An automatic
modulation classification task aims at detecting the modulation type of a
received signal and recovering the signal by demodulation. Currently, it has
been widely used in military electronic warfare, surveillance and threat
analysis [1,2]. The likelihood-based (LB) method [3] and feature-based (FB) method [4] are two conventional methods for automatic modulation
classification. LB method mainly includes the average likelihood ratio test
(ALRT) method [5] and the generalized likelihood ratio test (GLRT) [6].
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Although the LB
method obtains high accuracy, it requires more calculating time to fulfill
parameter estimation, which greatly limits its application [7]. FB methods usually work in two steps: Feature extraction
and classification. In previous papers based on FB methods, many signal
features, such as spectrum [8], high-order cumulant [9] and wavelet coefficients [10], are used to classify the modulation types.
With the emergence and development of machine learning (ML), many researches
employ ML to implement classification in FB method. For examples, Aslam et al.
[11] reported a modulation classifier based on
genetic programming and K-nearest neighbor (GP-KNN), but this classifier only
worked well for PSK. Han et al. [12] employed the support vector machine (SVM)
to classify the phase shift keying (PSK) and quadrature amplitude modulation (QAM)
and obtained a good classification accuracy under the known channel. Although
the FB method shows great advantages in automatic digital modulation
classification, there are still two challenges: Artificial feature extraction
and noise covering. The performance of FB methods severely depends on the
quality and quantity of extracted features, but the artificial feature
extraction is complex and difficult for various modulated wireless signals.
Moreover, when the signal-noise ratio (SNR) of the modulated signal is very
low, the performance of classifier is unsatisfied due to the limited quantity
of features extracted.
The neural network [13] is a fascinating classification method with
a series of state-of-the-art achievements automatic modulation classification [14,15]. For instance, O’Shea et al. [16] trained a deep neural network (DNN) using a
baseband IQ waveform to identify modulation. They reported that it was feasible
to use DNN for automatic modulation classification and had a better accuracy
with low SNR. Ramjee et al. [17] verified the classification performance of
long short-term memory (LSTM), convolutional long short-term memory deep neural
network (CLDNN) and deep residual network (ResNet) structures. Experimental
results showed that the three methods could achieve good classification results
on the dataset RadioML2016.10b [16]. The paper also verified the impact of
training data with different SNRs, and minimized the training data to reduce
training time. However, a neural network is very easy to over fit and memorize
data noise when using it in modulation classification [18]. Noises will be introduced into the signal
when it goes through channels, inducing a sharp decrease in SNR. If this low
SNR data is used to train the neural network, local optimum could appear and
cause significant decline in the performance of classifier.
To solve the over
fitting of neural network, we propose a novel automatic digital modulation
classifier with two neural networks, namely the StudentNet and MentorNet. The
StudentNet is used to classify the signal, and the MentorNet is employed to
supervise the training of StudentNet according to curriculum learning.
Experimental results show that our classifier can accurately identify 11 common
digital modulated signals, including 2-ary amplitude shift keying (2ASK), 2-ary
Frequency Shift Keying (2FSK), 2PSK, 4ASK, 4FSK, 4PSK, 8ASK, 8FSK, 8PSK, 16QAM
and 64QAM. The overall classification accuracy can be up to 99.3%, which is
much higher than other classifiers.
The structure of this
paper is organized as follows. Section 2 shows the signal model and relative
theories. Section 3 presents the performance improvement in
modulation classification by curriculum learning. Section 4 reports the experimental results and
discussion, and concludes this paper in Section 5.
