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Abstract
Photo-multiplier tube can be adopted for optical signal detection under weak signal and ambient light intensity, where the signals can be classified into three regimes, discrete-pulse regime, continuous waveform regime and the transition regime between the discrete-photon and continuous waveform regimes. While Poisson and Gaussian distributions can well characterize the discrete-photon and continuous waveform regimes, respectively, a statistical characterization and the related signal detection in the transition regime are difficult. In this work, we resort to a learning approach for the signal characterization and detection under pulse and transition regimes. We propose a support vector machine (SVM)-based approach for signal detection, which extracts eight key features on the received signal. We optimize the hyper-parameters to improve the SVM detection performance. The proposed SVM-based approach is experimentally evaluated under different symbol and sampling rates, and outperforms that of various statistics-based comparison benchmarks.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Visble light communication (VLC) serves as a complement to radio frequency (RF) communication due to its potential large transmission bandwidth, no penetration through walls, and no electromagnetic radiation [1–3]. Recently, various VLC transmission strategies have been proposed to increase the transmission rate [4–9].
A typical VLC system consists of a low cost light emitting diode (LED), and an optical receiver which can be photodiode (PD), avalanche photodiode (APD), single-photon avalanche diode (SPAD) or photo-multiplier tube (PMT). The PD, APD and PMT can be adopted to detect continuous waveform signal [10–12]. The photon-level signals [13,14] can be detected by both SPAD and PMT devices. Recently, most research works on VLC focus on the communication system design under strong illumination, where the received signal shows a continuous waveform. Work [9] proposed a building-to-building free-space VLC system with over 72m link distance using a standard CMOS APD, which realized on–off-keying (OOK) data rate of 2 Gb/s and forward-error-correction-compliant bit error rate (BER) below $3.8\times 10^{-3}$. Work [15] designed a fully integrated 800 $\mu m$ diameter APD optical receiver through a standard 0.35 $\mu m$ BiCMOS technology without any process modifications, which reaches the sensitivity of –33 dBm at 1 Gbit/s and –29.3 dBm at 2 Gbit/s.
In realistic communication scenarios, the received signal may be extremely weak under weak ambient light intensity, for example in deep sea. In such a scenario, PMT or SPAD needs to be adopted due to higher gain than the SPAD and APD. Work [16] realized 1 Gbit/s NRZ-OOK underwater wireless optical transmission experiment using wideband PMT, and demonstrated a huge receiver sensitivity improvement of about 17 dB at 1 Gbit/s than an APD receiver with the same bandwidth. The comparison between SAPD and a APD receivers for VLC is investigated in [17], demonstrating that the SPAD-based receiver is more sensitive in the dark condition.
Since extremely weak optical signal cannot be detected by PD or APD, we adopted a PMT based receiver. Works [18] and [19] theoretically and experimentally analyze the characteristics of the practical PMT receiver in a wide range of signal intensity, from discrete pulse signal to continuous waveform signal, respectively. Note that the PMT signal range can be divided into three regimes, pulse regime, transition regime and waveform regime, according to the received signal intensity [18]. Work [12] realized a PMT based VLC system, where the PMT output signal is continuous waveform signal. Work [20] adopted hidden Markov model (HMM) to characterize the LED transmission under weak illumination, where the PMT output signal is discrete pulse signal, and applied Viterbi algorithm to detect the signals. Work [19] considered three regimes of the PMT output signal with symbol rate 100Kbps, and proposed the combined detection under ML criterion.
In this work, a practical PMT is adopted, where the received signal is extremely weak and cannot be detected by APD. We propose a signal detection algorithm based on support vector maching (SVM), working in both pulse regime and transition regime. We optimize the hyper-parameters of the SVM to improve the detection performance. We experimentally evaluate the proposed algorithm under different symbol and sampling rates, and compare the performance of the proposed approach with that of various statsitics-based detection approaches. Due to the same type of optical receiver, such approach can be readily extended to ultra-violet communication if PMT is also adopted.
The remainder of this paper is organized as follows. We demostrate the system model and signal characteristics in Section II. We propose SVM-based signal detection algorithm with hyper-parameter optimization in Section III. Experimental results on the proposed and the comparison with statistics-based benchmarks are demonstrated in Secion IV. We conclude this work in Section V.
