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Abstract
Automatic modulation recognition (AMR) is an integral part of an intelligent transceiver for future underwater optical wireless communications (UOWC). In this paper, an orthogonal frequency division multiplexing (OFDM) based progressive growth meta-learning (PGML) AMR scheme is proposed and analyzed over UOWC turbulence channels. The novel PGML few-shot AMR framework, mainly suffering from the severe underwater environments, can achieve fast self-learning for new tasks with less training time and data. In the PGML algorithm, the few-shot classifier, which works in the presence of Poisson noise, is fed with constellations of noisy signals in bad signal-to-noise ratio (SNR) scenarios directly. Moreover, the data augmentation (DA) operation is adopted to mitigate the impact of light-emitting diode (LED) distortion, yielding further classification accuracy improvements. Simulation results demonstrate that the proposed PGML scheme outperforms the classical meta-learning (ML) approach in training efficiency, robustness against Poisson noise and generalization performance on a new task.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Prompt and effective recognizing of modulation schemes, particularly sensing the severely distorted data, is one of the critical techniques in underwater optical wireless communications (UOWC). It directly affects the data transmission quality and speed in UOWC, promoting the smart space-ground-aqua integrated network [1,2]. Traditionally, based on massive amounts of received data, deep learning (DL) is applied in automatic modulation recognition (AMR) systems due to its strong computational ability [3–5]. However, the complex and changeable underwater environments as well as the distortion caused by the light-emitting diode (LED) limit the generation of effective signals, which brings us new AMR challenges. In this regards, the meta-learning (ML) paradigm can be used with a smart receiver, coping with severe communication conditions, as no big data or preprocessing is required [6]. Furthermore, the ML approach, by taking advantage of the prior knowledge, has emerged as a promising way to achieve fast self-learning on new tasks [7]. These works have proved that the few-shot ML technique is essential for the implementation of smart UOWC AMR systems.
In view of the strong feature extraction ability of convolutional neural networks (CNN), many conventional CNN-based AMR methods were studied recently [8–10]. However, to improve the robustness against noise, received signals are classified by a signal-to-noise ratio (SNR) prediction module [8] before they are fed into the CNN-based classification model. It is noticed that, in the CNN-based AMR architecture, complex preprocessing is carried out for higher classification accuracy, such as re-ordering the signals samples [9], and rough SNR estimation [10]. Besides, the traditional CNN approaches require considerable training time and costly computational overhead [11,12]. Unlike the aforementioned methods, in this paper, small samples are directly fed into the few-shot classifier to get rid of complex preprocessing. Noting that, since the complexity of the underwater environment renders the signals of UOWC system vulnerable to damage [1,2], high-quality sample data of which is often difficult to obtain. In such a case, our proposed scheme has incomparable advantages.
The impact of LED distortion is a crucial limitation for high-quality data transmission in UOWC [13–15]. Without the predistortion illustrated in [13], the constellation diagram is largely distorted by the LED. Moreover, for gallium nitride (GaN)-based LEDs, the impact from the nonlinearity of LED will aggravate the distortion of signals in the UOWC system using the orthogonal frequency division multiplexing (OFDM) technology [14]. Although a pre-distorter at the transmitter, designed in [15], can mitigate the detrimental LED nonlinear distortion, the micro-LED distortion impact on UOWC AMR has not been thoroughly investigated in the literature so far. In order to improve the resistance to micro-LED array distortion, we explore a smart approach over the UOWC AMR system, that is, the data augmentation (DA) operation.
In recent years, transfer learning has received much attention for its excellent generalization performance and learning efficiency [16–18]. In [16], the transfer learning is introduced, reducing the time cost of the training period. According to [18], knowledge transfer is employed to mine prior knowledge from the source domain, and the training data is greatly reduced. It is worth mentioning that the capability of generalization and the demand for training data have become important indicators for evaluating network performance.
Against this background, we set out to exploit a progressive growth meta-learning (PGML) based smart UOWC few-shot AMR system with the enhanced generalized ability of fast self-learning.
More explicitly, our major contributions are summarized as follows:
1) Compared with the other existing schemes for AMR [5,11,19], the proposed PGML few-shot AMR framework shows strong adaptability to new tasks and small samples. Also, the PG strategy accelerates the training process of the few-shot classification model, significantly reducing the training time. Simulation results are shown in Fig. 6 and Fig. 9, respectively.
2) Propose a smart DA approach to alleviate the impact of micro-LED distortion on AMR. It effectively improves the recognition rate of modulated signals hampered by micro-LEDs. As shown in Fig. 8, $3\%\sim 12\%$ increment can be achieved in the probability of correct classification $(P_{cc})$ on various trained models.