2. Signal Model and Relative Theories
2.1. Signal Models
The received
modulated signal can be expressed as:
x(t)=(Ai+jAq)ej(2π(fc + Δf)t + Δθ),
(1)
Where Ai and Aq are the in-phase
and quadrature components of IQ modulation, respectively, fcis the carrier frequency, Δf is the offset of
carrier frequency and Δθ is the phase
offset. Aq=0 in ASK and FSK, and fc is
a variable in FSK. For PSK, the amplitude of modulated signal is fixed but the
phase is variable. Therefore, both Ai and Aq are varied while |Ai+jAq| is fixed
in PSK. QAM is a hybridization of ASK and PSK, whose amplitude and phase are
variables. These features provide possibility for us to classify the modulation
type, so that the original signal can be recovered accurately. However, the
emerged noise in signal transmission often leads to signal distortion, which
imposes a big obstacle in the recovery of the original signal.
Among various noises,
additive white Gaussian noise (AWGN) and Rayleigh fading are two most common
noises. Therefore, we built models to test the performance of our method in the
two above-mentioned noisy environments. Firstly, since AWGN cannot cause the
amplitude attenuation and phase offset on signal, the received signal can be
expressed as:
r(t)=(Ai+jAq)ej(2π(fc + Δf)t + Δθ)+n(t),
(2)
Where n(t) is the additive white noise obeying the zero-mean
Gaussian distribution. This model is an effective model to depict the
propagation of wired signal, satellite signal and deep space radio frequency
communication signal.
Rayleigh fading
describes the amplitude attenuation and Doppler shift induced by reflection,
refraction, scattering and relative motion between the receiver and the
transmitter in the propagation of wireless signal. Once a signal passes through
a wireless channel, its amplitude becomes random and its envelope obeys the
Rayleigh distribution. According to the central limit theorem, the amplitude of
received signal approaches to the zero-mean Gaussian distribution. Since there
is no line of sight in Rayleigh channel, the received signal is composed of
multi signals suffering reflection, refraction or scattering. Hence, the
received signal can be described as:
r(t)=∑nk=1ak(t)(Ai+jAq)ej(2π(fc + Δf)(t − τk(t)) + Δθ)+n(t)=(Ai+jAq)ej(2π(fc + Δf)t + Δθ)∑nk=1ak(t)e−j2πτk(t)+n(t),
(3)
where n means the number of paths, ak(t) is the path gain of the k-th path and τk(t) is the path
gain of the k-th delay.
2.2. Deep Residual
Network
For the neural
network, its classification accuracy depends on the depth of network. With the
increase of depth, the classification accuracy firstly improves and then
reduces. Researches show that the reduction of classification accuracy is
caused by the disappearance of variation in network weight gradient. Aiming at
solving this problem, we employ a deep residual network (ResNet), which
contains multiple residual blocks as shown in Figure 1a. The residual block mainly includes three convolution
layers (Conv layer 1, Conv layer 2 and Conv layer 3) and a summator. There are
two routes between these layers and summator: Sequential connection and
shortcut connection. Firstly, the sequential connection conducts three
consecutive convolutions on x to get F(x),
which is used as an input for the summator. Then, the other input of the
summator, x, is obtained by shortcut connection. Finally, the
output of whole residual block can be expressed as H(x)
= F(x) + x. As F(x) = 0
indicates the gradient disappearance of network weight, H(x)
= x is an identity mapping that removes the three convolution
layers and decreases the depth while the classification accuracy is ensured.
Figure 1. The
architecture of the (a) residual block and (b) ResNet.
The complete
architecture of ResNet used in this paper is shown in Figure 1b. It contains a convolution layer, a full connection
layer and 33 residual blocks. Every residual block contains three convolution
layers. Therefore, the utilized ResNet is a 101-layer DNN. The detailed
parameters of ResNet are the same as the 101 layers ResNet parameters [19]. We only modified the input size and output
size of the network.
