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Abstract
Low-cost underwater wireless optical communication (UOWC) systems are attractive for high-speed connections among unmanned vehicles or devices in various underwater applications. Here we demonstrate a high-speed and low-cost UOWC system using a low-resolution digital to analog converter (DAC), a single-pixel mini-sized light-emitting diode (mini-LED), and digital pre-compensation (DPC). The enabled DPC scheme comprises digital pre-distortion (DPD), digital pre-emphasis (DPE), and digital resolution enhancer (DRE), which pre-compensate for mini-LED nonlinearity, the bandwidth limitation of the mini-LED and avalanche photodiode detector, and DAC resolution limitation, respectively. The simulation results show that the in-band signal-to-quantization noise ratio can be increased by 6.8 dB using DRE based on a 4-bit DAC. To further improve the system capacity, we tune the level of DPE in order to optimize the trade-off between the residual inter-symbol interference and signal-to-noise ratio. With the combination of optimized DPE and DRE, we obtain a 21.1% higher data rate compared with full DPE only and demonstrate the transmission of 6.9 Gb/s PAM-8 signal over a 2-m distance underwater based on a single-pixel mini-LED and 4-bit DAC. This paper reports a cost-effective UOWC system first using a low-resolution DAC and DPC, which offers a promising path toward low-cost underwater optical wireless networks.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Underwater wireless optical communication (UOWC) plays a critical role in various underwater applications, including pollution and climate monitoring, offshore explorations, and oceanography research. Driven by a high-bandwidth connection between unmanned vehicles or devices/sensors, low-cost and high-speed UOWC systems attract interest from the industry and the research community [1,2]. Compared with acoustic and radio frequency-based underwater communication systems, UOWC systems have the advantages of higher capacity and lower latency [3,4]. Light-emitting diodes (LEDs) are suitable optical sources for UOWC systems due to the advantages including low-cost, high-power efficiency, mature fabrication process, and long working life compared with laser diodes. For higher communication bandwidth, micro/mini-sized LEDs (micro/mini-LEDs) have been designed and fabricated [5–7], and high-speed UOWC systems have been demonstrated based on these high-bandwidth micro/mini-LEDs [8–10]. A 2 m UOWC system with a net data rate of 1.87 Gb/s was achieved using a single-pixel 75 $\mathrm \mu$m blue micro-LED with 1 GHz 3-dB bandwidth [8]. With more spectrally efficient higher-order modulation formats, UOWC can achieve higher data rates. Zhang et al. transmitted a net 3.55 Gb/s 4-level pulse amplitude modulation (PAM-4) signal over a 2 m underwater channel using a single-pixel 175 $\mathrm \mu$m blue mini-LED with a 3-dB modulation bandwidth of 580 MHz and a Volterra nonlinear equalizer (VNLE) [9]. We demonstrated a net 4 Gb/s UOWC system over 2 m using a single-pixel 150 $\mathrm \mu$m blue mini-LED and linear equalization, including a digital pre-emphasis (DPE) equalizer and a feedforward equalizer (FFE) [10]. Note that these previously reported high-speed UOWC systems are based on digital to analog converters (DACs) having more than 8-bit resolution. To fulfill the need for low-cost UOWC systems for potential dense and high-speed underwater connections, low-resolution DACs are more desirable for UOWC implementation.
Compared with a high-resolution DAC, a low-resolution DAC has the advantage of low-cost and low power consumption. However, it also introduces stronger quantization noise, which degrades the signal-to-quantization noise ratio at the transmitter and impedes the use of higher-order modulation formats. The digital resolution enhancer (DRE) has been proposed and used in fiber-optical communication systems to suppress the quantization noise [11–13]. A 4-bit DAC-based 64-quadrature-amplitude-modulation (QAM-64) transmission was demonstrated with digital pre-emphasis (DPE) and DRE in a bandwidth-limited channel [11]. A 4-bit DAC-based QAM-64 transmission was achieved using nonlinear digital pre-distortion (DPD) and DRE [12]. A 4-bit DAC-based 80-km direct-detection PAM-4 transmission was demonstrated by using chromatic dispersion digital pre-compensation and DRE [13]. However, there are few studies to investigate quantization noise shaping in cost-effective UOWC systems using low-resolution DACs.
