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Abstract
The use of Alamouti-coded polarization-time block code (A-PTBC) in combination with a simple single polarization coherent receiver enables phase-diverse coherent detection without any optical polarization tracking. However, applying this technique to high-speed single-carrier systems is not straightforward, as it requires specialized digital signal processing (DSP) algorithms for data recovery, which increases DSP complexity. In this paper, we propose a novel Alamouti-coded coherent algorithm designed to significantly reduce the complexity of the receiver DSP for data recovery. The proposed algorithm achieves the comparable performance to the conventional algorithm but requires only half the number of necessary equalizers for data recovery. We validate its performance through simulations and also experimentally demonstrate a 100 Gb/s 16-quadrature amplitude modulation (QAM) single-carrier coherent system employed the single-polarization coherent receiver over 20 km of standard single-mode fiber (SMF). Through the performance verification, the coherent system with the proposed algorithm exhibits performance comparable to that of the conventional Alamouti-coded coherent system and achieves a power budget of 34 dB when the transmit launch power is set to 7 dBm at a Bit Error Rate (BER) of 1 × 10−2 for 0-20 km fiber transmission.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The era of the sixth generation (6 G), characterized by digital convergence that includes cloud computing, artificial intelligence (AI), virtual reality (VR), augmented reality (AR), and metaverse is extending its influence across various industries and social spheres. It is anticipated that the bandwidth of optical access networks will continue to expand in response to the ongoing surge in data traffic driven by extensive, high-capacity broadband services. While intensity modulation/direct detection (IM/DD), known for its cost-effectiveness and low-power consumption, has been the dominant technology in short-reach interconnects and optical access networks for over two decades, it is now approaching the typical bit rate limits due to constrained power budgets and decreasing chromatic dispersion tolerances. To overcome these challenges, coherent receivers can be considered as a reasonable alternative for future short-reach interconnects and optical access networks. Compared to direct detection (DD) receivers, coherent receivers offer higher sensitivity and ease of digital compensation of transmission impairments through digital signal processing (DSP). This enables significantly higher access capacities, larger power budgets, higher split ratios and extended coverage reaches with supporting data rate of hundreds of Gb/s per wavelength. For these reasons, numerous studies have aimed to investigate field trials and verify the feasibility of coherent transmission exceeding hundreds Gb/s in short-reach interconnects and optical access networks [1,2].
Although coherent optical transmission offers significant advantages, the traditional coherent transceivers designed for long-haul systems are not directly applicable to the optical access network markets. This is due to their high complexity and established prices, which are considerably higher compared to traditional IM/DD transceivers. The bulky design of the conventional polarization-diverse coherent receiver imposes a burden on markets that prioritize low-cost and compact form factors in the optical access networks. Due to this issue, the application of the conventional coherent transceivers to optical access networks has faced delays. Recently, a new related application called “coherent-lite”, has been under investigation and development in the industry. Coherent-lite technologies aim to simplify conventional optical coherent transceivers and apply them to short-reach interconnects and optical access networks [3,4].
An effective way to reduce receiver complexity is to utilize a single-polarization receiver. This approach offers the advantage of halving the number of components compared to conventional polarization diverse coherent receivers. However, the primary challenge with such receivers is that the receiver sensitivity depends on the state of polarization (SOP) of the received signal and measures need to be taken to ensure polarization independent. In real systems, it is unlikely that the polarization of the incoming signal remains aligned with the SOP of the LO due to the random changes in birefringence of the transmission fiber. To address this issue, the polarization-insensitive coherent receiver using the Alamouti-coded polarization-time block code (A-PTBC) was proposed. This approach eliminates the need for optical polarization tracking in the single-polarization receiver. While A-PTBC incurs a 3-dB sensitivity penalty due to its half-rate coding compared to a polarization division multiplexed (PDM) system at same bit rate, the reduction in the number of optical components allows for a simplified receiver, cut in half compared to a PDM coherent receiver [5–7]. Coherent optical systems employing A-PTBC require a special encoder and decoder for Alamouti encoding and decoding in the digital signal processing (DSP) of the transmitter and receiver, respectively. DSP algorithms for the A-PTBC have been explored in various application for optical access networks [8–11] and validated for the bit rate 100/200 Gbps transmission in both single-carrier systems [12–14] and orthogonal frequency division multiplexing (OFDM) systems [11]. In addition, research [15] proposed polarization-time coding techniques such as polarization scrambling and differential group delay (DGD) pre-distortion instead of the Alamouti-type polarization-time coding. Our approach in this paper is based on a novel algorithm aimed at simplifying the complexity of the Alamouti-coded receiver DSP. We propose suitable encoder and decoder structures for both transmitter and receiver DSP based on this algorithm. The simplified PTBC decoder, utilizing this algorithm, reduces the complexity of receiver DSP for data recovery by half compared to that of conventional Alamouti-code PTBC decoder. We conduct a performance comparison between the proposed PTBC coherent system operating at a net data rate of 100 Gb/s and the conventional A-PTBC coherent system. This evaluation is carried out through intensive simulations and validated through off-line experiments over a 20 km fiber transmission.
