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Abstract
We designed a photon-counting receiver system for long-distance underwater wireless laser communication at different code rate Reed-Solomon (RS) and low-density parity check (LDPC) codes. The symbol error rate (SER) performance of the LDPC and RS codes with different signal-to-noise ratios was analyzed. The effects of the background noise, pulse stretching, and frame synchronization were considered in our receiver system. A water tank experiment confirmed that the 1/2-code-rate RS (255,127) is an excellent coding strategy for communication distances in the range of 90–130 m in Jerlov II water. We constructed a communication link with a SER of 6.31 × 10−4 in a distance of 120-m distance in Jerlov II water for RS (255,127) with 256-pulse-position modulation (PPM) at bandwidth of 13.7 MHz. The maximum link loss was −136.8 dB at λ = 532 nm. The attenuation lengths Natt were 35.88, which were equal at link distances up to 249.2 m in clear ocean water (Jerlov IB water type). The photon counting receiver system can achieve a receiving performance of 3.32 bits/photon. To the best of our knowledge, this is the longest communication attenuation length ever reported under 1 mJ single pulse energy for a narrow field-of-view photon-counting receiver system.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High-sensitivity optical communication has recently received significant interest in the field of free-space optics, owing to its potential to provide cost-efficient, high-rate communications with reduced size, weight, and power constraints [1–3]. Underwater wireless communication has the capacity to increase data rates beyond those practically achievable, with link lengths potentially extending to hundreds of meters [4]. However, owing to the strong absorption and scattering processes, a water channel is a very challenging link for long-distance and high-data rate laser communication [5].
Compared to atmospheric or space-based wireless optical communication, underwater communication faces certain special challenges. The absorption spectrum of water determines that the communication wavelength needs to be in the blue or green range, in contrast to the infrared wavelengths used in air or space links [6, 7]. Unfortunately, light pulses propagating in water suffer from high levels of attenuation by both bulk absorption and scattering mechanisms [8]. The main problem for long-distance, high-data rate underwater laser communication systems is the degradation of communication as a result of absorption and scattering due to water, dissolved substances, and suspended particulates [9].
Photon-counting receiver architectures, exhibiting a great potential to achieve an ultimate, multiple bits per photon sensitivity, have been previously proposed [10]. However, the high sensitivity of a photon-counting detector can also result in the receiver being sensitive to the background noise, and for long distance underwater wireless laser communication, the signal light is reduced to the photon level and the receiver suffers from shot noise. Considering these difficulties and challenges for a photon-counting receiver, an appropriate solution is to use the photon-counting receiver with high M-ary PPM using forward error correction (FEC), suitable for high-rate background-limited links [11].
Researchers at the Fudan University proposed a laser communication system, and it was experimentally demonstrated that it can achieve a distance a of 34.5 m with a data rate of 0.15 Gbps and an attenuation coefficient of ∼ 0.44dB/m. This result is equivalent to a 90.7 m distance communication [12]. The Japan Agency for Marine-Earth Science and Technology (JAMSTEC) have completed an underwater wireless optical communication of 20 Mbps in a communication distance of 120 m in 700 m deep ocean water [13]. In these studies, the type of water was close to the type of Jerlov IB water. In order to achieve the ultimate performance of long distance underwater laser communication, we set up a water tank experiment using 256-PPM with different code rates using RS and LDPC codes. The experiment focused on the most fitting encoding strategy for long distance underwater communication using a photon-counting receiver system, and studied the ultimate performance of the narrow field-of-view (FOV) photon-counting receiver system.