In this paper, we realize a low-cost and high-speed UOWC system based on a 175 $\mathrm \mu$m single-pixel blue mini-LED and a low-resolution DAC enabled by DPC. The DPC scheme consists of DPE, DPD, and DRE. The quantization noise resulting from the low-resolution DAC is handled by DRE, which optimizes the quantization level for each data sample and leads to suppressed in-band quantization noise. Meanwhile, to overcome the limited bandwidth and nonlinearity of the light source, DPE and DPD are used as the pre-equalizer in the transmitter digital signal processing (DSP). We firstly show the performance gain of DRE for PAM-4 and PAM-8 signals with full DPE employed at the transmitter. Next, we control the level of DPE, i.e., partial DPE (p-DPE), in order to optimize the trade-off between the residual inter-symbol interference (ISI) and signal-to-noise ratio (SNR) at the receiver. By combining DRE and optimized p-DPE, we achieve a 21.1$\%$ higher data rate compared with full DPE only and experimentally demonstrate a 4-bit DAC-based UOWC system operating at 6.9 Gb/s over a 2-m underwater channel using a single-pixel LED. This paper reports the first use of DRE in a low-resolution DAC-based UOWC system, realizing cost-effective and high-speed underwater optical information delivery.
The rest of this paper is organized as follows. In section 2, we explain the principle of DPC in the transmitter DSP block. The experimental setup and DSP blocks are presented in section 3. In the first part of section 4, the results under the full DPE and DRE employed are presented and discussed. In the second part of section 4, the results under the optimal p-DPE and DRE used are shown, and the influences of p-DPE coefficients $\alpha$ on the SNR are also discussed. Finally, the conclusion of this paper is presented briefly.
2. DPC principle
The limited bandwidth, nonlinearity, and low output optical power of micro- or mini-LEDs constrain the transmission performance of UOWC systems. In order to pre-compensate these impairments induced by LEDs, we adopt DPC in the transmitter including DPD, DPE, and DRE. In the DPD part, a full third-order VNLE with the memory lengths of (9,9,7) including the cross-terms is employed for the nonlinearity pre-compensation. The VNLE coefficients are trained at 1 SPS after a T/2-spaced FFE equalizer is used to remove the ISI at the receiver [14,15].
In the following DPE part, a linear 55-tap finite impulse response (FIR) is adopted in the transmitter DSP to alleviate the bandwidth limitation of the mini-LED and avalanche photodiode (APD) detector. The DPE is performed by convolving with the FIR filter in the time domain, which is obtained in the prior post-equalization process [16,17]. Figure 1 shows the normalized power spectral density (PSD) of the signal and the signal after DPE shown as the red and green line, respectively. The high-frequency part of the signal is raised to overcome the bandwidth limitation. However, a side effect of the DPE is an increase in peak to average power ratio (PAPR), resulting in more quantization noise [18,19]. As PAPR increases, the output power of DAC decreases considering the fixed Vpp of 1 V for the DAC output. The decreased DAC output power will lead to reduced optical modulation amplitude (OMA), which consequently degrades the SNR at the receiver. The OMA is the difference between the highest and lowest modulated optical power level. Hence, it is necessary to optimize the level of DPE. The p-DPE coefficient $\alpha$ is optimized to reach a balance between the residual ISI and SNR. The amplitude-frequency response of p-DPE can be explained by the equation below:
In the final DRE part, DRE with a block length of 55 is adopted to dynamic convert the digital signal to the discrete digital signal after DPD and DPE. The level number of the discrete digital signals is set to $2^{r}$, where r is the DAC bit number. The DAC quantization process is a round-off (RO) function, which is a nonlinear function and generates white quantization noise [20,21]. Unlike a typical RO quantization processor, the DRE selects a new dynamic quantization path in the time domain, as shown in Fig. 3, and reduces the in-band quantization noise in the frequency domain based on the prior knowledge of the channel frequency response $\boldsymbol {h}_{ch}$. The channel response is comprised of DAC, ADC, RF amplifier, mini-LED, APD, and underwater channel. The $\boldsymbol {h}_{ch}$ is shown as the blue line in Fig. 4. The DRE output $x_{DRE}(n)$ is obtained by:
where $x_{ro}(n)$ is the result of the RO function, $u(n)$ is the path selection control parameter, and $\bigtriangleup$ is the DAC quantization step size, which is inversely correlated to DAC resolution. The $u(n)\in \left \{-1,0,1\right \}$ means the path selection only needs to consider the RO result $x_{ro}$ and two adjacent quantization levels. If $x_{ro}$ is the least significant bit (LSB) of DAC, $u(n)$ is belong to $\left \{0,1\right \}$. In contrast, if $x_{ro}$ is the most significant bit (MSB) of DAC, $u(n)$ is belong to $\left \{-1,0\right \}$. When $x_{ro}$ is neither LSB nor MSB, the quantization noise of the three paths after the channel is represented as follows:The position of the minimum value in the 3$\times$1 vector $\boldsymbol {P_s}$ corresponds to the value of $u(n)$ taking as 1, 0, and -1 in the Eq. (3). The PSD of the quantization noise with RO and DRE are shown in Fig. 4 as the green line and red line, and signal-to-quantization noise ratio gain of DRE from DC to 1 GHz is around 6.8 dB.