The structure of the paper is outlined as follows: In the next section we will first present a DSP algorithm describing the principles of the proposed PTBC algorithm, along with a detailed explanation of its least-mean-square (LMS) based adaptive equalizations. Section 3 presents simulations to verify the effectiveness of the algorithm, and experimental findings for the single-carrier 29.7-Gbaud 16-quadrature amplitude modulation (QAM) signal employing the proposed PTBC algorithm. In conclusion, we summarize the results and findings in Section 4.
2. Proposed PTBC algorithm
2.1 Transmitter digital signal processing
Figure 1 illustrates the polarization diversity transmitter structure. To enable polarization time block coding, The transmitter requires a dual-polarization (DP) configuration. In detail, two data symbols ${x_1}$ and ${x_2}$ are encoded in both polarization and time domains through the following process. In the first symbol period, the symbols ${x_1}$ and $x_2^\ast $ are transmitted, while in the second symbol period, $- {x_2}$ and $x_1^\ast $ are sent on the ${E_x}$ and ${E_y}$ polarization modes respectively, where * denotes the complex conjugate. This presents a notable contrast with Alamouti-coded PTBC transmission, where two data symbols ${x_1}$ and ${x_2}$ are transmitted and in the first symbol period, followed by $- x_2^\ast $ and $x_1^\ast $ are sent in the second symbol period on the ${E_x}$ and ${E_y}$ polarization modes respectively.
Fig. 1. A polarization diversity transmitter for PTBC system.
(Adapted from M. S. Faruk et al. Opt. Exp. 2016;24:24088 [7]). Tx-DSP : transmit digital signal processing, PBS : polarization beam splitter, PBC : polarization beam combiner, IQM : IQ modulator, DAC : digital analog converter, PTBC : polarization time block code
Figure 2 illustrates the comparison between A-PTBC and proposed PTBC encoding sequences. In both approaches, the orthogonality between the odd-numbered symbol pairs and the adjacent even-numbered symbol pairs remains consistent. However, the difference is that A-PTBC employs the conjugate operation to every even-numbered symbol on both ${E_x}$ and ${E_y}$ polarizations, whereas PTBC applies it to all signals of ${E_y}$ polarization modes only.