3) For severe UOWC environments, develop a PGML few-shot classifier which performs superiority in low SNR scenarios. Moreover, it has better robustness to accurately recognize modulation formats spreading in a wide-ranging SNR (from 6 dB to 15 dB SNR), as shown in Fig. 7.
The rest of the paper is arranged as follows: Section 2 introduces the overall structure of the smart UOWC AMR system. Section 3 gives a more profound description on the proposed PGML based few-shot AMR framework, including the operating mechanism of the PGML algorithm, and datasets division. Section 4 conducts simulation comparisons and makes a performance analysis. Section 5 validates the performance gain of the proposed approach through experimental demonstration. Finally, the conclusions are drawn in Section 6.
2. System model
Figure 1 shows a smart UOWC AMR system relying on the proposed PGML algorithm, which consists of a direct-current-biased (DC-biased) optical OFDM transmitter and a receiver with a few-shot classifier.
Fig. 1. The block diagram of our simulated smart UOWC AMR system. OFDM Tx: a typical DC-biased optical OFDM transmitter; OFDM Rx: an OFDM receiver with a PGML few-shot classifier.
2.1 Transmitter design
The DC-biased optical OFDM transmitter is described in Fig. 1. Consider an OFDM system with $2N$ subcarriers. The original information bitstream (e.g., $101100\cdots$) is fed into a serial-to-parallel (S$/$P) converter at first. Then, the input data are mapped using quadrature amplitude modulation (QAM)$/$amplitude-shift keying (ASK)$/$phase-shift keying (PSK) constellations, producing modulated symbols denoted by $\boldsymbol {X}= [X_0,X_1,X_2,\ldots ,X_{N-1}]$.
To achieve real-valued OFDM signals, Hermitian symmetry is applied [20]. Hence, the frequency symbols $\boldsymbol {X}$ assigned to $2N$ subcarriers should be expressed in the form of $\boldsymbol {X}= [0,X_1,X_2,\ldots ,X_{N-1},0,X_{N-1}^{*},\ldots ,X_2^{*},X_1^{*}]$, where $*$ denotes the complex conjugation.
Time-domain signals $\boldsymbol {x}= [x_0,x_1,\ldots ,x_{2N-1}]$ are then generated by a 2$N$-points inverse fast Fourier transform (IFFT) of $\boldsymbol {X}$, in which the $k^{th}$ sample of $\boldsymbol {x}$ is given as
After the IFFT output, a cyclic prefix (CP), which represents a copy of the last $G$ samples of the OFDM symbol, is then appended, yielding signals $\boldsymbol {\hat {x}} = [x_{2N-G},x_{2N-G+1},\ldots ,x_{2N-1},x_0,x_1,\ldots ,$
$x_{2N-G-1},x_{2N-G},\ldots ,x_{2N-1}]$. In general, the CP insert operation combats inter symbol interference (ISI) [21].
Finally, a certain bias value (denoted by $B_{DC}$) is added to the resulting OFDM symbol frame vector, clipping all of the real-valued signals to be non-negative [22]. And then the DC-biased OFDM signals enter the electrical-to-optical conversion block, expressed as $\boldsymbol {\hat {x} _b}= \boldsymbol {\hat {x}}+B_{DC}$. Here, we assume that a DC-bias value of 7 dB is used.
In this paper, the light emitter at the transmitter is a 445 nm blue GaN-based micro-LED array, as shown in Fig. 2(a). Figure 2(b) depicts the P-I-V curve of the micro-LED array we investigated. For GaN-based micro-LED array, the output power varying with the injected current has the nonlinearity and linearity, which will blur the received signals and destroy the phase information of the constellation diagrams [13,14].
The micro-LED array transfers the electrical signals to optical signals which are then transmitted into the underwater channel.
2.2 Underwater channel model
Considering both scattering/absorption and turbulence in the UOWC environments, attenuation and fading will be added into the transmitted optical signals [23]. Under this condition, the received optical signal intensity can be expressed as
where $I_r$ is the received optical signal intensity, $I_t$ is the transmitted power, $h_a$ represents the attenuation caused by scattering/absorption effect, and $h_f$ signifies the normalized channel fading.In the UOWC system, the optical energy loss factor due to absorption and scattering is given by [24]
where $c(\lambda )$ is the extinction coefficient, and $L$ is the transmission distance.Meanwhile, the fading irradiance caused by underwater optical turbulence can be modelled as a log-normal distribution, which satisfies a certain probability density function (PDF) defined as [23]
Optical signals are seriously distorted after propagating through the underwater channel, which leads to signal-to-noise ratio (SNR) degradation of the system. In such a case, both attenuation ($h_a$) and fading ($h_f$) should be carefully considered for recognizing received modulated signals.