2. System model and signal characteristic
2.1 System model
Consider a VLC system with weak ambient light and signal intensity, where the received signals cannot be detected by an APD. In such a scenario, a PMT based receiver is adopted, as shown in Fig. 1. At the transmitter side, the alternate current (AC) signal and direct-current (DC) supply are used for communication and driving the LED, respectively. At the receiver side, the extremely weak signal is detected by the PMT, whose output signal is sampled by an analog-to-digital converter (ADC) for further processing.
The photon-level detector can be adopted under weak signal and ambient light scenario, for example deep-water underwater VLC. Such scenario is different from the indoor application one with strong signal and background radiation, where an APD receiver needs to be adopted.
2.2 PMT output signal characterization
Assuming $Y_j$ denotes the photon impulse response in the $i-th$ symbol duration, we have,
where $h\left ( t \right ) =u\left ( t \right ) -u\left ( t-\tau \right )$ and $u\left ( t \right )$ is the step function; $G_{i}^{k}$ denotes the PMT gain for a single photon after multi-stage amplification; $t_{i}^{k}$ and $N_i$ represent the arrival time of the $k^{th}$ photon and the number of arrived photon during the $i^{th}$ symbol duration, respectively; $N_i$ obeys Poisson distribution with $\mathbb {P}\left ( N_i=n \right ) =\frac {\lambda ^{n}}{n!}e^{-\lambda }$ and $\lambda$ is the mean of the arrived photons during a symbol duration.We aim for characterizing this phenomenon based on experimental measurements. Figure 2 shows the experimental system diagram. At the transmitter side, Rigol DG5252 arbitrary signal waveform generator is used to generate OOK modulated data signals for driving commercial LED, whose $3$dB bandwidths before and after the blue filter are 1.71MHz and 6.30MHz, respectively. The OOK modulated signal is sent to a MINI-CIRCUITS ZFBT-4R2GW+ Bias-Tee. At the receiver side, Hamamatsu CR315 series PMT is adopted to detect the optical signals. Thorlabs FB450-10 filter and Thorlabs NDUV40A attenuator are placed in front of the PMT detector to remove the light in other wavelentghs and attenuate the signal, respectively. Note that the attenuator is adopted to emulate the signal attenuation due to long transmission distance. The filter center wavelength and bandwidth are 450nm and 10nm, respectively. The gain of the optical attenuator is 0.0003. Agilent MSOX6004A oscilloscope is adopted to capture the output signal of the PMT for offline processing in the computer side. Note that the LED and PMT are placed in a sealed black box to avoid the influence of ambient light.
Figure 3 shows the typical signal of three PMT output signal regimes. The curves labeled by “Pulse”, “Transition” and “Waveform” represent the signals belonging to photon counting regime, transition regime and waveform regime, respectively. We can see that the output signal amplitude in the waveform region is lower than that in the transition region. The reason is that the PMT outputs first increase and then become saturated as the input signal intensity increases.
The difficulty lies in designing the detection algorithm for the PMT, especially in the transition regime. Since the signal detection in the waveform regime is standard, the signal detection approach working in both pulse regime and transition regime is of interest. As the nonlinearity in the transition regime cannot be well characterized by an analytical model, in this work we resort to a learning-based approach under the SVM framework.
More specifically, as the nonlinearity of the transition regime cannot be well characterized by an analytical model, the conventional detection based on approximate statistical distribution does not perform well, especially in the case with ISI. Therefore, we investigate the characteristics of transition regime signal, extract more effective features from the received signal, and propose a signal detection algorithm based on SVM. As seen from experimental results, the proposed SVM shows lower BER compared with the detection based on approximate statistical distribution.
3. SVM-based signal detection
We propose an SVM-based signal detection algorithm for the pulse and transition regime signal with nonlinear distortion, as shown in Fig. 4. Firstly, we extract the features containing the average of the signal samples during a symbol duration and the average of the pilot signal samples from the received signal. Secondly, we adopt the adaptive threshold calculated through smooth filtering and minimum threshold constraint for edge detection. Then, we extract the features via pulse counting and sampling, normalize the feature vectors containing the pulse numbers and samples, and finally adopt SVM to fit the mapping relationship between the feature vectors and the corresponding symbol labels. A genetic algorithm is employed to optimize the hyper-parameters of SVM. Note that the change of sampling rate or transmission rate may affect the samples and number of pulses of each symbol. Therefore, the SVM detector needs to be retrained when the transmission rate or sampling rate changes.