Fig. 2. Illustration on two PTBC transmission in two polarization modes. (Adapted from M. S. Faruk et al. Opt. Exp. 2016;24:24086 [7]). (a) Alamouti-PTBC transmission, (b) proposed PTBC transmission, PTBC : polarization time block code
2.2 Receiver digital signal processing
Now the two symbol pairs [${x_1}$, $x_2^\ast $] and [$- {x_2}$, $x_1^\ast $] are transmitted through two orthogonal polarization modes [${E_x}$, ${E_y}$] at the transmitter. For simplicity of exposition, we consider only one pair of data symbols [${x_1}$, ${x_2}$] to be transmitted on the channel. Once the single-polarization receiver detects optical signals on a polarization mode, i.e. ${E_x}$ polarization, the received symbol pair can be expressed as:
The received symbols, denoted as ${y_1}$ and ${y_2}$, correspond to the first and second transmit instants respectively. Here ${h_1}$ and ${h_2}$ represent the channel coefficients for the ${E_x}$ and ${E_y}$ polarization modes respectively. The $\theta $ is phase rotation resulting from the carrier frequency offset (CFO) and phase noise. Additionally, ${n_1}$ and ${n_2}$ denote channel noises at the time of the first and second symbols respectively. To take into account that the second received symbol ${y_2}$ is conjugated, the received symbol vector $\mathbf{Y} = {[{{y_1},\; y_2^\ast } ]^T}$ can be organized in matrix form with the channel transfer function H1 as:
Moreover, considering the conjugation of the first receiver symbol ${y_1}$, the received symbol vector ${\mathbf{Y}^{\boldsymbol \ast }} = {[{y_{1}^{\ast} ,\; {y_{2}}} ]^{T}}$ can also be organized in matrix form with the channel transfer function H2 as:
The noise terms, $n_1^\ast $ and $n_2^\ast $ is statistically identical to ${n_1}$ and ${n_2}$. Now, we can establish the first column, ${\mathbf{c}_1}$, of the channel matrix ${\mathbf{H}_1}$ and the second column, ${\mathbf{c}_2}$, of the channel matrix ${\mathbf{H}_2}$ as estimated channel coefficients:
Here, $\mathbf{h}$ represents $\sqrt {{{|{{h_1}} |}^2} + {{|{{h_2}} |}^2}} $. Now we can use these coefficients to derive the restored symbols, as follows:
Both systems have in common the joint performance of channel equalizations and carrier phase recoveries using multi-tap finite impulse response (FIR) filters and single-tap phase estimators. The main difference in the two PTBC decoders is that the A-PTBC decoder has four equalizers and four phase trackers, while the proposed PTBC decoder has only two equalizers and two phase trackers. To compare the complexity of these two decoders fairly, they must be evaluated under the condition of the same equalization operating rate. For this reason, the input vector $\mathbf{y}[m ]$ of the A-PTBC, as shown in Fig. 3(a), is applied at a two-fold oversampled symbol rate (oversampling factor: OV = 2), while the input vector $\mathbf{y}[n ]$ of the proposed PTBC decoder, as shown in Fig. 3(b), is applied at the symbol-spaced rate (OV = 1), where $m$ represents the half-symbol spaced sample index and n represents the symbol spaced sample index. A serial-to-parallel converter located in front of the A-PTBC decoder reduces the rate of the input signal by half, Consequently, both the A-PTBC decoder and the proposed PTBC decoder operate at the same symbol-spaced (${T_s})\; $ equalization rate.
Fig. 3. Illustration on two PTBC decoders for equalization, polarization tracking and carrier phase recovery. (a) Alamouti-PTBC Decoder (Adapted from M. S. Faruk et al. Opt. Exp. 2016;24:24087 [7]), (b) Proposed PTBC Decoder, OV : oversampling factor, SP : serial-to-parallel, PS : parallel-to-serial, LMS : least mean square, PTBC : polarization time block code
When the input vector of the A-PTBC decoder is configured to the symbol-spaced rate (OV = 1), significant performance degradation occurs under limited bandwidth conditions, as shown in Fig. 7(b). This degradation stems from insufficient equalization performance of the equalizers of the A-PTBC decoder, which operate at a two-symbols-spaced rate due to the serial-to-parallel conversion. Therefore, for a fair DSP complexity comparison between the two systems, the operating rate for the equalizers must be the same so that both systems can achieve comparable performance. With the equalizers operating rates matched, the A-PTBC (OV = 2) decoder requires four multi-tap adaptive FIR filters and four single-tap phase trackers in terms of DSP complexity, whereas the proposed PTBC decoder only requires two multi-tap adaptive equalizers and two phase trackers.
The proposed PTBC decoding progresses are schematically illustrated in Fig. 4. Initially, the data symbols are encoded on the ${E_x}$ and ${E_y}$ polarization modes at the transmitter, and the received symbol vector $\mathbf{y}[n ]$ from the single polarization coherent receiver generates signal $\mathbf{u}[n ]$ after passing through a multi-tap FIR filter ${\mathbf{w}_1}$ and a single-tap phase tracker p at the upper side of the decoder. Simultaneously, at the lower side of the decoder, after the received symbol $\mathbf{y}[n ]$ performing a conjugate operation, a signal $\mathbf{v}[n ]$ is generated by passing through a FIR filter ${\mathbf{w}_2}$ and a phase tracker ${p^\ast }$.