2.3 Receiver design
The smart receiver, which contains a few-shot classifier, is designed to process the resulting severely distorted modulated OFDM signals. With a few effective received samples, the modulation formats can be recognized by the proposed few-shot classifier.
2.3.1 Received signal model
At the receive-side, a SPAD array is employed as an optical-to-electrical converter. During the $k^{th}$ symbol interval, the average photons number $n_r[k]$ arrived at the receiver can be expressed as
where $n_s$ is the average transmitted photons number per bit, $\hat x_b[k]$ is the transmitted DC-biased OFDM signal corresponding to the $k^{th}$ symbol interval, and $n_b$ is the number of equivalent photons per bit imposed by the background radiation.The photoelectrons $r[k]$ received for the $k^{th}$ symbol interval obeys the Poisson distribution given by
Obviously, the noise at the receiver is Poisson-distributed. The resulting received electrical signals with nonlinear noise are then fed into the demodulator block. After removing the CP, the received symbols can be obtained by using $2N$-points FFT operation. Furthermore, the generated OFDM signals will be converted to constellation diagram samples which are utilized to train and validate the few-shot classifier.
2.3.2 Network architecture of the few-shot classifier
In our proposed few-shot classifier, as illustrated in Fig. 3, a CNN structure is the core function block. The input labeled constellation diagrams are vectored to form feature tensor $\boldsymbol {\chi } \in \mathbb {R}^{M_b\times S_{num}\times C_{num}\times H\times D}$, where $M_b$= 32 denotes the meta-batch size, $S_{num}$= 2 is the number of constellation classes in one task, $C_{num}$= 1 is the number of color channels that the input data contains, and $H\times D$= $28\times 28$ is the size of input samples.
Fig. 3. Illustration of the proposed few-shot classifier based smart AMR system. In one task, types of constellations are mutually exclusive in training/validation datasets (e.g., $\boldsymbol {\chi _{1}}, \boldsymbol {\chi _{2}}$ and $\boldsymbol {\chi _3}, \boldsymbol {\chi _4}$). Constellations diagrams in support/query sets are denoted by $[\chi _i^{j}(1),\chi _i^{j}(2),\ldots ,\chi _i^{j}(28\times 28)]$, where $j\in [1,20]$ is an integer corresponding to different input sample. Besides, $\beta$ is a hyperparameter, being set to $1.0\times 10^{-3}$.
The pixel matrix $\boldsymbol {\chi }_i\in \mathbb {R}^{H\times D}$ in feature tensor $\boldsymbol {\chi }$ represents the input constellation sample of category $i$, where $i\in \{1,2,3,\ldots ,14,15\}$ is the real-label corresponding to 15 modulation modes. For any constellation in the dataset, the input vector converted from $\boldsymbol {\chi }_{i}$ takes the form of $\boldsymbol {\chi }_{i,j}=[\chi _i^{j}(1),\chi _i^{j}(2),\ldots ,\chi _i^{j}(m),\ldots ,\chi _i^{j}(H\times D)]$, where $\chi _i^{j}(m)$ (for $m\in \{1,2,\ldots ,H\times D\}$, $j\in \{1,2,\ldots ,20\}$) denotes the $m^{th}$ pixel value of the $j^{th}$ input sample vector for class $i$.
After stacked convolution layers and pooling layers (denoted as hidden layers in the Fig. 3), the output vectors are flattened by the fully-connected layer $l$. What’s more, a rectified linear unit (ReLU) [25] and batch normalization (BN) follow behind each layer (except for the fully-connected layer). Giving the output vector $\boldsymbol {\chi }_{i,j}^{l-1}$ of the previous layer $l-1$, the output of the fully-connected layer $l$ is then calculated as
Then, an activation function softmax is added to normalize the output layer. The final output is a probability distribution of classification accuracy, which describes the possibility of target modulation types
The cross entropy error is selected as the object loss function, and for a learning task it can be written as
Especially, the meta-learner in the PGML AMR architecture is designed to optimize the few-shot classification model $M_{ft}$ via meta-gradient update. In this paper, our proposed PGML architecture for AMR is different from the conventional ML structure. And it will be thoroughly described in following Section 3.
3. Proposed PGML based few-shot AMR framework
This section introduces the operating mechanism of the PGML based few-shot AMR framework, which is illustrated in Algorithm 1. The proposed framework consists of two crucial technical parts: a meta-learner implemented with ML paradigm [7] for rapidly adapting to new tasks, and a PG training procedure proposed for accelerating the training speed.
