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Abstract
We propose and experimentally demonstrate an underwater wireless optical communication (UWOC) system using a 520-nm laser diode (LD) and 32-quadrature amplitude modulation (32-QAM) single carrier signals. To mitigate the inter-symbol interference (ISI), a frequency domain equalizer combined with a time-domain decision feedback noise predictor is employed at the receiver. However, this structure cannot apply channel coding conjunctively. Therefore, an interleaver/deinterleaver pair is applied to handle the decoding delay, and thus systematic Reed-Solomon (RS) code can provide reliable feedback signals. With a 3-dB bandwidth of 200 MHz, the proposed system with the frequency domain equalization and noise prediction (FDE-NP) scheme can achieve a maximal net data rate of 3.48 Gbps, which is 17.2% higher than that of orthogonal frequency division multiplexing (OFDM) scheme. At a net data rate of 3.31 Gbps, we have successfully achieved a transmission distance up to 56 m. To the best of our knowledge, this is the first time to employ FDE-NP in UWOC where OFDM conventionally plays a prevailing role for high-speed transmission.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
With the increasing depletion of land resources, how to explore the ocean, with a great reserve of resources, has gradually become a hot topic. High-speed and long-distance underwater wireless communication is an essential requirement in underwater activities including the submarine exploration and seafloor monitoring. The most widely used underwater acoustic communication and radio frequency (RF) communication suffer from a low data rate and a limited transmission range, respectively [1,2]. Underwater wireless optical communications (UWOCs) with blue and green light have drawn more and more attention, in recent years, additionally, UWOC with a higher speed and longer transmission distance have been pursued by researchers [3–13]. In 2016, a 1.5-Gbps non-return-to-zero on-off keying (NRZ-OOK) UWOC link through a 20-meter underwater channel was demonstrated [3]. In the same year, a UWOC system employing a two-stage injection-locked 405 nm-laser with a 3-dB bandwidth of 5.4 GHz was firstly proposed and achieved a data rate of 9.6 Gbps over an 8-m underwater channel [4]. Over a 5-m air channel and a 21-m water channel, a 5.5-Gbps transmission with a power loading scheme was achieved in [5]. Subsequently, a low-power green laser of 520 nm was employed to implement a UWOC link at 2.7 Gbps over a 34.5-m channel [6]. By using red, green and blue (RGB) wavelength division multiplexing (WDM), a 9.51-Gbps orthogonal frequency division multiplexing (OFDM) UWOC system over a 10-m fresh tap water channel [7] and a 9.7-Gbps OOK UWOC system over a 2.3-m tap water channel [8] have been demonstrated, respectively. A 500-Mbps NRZ-OOK UWOC system with the transmission distance up to 100 m and attenuation coefficient measured to be about 0.05 m-1 was reported in [9]. Recently, the authors in [10] pioneered the application of probabilistic shaping (PS)-quadrature amplitude modulation (QAM)-OFDM in UWOC and realized a net data rate of 12.64 Gbps at a distance of 35 m.
Due to its simplicity, OOK is one of the most popular modulation formats in UWOC [14]. Nevertheless, the inter-symbol interference (ISI) induced by limited device bandwidth and multi-scattering [15,16] restricts the system capacity. Simple modulation schemes are gradually unable to satisfy the increasing needs of future networks that require high-speed transmissions. Advanced modulation formats with higher orders including pulse amplitude modulation (PAM) and OFDM have attracted the attention of researchers worldwide [17–19]. OFDM offers the advantages of low complexity and high spectral efficiency and is the optimal solution for ISI when applying minimum mean square error (MMSE) criteria [20]. However, the deployment of OFDM in UWOC faces a serious challenge of large peak to average power ratio (PAPR), hence the performance will be severely degraded by the nonlinearity of the system [21]. For this reason, single carrier with frequency domain equalization (SC-FDE) is a promising alternative to OFDM. By applying the Nyquist filter, SC-FDE can have a similar structure, complexity and spectral efficiency to OFDM, while have a smaller PAPR due to its single carrier characteristic [21,22]. In SC-FDE, the inverse fast Fourier transform (IFFT) and fast Fourier transform (FFT) are both located at the receiving end, which can reduce the transmitter complexity and potentially improve the battery life of mobile transmitters such as autonomous underwater vehicles (AUVs) and unmanned ships. To further improve the performance of single carrier system with linear frequency domain equalization, a hybrid frequency domain equalization with time domain nonlinear decision feedback equalization (FDE-DFE) was proposed. FDE-DFE schemes are used to eliminate the ISI and reduce noise enhancement [23,24]. However, the symbols after decision are highly unreliable at low signal-to-noise ratios (SNRs), which may induce the performance degradation and error propagation [25]. Therefore, by further combining channel coding and feedback equalization, a frequency domain equalization with noise prediction (FDE-NP) scheme was proposed to improve the signal reliability [26–28].