2. Theoretical analysis
Photon-counting receiver systems have been demonstrated with PPM to achieve high sensitivity. In M-PPM, a symbol representing log2(M ) bits of information is transmitted by sending a single pulse in one of the M transmission slots [14]. When coupled with an average-power limited transmission laser, a near-theoretical communication rate can be achieved by increasing the size M of the symbol [15]. Lasers can operate under high peak power and low average power with PPM. For underwater laser communication systems, the received signal photon counts correspond to the transmitted single laser pulse energy. If the intensity of the optical pulses at the receiver is at a single-photon level, the probability of single optical pulse photon counts can be determined from a Poisson distribution associated with the average number of photons per pulse incident at the detector. The mean values of signal photon counts in one symbol ns cannot be detected directly due to the effect of the noise photon counts. If we denote the mean values of the noise photon counts in one symbol by nb, then n1 represents the photon counts in symbol “1” and n0 represents the average photon counts in symbol “0”. Counts ns can be calculated by ns = n1 − n0 and nb = n0. We choose 256-PPM for the communication system, and each pulse represent 1 byte of information. The symbol error rate (SER) and signal-to-noise ratio (SNR) equations can be expressed as
where nt denotes the threshold photon number for demodulation and M = 256. For a received photon count n corresponding to a transmitted symbol, the log likelihood ratios (LLR) are [9] The LLR generates hard decisions: for each symbol, if LLR ≥ 0, the corresponding hard decision is “1”, and this symbol is selected for the pulse position of 256 symbols. Otherwise, the hard decision is “0”. This hard-decision threshold nt can be expressed asA balance between the communication rate and the code rate is required in the communication system. A low code rate can result in good SER performance; however, it also limits the communication rate. The code rate can be expressed as
where k denotes the information symbol length and n denotes the code length.3. Design considerations for the photon-counting communication system
Owing to the variability in the water channel, the underwater communication system needs to be able to handle the effects of laser pulse stretching, background noise, and frame synchronization.
3.1. Laser pulse stretching
Laser pulse stretching affects the design of the slot time. The effect of the laser pulse stretching depends on the communication distance and the clarity of water. Monte Carlo simulation is one of the numerical methods used in underwater laser communication research to study underwater channel links [16–18]. We used a Monte Carlo method to simulate the characteristics of a laser pulse during a long distance underwater transmission. The steps of the simulation were presented in our previous work [19]. We set the laser wavelength to 532 nm, the single-pulse energy to 1 mJ, the laser spot as a Gaussian distribution with a radius (full width at half maximum (FWHM)) of 1 mm, the laser divergence angle to 2 mrad, the laser pulse width (FWHM) to 10 ns, and the number of simulated photon packets to 2.67 × 107. Each packet contained 108 photons (each photon had an energy of 3.74 × 10−19 J at a wavelength of 532 nm; thus, the total energy can be calculated as 2.67 × 107 × 108 × 3.74 × 10−19 J = 1 × 10−3J). The water channel parameters included the attenuation coefficient c, the scattering albedo ω, and we applied the Jerlov water channel parameters. The detailed values of c and ω for the Jerlov IB, II, and III water channels are shown in Table 1. The simulation results of the pulse stretching are shown in Fig. 1. For an underwater communication link with a communication distance less than 140 m, the FWHM of the received laser pulse is less than 95 ns in the Jerlov IB, II, and III water channels. The pulse stretching requires a system slot time exceeding 95 ns to avoid inter-symbol interference. The pulse stretching limits the bandwidth of the receiver system, as shown in Fig. 1. In this paper, we focus on the receiver performance. The maximum communication rate is limited by the communication bandwidth. In this water tank experiment, the repeat frequency of the laser was 1.5 kHz, the communication rate was limited by the laser repeat frequency, the communication bandwidth for receiver was limited by the pulse stretching. In the following analysis, we focus on the communication bandwidth, which determines the ultimate performance of receiver.
Table 1. Jerlov IB, II, and III water channel parameters.
3.2. Frame structure
The transmitted data was organized into frames. In order to mark the start of the frame and to achieve an easier synchronization, the two special frame headers were fixed at the beginning of the frame, while their pulse separation was greater than the maximum 256-PPM separation. The receiver can distinguish the start of the frame from the data sequence by using this method. The frame header is followed by the frame estimation sequence (FES), which is a fixed sequence shared by the transmitter and receiver. The receiver uses the FES to determine the n0 and n1 after the receiver finished the frame synchronization. The FES is followed by the data sequence and encoded by RS or LDPC code. We considered eight different code rate strategies for the RS and LDPC codes for underwater photon-counting links to obtain the coding gain of different code rates. The RS (255,127), RS (255,171), RS (255,191), RS (255,203), LDPC (2304,1152), LDPC (2304,1536), LDPC (2304,1728), and LDPC (2304,1920) codes programmed in the encoder and decoder can be selected and changed during the experiment.