2.3. Curriculum
Learning
As known, overfitting
occurs easily in the application of a neural network, and curriculum learning
provides the possibility to solve this problem. Curriculum learning is inspired
by the learning principles behind the cognitive processes of human and animal,
which usually begin with learning the easy contents and then gradually consider
the more complex parts. According to this learning principle, curriculum
learning can assign priority to samples of the training set, such as D = {(x1,y1),⋯(xi,yi),⋯(xn,yn)},
by associating the learning model parameter w and the weight of sample in
training set v as follows [20]:
minw∈Rd,v∈[0,1]nF(w,v)=1n∑ni=1viL(yi,f(xi,w))+G(v;λ)+θ∥w∥22,
(4)
where xi is
the ith training sample, yi is the
corresponding label, f(xi,w) is the discriminative
function of a neural network called StudentNet, L(yi,f(xi,w)) is
the loss function of StudentNet, G(v;λ) represents a
curriculum and λ is a variable parameter to
tune the learning pace. Although the alternating minimization algorithm is
usually employed to minimize Equation (4), it is too complex and requires too
much calculation resources. Herein, we employ the scholastic gradient partial
descent (SPADE) algorithm [21] based on another neural network named
MentorNet to minimize the association of the parameter w of StudentNet and the
weights v of random mini-batch samples, so that the bad local minima can be
avoided and the better generalization results can be gained.
3. Curriculum Learning Based Modulation
Classification
3.1. Architecture of
Automatic Digital Modulation Classifier
The diagram of our
automatic digital modulation classifier is shown in Figure 2. The input of this classifier is an intermediate
frequency signal-containing carrier, which is different from the baseband
signal used in previous studies [22,23,24]. Then, the input signal is sampled and
normalized to obtain a one-dimensional sequence. Next, the one-dimensional
sequence is sliced into multiple short sequences, and a grayscale image is
gained by arranging these multiple short sequences row by row. Finally, this
grayscale image is considered as the input of StudentNet. In practical
applications, the StudentNet needs to be trained under the supervision of
MentorNet. Later, we would interpret the training of StudentNet in details.
Figure 2. The diagram of
the automatic digital modulation classifier.
3.2. Implementation
of MentorNet
The structure of
MentorNet is shown in Figure 3. The MentorNet including 10 LSTM (long short-term
memory) units can receive new data input and remember the last output. While
the input loss value and the difference between loss and the moving average [25] have a time correlation due to the increase
of training iteration times, so that the LSTM can predict the weight of samples
better. In addition, an embedding layer (size = 5) is employed to receive the
integer epoch percentage as its input. Meantime, two fully connected layers fc1
and fc2 contain 20 hidden nodes and one node, separately. The fully connected
layer fc2 uses sigmoid as the activation function, ensuring that its output is
between 0 and 1. The output layer is a probability sampling layer and its
application is to dropout samples with a specific probability. The input of
MentorNet is some sample features including aforementioned loss, loss
difference to the moving average, and training epoch percentage. The output of
MentorNet is weighted corresponding to these features. The loss is calculated
by the difference between the actual and predicted modulation types of samples in
training set. The moving average is the value of the p-th largest loss of features. The training epoch
percentage ranging from 0–99 shows the training progress of StudentNet. Zero
represents the first training epoch, while 99 symbolizes the last training
epoch.
Figure 3. MentorNet
architecture.
The MentorNet is used
to supervise the training of StudentNet, so the training of MentorNet should be
measured before the StudentNet training. However, in order to obtain the loss,
the StudentNet needs to be pre-trained to get the predicted modulation types of
samples in training set. In terms of pre-train procession of StudentNet, 18
epoch percentages are trained by using noisy samples, and then we use this
trained network to evaluate a noisy test set and get the losses. The average
losses under different SNRs are presented in Figure 4. It can be found that when the SNR is larger than 0
dB, the loss varies in a small range, and these samples can be considered as
the easy learning samples. Therefore, weights of these samples should be marked
as v∗i=1. Once the SNR of
samples is less than 0 dB, the loss shows a continuous increase indicating
these samples are difficult to learn. Then these samples’ weights could be
marked as v∗i=0. These losses and
weights obtained by StudentNet are used to train the MentorNet. After training
MentorNet, MentorNet has learned this curriculum corresponding to the features
mentioned above.