In this paper, single carrier scheme is adopted as a promising alternative to OFDM due to its low PAPR. Considering that more severe ISI will be induced in order to achieve the same spectral efficiency as OFDM, a cascade FDE-NP structure is applied for efficient equalization. A block interleaver/deinterleaver pair is used to handle the decoding delay and thus improves the reliability of the feedback signals. As far as we know, this is the first time in UWOC that feedback equalization is combined with channel coding to provide reliable feedback signals. The simulation and experimental results show that FDE-NP has a better performance than FDE and FDE-DFE. Due to its low PAPR and high equalization efficiency, single carrier with FDE-NP scheme performs better than OFDM scheme with similar spectral efficiency. The experimental results show that, with a 3-dB bandwidth of 200 MHz, FDE-NP scheme can achieve a maximal net data rate of 3.48 Gbps, which is 17.2% higher than that of OFDM scheme. Furthermore, with the proposed system, we demonstrate a 56-m transmission with a net data rate of 3.31 Gbps.
The rest of the paper is organized as follows. Section 2 introduces the principle of FDE-NP. In Section 3, we describe the proposed single carrier system. The experimental results of the proposed system are presented and analyzed in Section 4. Finally, Section 5 concludes the paper.
2. Principle of FDE-NP
The receiver structure of the conventional FDE-DFE for coded systems is shown in Fig. 1(a) [28]. The structure can be divided into three cascaded parts, namely frequency domain feedforward linear equalizer, time domain nonlinear feedback equalizer and decoder. After IFFT, the output of the frequency domain equalizer will be
where ${\textbf s} = {[{s_0}\textrm{ }{s_1}\textrm{ } \cdots {s_{N - 1}}]^T}$, and ${{{{\textbf F}^H}} / N}$ performs IFFT operation. ${{\textbf G}_{FF}}$ is the tap coefficient of the frequency domain feedforward equalizer. ${{\textbf Y}_K}$ is the received signal in the frequency domain. In the following content, capital letters are always used to represent entities in the frequency domain, and lowercase letters are used to represent entities in the time domain.Then, the input signal of the decision module is
where ${\textrm{g}_{F{B_\textrm{m}}}}$ for $m = 1, \cdots ,B$ is the tap coefficient of the time domain feedback equalizer with B being the tap number of the equalizer. ${\hat{x}_n}$ is the hard decided symbol.Due to the decoding delay (for example, the trace back length of convolutional codes using Viterbi decoder or the block size of the block codes), the decoded signal cannot be applied directly to the feedback equalizer in time. The signals are sent to the decoder after the feedback equalizer. Once encountering the situation of low SNR, unreliable signals passing through the feedback filter will cause error propagation, which may bring a large number of error bits to exceed the capacity of decoder and severely degrade the system performance.
We adopt the structure with a linear feedforward frequency domain equalizer, a time domain noise predictor and a block deinterleaver as proposed in [27], shown in Fig. 1(b). The signal processing in the frequency domain equalizer is similar to Eq. (1), except that a deinterleaver is added. ${{\textbf W}_k}$ are the tap coefficients of the frequency domain feedforward equalizer in FDE-NP. To deal with the decoding delay, a simple block deinterleaver is applied to rearrange the order of the received symbols. The output symbols from IFFT are written row-by-row into the deinterleaver and read out column-by-column. After that, two adjacent symbols in the time domain will be separated by a distance of deinterleaver column length. If the distance of the two adjacent symbols is larger than the decoding delay, the decoded reliable signals can be fed back to cancel the ISI in the time domain. Since the symbols in the first column cannot benefit from the feedback, this column is filled with known symbols to further mitigate the error propagation. Since both ISI and noise can be regarded as distortion term, the noise predictor is used to predict the distortion of the current symbol according to the distortion part of the previous decided symbols and then feedback to remove it.
The detailed derivation of the tap coefficients of FDE-DFE and FDE-NP can be found in [24] and [27], respectively. Another advantage of FDE-NP is that the feedforward frequency domain equalizer and the feedback equalizer are independently designed, which makes it easier to change the tap number of the feedback equalizer, while in FDE-DFE the two equalizers are jointly designed. Therefore, with FDE-NP, it is convenient to obtain the tradeoff between complexity and performance by only changing the order of the noise predictor. Unlike in [27], in this paper, systematic Reed-Solomon (RS) code instead of convolutional code is selected for error correction. The systematic code consists of information bits and check bits. The decoder can correct the errors in the information bits and the check bits. The post-decoded information bits and check bits can be remapped to symbols for feedback without recoding. The post-decoded information bits are used for bit error rate (BER) calculation.