According to the simulation results shown in Fig. 1, we set the slot time to 100 ns. Thus, using a 100-ns slot time, the inter-symbol interference introduced by the pulse stretching can be avoided. The 256-PPM timing sequence is shown in Fig. 2. As the PPM timing sequence has to be compatible with the repeat frequency range of the pulse laser, the repeat frequency of the laser is 1.5 kHz. Therefore, we set the silence time to 650 µs, and combining it with the 100 ns slot time, the laser was operating in the interval between 1.427 kHz (the previous symbol position present at the first symbol and the current symbol position present at the last symbol) and 1.538 kHz (the previous symbol position present at the last symbol and the current symbol position present at the first symbol). Finally, each PPM sequence can achieve the operation of the solid-state laser under its repeat frequency. The two fixed separation were set to 680 µs as frame head and followed by ten fixed pattern as FES for the receiver to finish the frame synchronization and channel estimation. The following ten pulses were FES and the next 255 pulses were data sequence. The frame structure is shown in Fig. 3
3.3. Transmitter and receiver parameters
The underwater laser communication system is shown in Fig. 4. The message from the computer was sent to a field-programmable gate array (FPGA) through a universal asynchronous receiver-transmitter (UART). The FPGA encoded the message and modulated the laser by 256-PPM. The transmitter parameters are shown in Table 2. The laser pulse suffers from attenuation and stretching due to water channel. The receiver is consisted of a single-photon detector (SPD), FPGA, and computer.
Table 2. Transmitter parameters.
Table 3. Receiver parameters.
The high sensitivity of the photon-counting receiver with a large FOV induces increased background counts coupled into the receiver. The time-of-flight (TOF) of photons refracting or scattering from the water channel is longer than the TOF of photons with a direct path from the transmitter to the receiver. The distribution of the TOF of photons in an individual pulse widens as the FOV of the receiver is increased. If the distribution of the TOF becomes sufficiently wide, the instrumental response of the system can limit its the bandwidth. [8]
In order to address the problems mentioned above, the full FOV of the photon-counting receiver system was limited to 52 mrad. A Hamamatsu H11870-02 photomultiplier tube was used as an SPD. The FPGA detected the TTL edge from the SPD and finished the demodulation and decoding. The receiver consists of a Xilinx Spartan 6 FPGA board. The output of the SPD was DC-coupled low-voltage TTL. The FPGA sampled the SPD output 400 Msamples/s. The parameters of the receiver are shown in Table 3
3.4. FPGA functions
The FPGA performed frame synchronization, demodulation, and decoding, and continuously processed the frame data in real time. Fig. 5 shows a block diagram of the FPGA used to perform these functions. The duration of the SPD output pulse was 9 ns and the dead time was 3.5 ns. The generated TTL duration was significantly longer than the sampling period of 2.5 ns of the FPGA. Therefore, the FPGA registered the SPD events as the rising edges of the SPD output.