Fig. 4. Illustration on the process of proposed PTBC from encoding to decoding, PTBC : polarization time block code
Subsequently, the crossed branches exchange odd and even numbered symbols of the signal $\mathbf{u}[n ]$ and $\mathbf{v}[n ]$ through the symbol space delayers (D). At the adders, they are combined together and down-sampled by a factor of two. Following this, the parallel-to-serial converter arranges the recovered symbols sequentially. The odd and even numbered recovered symbols are expressed as:
The tap coefficients of the FIR filters are adjusted through the LMS algorithm with a step-size parameter ${\mu _f}$, as follows:
The LMS algorithm of the proposed PTBC does not necessitate greater DSP complexity than that of A-PTBC [7]. While it might appear to involve more multiplications compared to the A-PTBC algorithm, in reality, the complexity is at least comparable. This is because A-PTBC updates the channel coefficients for four equalizers, whereas the proposed PTBC updates the channel coefficients for only two equalizers. Hence, in terms of DSP complexity, the proposed PTBC algorithm is either less complex or equivalent to the A-PTBC algorithm from the perspective of the LMS algorithm.
3. Simulations and experimental results
3.1 Simulation conditions
We conduct computer simulations using the proposed transceiver for 29.7 Gbaud 16-QAM transmission system to verify its performance. This includes a net data rate of 100 Gbps, forward error correction (FEC), pilot symbols, training symbols and preambles. The FEC (76176, 65536) employs the one-step-ahead (OSA) algorithm to enhance the error correction capability of the Bose-Chaudhuri-Hocquenghem (BCH) code [18]. A single-carrier PTBC coded signal is generated by a dual-polarization transmitter configured in Fig. 1. Pulse shaping employs a square-root raised cosine (SRRC) filter with a roll-off coefficient of 0.1. The signal is transmitted over 20 km through standard single mode fiber (SMF) characterized by a dispersion coefficient of 17 ps/nm/km, an attenuation coefficient of 0.2 dB/km, and a nonlinearity coefficient of 1.3 W/km. The optical signal is detected through a single polarization intradyne coherent receiver. To control the input signal power at the receiver, the transmit power is adjusted and the receiver noises are considered using the parameters for the coherent receiver, such as, a shot noise, a thermal noise and a laser relative intensity noise (RIN) known as the main noise source of unamplified coherent transmission. To simulate the bandwidth effect on the optical components of coherent receiver, a 3-dB cutoff 5-tap Butterworth low-pass filter is used. For the conversion of the received optical power (ROP), we utilize the equations presented in [19]. The following parameters considered in the simulations refer to the datasheet of integrated tunable transmitter and receiver assembly (ITTRA: FIXQ6410C1mf), which is used in the offline test : optical power of the local oscillator ($P_L^{CW}$) = 12 dBm, LO-RIN = -140 dB/Hz, input-referred noise current density of TIA (iTIA) = 30 pA/$\sqrt {Hz} $, common mode rejection ratio (CMRR) of the balanced photodiode = -18 dB, responsivity of receiver (R) = 0.1 A/W, and effective number of bits (ENOB) of ADC = 4 bits.
Figure 5 shows the structure of the transmitter and receiver DSP for the PTBC coherent simulations. First, the transmitter DSP consists of a 16-QAM mapper, pilot symbols insertion, PTBC encoding, preamble symbols insertion, and matched filtering. The transmission frame format includes preamble symbols, training symbols and data symbols. The training symbols and the data symbols are mapped using a pseudo random binary sequence (PRBS) ${2^{23}} - 1$. The processing involves a total of 38,400 data symbols, of which 6,400 symbols are allocated for training symbols, Subsequently, these symbols are PTBC encoded. After passing through the optical transmission channel, the received signal is converted to a two-fold oversampled symbol rate. Subsequently, several DSP operations are carried out, including direct current (DC) cancellation, automatic gain control (AGC), chromatic dispersion (CD) compensation, sampling timing error compensation, frame synchronization, carrier frequency offset compensation, and matched filtering. Finally, in the PTBC decoder, adaptive equalization, polarization tracking and carrier phase recovery are performed. After the symbols are decoded, the bit-error-rate (BER) is calculated [20].