3.1 SVM-based signal detection algorithm
We extract the feature vectors including eight features from the received signal. The feature vector corresponding to the $k^{th}$ symbol is characterized as follows,
where $v_{k,1}$ represents the mean of the signal pilot samples; $v_{k,2}$ and $v_{k,3}$ represent the mean signal samples and the number of pulses corresponding to the $k^{th}$ symbol, respectively; $v_{k,4}$, $v_{k,5}$ and $v_{k,6}$ represent the number of pulses of the first, second and third parts of the $k^{th}$ symbol, respectively; $v_{k,7}$ and $v_{k,8}$ represent the numbers of pulses corresponding to the $(k-1)^{th}$ and $(k+1)^{th}$ symbol, respectively.The mean of pilot samples $v_{k,1}$ characterizes the threshold between symbol zero and symbol one. Inspired by the conventional maximum likelihood (ML) detection algorithm based on Gaussian-approximation and Poisson-approximation, the number of pulses and samples corresponding to each symbol are beneficial for symbol decision. Therefore, $v_{k,2}$ and $v_{k,3}$ are extracted. To reflect the short inter-symbol interference (ISI), it is beneficial to divide the symbols and adopt them for symbol decision. Therefore, $v_{k,4}$, $v_{k,5}$ and $v_{k,6}$ are selected. To further reflect the long ISI, the information from the previous and the subsequent symbols are needed. Therefore, $v_{k,7}$ and $v_{k,8}$ are selected.
Specifically, let $\left \{ x_n \right \} _{n=1}^{MK}$ represent the signal samples and $X_i$ denote the mean of samples corresponding to the $i^{th}$ transmitted symbol, where $M$ and $K$ denote the sampling rate per symbol and transmitted symbol number, respectively. Let $X_i^{pilot}$ denote redthe mean of samples corresponding to the $i^{th}$ pilot symbol. The average of the pilot signal samples $v_{k,1}$ can be calculated by,
where $L_{pilot}$ represents the length of the pilot.The mean of signal samples corresponding to the $k^{th}$ transmitted symbol can be calculated by
Sample $n$ filtered by moving mean filter with window of $2L+1$, is given by,
We also calculate the long-term mean in the window of length $2D+1$, given by,
The adaptive threshold for edge detection is given by,
where $max \left ( \cdot \right )$ denotes the maximum function. Note that Eq. (5) and Eq. (6) provide the short-term and long-term means of the signals samples, respectively, and such maximum one provides a more accurate threshold for rising edge detection.The position of the pulse in the sampled signal can be marked as follows,
We divide a symbol duration into three parts with equal duration, and count the pulse numbers separately. The pulse number of the first part of the $k^{th}$ symbol is calculated by,
The pulse number of the second part of the $k^{th}$ symbol is calculated by,
The pulse number of the third part of the $k^{th}$ symbol is calculated by,
The number of pulses of the $(k-1)^{th}$ and $(k+1)^{th}$ symbol can be calculated by,
We normalize the feature vector as follows,
SVM is designed to fit the nonlinear relationship between the feature vectors and symbol labels, and construct function $y_{i}^{'}=f\left ( v_i \right )$ that approximates the signal detection. The error between true value $y_{i}$ and predicted value $y_{i}^{'}$ is minimized by the SVM algorithm. The optimization problem is given by,
The above optimization problem can be solved by a standard Lagrangian multiplier method, where the Lagrangian function is given by,
Taking partial derivative of $L\left ( w,b,\alpha,\beta \right )$ with independent variables $w$ and $b$, and setting the results as 0, we have,
Bringing $w$ and $b$ into Eq. (17) and Eq. (18), the original optimization problem is converted into its dual form, given by,
The above optimization problem can be solved by the sequential minimum optimization (SMO) algorithm. Then, the SVM classification model can be calculated as,
3.2 Training and hyper-parameters optimization
The goal of SVM training is to obtain an efficient signal detector. In this work, the feature vectors and the corresponding symbol labels under different signal-to-noise ratios (SNRs) are collected for SVM training. The training samples are collected at different AC signals, whose size in the SVM training is 260000. Note that ten-fold leave-one-out cross-validation is adopted in this paper. The testing samples size at each voltage is 1000000.
In this paper, RBF is adopted for its outstanding performance in vast majority of occasions. Hyper-parameters $C$ and $g$ are the penalty factor and kernel radius, respectively. They weigh the empirical risk and structural risk, where lager $C$ or smaller $g$ may lead to over-fitting, and smaller $C$ or lager $g$ easily leads to under-fitting. Therefore, in the SVM training process, hyper-parameters $C$ and $g$ need to be optimized to further improve the classification performance.