Figure 4. Average loss of
actual and predictive modulation type at different signal-to-noise ratios
(SNRs).
Figure 5 illustrates the performance of trained
MentorNet. Figure 5a,b represents the schematic diagram of MentorNet
assigning weights to samples when training is completed by 20% and 90%. In
the Figure 5, epoch percentage represents the percentage of the
current training progress, and the z axis represents the weights computed by
trained MentorNet, The y axis and the x axis are the sample loss and the
difference between sample loss and moving average. For samples with larger
loss, the corresponding weight should be smaller, and the rapid decline in
different locations means that the courses in these two phases are different.
The diff to loss mv can be used to capture the prediction variance [25]. It can be seen that the MentorNet tends to
assign high weights to samples with low loss and it can be updated in real
time, which provides a great generalization capability for the StudentNet.
Figure 5. The data-driven
curriculum learned by MentorNet: (a) Epoch percentage = 20 and (b)
epoch percentage = 90.
3.3. Implementation
of the StudentNet
In our design, the
StudentNet should be trained twice. The first training is the pre-training
process. Firstly, the pre-training was carried out without the supervision of
MentorNet to obtain features of sample in training set. Subsequently, the
obtained features were transferred to MentorNet for the extraction of
curriculum. Herein, we focus on training the StudentNet under the supervision
of MentorNet and testing the performance of the proposed classifier.
The diagram of the
second training under the supervision of MentorNet is shown in Figure 6a. Obviously, the StudentNet training can be divided
into two steps. The first step is called forward propagation, in which
StudentNet obtains the predicted label of training samples by convolution
operations and pooling, and then computes the loss between the actual label and
predicted label. According to the value of computed losses, the MentorNet
assigns corresponding weight to loss. In the second step, named back
propagation, the weighted loss is passed back to the upper layer and each layer
needs to manipulate own its parameters according to the received loss. After
training the StudentNet, the parameters of each layer are saved in a memory.
Figure 6. The diagrams of
(a) training StudentNet under the supervision of MentorNet training and
(b) testing the performance.
During verifying the
performance of our classifier, the parameters are loaded into the StudentNet
from memory. Afterwards, the samples in test set are transferred into
classifier and processed into grayscale images before coming into the
StudentNet. Finally, the predicted labels are obtained by forward propagation.
The diagram of performance testing is shown in Figure 6b. Unlike the training of StudentNet, the testing
process does not require the involvement of MentorNet and back propagation.
4. Results and Discussion
In this section, a
series of measurements are implemented to verify the classification accuracy of
the automatic digital modulation classifier. In our experiment, various
modulated signals were tested, including 2ASK, 4ASK, 8ASK, 2FSK, 4FSK, 8FSK,
2PSK, 4PSK, 8PSK, 16QAM and 64QAM. The relative parameters are shown in Table 1. We generated a training set and test set by using
Matlab2018a. Every training set included 110,000 samples, while each validation
set and test set included 11,000 samples. All these samples possessed the same
length of 1024 and various SNRs obeying uniform distribution. The training,
validation and test sets were used to implement the training, evaluation and
exam of classifier, respectively. In addition, the classifier with only
StudentNet was named as the Baseline classifier, and the one containing both
StudentNet and MentorNet was called the MentorNet classifier.
Table 1. Modulation
parameter.