In any communication system it is crucial that the transmitter and receiver share a common timing reference, as the two remote clocks operate at slightly different frequencies even if both of them are atomic clocks. The clocks on the transmitter and receiver need to be phase-locked and share a common frame header pattern, which marks the key positions at the start of each frame. In our receiver, the FPGA uses an equalizer to acquire the best matching symbol, which can perform frame synchronization and pre-demodulation. The equalizer accumulates the photon counts in a slot time. Hence, the width of equalizer was 100 ns. First, the equalizer needs to finish the frame synchronization. The slide step of the equalizer was 2.5 ns, and it selected the best matching position and the photon counts in every 680 µs. The equalizer function is shown in Fig. 6. When two frame heads were matched, the frame synchronization was finished. The synchronization error was less than 2.5 ns. Then, the equalizer needed to estimate the channel condition. The equalizer maintained the same 100 ns width, but changed the slide step to 100 ns (equals to slot time), and it selected the best matching position and the photon counts in every 675.5 µs(650 µs+255×100 ns). The second step was repeated until the end of the FES, which activated the FPGA to finish the channel estimation, obtain the n0, n1, and calculate the decision threshold nt. Finally, when the channel estimation was finished, the equalizer used the threshold nt to judge the symbol position for the PPM sequence and sent the location and photon counts information to a first-in-first-out (FIFO) buffer. When the FIFO was full, the microblaze read the data from it, and sent the demodulated message to the decoder. After the decoder finished the decoding, the microblaze received the decoded message and transmitted them to the computer via an UART.
4. Water tank experiment
4.1. Description of the experiment
A diagram of the water tank experiment is shown in Fig. 7. Firstly, we elevated the lift platform to the water surface, then installed the transmitter on the platform and connected the cable between vehicle-1 and the transmitter. As the laser signal is hard to align with the receiver due to the extremely high attenuation in water, we adjusted the initial transmission direction to align it with the water surface. Then, the lift platform with the transmitter was lowered to the bottom of the water tank. Vehicle-1 was located above the transmitter and standing still during the experiment. In order to ensure the vertical alignment of the receiver with the transmitter, we installed the receiver to a cushion block, with the same height as the lift platform. The supporting frames for the transmitter and the receiver also had the same height. In order to ensure the horizontal alignment, the transmitted direction scan along the horizontal direction, stopped scanning when the receiver received the maximum energy. During the experiment, we moved vehicle-2 to change the communication distance. To obtain the specified distance, we stopped vehicle-2 and lowered the receiver to the bottom of the water tank to test the performance of the communication. Different code rates of RS and LDPC codes were tested in the same communication distance. Then, vehicle-2 was moved to another position to change the communication distance and the above steps were repeated until the communication link was lost. Here, the lost link is defined as the state when the receiver can not receive a full correct frame.
4.2. Link loss
Owing to variability of the underwater channel, the effect of the link loss on the communication system needs to be considered. The clarity of water can significantly affect the performance of the underwater communication. The link loss due to water absorption and scattering is determined by the Beer–Lambert law [20,21]:
where a and b represent the absorption and scattering coefficients, respectively, c is the attenuation coefficient, and z is the distance. In order to obtain the attenuation coefficient c of the experimental water tank, we used an absorption-attenuation spectra (ACS) to acquire the attenuation coefficients c = 0.299m−1. The quality of water was close to that of the Jerlov II water. However, the Beer–Lambert law does not consider the scattering effects. Therefore, we used a Monte Carlo simulation to simulate the received signal. According to the Jerlov II water parameters in Table 1, the parameters in Table 2, Table 3, and the pulse stretching simulation result shown in Fig. 1, we can simulate the received photon number for our system. The results are shown in Table 4.Table 4. Simulated received photon number and link loss.
4.3. Comparison of simulation and experimental results
The received photon counts per symbol in different communication distances are shown in Fig. 8. The average received photon counts in symbol “1” n1 for distances of 90 m, 100 m, 110 m, 120 m and 130 m are 4.91, 3.94, 3.20, 2.41, and 1.68, respectively. The average received photon counts in symbol “0” n0 for all distances is 0.87. The difference between the simulated received photon number and experimental received photon number results from the SPD working mechanism, including the 80 MHz count rate, which enables the SPD to detect one photon at 12.5 ns, while the SPD can not distinguish the photon numbers at one acquisition period. Combining this statistical result with Eq. (4), we obtained the threshold photon counts nt for the previously mentioned five distances as 2.33, 2.03, 1.82, 1.51, and 1.23, respectively. The results are shown in Fig. 9. According to Eq. (2), the SNR of the photon-counting receiver system at distances of 90 m, 100 m, 110 m, 120 m, and 130 m are 6.66 dB, 5.47 dB, 4.41 dB, 2.48 dB, and −0.20 dB, respectively.