3. Experimental setup
Figure 5 shows the experimental setup of the single-pixel mini-LED-based UOWC system, in which the DSP modules of the transmitter and receiver are included. In the transmitter DSP, the generated random PAM-4/8 symbols are digitally pre-distorted by a VNLE to compensate for the LED nonlinearity. The equalizer has a memory length of [9,9,7] and operates at 1 sample per symbol (SPS). The tap coefficients are obtained by the training procedure when the equalizer is applied at the receiver. Next, the pre-distorted symbols are upsampled to 2 SPS and then filtered by a root-raised cosine (RRC) filter with a roll-off factor of 0.01. Afterward, the filtered signal is resampled at 4 GSa/s to match the arbitrary waveform generator (AWG, AWG7000A, Tektronix). The following DPE module is implemented by a finite impulse response (FIR) filter in the time domain. The FIR filter coefficients are trained by sending an OOK signal to calculate the frequency response of the UOWC system from the DC to the 2 GHz band. To handle the high PAPR caused by DPD and DPE, the signal after DPE is clipped with a clipping probability of 1$\%$. The optimization of the clipping probability has not been considered in this paper. Next, the DRE is used to select a dynamic quantization path in the time domain for shaping the in-band quantization noise in the frequency domain. The analog electric signal is generated by following AWG, which has the variable DAC resolution by setting the number of digital signal levels. The output of DAC is then amplified by an RF amplifier (SHF P101A) and then combined with 35 mA direct current (DC) via a Bias-Tee (ZFBT-6GW+, Mini-circuit). The combined signal is used to drive the single-layer GaN-based mini-LED, which has an output wavelength of 484 nm. The emitted intensity-modulated optical signal is then converged by a plano-convex lens and passes through a 2-meter-long water tank filled with fresh water. The water tank has a transmission loss of around 3.5 dB. At the receiver end, with another plano-convex lens, the light beam focuses on the light-sensitive area of an APD (APD210, Menlo System) with 3-dB bandwidth of 1 GHz. The detected signal by APD is sampled by a real-time oscilloscope (RTO, MSO73304DX, Tektronix) with a fixed sampling frequency of 12.5 GSa/s. In the receiver DSP section, the sampled signal is resampled to 2 SPS and then filtered for removing out-of-band noise by an RRC matched filter. A T/2-spaced linear FFE is then used as a post-equalizer to compensate for residual ISI. Finally, the equalized signal is downsampled to 1 SPS and demapped for BER courting.
Fig. 5. Experimental setup of the single-pixel mini-LED-based UOWC system and DSP block diagram of the transmitter and receiver.
4. Results and discussion
4.1 Results of full DPE and DRE
Fig. 6. BER versus various raw data rates with different resolution DAC with and without DRE in (a) PAM-4 and (b) PAM-8 transmission.
Firstly, we evaluate the UOWC BER performances of PAM-4 from 2.0 GBaud to 2.4 GBaud and PAM-8 from 1.9 GBaud to 2.3 GBaud systems with the full DPE scheme. Figure 6(a) plots BER versus raw data rate in PAM-4 cases with 3, 4, and 8-bit resolutions used. The result with 8-bit DAC is used as a benchmark for comparison. With 4-bit DAC used, the data rates of 4.4 Gb/s and 4.6 Gb/s can be obtained with $2\times 10^{-2}$ BER threshold under without (w/o) and with (w/) DRE, respectively. The DRE brings the limited 4.5$\%$ gain for the date rate. Figure 6(b) represents the PAM-8 BER performances with the DAC resolutions of 4, 5, and 8-bit when the DRE is applied or not. The raw data rate can be improved by 10.5$\%$ with DRE employed, and the maximum data rate of 6.3 Gb/s is achieved with $2\times 10^{-2}$ BER threshold. An 8-bit DAC is essential to achieve a transmission data rate of 6.6 Gb/s UOWC system without DRE, and the DRE enabled a 5-bit DAC to achieve the same data rate for hardware cost-saving. With the required sample rate of DAC increasing, the DRE will play a bigger role in UOWC system cost-saving.