3. Experimental setup
The schematic diagram of our proposed single carrier-based UWOC system is shown in Fig. 2(a). The signal processing is operated offline in MATLAB, as depicted in Fig. 2(b) and Fig. 2(c). At the transmitter, a pseudo random binary sequence (PRBS) was generated and then encoded by a systematic RS (15,11) encoder over Galois field GF(24). The encoded bits were mapped to 32-quadrature amplitude modulation (32-QAM) symbols and reordered by a 12${\times} $84 block interleaver. Because of the excellent property with constant amplitude zero autocorrelation (CAZAC) in both time domain and frequency domain, four identical Chu sequences with a length of 512 were used for synchronization and channel estimation, followed by 150 data frames. Additionally, a Chu sequence with a length of 16 was added to the beginning of each data frame as a cyclic prefix (CP) to mitigate both precursor ISI and postcursor ISI. Each data frame contained 1024 symbols and the FFT size was 1024. The signal was up-sampled by 5 times and reshaped using a root-raised cosine (RRC) filter with a roll-off coefficient of 0 and a length of 50, which can assure that the spectral efficiency of the single carrier signal equalled to that of OFDM. The real part and imaginary part of the signal were multiplied by a sine carrier and a cosine carrier with the same frequency, respectively, to realize up-conversion. The carrier frequency was the sum of the frequency gap near zero frequency and half of the signal bandwidth. The transmitted single carrier signal was loaded to an arbitrary waveform generator (AWG) (Tektronix AWG70002A, 5 GSamples/s), and the signal amplitude was adjusted by a 25-dB amplifier (AMP) (Mini-Circuits ZHL-6A-S+) and a variable electrical attenuator (VEA). The signals combined with a DC bias were injected to a 520-nm laser diode (LD) (PL-520). The 7-m water tank was filled with tap water. Mirrors (Thorlabs BB2-E02) were attached to the inner sides of the tank to reflect the optical signals. At the receiver, focused by a lens, the optical signals were detected by an APD (APD210, 1 GHz) and recorded by a mixed-signal oscilloscope (MSO) (Tektronix MSO 71254C, 6.25 GSamples/s). The received signals were resampled to 5 GSamples/s and processed in the reverse order to the transmitter. In view of convenience, the parameter settings are listed in Table 1. Equalization methods for single carrier signals including FDE, FDE-DFE and FDE-NP were adopted here. The tap number of the feedback equalizer was set to 5. For comparison, OFDM signals with the same channel coding and interleaving and without bit and power loading were also employed in the experiment.
Fig. 2. (a) Experimental setup of the proposed single carrier-based communication system. (b) Signal processing at the transmitter. (c) Signal processing at the receiver.
Table 1. Parameter settings in the experiment
4. Results and discussion
Figure 3 illustrates the normalized frequency response of the proposed system. The 3-dB bandwidth is about 200 MHz. To verify the feasibility of the algorithm, the measured frequency response was used for simulation. The signal bandwidth was set to 1 GHz. Due to the existence of low-frequency noise induced by the laser diode, the frequency gap near zero frequency was set to 100 MHz. OFDM signals were equalized using MMSE. The simulation results are depicted in Fig. 4(a). The SNR is defined as the ratio of the signal power to the noise power, where the noise bandwidth is equal to the signal baud rate. Since nonlinear effects are not considered here, with RRC bringing additional ISI, FDE scheme has a worse performance than OFDM scheme. In the case of low SNR, due to severe error propagation, the BERs of FDE-DFE and FDE-NP schemes are higher than that of OFDM scheme. At higher SNRs, with an additional efficient feedback equalizer, FDE-DFE and FDE-NP schemes perform better than OFDM scheme. The SNR required by FDE-NP scheme is about 0.6 dB, 1.4 dB and 3.8 dB less than that of FDE-DFE, OFDM and FDE schemes, respectively. Figure 5 depicts the bit error distribution of different equalization methods at an SNR of 19 dB. With ideal feedback, assuming that all the feedback symbols are correct, FDE-NP can eliminate the error propagation and has only some individual error bits, as shown in Fig. 5(a). However, without ideal feedback, the individual error bits are mapped to wrong QAM symbols and some of them will bring error propagation after feedback, as shown in Fig. 5(b). For the FDE-DFE scheme, shown in Fig. 5(c), with unreliable feedback signals, the error propagation is more severe than FDE-NP scheme, leading to a higher BER.