3.1 Implementation of PGML based few-shot AMR
The illustrative structure of our designed few-shot AMR is shown in Fig. 3. The meta-learner executes meta-gradient update to obtain the trainable parameters (denoted by $\boldsymbol {W}^{*}$ and $\boldsymbol {B}^{*}$) of the model $M_{ft}$, such that few gradient steps will lead to fast adaptation on a new task. As shown in Algorithm 1, the classification model $M_{ft}$, which is optimized by the meta-learner, is further trained with the proposed training procedure that simulates the human cognition process to achieve smart AMR. Moreover, on the basis of the smart humanoid problem setting, it is assumed that each epoch’s learning tasks will increase, step by step, along with the increase in epoch times.
3.1.1 Training process with PG strategy
The PG strategy is designed to speed up the training process, while assisting to improve the self-learning ability of the classical ML algorithm. As shown in Algorithm 1, the proposed PG strategy is combined with the ML paradigm to achieve a smart AMR algorithm which is called as the PGML few-shot AMR framework.
In the whole training procedure, the PGML AMR is trained epoch by epoch, and in an epoch, the training dataset $D^{tr}$ is split into batches with size being $N_B$. Among the batches, the meta-batch size is fix at 32, that is, there are 32 prior tasks in each batch. The model $M_{ft}$ is then trained batch by batch. At the end of each epoch, the trained model $M_{ft}$ is fine-tuned and validated on new tasks in evaluation batches. In this paper, we assume that the size of evaluation batches is 20, and each of them contains 32 new tasks sampled from the validation dataset $D^{val}$.
Formally, in the $2$-way $1$-shot learning setting, the model is trained with 2$\times (2\times 1)$ samples in one task. In our work, each prior task $\mathcal {T}_{p}$= $\{\boldsymbol {\chi }_{i_{1},j_{1}}\in D_s^{tr},\boldsymbol {\chi }_{i_{1},j_{2}}\in D_q^{tr},\boldsymbol {\chi }_{i_{2},j_{3}}\in D_s^{tr},\boldsymbol {\chi }_{i_{2},j_{4}}\in D_q^{tr},L(f_{W,B})\}$ consists of a loss function $L(f_{W, B})$, and four constellation samples ($\boldsymbol {\chi }_{i_{1},j_{1}}$, $\boldsymbol {\chi }_{i_{1},j_{2}}$, $\boldsymbol {\chi }_{i_{2},j_{3}}$, $\boldsymbol {\chi }_{i_{2},j_{4}}$) of two classes (labeled as $i_{1}$, $i_{2}$). More explicitly, $\{\boldsymbol {\chi }_{i_{1},j_{k}}\}_{k=1}^{2}/\{\boldsymbol {\chi }_{i_{2},j_{k}}\}_{k=3}^{4}$ denote the $\{(j_{k})^{th}\}_{k=1}^{2}/\{(j_{k})^{th}\}_{k=3}^{4}$ data sampled from the support/query set ($D_s^{tr}$/$D_q^{tr}$) of the training dataset $D^{tr}$, respectively. Note that $\{j_{k}\}_{k=1}^{4}\in \{1, 2,\ldots , 20\}$ and $j_{1}\ne j_{2}$, $j_{3}\ne j_{4}$; $i_{1}/i_{2}\in \{1, 2,\ldots , 8\}$ and $i_{1}\ne i_{2}$. Similarly, a new task sampled from the validation dataset $D^{val}$ can be expressed as $\mathcal {T}_n$= $\{\boldsymbol {\chi }_{i_{3},j_{1}}\in D_s^{val},\boldsymbol {\chi }_{i_{3},j_{2}}\in D_q^{val},\boldsymbol {\chi }_{i_{4},j_{3}}\in D_s^{val},\boldsymbol {\chi }_{i_{4},j_{4}}\in D_q^{val},L(f_{W,B})\}$. Moreover, here, we assume that $i_{3}/i_{4}$ represents the $(i_{3})^{th}/(i_{4})^{th}$ class in support/query set ($D_s^{val}$/$D_q^{val}$) of the validation dataset $D^{val}$, in which $i_{3}/i_{4}\in \{9, 10,\ldots , 15\}$ and $i_{3}\ne i_{4}$.
After a certain number of iterations, it is observed that the validation accuracy improvements become marginal. Accordingly, we set epoch times as 13, while the batch size is set as $N_B$= $10*epoch$, in which $N_B$ represents the number of batches in current epoch times $epoch$. In this case, the hyperparameters of our proposed PGML based few-shot AMR framework are depicted in Table 1.