4.1. The Accuracy of
MentorNet Classifier
4.1.1. Overall
Accuracy of MentorNet Classifier Under Different SNRs
Before investigating
the performance of MentorNet classifier, the Baseline classifier was
established and trained by four training set with different SNR ranges. Herein,
samples in the training set and test set were the signals passing through
additive white Gaussian channel without phase drift and frequency drift
Therefore, SNR was the ratio between the amplitudes of Gaussian noise and
signal. Then the performance of trained Baseline classifiers was measured on
one test set with SNRs ranging from −20 to 18 dB and
the results are shown in Figure 7a. It is obvious that when the SNR of the training set
was relatively high (such as 10–18 dB, Black line in Figure 7a), the Baseline classifier possessed higher
classification accuracy, whereas an unsatisfactory performance occurred on the
samples with low SNR in the test set. Unfortunately, once the SNR range of the
training set broadened to −20–18 dB (Purple line
in Figure 7a), the performance of the Baseline classifier showed
an improvement on samples with low SNR in the test set but deterioration on
samples with high SNR in the test set. We suppose this phenomenon should be
induced by the overfitting of StudentNet in the Baseline classifier. To
overcome this problem, the MentorNet classifier was proposed and tested. The
MentorNet classifier was trained by only one training set with −20–18 dB SNR and its
performance was verified on the same test set with the Baseline classifier. The
green and magenta curves in Figure 7a revealed that for the training set with −20–18 dB SNR, the
MentorNet classifier could overcome the overfitting, and results in a 1.7%
improvement in classification accuracy.
Figure 7. The performance
of various classifiers under different SNRs: (a) Curves about the
classification accuracy versus the SNR range of the training set, and (b)
classification accuracy of different methods with −20–18 dB SNR.
Besides, we also
compared the accuracy of the MentorNet classifier with several existing
modulation classifiers, including the classifiers based on the Inception [26], the fusion model of convolutional neural
network and long short-term memory (CNN-LSTM) [27], and SVM [27]. The five classifiers were trained and
tested with the same training set and test set, and then the classification
accuracy are shown in Figure 7b. Comparison results indicated that both the accuracy
of the MentorNet classifier and Baseline classifier was higher than others,
which verifies that ResNet could improve the classification accuracy
significantly. Due to the existence of overfitting in the Baseline classifier,
its performance was worse than the MentorNet classifier. Therefore, we can
conclude that the MentorNet classifier proposed by us could achieve the higher
classification accuracy.
4.1.2. Intra-Class
and Inter-Class Accuracy of the MentorNet Classifier Under Different SNRs
In addition to the
overall accuracy, the intra-class and inter-class accuracy of the classifier is
also worthy to mention. The common modulation signals can be divided into four
classes including ASK, FSK, PSK and QAM according to the modulation method.
According to the modulation order, these four classes also can be divided into
eleven types, including 2ASK, 4ASK, 8ASK, 2FSK, 4FSK, 8FSK, 2PSK, 4PSK, 8PSK,
16QAM and 64QAM. The intra-class accuracy of MentorNet classifier for each
modulation class at different SNR is reported in Figure 8, which denotes that all classification accuracy
increased with SNR until approaches closed to 100%. In details, when SNR was
larger than –10 dB, the classification accuracy of 2ASK was largest in ASK and
saturated at 10 dB. Meantime, the classification accuracy of 2PSK was also the
largest in PSK and saturated at −10 dB. Besides, the
modulation order had few impacts on the classification accuracy of FSK as SNR
was lower than 0 dB. However, the intra-class accuracy of QAM was almost
unaffected by the modulation order. These results suggest that the modulation
order has a different influence on the intra-class accuracy of different
classes.
Figure 8. Curves about intra-class
classification accuracy versus SNR.
