.66  14.64  22.89  35.78 
Std  0.21  0.23  0.30  0.62  1.11  1.31  1.31  
CLDNN  Mean  9.19  9.35  9.56  11.76  15.39  23.98  36.16 
Std  0.16  0.22  0.23  0.74  1.17  1.38  1.61  
CNN  Mean  9.15  9.23  9.64  11.68  15.24  23.51  33.98 
Std  0.13  0.26  0.40  0.79  0.98  1.31  0.82  
Model  6dB  4dB  2dB  0dB  2dB  4dB  6dB  
DAE  Mean  53.31  67.88  79.97  87.62  89.98  91.81  92.61 
Std  1.56  1.23  1.08  0.74  0.60  0.45  0.23  
LSTM  Mean  52.14  65.26  77.29  86.20  89.18  90.37  91.20 
Std  0.94  1.07  0.65  0.85  0.64  0.81  0.52  
CLDNN  Mean  50.54  63.66  75.20  81.30  82.45  82.68  84.18 
Std  1.30  1.57  1.53  0.83  0.91  1.43  0.96  
CNN  Mean  46.56  58.43  68.05  72.62  72.40  73.57  74.32 
Std  1.06  0.92  0.65  1.14  0.91  1.56  1.15  
Model  8dB  10dB  12dB  14dB  16dB  18dB  Overall  
DAE  Mean  92.31  92.17  91.64  93.40  91.34  92.75  61.72 
Std  0.31  0.34  0.46  0.31  0.17  0.31  0.18  
LSTM  Mean  90.89  90.77  90.39  92.05  90.24  91.33  60.49 
Std  0.50  0.58  0.78  0.63  0.69  0.78  0.37  
CLDNN  Mean  84.21  84.32  82.02  84.38  83.41  84.16  56.78 
Std  1.14  0.82  0.90  0.79  1.02  0.99  0.46  
CNN  Mean  74.61  74.59  73.51  74.76  73.49  75.10  51.29 
Std  0.97  1.31  1.33  1.29  1.60  1.54  0.40  
The twolayer LSTM denoising autoencoder is trained on SNRs ranging from 20dB to 18dB. The top1 classification accuracy of CNN [16], CLDNN [22], LSTM [19] and our proposed model is shown in Figure 5 and Table I. The classification accuracy computed over all SNRs achieved by CNN, CLDNN, LSTM and our proposed model is 51.29%, 56.78%, 60.49% and 61.72%, respectively. It is worth pointing out that training with noise helps increase the classification accuracy (computed across all SNRs) by 1.1% as compared to training with the original signal. The autoencoder enables extraction of stable lowdimensional features with a significantly reduced dimension of hidden LSTM states and thus contributes to the improvement in classification accuracy and the reduction of computational complexity. The average classification accuracy for SNRs ranging from 0dB to 18dB achieved by CNN, CLDNN, LSTM and our proposed model is 73.9%, 83.31%, 90.26% and 91.55%, respectively. The proposed model outperforms selected models for almost all SNRs. The considered softwares were executed with their default settings, i.e., we use the same hyperparameters as the authors of existing methods did when running their methods on RadioML10.A dataset. The results in Figure 5 are averaged over 10 experiments. Model parameters were initialized at the beginning of each experiment. Note that the benchmarking results for the preexisting methods that we obtained closely match those reported in [19]. It is worth pointing out that our proposed model significantly outperforms CLDNN and CNN in high SNR regimes, while marginally outperforming LSTM in terms of top1 classification accuracy. Figure 68 illustrate the confusion matrices in the experiment that achieved the highest overall top1 classification accuracy for the proposed model and LSTM for SNRs 18dB, 0dB and 4dB. For the SNR of 18dB, the diagonal is much more sharp even though there are some confusions in separating AMDSB from WBFM signals, which are mainly due to the silence periods of audio [19]. Similar to Figure 7, there are some difficulties in separating AMDSB and WBFM at the SNR of 0dB. Besides, there is some level of confusion between QAM16 and QAM64 since QAM16 is a subset of QAM64. It is also worth mentioning that the proposed model performs better on AMSSB signals and on distinguishing QAM64 from QAM16 signals at high SNRs. As shown in Figure 8, it becomes much more difficult to distinguish the signals at low SNRs.
Model  # Parameters  # FLOPs  Memory 

DAE  14637  45040  224KB 
LSTM  200075  660239  2.32MB 
CLDNN  248817  588974  2.91MB 
CNN  5456219  80548043  61.4MB 
Platform  DAE  LSTM  CLDNN  CNN  