Table 1. Settings in the proposed framework
The PGML based few-shot AMR is described in Algorithm 1. With the aid of the proposed PG training procedure, it is not necessary to restart a new training process from the very beginning after each epoch. Within an epoch, the trained model $M_{ft}$ with the lowest validation loss is stored, and the corresponding parameters of the optimizer/$epoch$ are saved simultaneously. Before starting next epoch, the path information of the saved model $M_{ft}$ is given to confirm that $M_{ft}$ as well as the parameters of the optimizer/$epoch$ are valid. Subsequently, batches of prior tasks are loaded according to the current epoch times ${epoch+1}$, which then are used to train the restored model $M_{ft}$. It has to be noted that the batch size relying on the current epoch times is employed to speed up the training process. Particularly, before training the whole framework, we have to ensure that there does not exist any model in the designated path.
3.1.2 Fast self-learning with ML paradigm
In our ML scenario for few-shot AMR, the goal of the trained model $M_{ft}$ is to solve quickly a new task $\mathcal {T}_n$ sampled from the validation dataset $D^{val}$, and the model is trained by the meta-learner. In effect, the meta-learner aims to find the parameters ($\boldsymbol {W}^{*}$, $\boldsymbol {B}^{*}$) of the model $M_{ft}$ for fast adaptation, using prior tasks $\mathcal {T}_p$ sampled from the training dataset $D^{tr}$.
In the meta-learner, a fast model $M_{ft}^{{W,B}}$ is created to find the meta-gradient descent direction, which applies the same forward propagation as the model $M_{ft}$ and uses a set of specified parameters $\{\boldsymbol {W},\boldsymbol {B}\}$ shared by $M_{ft}$. Guided by the direction of the meta-gradient, the parameters $\varTheta$= $\{\boldsymbol {W}, \boldsymbol {B}\}$ of model $M_{ft}$ become ${\varTheta }^{*}$= $\{\boldsymbol {W}^{*}, \boldsymbol {B}^{*}\}$. Then the model $M_{ft}$ can share the learned parameters ${\varTheta }^{*}$ with the fast model $M_{ft}^{{\varTheta }^{*}}$ for further optimization in next batch.
The process of the meta-gradient update implemented with the meta-learner is described in Algorithm 2. Given a classification model $M_{ft}$ with random parameters $\varTheta$= $\{\boldsymbol {W}, \boldsymbol {B}\}$ initialization, we consider a fast model represented by $M_{ft}^{\varTheta }$ whose parameters are shared by the model $M_{ft}$. In the fixed-size $(M_b$= $32)$ meta-batch, we first update the model parameters $\varTheta$ manually, using data ($D_s^{tr}$) drawn from the ${(mb)}^{th}$ prior tasks $\mathcal {T}_{p,mb}$, such that the fast parameters $\varTheta ^{'}$ are updated as follows
After the fast parameters $\varTheta ^{'}$ are shared with the fast model, data ($D_q^{tr}$) in the current task $\mathcal {T}_{p,mb}$ are passed forward through the fast model $M_{ft}^{{\varTheta }^{'}}$, so as to get the cumulative loss of the meta-batch. In this paper, we calculate the meta-gradient with respect to $\varTheta$, which is expected to represent the meta-gradient descent direction, using the mean value of the cumulative loss $meta$-$loss$ in a meta-batch. The parameters of model $M_{ft}$ are then updated through back propagation
To evaluate the rapid adaptation of the trained model $M_{ft}$, the fine-tuning and validation across new tasks $\boldsymbol {\mathcal {T}}_n$ are performed. As shown in Fig. 3, the optimized model $M_{ft}$ with updated parameters $\varTheta ^{*}$= $\{\boldsymbol {W}^{*},\boldsymbol {B}^{*}\}$ can achieve fast self-learning on new tasks with one or few gradient steps.
3.2 Dataset description
In our system, 15 modulation candidates are considered, including $M$-ary QAM ($M$= $2^{n}$, $n$= 2, 3,…, 8), $M$-ary ASK ($M$= $2^{n}$, $n$= 1, 2, 3), $M$-ary PSK ($M$= $2^{n}$, $n$= 2, 3, 4, 5), and BPSK. Figure 4 demonstrates that constellation diagrams present different modulation formats, and each sample has an ordered integer label converted from the corresponding modulation class name.
Fig. 4. The division of the training/validation dataset ($D^{tr}$/$D^{val}$). The entire dataset contains 15 modulation types, among which eight classes for training and seven classes for validation. In one task, constellations in support/query set are of the same class but different samples.