The inter-class
accuracy of MentorNet classifier was obtained by its confusion matrix as shown
in Figure 9. The confusion matrix illustrates the prediction
error of the classifier, where the horizontal and vertical axes represent the
actual and predicted modulation types. The inter-class accuracy was calculated
by ignoring the modulation order and adding the probability of achieving the
correct modulation class. From Figure 9, we can conclude that it was difficult to identify
both the modulation order and the modulation class accurately at low SNR (such
as −20 dB) due to the large noise
interference, which is consistent with Figure 7 and Figure 8. It is well-known that the wrong modulation order
cannot pose a fatal threat to the demodulated signal so that the demodulated
signal showed a large deviation with the original signal. The correct
modulation class was the most urgent need for us. Hence, we presented the
inter-class accuracy of MentorNet classifier in Figure 10. As shown in Figure 10, the MentorNet classifier could effectively
distinguish modulation classes such as ASK, FSK and PSK even if SNR was very
low (such as −20 dB). However, the inter-class
accuracy of QAM was relatively low as SNR was lower than –10 dB, because QAM
was easy to be recognized as PSK according to Figure 9. However, the original signal of QAM can be recovered
by conventional demodulation in the case of misjudgment. Therefore, the
performance of the MentorNet classifier could satisfy the accuracy requirements
for modulation recognition in most applications.
Figure 9. Confusion
matrix with different SNRs: (a) SNR = −20 dB; (b) SNR
= −10 dB; (c) SNR = 0 dB and (d)
SNR = 10 dB.
Figure 10. Curves about
inter-class classification accuracy versus SNR.
4.2. The Robustness
of the MentorNet Classifier
4.2.1. The Impact of
Rayleigh Fading
As known, AWGN and
Rayleigh fading are two common noise sources. The samples with AWGN have been
tested above. Hence, this subsection will investigate the impact of Rayleigh
fading on the accuracy of the MentorNet classifier. In the experiment, the
modulation parameters and the number of samples in the test set were the same
as above. Besides, we assumed that the received signal was a combination of two
signals coming from two reflection paths. The gains of these two paths were 0
dB and −10 dB, respectively, while the delay
between them was 10−7 s. In the meantime, the
maximum Doppler frequency shift (fd), induced by the relative motion between
the receiver and the transmitter in the propagation of two signals, was
supposed as 0 Hz, 1 kHz, 5 kHz and 10 kHz.
The experimental
results are shown in Figure 11. It is worth mentioning that the black and red
curves both represent the classification accuracy of test samples with a 0 Hz
Doppler shift, but a multipath fading existed in the test samples of the red
curves, leading to the relatively low classification accuracy. However, the red
curve could also reach 20% at −20 dB SNR and 99% at
10 dB SNR, which was close to the black curve. When the different Doppler
shifts existed, the classification accuracy at very low SNR (such as −20 dB) was very
similar until the SNR was up to −5 dB. With the
further increase of SNR, the difference of classification accuracy increased
and a larger Doppler shift corresponded to a lower classification accuracy
classifier. When the SNR was 10 dB the classification accuracy of test samples
containing Rayleigh fading ranged from 85% to 98%, which is enough for the
application in military electronic warfare equipment. These results indicate
the MentorNet classifier possesses a great robustness to endure the Rayleigh
fading.
Figure 11. Classification
accuracy of the MentorNet classifier under the interference of Rayleigh fading.
4.2.2. The Impact of
Carrier Frequency Offset and Phase Offset
As shown in Equation
(1), the carrier frequency offset and phase offset induced by the drift of the
clock could also increase the difficulty of modulation classification. In this
subsection, we would explore the impact of carrier frequency offset and phase
offset on the classification accuracy of the MentorNet classifier. Firstly, the
ratio of carrier frequency deviation to sampling frequency Δf/fswas set within 1×10−4 to 2×10−4 to
investigate the anti-interference ability of the MentorNet classifier to
carrier frequency offset. For a fair comparison, the Inception classifier,
Baseline classifier and MentorNet classifier were trained by a training set
with −20–18 dB SNR, and then they were
tested in a test set with an SNR of 10 dB. The experimental results are
reported in Figure 12a. We could find the accuracy of all classifier
decreased monotonously with Δf/fs, but the reduction
of Inception classifier was the smallest (around 5%), due to its simple network
structure [28] Meanwhile the reductions of the Baseline
classifier and MentorNet classifier were around 13% and 12% separately.