Genetic algorithm, which contains selection, crossover and mutation operation, is adopted to optimize the hyper-parameters $C$ and $g$ of SVM. The proportional selection operator, as one of the most commonly used selection operator, is also adopted. In the proportional selection operator, the probability of each individually selected is proportional to its fitness. The probability of the $i^{th}$ individual being selected can be calculated by,
where $F_i$ denotes the fitness of the $i^{th}$ individual, as the correct prediction rate of the SVM; and $P$ represents the population size.Simulated binary crossover operator [21] is adopted in this work, calculated as follows based on weighting average,
In addition, the mutation operator is polynomial mutation operator, calculated by,
The detailed process of optimizing hyper-parameters $C$ and $g$ based on the GA is summarized in Algorithm 1.
Algorithm 1. Optimize C and g via generic algorithm.
Since the relationship between the hyperparameters $C$ and $g$ of SVM and the target result is highly nonlinear, the genetic algorithm has lower computational complexity compared with exhaustive search approach. In addition, the cost function for all individuals of the group in genetic algorithm can be computed in parallel to increase the processing speed. Moreover, given the transmitter and receiver devices, for specific transmission rate and sampling rate, parameters $C$ and $g$ can be optimized in prior and adopted for all peak voltages at the receiver side. Experimental results show that the optimized parameters are universally good under all received optical power for specific transmission rate and sampling rate, given transmitter and receiver devices. Moreover, parameters $C$ and $g$ must be retrained if the above conditions change. In real applications, note that the transmitter and receiver devices can be standardized, and the transmission rate and sampling rate are selected from a discrete set. Thus, the genetic algorithm parameters for the transmission rates and sampling rates in such a discrete set can be optimized in an offline manner, and stored for online table look-up operation. Therefore, genetic algorithm can be adopted to optimize parameters for real applications.
4. Experimental results
The experiment environment is shown in Fig. 5. We place an optical filter at center wavelength 450nm in front of PMT to increase the system bandwidth. In addition, an optical attenuator is placed in the front of PMT to ensure that the received signal intensity lies in the pulse and transition regimes. Note that both PMT and Philips LED are placed in a sealed black box to avoid the ambient light. The I-V curve of the LED adopted in this paper is shown in Fig. 6, and the electric peak voltage of the LED is 18V.
We experimentally investigate the performance of the proposed SVM based signal detection algorithm in the weak signal communication, and compare it with the traditional counting-based threshold detection, sampling-based threshold detection, Poisson approximation-based maximum likelihood (ML) detection, Gaussian approximation-based ML detection, combined detection, and linear minimum mean square error (LMMSE) equalizer. Note that the combined detection is based on the summation of LLRs from Poisson approximation-based detection and the Gaussian approximation-based detection [19].
Let $LLR_P$ and $LLR_G$ represent the LLR of Poisson approximation-based and Gaussian approximation-based ML detection, respectively, calculated by,
Assuming that $LLR_C$ represents the LLR of the combined symbol detection, we let,
where symbol 1 is detected if $LLR_C \ge 0$ and symbol 0 is detected otherwise.4.1 Comparison of adaptive threshold and conventional fixed threshold
We adopt the edge detection algorithm for pulse counting. However, accurate counting is a big challenge when the signal falls into the transition regime. Therefore, we design a pulse counting method based on adaptive threshold, which is given by Eq. (7). Figure 7 shows the received signal in the transition regime, along with the corresponding fixed thresholds and adaptive thresholds with symbol rate 20Mbps. The curves labeled by “Received signal”, “Adaptive threshold” and “Fixed threshold” represent the received signal, adaptive thresholds and fixed thresholds, respectively. The fixed threshold is the mean of pilot samples. We can see that the proposed pulse counting algorithm can track the signal intensity changes more accurately compared with fixed threshold.