In our scheme, there are eight modulation formats in the training dataset, which are labelled as $\{\boldsymbol {\chi }_1,\boldsymbol {\chi }_2, \boldsymbol {\chi }_3, \boldsymbol {\chi }_4, \boldsymbol {\chi }_5, \boldsymbol {\chi }_6, \boldsymbol {\chi }_7, \boldsymbol {\chi }_8\}$ respectively. Note that the validation dataset consists of seven modulation classes labelled as $\{\boldsymbol {\chi }_9,\boldsymbol {\chi }_{10}, \boldsymbol {\chi }_{11}, \boldsymbol {\chi }_{12}, \boldsymbol {\chi }_{13}, \boldsymbol {\chi }_{14}, \boldsymbol {\chi }_{15}\}$, which are completely different from those in the training dataset. In one prior task, the support/query set of the training dataset can be denoted as $D_s^{tr}$/$D_q^{tr}$, respectively. Similarly, in a new task, the support/query set of the validation dataset can be expressed as $D_s^{val}$/$D_q^{val}$. The approach of datasets division is extremely important to the generalization of adapting to new tasks.
Based on the above system, we collect 20 constellation diagram images (in "png" format) for each SNR value of each modulation format. More specifically, each format has 80 constellation diagrams taken from four different SNRs ranging from 6 dB to 15 dB with an interval of 3 dB. In a whole training procedure, we chose 20 samples from the collected constellation diagram images for each type of modulation, building datasets at various SNR levels. Thus, the entire dataset ($D^{tr}$ and $D^{val}$) comprises 300 (20$\times 15$) samples in total.
As illustrated in Fig. 5, the input constellation diagrams are processed into a size of 28x28 pixels after grayscale conversion, so as to facilitate the samples processing of the overall framework. In the case that the amount of data is limited, DA operation is implemented over datasets, which expects that the impact of micro-LED distortion on the classification effect can be mitigated. Specifically, when training the model $M_{ft}$, we rotate the preprocessed images for six angles from $0^{\circ}$ to $360^{\circ}$ with a stride of $60^{\circ}$. Then evaluation constellation diagrams are fed into the trained model $M_{ft}$, and these samples are rotated for 71 different angles from $0^{\circ}$ to $360^{\circ}$ with a stride of $5^{\circ}$. The effect of evaluation samples after DA operation is shown in Fig. 5.
3.3 Implementation platform
The PGML based few-shot AMR architecture, designed in this paper, is conducted in the platform with one NVIDA GeForce GTX 1060 GPU which are applied for training and validating the network. The implementation of the network architecture relies on Torch.nn with Pytorch 1.2.0 and Python 3.6.4 as the backend. Besides, MATLAB R2018b is applied to simulate UOWC systems, generating constellation diagram samples to build our datasets.
4. Simulation results and analysis
In this section, the classification performance of the proposed PGML based few-shot AMR is evaluated over the micro-LED UOWC system in the presence of Poisson noise.
4.1 Classification performance comparisons
4.1.1 Benefit 1: the promotion of fast self-learning ability
The performance of training/validation accuracy of our proposed PGML approach is studied, which compares with that of the classical ML algorithm served as the baseline model.
These comparisons focus on four cases: 1) training with datasets at bad SNR (SNR= 6 dB). 2) training with datasets at median SNR (SNR= 9 dB). 3) training with all samples at high SNR (SNR= 12 dB). 4) training with constellation diagrams in training/validation dataset ($D^{tr}/D^{val}$) are proportionally mixed for SNR= $j$ dB ( $j\in$[6 dB, 12 dB]). The SNR model at the receiver is given by $\textrm {SNR}$= $10\textrm {log}_{10}({n_{s,ave}^{R}}/{n_b})$, where $n_{s,ave}^{R}$ denotes the average received number of photons per bit, $n_b$ is the number of equivalent photons per bit imposed by the background radiation.
We measure the training/validation accuracy of the two approaches under different epoch times. As the epoch times grow, the parameters $\varTheta$= $\{\boldsymbol {W}, \boldsymbol {B}\}$ of the classification model are further optimized, contributing to the improved training/validation accuracy. When the epoch times arrive at 13, the validation accuracy improvements become marginal, such that the training is terminated. Based on the datasets of various SNR levels, four types of trained classification models ($M_{bad}, M_{median}, M_{high}, M_{mix}$) are stored.
After each epoch, the trained classification model is generalized into new tasks drawn from the validation dataset $D^{val}$ to evaluate the fast self-learning ability of the model. As shown in Fig. 6, the proposed PGML scheme can achieve validation accuracy of $95.63\%$, $93.36\%$, $95.23\%$, and $89.3\%$ trained with datasets corresponding to SNR of 6 dB, 9 dB, 12 dB, and mixed values respectively.