3.2 Performance for the simulations
To evaluate the polarization-insensitive operation of the proposed proposed PTBC algorithm, we investigate the BER performance in response to changes in polarization state across the entire the Poincaré sphere. The state of polarization (SOP) of the incoming signal to the receiver is simulated using the Jones matrix by sweeping the parameters $\theta $ and $\phi $ of Eq. (13) from $- \pi /2$ to $\pi /2$ [12].
Fig. 5. DSP structure for PTBC coherent simulations. PTBC : polarization time block code, QAM : quadrature amplitude modulation, DC : direct current, AGC : automatic gain control, CD : chromatic dispersion, CFO : carrier frequency offset
In the Eq. (12), $\theta $ and $\phi $ represent the azimuth and elevation rotation angles, respectively, for the transition between two polarization states. Figure 6 shows the BER performance through a two-dimensional sweep considering these angles. Based on simulations regarding the number of taps of the equalizers, optimal performance was achieved with more than 11 taps. Therefore, we chose 17 taps for the equalizers in both simulations and experiments. For the step size used to update the weights of the LMS algorithm, we applied a phase step-size parameter (${\mu _p}$) of 0.15 and a channel FIR filter update step-size parameter (${\mu _f}$) of 4.5e-4. During the simulation, the received power is set to -27.5 dBm. The high-speed standards for passive optical network (PON) in recent ITU-T have adopted $1 \times {10^{ - 2}}$ as the FEC limit for BER, and we also align with this target. As shown in Fig. 6, the proposed proposed PTBC coherent receiver demonstrates insensitivity to polarization, and no significant performance variation is observed concerning polarization rotations.
Now, we investigate the performance of both the A-PTBC and proposed PTBC by considering a coherent receiver with the PTBC decoder illustrated in Fig. 3. Figure 7(a) shows the BER performance as a function of received power for both systems under an additive white Gaussian noise (AWGN) condition without any linear or non-linear impairments. In the absence of bandwidth limiting effects, as shown in Fig. 7(a), the receiver sensitivities are all similar, achieving about -27.5 dBm at BER of $1 \times {10^{ - 2}}$. However, in practical systems, SRRC filters are commonly used in both the transmitter and receiver to mitigate inter-symbol interference (ISI) and enhance bandwidth efficiency. While the application of the SRRC filter improves bandwidth efficiency, it causes interference between adjacent symbols due to its bandwidth limiting effect. The smaller the roll-off factor ($\alpha \; :0 < \alpha \le 1$) of the SRRC filter, the more pronounced the impact of interference from adjacent symbols. As shown in Fig. 7(b), BER performance degradation occurs when the receiver bandwidth is limited to 26.7 GHz (0.9 times the baud rate), and the SRRC filters a roll-off factor of 0.1 are employed in both the transmitter and receiver. No significant BER degradation is observed for the proposed PTBC, while A-PTBC (OV2) shows a slight performance degradation of about 0.2 dB at a BER $1 \times {10^{ - 2}}$, and A-PTBC (OV1) shows a more significant performance degradation of about 1.7 dB at a BER $1 \times {10^{ - 2}}$. Therefore, unless otherwise stated, the A-PTBC (OV2) is used for simulations and experiments and is referred to as A-PTBC throughout the paper.
Fig. 7. BER performance as a function of received power, (a) without an SRRC filter, (b) with SRRC filters and limited receiver bandwidth, SRRC : square-root raised cosine
Next, as the proposed PTBC decoder reduces the complexity of the equalizations by half compared to the A-PTBC decoder, we investigate its performance impact on carrier frequency offset, phase noise at both transmitter and receiver, and polarization mode dispersion (PMD).