4.3.1. Simulation results
The performance of the SER can be improved by using a channel coding technology, allowing the communication system to receive less power for the same target SER. In this study, we focus on RS and LDPC codes. According to the result of the water tank experiment, n0 for all distances remained at a constant value of 0.87. Therefore, we set n0 to 0.87. The value of n1 was changed to vary the SNR in the range of 1–6 dB. The performance curve of the non-coded SER for 256-PPM can be obtained from Eqs. (1) and (2). Combing RS (255,127), RS (255,171), RS (255,191), and RS (255,213) with 256-PPM, we can obtain the theoretical SER performance for a photon-counting receiver system by simulation. The results are shown in Fig. 10. The SER performances of LDPC (2304,1152), LDPC (2304,1536), LDPC (2304,1728), and LDPC (2304,1920) with 256-PPM are shown in Fig. 11.
The results reveal that the SER performance is related to the SNR and code rate. For 256-PPM with a 5/6 code rate, LDPC (2304,1920) has better performance than RS (255,213) for SNR ≤ 3dB; however, the SER curve of the RS codes exhibits a better performance than the LDPC codes for SNR ≥ 3.5dB. For a 3/4 code rate, LDPC (2304,1728) has better performance than RS (255,191) for SNR ≤ 2.5dB; however, when the SNR exceeds 3 dB, the SER curve of the RS codes exhibits a better performance than the LDPC codes. For a 2/3 code rate, LDPC (2304,1536) has better performance than RS (255,171) for SNR ≤ 2.5dB; however, when the SNR exceeds 3 dB, the SER curve of the RS codes exhibits a better performance than the LDPC codes. For a 1/2 code rate, RS (255,127) has better performance than LDPC (2304, 1536) for SNR ≥ 1dB.
4.3.2. Results of the water tank experiment
We tested the different code rates of RS and LDPC codes with 256-PPM for different communication distances. All encode strategies were tested for more than 1 × 107 symbols. For RS codes, we tested RS (255, 127), RS (255, 171), RS (255, 191), and RS (255, 213). The SER performances of the RS codes are shown in Fig. 12. For LDPC codes, we tested LDPC (2304, 1152), LDPC (2304, 1536), LDPC (2304, 1728), and LDPC (2304, 1920). The SER performances of LDPC codes are shown in Fig. 13. For the 90-m distance communication, the SNR was 6.66 dB. The SER of the 1/2, 2/3, 3/4, and 5/6 code rate LDPC and RS codes were all less than 1 × 10−6. Due to the high SNR in the distance of 90 m, all encoding strategies exhibit excellent performance. For the 100-m distance communication, the SNR was 5.47 dB. The SER of the 1/2, 2/3, 3/4, and 5/6 code rate RS codes and 1/2, 2/3 code rate LDPC codes were all less than 1 × 10−6, while the SER of the 3/4 code rate LDPC code was 9.26 × 10−6 and the SER value of the 5/6 code rate LDPC code was 8.3 × 10−5. For the 110-m distance communication, the SNR was 4.41 dB, the SER of the 1/2, 2/3, 3/4, and 5/6 code rate RS codes were < 1 × 10−6, 9.3 × 10−6, 4.21 × 10−5, and 8.62 × 10−5 respectively. The SER values of the 1/2, 2/3, 3/4, and 5/6 code rate LDPC codes were 4.31 × 10−6, 5.17 × 10−5, 5.55 × 10−4, and 4.61 × 10−3, respectively. The results for the distance of 100-m and 110-m reveal that the RS codes with 256-PPM exhibit better SER performance than the LDPC codes with 256-PPM in Jerlov II water in a distance of ∼ 100 − 110-m. For the 120-m distance communication, the SNR was 2.48 dB, the SER values of the 1/2, 2/3, 3/4, and 5/6 code rate RS codes were 6.31 × 10−4, 2.68 10−2, 6.75 × 10−2, and 8.38 × 10−2 respectively. The SER values of the 1/2, 2/3, 3/4, and 5/6 code rate LDPC codes were 7.08 × 10−3, 2.03 × 10−2, 4.31 × 10−2, and 5.13 × 10−2, respectively. These results indicate that with the decrease of the SNR, the performances of the 2/3, 3/4, and 5/6 code rate RS codes degrade, compared to those of the LDPC codes; however, the 1/2 code rate RS codes still have excellent performance. For the 130-m distance communication, as the SNR is extremely low, −0.20 dB, most encoding strategy exhibit high SER. Under this condition, the 1/2 code rate RS codes still has an SER of 0.0937. For the 2/3, 3/4, and 5/6 code rates, LDPC has better performance than the RS in short-distance communication, while the RS has better performance than the LDPC in long-distance communication.