GTX 1080Ti  Mean  8456  7325  10257  19162 
Std  153.97  138.72  102.28  346.64  
Intel i78700K  Mean  1255  869  871  1578 
Std  7.72  21.62  15.70  14.36  
Raspberry Pi 4  Mean  241  42  45  127 
Std  14.61  0.51  1.36  1.01  
Raspberry Pi 3  Mean  119  19  20  45 
Std  1.45  1.97  0.23  2.39 
Next, we compare considered models in terms of the number of trainable parameters, the number of floating point operations (FLOPs), the memory cost, and the number of classifications per second on different computational platforms. As shown in Table II, the proposed model has the smallest number of trainable parameters and requires the fewest FLOPs and the smallest memory space. Table III shows that in terms of the number of classifications per second on Raspberry Pi 4, the proposed model is on average approximately , and faster than LSTM, CLDNN and CNN, respectively. On Raspberry Pi 3, the proposed model is on average approximately , and
faster than LSTM, CLDNN and CNN, respectively. The mean and standard deviation of the number of classifications per second are averaged over 10 experiments. Note that the complexity of existing methods cannot be reduced without causing severe deterioration of classification accuracy
[19].IiiB Performance Comparison on RadioML2018.01A
We next evaluate performance of the proposed model on the modulation classification task using the realistic overtheair RadioML2018.01A data with specific radio channel effect settings including carrier frequency offset, symbol rate offset, delay spread and thermal noise [15]. Signals over the socalled Normal Classes that are commonly seen in impaired environments, including OOK, 4ASK, BPSK, QPSK, 8PSK, 16QAM, AMSSBSC, AMDSBSC, FM, GMSK and OQPSK, are utilized. The data contains 11 modulations and the SNR range is from 20dB to 30dB with 2dB step size. For each SNR and modulation scheme there are 4096 samples, leading to about 1.17M samples in total. The sample length is 1024 and each sample is composed of IQ components. 50%, 25% and 25% of the entire dataset are used for training, validation and testing, respectively.
Table IV shows the mean and standard deviation of top1 classification accuracy over the range of SNRs for a number of models computed over 10 experiments. The classification accuracy computed over all SNRs achieved by VGG, RN and our proposed model is 64.03%, 66.00% and 67.30%, respectively. Note that training with noise helps increase the classification accuracy (computed across all SNRs) by 0.9% as compared to training with the original signal. As before, the autoencoder enables extraction of stable lowdimensional features with a significantly reduced dimension of hidden LSTM states, hence contributing to the improvement in classification accuracy and the reduction of computational complexity. The classification accuracy over the range of SNR from dB to dB achieved by VGG, RN and our proposed model is 92.16%, 94.89% and 96.56%, respectively. The proposed model outperforms stateoftheart models for almost all SNRs.
The top1 classification accuracy of the VGG and residual networks (RN) used in [15] and the proposed model across different SNRs are shown in Figure 9. Results in Figure 9 are averaged over 10 experiments.
Figure 1012 illustrate the confusion matrices for the experiment with the highest overall top1 classification accuracy for the proposed model and LSTM at the SNRs 18dB, 6dB and 0dB. For the SNR of 18dB, the diagonal is very sharp for the proposed model while there are some confusions between AMSSBSC and 4ASK signals for RN and VGG. At the SNR of 0dB, it becomes more difficult for the proposed model to separate AMSSBSC and 4ASK. As shown in Figure 12, it becomes much more difficult to distinguish the signals at low SNRs and all considered models start making mistakes differentiating between GMSK, OQPSK and BPSK signals.
Model  20dB  18dB  16dB  14dB  12dB  10dB  8dB  

DAE  Mean  9.86  9.73  10.03  11.05  12.84  17.33  20.43 
Std  0.32  0.32  0.40  0.48  0.42  0.46  0.43  
RN  Mean  9.28  9.42  9.69  10.49  11.81  16.21  19.87 
Std  0.50  0.60  0.46  0.43  0.89  0.77  0.87  
VGG  Mean  9.82  9.17  9.69  10.59  11.50  15.41  19.87 
Std  0.47  0.40  0.38  0.41  0.48  0.67  0.39 
Model  6dB  4dB  2dB  0dB  2dB  4dB  6dB  

DAE  Mean  26.71  35.84  52.41  72.04  85.31  92.10  97.19 
Std  0.32  0.43  0.51  0.26  0.32  0.38  0.16  
RN  Mean  26.54  34.33  50.34  68.65  80.90  87.88  93.54 
Std  1.35  0.95  0.98  1.21  0.72  0.69  0.50  
VGG  Mean  27.69  34.57  47.91  65.43  78.04  85.29  91.25 
Std  0.46  0.66  0.82  0.65  0.62  0.56  0.20 
Model  8dB  10dB  12dB  14dB  16dB  18dB  20dB  