Fig. 4. Simulation results of 1 GHz signals through the measured frequency response (a) without amplifier limitation and nonlinear clipping, (b) with amplifier limitation and nonlinear clipping.
Fig. 5. Bit error distribution of (a) FDE-NP with ideal feedback, (b) FDE-NP, and (c) FDE-DFE schemes.
Furthermore, the limitation of the amplifier and the nonlinear clipping are considered. Due to the high PAPR, with the same signal peak-to-peak amplitude, the received OFDM signal has a lower SNR compared with single carrier signal. The simplified double-sided clipping can be expressed as Eq. (4) to meet the dynamic range constraint.
The simulation results with amplifier limitation and nonlinear clipping are depicted in Fig. 4(b). The nonlinear effects have little effect on single carrier signals, however OFDM scheme suffers from performance degradation due to its high PAPR characteristics. In this case, FDE scheme performs better than OFDM scheme. The SNR required by FDE scheme is about 2.3 dB less than that of OFDM scheme.
After the simulation, the feasibility of the proposed system is experimentally proved. Finding the optimal operating state is a significant step in the experiment. Note that when the incident optical power is too high, APD will be saturated. Therefore, a tunable optical attenuator (GCC-3030) was placed in front of the laser to adjust the optical power so as to maximize the peak-to-peak value of the received electrical signal. By adjusting the bias current and the attenuation value of the VEA, Fig. 6 shows the corresponding error vector magnitudes (EVMs) of 1-GHz single carrier signal employing FDE-NP with ideal feedback under different operating states of the laser. With a small bias current, the lower part of the signal falls outside the linear range of the laser, resulting in a large EVM. In this case, we can find a better performance with a larger attenuation value. As the bias current increases, the influence of nonlinear distortion decreases and the EVM performance is improved. However, with the further increase of the bias current, the EVM performance starts to decline due to the decrease of extinction ratio, and a smaller attenuation value results in a better performance. Therefore, to achieve the optimum operating state, in all the following experiments, for single carrier signals, the bias current and attenuation value of VEA were fixed at 70 mA and 6 dB, respectively. By the same way, for OFDM signals, the bias current and attenuation value of VEA were fixed at 70 mA and 5 dB, respectively. Under these parameters, the transmitted optical power of single carrier signals and OFDM signals were both 12.5 dBm (17.8 mW). The optical power was measured using an optical power meter (Thorlabs PM200) with an active detector area of $9.7mm \times 9.7mm$.
Fig. 6. EVM versus bias current of the laser with different attenuation values of VEA with 1-GHz single carrier signal employing ideal feedback-FDE-NP.
To show the superiority of single carrier signal with low PAPR compared with OFDM signal, the BER under different peak-to-peak amplitude adjusted by the attenuation value of VEA is depicted in Fig. 7. The bias current was fixed at 70 mA. When the attenuation value of VEA is around 0 dB, both single carrier signal and OFDM signal suffer from severe nonlinear clipping, making the BERs close to 0.1. With the decreasing of the signal amplitude, the BER of single carrier signal is improved below the FEC threshold of $3.8 \times {10^{ - 3}}$, while the BER of the OFDM signal is still higher than the FEC threshold due to the low SNR induced by amplifier limitation.
To demonstrate the achievable data rate of the proposed single carrier-based UWOC system, we have experimentally studied the BER performance of different equalization methods under different signal bandwidths. The tunable optical attenuator was also employed here to maximize the peak-to-peak value of the received electrical signal, and the received optical power was around -8 dBm. As depicted in Fig. 8, for the BER under the FEC threshold of 3.8×10−3, the maximal achievable signal bandwidth of FDE-NP scheme is 1.05 GHz (corresponding to a net data rate of 3.48 Gbps). Besides, FDE-DFE and FDE schemes reach maximal signal bandwidths of about 1.03 GHz and 1 GHz (corresponding to a net data rate of 3.41 Gbps and 3.31 Gbps), respectively. In real system, due to the nonlinear effect, the disadvantages of large PAPR of OFDM signal begin to appear. As a result, different from the previous simulation results, FDE scheme performs better than OFDM scheme, which only achieves a maximal signal bandwidth of 0.90 GHz (corresponding to a net data rate of 2.97 Gbps). Compared with OFDM scheme, FDE-NP scheme has the advantages of low PAPR and an additional feedback equalizer, leading to a 17.2% improvement in achievable data rate. To further improve the BER, linear digital pre-equalization was employed here to compensate for the high frequency distortion. The bandwidth of the single carrier signal was set to 1 GHz. As the pre-equalization slope increases from 0 to 6 dB/GHz, the BER decreases from 2.25×10−4 to 4.73×10−6, as shown in Fig. 9. Figure 10 shows the spectra of received single carrier signals with and without pre-equalization. It is obvious that after pre-equalization, the spectra of the received signals become flatter. However, an excessive increase in pre-equalization slope will suppress the low frequency part of signal and decrease the SNR, resulting in an increase of BER. For different bandwidths and modulation formats, the optimal pre-equalization slopes are not exactly the same. For simplicity, no pre-equalization was used in subsequent experiments.