The 1/2 code rate RS codes represent the most fitting encoding strategy among the encoding strategies we have tested. The experimental results are in agreement with the simulated analysis in Section. 4.3.1, where we summarized the SER of the 1/2 code rate RS codes, present the attenuation lengths (Natt = L×c), obtained the Jerlov IB equivalent distance by useing Eq. (6) and Table 1, determined the communication bandwidth from Fig. 1, and obtained the received bits per photon from Fig. 9. The result is shown in Table 5. The theoretical receiving limit for 256-PPM is 8 bits/photon; however, the intensity of the optical pulses at the receiver is at a single-photon level while the probability of the single optical pulse photon counts is determined from a Poisson distribution. Combining this condition with the SER requirement for underwater communication system and the dark count rate of detector, it is not possible to achieve the theoretical receiving limit.
Table 5. Communication performance of the 1/2 RS codes.
In applications such as communication between underwater vehicles and the collection of information pollution through hydrophones submerged in water, the required SER is in the range of 10−3–10−4 [22]. Table 5 reveals that the 1/2 code rate RS codes can achieve 120 m distance communication with a SER of 6.31 × 10−4 in Jerlov II water at a bandwidth of 13.7 MHz. The Natt is 35.88 and equivalent to link distances up to 249.2 m in clear ocean water (Jerlov IB water). Considering a total link loss of −136.8 dB and the experimentally obtained photon counts in symbol “1” n1 of 2.41 and the 256-PPM makes one laser pulse represent 8 bits information. Photon counting receiver system can achieve a receiving performance of 3.32 bits/photon.
5. Conclusion
We analyzed the simulated the SER performance for LDPC and RS codes with different SNRs, and designed a frame structure customized to our laser. A slot time of 256-PPM was designed according to the pulse stretching simulation. The attenuation coefficient was c = 0.299m−1. The clarity of water was close to that of the Jerlov II water. The total link loss for 120-m distance was −136.8 dB and the experimentally received photon counts in symbol “1” n1 was 2.41. In order to reduce the effects of the background noise and the waveform distortion due to the TOF, we limited the FOV to 52 mrad. An FPGA was used to perform frame synchronization, demodulation, decoding, and continuous processing of the frame data in real time. The experimental results reveal that for communication in the distance range of 90–130 m, the 1/2 code rate RS codes can be considered the most fitting encode strategy for 256-PPM in Jerlov II water.
We constructed a communication link with a SER of 6.31 × 10−4 at a distance of 120 m in Jerlov II water for RS (255,127) with 256-PPM at a bandwidth of 13.7 MHz. The Natt was 35.88 and equivalent to link distances up to 249.2 m in clear ocean water (Jerlov IB water). The photon counting receiver system can achieve a receiving performance of 3.32 bits/photon. To the best of our knowledge, this is the longest communication attenuation length ever reported under 1 mJ single-pulse energy for a photon-counting receiver system.
Funding
The National High Technology Research and Development Program of China (2014AA093301).
Acknowledgments
The authors wish to thank Xiaolei Zhu, Tingting Lu and Jian Ma for the development of laser. They also wish to acknowledge the structure design provided by Yuxin Deng, Dan Liu and Zhengyang Jiang.
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