DAE  Mean  99.33  99.77  99.91  99.87  99.95  99.95  99.91 
Std  0.09  0.05  0.05  0.05  0.05  0.08  0.05  
RN  Mean  97.26  98.29  98.81  99.12  99.26  99.24  99.28 
Std  0.28  0.41  0.50  0.29  0.32  0.37  0.30  
VGG  Mean  94.07  94.75  95.80  95.89  96.10  95.70  96.22 
Std  0.23  0.31  0.32  0.38  0.34  0.29  0.24 
Model  22dB  24dB  26dB  28dB  30dB  Overall  

DAE  Mean  99.94  99.97  99.95  99.91  99.93  67.30 
Std  0.01  0.03  0.06  0.04  0.02  0.17  
RN  Mean  99.21  99.17  99.22  99.15  99.28  66.00 
Std  0.38  0.39  0.35  0.36  0.40  0.22  
VGG  Mean  96.09  96.16  95.97  96.15  96.10  64.03 
Std  0.42  0.39  0.24  0.36  0.31  0.15 
In addition to the top1 classification accuracy, we also compare considered models in terms of the number of trainable parameters, the number of floating point operations, the memory cost and the number of classifications per second on different computational platforms. As shown in Table V, the proposed model has the fewest trainable parameters and requires the smallest number of FLOPs and memory space. It is noticeable in Table VI that the proposed model is on average approximately and faster than RN and VGG on Raspberry Pi 4 in terms of the number of classifications per second, respectively. On Raspberry Pi 3, the proposed model is on average approximately and faster than RN and VGG, respectively. The mean and standard deviation of the number of classifications per second are calculated over 10 experiments on 1024 signals.
Model  # Parameters  # FLOPs  Memory 

DAE  14989  288925  242KB 
RN  257009  8651090  3.41MB 
VGG  236344  8343647  3.42MB 
Platform  DAE  RN  VGG  

GTX 1080Ti  Mean  1327.45  902.71  1326.73 
Std  18.49  22.22  16.64  
Intel i78700K  Mean  119.25  85.73  155.77 
Std  1.66  2.36  1.63  
Raspberry Pi 4  Mean  24.43  10.32  15.43 
Std  0.26  0.36  0.61  
Raspberry Pi 3  Mean  12.12  5.28  9.06 
Std  0.17  0.40  0.43 
IiiC Performance Comparison on Electrosense Data
We further evaluate performance of the proposed model on realtime overtheair PSD data from Electrosense. The goal of Electrosense initiative is to enable more efficient, safe and reliable monitoring of the electromagnetic space by improving accessibility of spectrum data to general public [18]. The aggregated spectrum measurements collected from sensors all over the world could be retrieved from the Electrosense API^{2}^{2}2https://electrosense.org/openapispec.html. Six commercially deployed technologies (WFM, TETRA, DVB, RADAR, LTE and GSM) are collected from indoor sensors with omnidirectional antennas by setting frequency resolution to 100kHz and time resolution to 60s [19]
. 10k samples of length 2000 are retrieved for each technology and are padded with 0s accordingly for the consistency of the sample lengths. 50%, 25% and 25% of the entire dataset are used for training, validation and testing, respectively.
Figure 13 shows the confusion matrices of our proposed model and LSTM for technology classification on Electrosense data. The proposed model performs slightly better than LSTM. It is noticeable that distinguishing DVB from LTE based on PSD is difficult since the power spectra of DVB and LTE is highly similar and both of them are based on OFDM [19].
Next, we compare the considered models in terms of the number of trainable parameters, the number of FLOPs, the memory cost and the number of classifications per second on different platforms. As shown in Table VII, the proposed model has significantly fewer trainable parameters and requires much fewer FLOPs and memory space. Table VIII shows that the proposed model is on average approximately faster than LSTM on Raspberry Pi 4 in terms of the number of classifications per second. On Raspberry Pi 3, the proposed model is on average approximately faster than LSTM. The mean and standard deviation of the number of classifications per second are calculated over 10 experiments on 1024 signals.
Model  # Parameters  # FLOPs  Memory 

DAE  14572  279455  237KB 
LSTM  199563  7696283  2.31MB 
Platform  DAE  LSTM  

GTX 1080Ti  Mean  685.08  613.30 
Std  13.88  10.85  
Intel i78700K  Mean  77.72  64.08 
Std  1.69  0.76  
Raspberry Pi 4  Mean  12.79  2.92 
Std  0.04  0.02  
Raspberry Pi 3  Mean  6.45  1.27 
Std  0.06  0.01 
Iv Conclusions
In this paper, we introduce a denoising autoencoder to the problem of inferring the modulation and technology type of a received radio signal. In particular, an LSTM autoencoder is trained to learn stable and robust features from the noise corrupted received signals, reconstruct the original received signals and infer the modulation or technology type, simultaneously. Empirical studies show that the proposed framework generally outperforms top1 classification accuracy of the competing methods while requiring significantly smaller computation resources. In particular, the proposed framework employs a compact architecture that it can be implemented on affordable computational devices, enabling realtime classification of the received signals at required levels of accuracy.
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