Fig. 9. BERs of 1-GHz single carrier signal employing FDE-NP with different pre-equalization slopes.
Fig. 10. The spectra of transmitted signal (a) without pre-equalization and (b) with pre-equalization. The spectra of received signal (c) without pre-equalization and (d) with pre-equalization.
In order to evaluate the longest transmission distance of our proposed system, it is necessary to determine the minimum required received optical power with the BER under the FEC threshold. A tunable optical attenuator was used to adjust the received optical power. We present the BER performance as a function of received optical power after a 7-m transmission as shown in Fig. 11. The signal bandwidth was 1 GHz. It can be seen that the minimum required received optical power of FDE-NP scheme is about -11.6 dBm, which is 0.4 dB and 3.6 dB lower than that of FDE-DFE and FDE schemes, respectively. At the same BER, FDE-NP scheme requires lower received optical power, which means that it can achieve a higher data rate or a longer distance. It is worth noting that the BER of OFDM scheme is higher than FEC threshold at any received optical power. Based on the above results, the system can achieve the best performance with a received optical power of -6 dBm. When the received optical power reaches -5 dBm, the performances of all methods are reduced due to the severe nonlinear effect caused by detector saturation.
With the above-measured results, it is feasible to evaluate the maximum transmission distance with FDE-NP scheme. We first measured the received optical power with different transmission distances, as shown in Fig. 12. In order to mitigate measurement error, a first-order function is used to fit the measured values. According to the fitting curve, the attenuation coefficient of water in this experiment is about 0.38 dB/m. The measured received optical power at 49 m and 56 m are -8.53 dBm and -11.50 dBm, respectively. Therefore, as depicted in Fig. 13, a distance of 56 m is achieved at a signal bandwidth of 1 GHz (corresponding to a net data rate of 3.31 Gbps). With a single channel, the proposed system achieves a capacity-distance product of 185.36 Gbps-m. For the transmission distances below 42 m, corresponding to the received optical powers higher than -6 dBm, the received optical powers were fixed to about -6 dBm by the tunable optical attenuator. Due to alignment errors, there is a little fluctuation in BERs at different distances below 42 m. For the signal with a bandwidth of 1.1 GHz, due to the large ISI, the BER cannot be reduced below the FEC threshold of 3.8×10−3 by adjusting the received optical power.
Fig. 13. BER of FDE-NP versus transmission distance at the signal bandwidth of 0.9 GHz, 1 GHz and 1.1 GHz.
5. Conclusion
In this paper, we propose and experimentally demonstrate a high-speed long-distance UWOC system using a low-power 520-nm LD based on single carrier scheme with 32-QAM modulation and RS (15,11) code. At the receiver, FDE-NP is employed to mitigate ISI. By applying an interleaver/deinterleaver pair, the decoded symbols can be used for feedback to improve the reliability. According to the simulation and experimental results, the FDE-NP scheme performs better than traditional OFDM, FDE and FDE-DFE schemes. With the 3-dB bandwidth of only about 200 MHz, FDE-NP scheme achieves a maximal net data rate of 3.48 Gbps, which is 17.2% higher than that of OFDM scheme. A transmission distance of 56 m is also obtained with a net data rate of 3.31 Gbps by employing FDE-NP. This study suggests that efficient signal processing technology requires lower SNR at the same BER, which means that it can be applied either to improve the data rate or to extend the transmission distance.
Funding
National Natural Science Foundation of China (61971378, 61671409); Guangdong Science and Technology Planning Project (2019A050503003); National Key Research and Development Program of China (2016YFC1401202, 2017YFC0306100, 2017YFC0306601); Strategic Priority Research Program of the Chinese Academy of Sciences (XDA22030208).
Disclosures
The authors declare no conflicts of interest.
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