Firstly, we investigate the frequency offset tolerance of the proposed proposed PTBC system, as shown in Fig. 8. We measure the BER for various frequency offset values at a received power of -26 dBm, including an additional 1.5-dB margin to the received power required for a BER of $1 \times {10^{ - 2}}$. The frequency offset tolerance is highly affected by the receiver bandwidth (${B_{RX}}$). For A-PTBC, when the receiver bandwidth (${B_{RX}}$) is set at 26.7 GHz (0.9 times the baud rate), no significant BER degradation is observed for the frequency offset around ${\pm} $5 GHz. However, for the proposed PTBC, this tolerance range expands to ${\pm} $10 GHz. Specifically, with the proposed PTBC, no significant BER degradation is observed at frequency offsets around ${\pm} $5 GHz, even when ${B_{RX}}$ is set at 20.8 GHz (0.7 times the baud rate). The reason why the proposed PTBC outperforms the A-PTBC in terms of frequency offset tolerance is expected to be that the proposed PTBC is more robust against the bandwidth limiting effect than A-PTBC, as shown in Fig. 7(b).
Fig. 8. BER performance for different carrier frequency offset. (a) for A-PTBC (OV2), (b) for proposed PTBC, ${B_{RX}}$ : receiver bandwidth
Next, we investigate the tolerance of laser linewidth and the tolerance of PMD for both systems. Figure 9 shows the receiver sensitivity at a BER of $1 \times {10^{ - 2}}$ for a 3-dB linewidth of a transmitter laser and a receiver LO for both systems. In terms of the linewidth tolerance, the sensitivity penalty of both systems is very similar. The proposed PTBC system exhibits a sensitivity penalty of 0.37 dB at a 1 MHz linewidth and 0.79 dB at a 2 MHz linewidth.
Fig. 9. Received sensitivity as a function of 3-dB linewidth, A-PTBC : Alamouti-PTBC, PTBC : polarization time block code
Figure 10 shows the sensitivity penalty based on the first order PMD in terms of mean differential group delay (DGD). The PTBC coherent systems employing a single polarization receiver are inherently susceptible to PMD caused by different group delays of the two orthogonal polarizations. This vulnerability arises because PMD disrupts the orthogonality between two grouped symbols encoded on the ${E_x}$ and ${E_y}$ polarization modes [20]. In the absence of PMD, in the A-PTBC decoder, the equalizer coefficients ${\mathbf{w}_{11}}$ and $- \mathbf{w}_{22}^\ast $ converge to be equal, and ${\mathbf{w}_{12}}$ and $\mathbf{w}_{21}^\ast $ also converge to be equal. However, in the presence of PMD, these coefficients no longer converge to be equal, but diverge from each other. With the proposed PTBC system, which halves the number of equalizers compared to the A-PTBC system, it becomes more vulnerable to the loss of orthogonality in situations where the coefficients converge differently. For a DGD of 4 ps, the A-PTBC system exhibits a sensitivity penalty of 0.42 dB, while the proposed PTBC system exhibits a sensitivity penalty of 0.71 dB at a BER of $1 \times {10^{ - 2}}$. With a DGD of 6 ps, the A-PTBC system exhibits a sensitivity penalty of 0.97 dB, whereas the proposed PTBC system exhibits a sensitivity penalty of 1.77 dB at a BER of $1 \times {10^{ - 2}}$.
Fig. 10. Sensitivity penalty as a function of PMD. A-PTBC : Alamouti-PTBC, PTBC : polarization time block code, PMD : polarization mode dispersion, DGD : differential group delay
3.3 Experimental setup and results
To evaluate the performance of the proposed proposed PTBC technique, we conduct experimental investigations in 29.7 Gbaud 16-QAM single-carrier coherent transmission as shown in Fig. 11. The pseudo-random bit sequence (PRBS) is mapped to a 16-QAM baseband signal. A frame begins with 288 preamble symbols, which are inserted at the beginning of the frame to estimate CFO and retrieve the start of the frame. A training sequence of 6400 symbols is attached after the preamble symbols and is followed by a data sequence. The PTBC Encoding is applied to both the training sequence and the data sequence at the transmitter. The mapped signal is then generated in an arbitrary waveform generator (AWG) which operates at the sampling rate of 120 GS/s and leads to an optical bandwidth of 45 GHz. At the transmitter, an external cavity laser (ECL) with a linewidth of 300 kHz generates a continuous-wave signal at 1550 nm. The electrically modulated baseband signal, generated by the AWG, is input into a dual-polarization (DP) I-Q Mach-Zehnder modulator (MZM), and then the optical signal is transmitted through a 20-km standard single-mode fiber (SMF) link. A PMD emulator is inserted into the link to evaluate the influence of the first-order PMD. The polarization controller in front of the PMD emulator is adjusted to launch roughly equal power into two principal states of polarization of the PMD emulator.