Results in Fig. 6 show that the validation accuracy of the proposed PGML based few-shot classifier is higher than the classical ML enabled AMR classifier for various SNR scenarios. Clearly, our proposed approach has a superior capability of fast self-learning with a small number of samples from new tasks.
Fig. 6. Accuracy vs. epoch times. Training accuracy on prior tasks drawn from dataset $D^{tr}$, including $M$-ary ASK ($M$= $2^{n}$, $n$= 1), $M$-ary PSK ($M$= $2^{n}$, $n$= $2, 3, 4, 5)$, and $M$-ary QAM ($M$= $2^{n}$, $n$= $6, 7, 8)$ modulation constellations. Validation accuracy on new tasks drawn from dataset $D^{val}$, including $M$-ary QAM ($M$= $2^{n}$, $n$= $2, 3, 4, 5)$, $M$-ary ASK ($M$= $2^{n}$, $n$= $2, 3)$, and BPSK modulation constellations. Classification models are trained in different SNR scenarios: (a) SNR= 6 dB; (b) SNR= 9 dB; (c) SNR= 12 dB; (d) SNR= $j$ dB ($j\in$[6 dB, 12 dB]).
4.1.2 Benefit 2: stronger robustness against Poisson noise
To explore the robustness performance of the proposed PGML scheme, the few-shot classification model is trained on training datasets with single SNR. The restored trained model is then evaluated on validation datasets with SNR ranging from 6 dB to 15 dB, respectively. Moreover, the trained model can be employed into AMR of new modulation classes.
Additionally, $P_{cc}$ $(P_{cc}=\{P_{cc}^{snr}\}_{snr= 6}^{15})$ is applied to measure classification performance under different SNR scenarios. The probability of correct classification at $snr$ dB is $P_{cc}^{snr}$ which can be defined as $P_{cc}^{snr}= ({S_{correct}^{snr}}/{S_{total}^{val}})\times 100\%$; where $S_{correct}^{snr}$ is the constellation diagrams recognized correctly at $snr$ dB, $S_{total}$ is the total number of samples selected for validation in $D^{val}$.
As depicted in Fig. 7, $P_{cc}$ is evaluated and compared with that of classical ML method. According to the previous analysis in Section 4.1.1 Benefit 1, we can obtain four trained few-shot classification models ($M_{bad}, M_{median}, M_{high}, M_{mix}$). For datasets based on distinct values of received SNRs, i.e., 6 dB, 9 dB, 12 dB, 15 dB, the trained models are validated under all SNR conditions. In one task, $N\in \{1, 2, 3\}$ samples is/are selected for validation respectively.
Fig. 7. Classification performance comparison curves between baseline classical ML method and the proposed PGML scheme under SNR range being [6, 15] dB, based on saved models: (a) Model $M_{bad}$; (b) Model $M_{median}$; (c) Model $M_{high}$; (d) Model $M_{mix}$.
Figure 7 demonstrates that the proposed scheme can achieve a higher $P_{cc}$ at all testing SNRs values, it shows better robustness performance with varying SNRs and complex UOWC channels. Especially, even at a low SNR (SNR= 6 dB), the proposed scheme gives better classification performance no matter which saved model is tested on. Apparently, by comparing the results in Fig. 7, it is noted that the promotion of $P_{cc}$ using our proposed scheme is significant.
4.1.3 Benefit 3: excellent resistance to micro-LED array distortion
In this section, we investigate the effect of micro-LED array distortion on few-shot AMR. Considering the phase information of constellation diagrams distorted by the micro-LED, we rotate evaluation images for 71 different angles from $0^{\circ}$ to $360^{\circ}$ with a stride of $5^{\circ}$. With the results on the original datasets set as the baseline, the proposed few-shot classifier is evaluated on enlarged datasets to validate the resistance performance to the distortion caused by micro-LED arrays.
From Fig. 8, we can observe that the $P_{cc}$ can be improved at every SNR. Particularly, the improvement of $P_{cc}$ at low SNR values is significantly. When the SNR is 6 dB, the DA operation based classification model $M_{bad}$ can increase $P_{cc}$ from 83.67$\%$ to 95.85$\%$. Consequently, the DA operation accounts for making up the $P_{cc}$ performance loss and providing a meaningful solution to overcome the distortion caused by micro-LED arrays in few-shot AMR effects.