Although the accuracy of the Baseline classifier and MentorNet classifier was
significantly disturbed by the carrier frequency offset, their accuracy was
still 14% and 18% higher than the Inception classifier, respectively. Hence, it
was obtained that in the presence of frequency offset, the performance of the
MentorNet classifier was still the best, so that has actual importance in the
field of communication.
Figure 12. Classification
accuracy with (a) different carrier frequency offsets and (b)
different phase offsets.
Then, the impact of
the phase offset Δθ on the accuracy of the
classifier was studied and discussed. The experimental parameters are the same
as above, except the carrier frequency offset and phase offset. The phase
offset was set within 0–10°, while the carrier frequency offset
was set to 0 Hz. The results are shown in Figure 12b. It is obvious that the phase offset had little
effect on the accuracy of classifier, which suggests the strong robustness to
phase offset. Moreover, the accuracy of the MentorNet classifier could maintain
at 99% regardless of the phase offset, while the Inception classifier and
Baseline classifier could only achieve a classification accuracy of 96% and
83%, respectively. This phenomenon reveals that among these three classifiers,
the designed MentorNet classifier obtained a better performance.
4.3. Classification
Accuracy on a Generic Dataset
An additional
experiment was conducted to evaluate the classification performance on analog
modulation signals, and a GUN radio generated dataset (RML2016b) was used [16]. In the test, the dataset was divided into
a training set, validation set and test set. We used the training set to train
StudentNet, and used the validation set to evaluate the performance of the
current classifier and select the best classifier for testing. For the
MentorNet classifier, the trained MentorNet was used to supervise the training
of StudentNet. For the Baseline classifier, the StudentNet was trained without
MentorNet. As shown in Figure 13, the comparison of classification accuracy was made
among MentorNet classifier and some classical methods such as the Baseline,
ResNet and CLDNN [29] classifiers. When the SNR was greater than
0 dB, our proposed MentorNet classifier could achieve the overall
classification accuracy up to 85.5%, which was better than the Baseline
(82.2%), CLDNN (83.1%) and ResNet (80.5%). The comparison results indicate that
the proposed MentorNet classifier could also deal with the analog modulation
signals with better versatility and classification accuracy.
Figure 13. Classification
accuracy of various classifiers on dataset RML2016b.
5. Conclusions
In this paper, we
reported a novel automatic digital modulation classifier called the MentorNet
classifier, which consists of two neural networks: StudentNet and MentorNet.
The MentorNet supervises the training of StudentNet to overcome the overfitting
in the classification process. In order to verify the performance of this
classifier, several comparative tests with other classifiers were conducted in
the presence of AWGN, Rayleigh fading, carrier frequency offset and phase
offset. Experimental results showed the accuracy of the MentorNet classifier
and Baseline classifier was much higher than the Inception classifier and
classifier based on SVM, which suggests the deep residual network is suitable
for digital modulation classification. Meantime, the accuracy of the MentorNet
classifier at high SNR was higher than that of the Baseline classifier,
indicating the curriculum learning can solve the overfitting of the neural
network. In the interference of Rayleigh fading, the MentorNet classifier still
owned the highest accuracy, which ranged from 80%–90% at 10 dB SNR as the
Doppler frequency shift was within 0–10 kHz, which suggests the outstanding
robustness of MentorNet classifier. When the carrier frequency offset and phase
offset were taken into account, the accuracy of the MentorNet classifier
presented quite different tendencies. When only the carrier frequency offset
was considered, the accuracy of the MentorNet classifier showed a smooth
reduction from 98% to 85% with Δf/fs ranging
within 1×10−4 and 2×10−4, while it
maintained at 99% in the presence of a 0–10° phase offset.
Moreover, the proposed classifier could also achieve favorable classification
performance for analog baseband signals, indicating the transplantation
feasibility of the proposed classifier. Although the proposed MentorNet
classifier had outstanding performance, when SNR was −20 dB the classification
accuracy remains to be improved.
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