4.2 Hyper-parameters optimization
As mentioned in Section III, the detection performance is related to hyper-parameters $C$ and $g$, which which characterize the penalty coefficient and kernel function parameter in the SVM, respectively. We adopt the genetic algorithm to optimize the hyper-parameters. We set $C_l=0$, $C_u=10$, $g_l=0$ and $g_u=10$. The numbers of populations and iterations are set to 20 and 50, respectively. The training data is the feature vectors extracted from the received signal under different SNRs, while the training labels are the corresponding transmitted symbol “0” or “1”. We divide the samples into ten parts, and conduct ten times of training and verification processes. Each time nine parts are used for training and one part is used for verification. The average prediction accuracy is adopted as the metric. We optimize the hyper-parameters under different transmission rates and sampling rates. Figure 8 shows the fitness curves of GA adopted to optimize the hyper-parameters of SVM under different sampling rates at symbol rate 5Mbps. The curves labeled by “Optimal fitness” and “Average fitness” represent the optimal and average fitness of GA, respectively. It can be seen that the optimal fitness first increases and then tends to flatten with the evolution. We can also see that lower sampling rate leads to more significant fitness improvement. The optimized hyper-parameters are shown in Fig. 8, which are used for the SVM training.
4.3 Feature weights analysis
The weights of SVM are proportional to the importance of the corresponding features for the prediction performance. We conduct experiments to demonstrate the weights of the features under different sampling rates and symbol rates. Note that limited by the size of the black box, we set the distance between the LED and PMT to 15cm and adopt attenuator to attenuate the signal. Longer distance communication can be achieved after removing the attenuator.
Figure 9 shows the normalized weights of the features under different sampling rates, where the symbol rate is 5Mbps. The curves labeled by “50 times”, “25 times”, “10 times” and “5 times” represent the sampling rate per symbol of 50, 25, 10 and 5, respectively. The horizontal axis of Fig. 9 represents the feature index. No. 1 represents the average of the signal samples of the pilot; No. 2 and No. 3 represent the average of the signal samples and the number of pulses corresponding to the pending transmitted symbol, respectively; No. 4, No. 5 and No. 6 represent the numbers of pulses of the first, second and third parts of transmitted symbol, respectively; No. 7 and No. 8 represent the numbers of pulses corresponding to the previous and next transmitted symbol of the symbol to be judged, respectively. It can be seen that the normalized weight of No. 2 feature decreases with the sampling rate, since the accuracy of the Poisson approximation decreases with the sampling rate.
Figure 10 shows the normalized weights of the features with $50$ times symbol-rate sampling at different symbol rates. The curves labeled by “5Mbps”, “10Mbps” and “20Mbps” represent symbol rates 5Mbps, 10Mbps and 20Mbps, respectively. It can be seen that the normalized weight of No. 2 feature decreases with the symbol rate, due to lower accuracy of Poisson approximation. In addition, the weight of No. 8 feature under symbol rate 20Mbps is significantly higher than those under symbol rates 5Mbps and 10Mbps, since high rate leads to inter-symbol interference (ISI), where the features of neighboring symbols need to be adopted for symbol detection.
Fig. 10. The weights of feature vectors under different symbol rates for $50$ times symbol-rate sampling.
4.4 BER performance of the proposed symbol detection algorithm
We conduct experiments to compare the BER performance of the proposed detection algorithm with that of the benchmarks under different bit rates and sampling rates. The experiment system is shown in Fig. 5, where the distances between the LED and PMT are 15cm, 15cm and 10cm for symbol rates 5Mbps, 10Mbps and 20Mbps, respectively. We change the received optical power of PMT by adjusting the AC voltages of the Bias-Tee at the transmitter side. Note that the DC voltage and AC voltage are set to 7V and from 6V to 20V, respectively. The lengths of the pilot symbols and frame are 511 and 16384, respectively. The window size of the moving average filter is equal to the oversampling rate.
4.4.1 BER performance under symbol rate 5Mbps
Figure 11 shows the BER of the proposed and conventional detection algorithms under different sampling rates at symbol rate 5Mbps. The curves labeled by “Poisson-Mean”, “Poisson-ML”, “Gaussian-Mean”, “Gaussian-ML”, “Combine-ML”, “LMMSE” and “Proposed method” represent the counting-based threshold detection, Poisson approximation-based ML detection, sampling-based threshold detection, Gaussian approximation-based ML detection, combined detection, LMMSE equalizer and proposed SVM-based detection algorithm, respectively.