Fig. 8. $P_{cc}$ curves of model $M_{bad}$ and $M_{high}$ versus SNR in range [6, 15] dB. Classification performance with DA operation adopted are plotted with dotted lines, and it illustrated with solid lines when implemented on original datasets: (a) Model $M_{bad}$; (b) Model $M_{high}$.
4.1.4 Benefit 4: significant training speed improvement
Figure 9 presents the training time versus epoch times. With our PG strategy, batches in each epoch increase incrementally and the time consumption of our proposed scheme increases linearly.
Fig. 9. Training time consumption comparison between the proposed PGML scheme and classical ML method. The total time recorded under four SNR scenarios (SNR= 6 dB, SNR= 9 dB, SNR= 12 dB and mixed SNRs) is averaged as $T_{av}$.
The total time consumed by the proposed PGML scheme per training process (the sum of the training time on 13 epochs) is 15.083 minutes, 15.334 minutes, 14.868 minutes, and 15.134 minutes corresponding to datasets with SNR= 12 dB, SNR= 9 dB, SNR= 6 dB, and SNR= $j$ dB ( $j\in$[6 dB,12 dB]), respectively. By contrast, the classical ML method consumes 19.602 minutes, 19.768 minutes, 19.651 minutes, and 19.718 minutes, respectively.
The average time consumed per training process (denoted by $T_{av}$ ) is calculated for the two training approaches respectively, based on the total time consumption under the four different SNR scenarios mentioned above. Compared with the classical ML method, the average total training time implemented with the PGML approach is reduced by about 23.27$\%$. Therefore, the proposed PGML scheme reduces the training cost, promoting the learning efficiency of the classification models to prior tasks.
4.2 BER evaluation
Based on our proposed PGML few-shot AMR framework, we simulate an OFDM based photon-counting communication system over underwater channels to validate the feasibility of the smart UOWC AMR. The parameters of OFDM and underwater channel model in the simulation are shown in Table 2.
Table 2. Parameters setting in the simulation
Figure 10 depicts the BER performance over UOWC channels with both scattering/absorption and turbulence taken into consideration. In our simulations, a shot noise is considered at the receiver. Figure 10 also shows that the smart UOWC AMR system is capable of good BER performance in the low bit energy.
Fig. 10. BERs for $M$-ary QAM ($M$= $2^{n}$, $n$ = 2, 3,…, 7, 8) and BPSK modulation formats versus transmit energy in (dBJ).
5. Experimental validation
To demonstrate the practicality of the proposed PGML few-shot AMR approach, we also set up physical experiments for recognizing BPSK, $M$-ary QAM ($M= 2^{n}, n= 2, 3, 4, 5, 6$) signals over UOWC systems.
Based on the above simulated system, the transmission distance in our experiment is 2.3 meters. A 2.3 m water tank, which is filled with clear water, is used to emulate the underwater link. We collect constellations with SNR ranging from 6 dB to 15 dB at the receive-side, and validate the performance gain of the proposed approach on the trained models saved in Section 4.1.1. In our experiments, there are 20 samples with single SNR for each type of modulation format in $D^{val}$, and parts of them are presented in Fig. 11(a).
Fig. 11. (a) The received constellation diagrams for five modulation categories (BPSK, $M$-ary QAM ($M= 2^{n}$, $n$= 2, 3, 4)) with different SNRs over UOWC experiments. The $P_{cc}$ curves of the proposed PGML scheme and the classical method under varying received SNRs validated on the trained models: (b) $M_{bad}$; (c) $M_{high}$.
Figures 11(b) and (c) show the $P_{cc}$ versus received SNRs over the experimental demonstration. The measured $P_{cc}$ performance is improved by using the proposed PGML scheme at all received SNR values, as shown in Figs. 11(b) and (c).
6. Conclusion
In this paper, we have introduced a PGML based few-shot AMR scheme for smart UOWC system, which aims to solve modulation classification tasks in a small sample problem setting. The proposed PGML algorithm not only can recognize new types of modulation formats but also requires a small number of samples, achieving the enhanced generalized ability of fast self-learning. Notably, the PG strategy improves the training efficiency of the few-shot classifier. Besides, the DA operation is employed before training the classification models, which can effectively overcome the micro-LED distortion of UOWC systems. The results show that our proposed scheme can be well-performed in low SNR scenarios for recognizing a small number of samples of new modulation types, which is suitable in severe UOWC environments. In summary, the classifier designed in the smart UOWC system achieves superior generalized ability and strong robustness performance with the aid of our proposed PGML based few-shot AMR framework.
Funding
National Natural Science Foundation of China (61571135).
Acknowledgments
The authors would like to thank the anonymous reviewers for their constructive comments.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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