4.2 Results of partial DPE and DRE
Figure 7 shows the measured PSD of the received signals with different p-DPE coefficients. With the decreased p-DPE coefficient, the high-frequency components are attenuated obviously. This consequently leads to more residual ISI impairments, which will have to be compensated by FFE in the receiver DSP. Figure 8 shows the root means square (RMS) of the detected signal by APD under different p-DPE coefficients. As the p-DPE coefficient $\alpha$ increases, the measured RMS decreases. This can be explained by the fact that with the large $\alpha$, the increased PAPR will lead to a reduced OMA of the LED due to the output Vpp of DAC being fixed when all DAC quantization levels are used, which consequently reduces the RMS of detected signal of APD. The reduced RMS decreases the SNR of the detected signal due to the inherent electrical noise of APD. In the meanwhile, with the increased $\alpha$, the PAPR of the signal after DPE will become larger, which induces more quantization noise during the DAC process. At the receiver DSP, a 199-taps linear FFE is used to compensate for the bandwidth limitation effect. The high-frequency components are amplified during the equalization, along with the enhanced noise. Therefore, the smaller p-DPE coefficient indicates the more enhanced high-frequency noise after FFE. Figure 9 presents the measured PSD of the 2.3 Gbaud PAM-4 signal after FFE, marked as the black line, and the enhanced noise under different p-DPE coefficients of 1.0, 0.8, 0.6, and 0.4, respectively. With the decreased $\alpha$, the noise power below 0.8 GHz is suppressed effectively, which is consistent with the above RMS result shown in Fig. 8. However, the high-frequency noise in 1-1.15 GHz is enhanced significantly by the FFE process due to insufficient DPE in the transmitter DSP. Therefore, the p-DPE coefficient needs to be optimized to achieve a trade-off considering the following factors: the first one is the degraded RMS and full-band SNR under large $\alpha$, and the second one is the enhanced high-frequency noise under small $\alpha$.
Fig. 9. PSD of the 2.3 Gbaud PAM-4 signals after FFE and the noise with different p-DPE coefficients $\alpha$. ($\alpha$ = 1, 0.8, 0.6, 0.4)
The 2.3 and 2.4 GBaud PAM-4 and 2.3 GBaud PAM-8 transmission performances are investigated by optimizing the p-DPE factor, as shown in Fig. 10. In PAM-4 transmissions, we test 4.6 Gb/s and 4.8 Gb/s cases shown in Fig. 10(a). It is found that BER firstly decreases and then increases when the p-DPE coefficient $\alpha$ grows from 0.4 to 1.0. The lowest BER is obtained when $\alpha$ is around 0.6. When 20$\%$ FEC overhead and 3-bit DAC are used, the PAM-4 signal achieves a raw data rate of 4.8 Gb/s. In the PAM-8 transmissions, we test the performance at a data rate of 6.9 Gb/s, with the best performance obtained when the p-DPE coefficient $\alpha =0.5$ as shown in Fig. 10(b). When 20$\%$ FEC overhead and a 4-bit DAC are used, the raw data rate reaches 6.9 Gb/s. The corresponding net data is 5.75 Gb/s, which is the highest net data rate achieved in 4-bit DAC-based UOWC systems. In addition, the optimal p-DPE coefficients for PAM-4 and PAM-8 formats are different due to the fact that higher-order modulation formats are more sensitive to full-band noise, including quantization noise and channel noise. Therefore, the optimal $\alpha$ should be slightly lower under the higher-order modulation format.
Fig. 10. BER versus various p-DPE coefficients with different resolution DAC with and without DRE in (a) PAM-4 and (b) PAM-8 transmission.
5. Conclusion
The UOWC scheme over a 2-m underwater is experimentally demonstrated using a low-resolution DAC and a single-pixel mini-LED. The enabling DPC block in the transmitter is comprised of DPD, DPE, and DRE, which are employed together for nonlinear compensation, linear compensation, and quantization noise shaping, respectively. The simulation results show that with DRE, the in-band quantization noise is reduced by 6.8 dB in a 4-bit-based PAM-8 system. The p-DPE coefficient is experimentally optimized to reach the balance between residual ISI and SNR, and the optimal p-DPE coefficient in PAM-4 and PAM-8 systems is 0.6 and 0.5, respectively. With the combination of DRE and optimized DPE, the 21.1$\%$ data rate gain is obtained compared with full DPE only. Consequently, a 6.9 Gb/s 4-bit DAC-based PAM-8 transmission over a 2-m underwater channel is achieved successfully. To the best of our knowledge, a low-resolution DAC-based UOWC system enabled by DPC is investigated for the first time. We believe the DPC-enabled UOWC scheme using low-resolution DAC has the advantage of cost-efficiency, which will become increasingly important as DACs with higher sampling rates are adopted in the future to scale the capacity.
Funding
Science, Technology and Innovation Commission of Shenzhen Municipality (JCYJ20190806142407195, JCYJ20210324131408023); National Key Research and Development Program of China (2021YFA0716400); National Natural Science Foundation of China (61974080, 62150027); Shenzhen Municipal Science and Technology Innovation Council (JSGG20210818101404013).
Acknowledgments
We thank Prof. Lai Wang from Tsinghua University for providing mini-LED devices to support high speed wireless optical communication experiments.
Disclosures
The authors declare no conflicts of interest
Data Availability
Data underlying the results are not publicly available at this time but may be obtained from the authors upon reasonable request.
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