We can also see that the BER of the proposed method under 50 times symbol-rate sampling is similar to that under 25 times symbol-rate sampling, which is significantly lower than that under 10 times and 5 times symbol-rate sampling. This means that increasing the sampling rate can improve the performance, but limited gains are observed when the sampling rate exceeds 25 times. In addition, lower sampling rate leads to more significant performance improvement of the proposed algorithm over the benchmark algorithms. It can be seen that 50 times symbol-rate sampling rate may lead to slightly worse BER performance than 25 times symbol-rate sampling. This is due to the high-dimensional data from the 50 times symbol-rate sampling, which degrades the separation performance from eight features. We can also see that the BER of the LMMSE equalizer is slightly lower than that of the sampling-based threshold detection. The BER of the counting-based threshold detection and Poisson approximation-based ML detection first decreases and then tends to flatten or increases slightly as the AC voltage increases. This is because the received signal changes from the pulse signal to the transition signal as the AC voltage increases, where the pulse counting approach based on rising edge detection becomes less accurate. It can also be seen that the combined detection has no significant performance improvement compared with Gaussian approximation-based ML detection. However, both the combined detection and Gaussian approximation-based ML detection shows lower BER than other algorithms except the proposed one.
4.4.2 BER performance under symbol rate 10Mbps
Figure 12 shows the BER performance of the proposed and conventional detection algorithms under different sampling rates at symbol rate 10Mbps. The representations of the curve labels are the same as those in Fig. 10. It can be seen that the proposed algorithm has the lowest BER, which also decreases with the AC voltage. Higher AC voltage or sampling rate leads to more significant performance improvement of the proposed algorithm. We can also see that the BER of the LMMSE equalizer is lower than that of the sampling-based threshold detection and worse than that of the Gaussian approximation-based ML detection and combined detection. The combined detection performs first better and then worse than the Gaussian approximation-based ML detection as the AC voltage increases, due to less accuracy of the Poisson approximation-based detection. The performance of the Gaussian approximation-based ML detection and combined detection outperforms other algorithms except the proposed one. Both the counting-based threshold detection and Poisson approximation-based ML detection performs first better and then worse than the Gaussian approximation-based ML detection and LMMSE equalizer, also due to less accuracy of Poisson approximation.
4.4.3 BER performance under symbol rate 20Mbps
Figure 13 shows the BER of the proposed and conventional detection algorithms under different sampling rates at symbol rate 20Mbps. The same representation of the curve labels as those in Fig. 11 and Fig. 12 is adopted. It can be seen that the proposed algorithm exhibits the lowest BER, which also decreases with the AC voltage. Higher AC voltage or sampling rate also leads to more significant performance improvement of the proposed algorithm. We can also see that the LMMSE equalizer performs first worse and then better than the Gaussian approximation-based ML detection and combined detection. In addition, higher sampling rate leads to more significant performance improvement of the LMMSE equalizer compared with Gaussian approximation-based ML detection and combined detection. The BERs of the counting-based threshold detection and Poisson approximation-based ML detection first decrease and then tend to flatten as the AC voltage increases, worse than other detection algorithms under high AC voltage.
4.4.4 Complexity Analysis
We also compare the computational complexity between the proposed approach and the benchmarks. Table 1 shows the average time needed for detecting a single symbol using the proposed approach and the comparison benchmarks via running MATLAB on a desktop computer. Labels “5 times”, “10 times, “25 times” and “50 times” represent 5 times sampling rate, 10 times sampling rate, 25 times sampling rate and 50 times sampling rate, respectibvely. The proposed detection algorithm needs higher computational complexity than the benchmark methods. In addition, it can be seen from Table 1 that for lower transmission rate or higher sampling rate, the proposed approach needs less time since symbols one and zero are more distinguishable.
Table 1. Time needed for detecting a single symbol via running Matlab (unit ns)
We have to concede that the proposed approach needs higher computational complexity compared with other benchmarks, which is the cost of lower detection BER. However, since the symbol detection realized in Field-Programmable Gate Array (FPGA) needs much shorter time (typically up to two orders) compared with that via running Matlab, we can predict that such operation can be realized in a real-time manner using FPGA.
5. Conclusion
We have proposed a signal detection algorithm based on SVM for the PMT output signal, especially in the pulse and transition regimes. Hyper-parameters of the SVM are optimized by genetic algorithm to improve the performance of the proposed method. We have demonstrated the weights of the features under different sampling rates and symbol rates. We have also compared the performance of the proposed algorithm and statistics-based conventional detection algorithms. Experimental results show that the proposed method demonstrates the lowest overall BER compared with the conventional statistics-based detection algorithms.
Funding
National Key Research and Development Program of China (2018YFB1801904); Key Program of National Natural Science Foundation of China (61631018); Key Research Program of Frontier Science, Chinese Academy of Sciences (QYZDY-SSW-JSC003).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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