Fig. 11. Experimental setup for PTBC coherent system. DSP : digital signal processing, PTBC : polarization time block code, ECL : external cavity laser, AWG : arbitrary waveform generator, DP : dual-polarization, TIA : transimpedance amplifier, LO : local oscillator, PC : polarization controller, SMF : single mode fiber, DSO : digital sampling oscilloscope
For receiver sensitivity measurements, the signal power is regulated using a variable optical attenuator (VOA). The single polarization coherent receiver consists of a 90-degree hybrid coupler and two balanced photodiodes (BPDs). After the photo-detection, the two electrical signals at the output of the trans-impedance amplifiers (TIAs) are digitized by a digital sampling oscilloscope (DSO) with a 8-bit analog-to-digital converter (ADC) operating at a sampling rate of 160 GS/s and a bandwidth of 36 GHz. The sampled digital signals are then post-processed on the computer after appropriate down-sampling at two samples per symbol through an off-line receive DSP for PTBC signal reception.
Figure 12 shows the BER performance as a function of transmit launch power for both A-PTBC and proposed PTBC systems. We conducted a comparative analysis of the both systems over a 20 km transmission distance using standard SMF, with received optical power levels set at -25 dBm and -10 dBm. It is noted that performance degradation occurs when the transmitted launch power exceeds 9 dBm due to optical fiber nonlinearity. Therefore, in our experiments for both systems, we chose a transmit launch power of 7 dBm to mitigate the effects of fiber optic nonlinearity. Next, to investigate the impact of PMD, we also measure the BER performance as a function of received power for different DGD values.
Fig. 12. BER as a function of launch power. A-PTBC : Alamouti-PTBC,
PTBC : polarization time block code
Figure 13(a) depicts the BER against received power for the A-PTBC system, while Fig. 13(b) shows the same for the proposed PTBC system. The A-PTBC system demonstrates a slight performance degradation as DGD increases, whereas the performance of the proposed PTBC system significantly degrades when the DGD exceeds 6.2 ps. However, if the DGD remains below 4.3 ps, the sensitivity penalty stays within 1 dB at a BER of $1 \times {10^{ - 2}}$. These findings are in good agreement with those obtained with the computer simulations in Section 3.2. Specifically, in the simulation, the proposed PTBC system exhibits a sensitivity penalty of 0.71 dB at a DGD is 4 ps and a penalty of 1.77 dB at a DGD of 6 ps. The time-averaged differential time delay, or DGD, between two orthogonal SOPs on a fiber link is described by the following equation:
where $\Delta \mathrm{\tau }$ is the differential group delay (DGD), L is the fiber link distance, and ${D_{PMD}}$ is the fiber PMD parameter measured in $\textrm{ps}/\sqrt {\textrm{km}} $. For a standard SMF with a fiber dispersion of 17 ps/nm.km in the C-band 1550 nm, the largest average PMD parameter is 0.6977 $\textrm{ps}/\sqrt {\textrm{km}} $ [21]. It corresponds to 3.12 ps of DGD when applying a distance of 20 km. Typically, the PMD of a carefully constructed link can be as low as 0.1 $\textrm{ps}/\sqrt {\textrm{km}} $.Fig. 13. BER as a function of received power for different PMD.
(a) Alamouti-PTBC transmission, (b) proposed PTBC transmission,
PMD : polarization mode dispersion, A-PTBC : Alamouti-PTBC, PTBC : polarization time block code, ROP : received optical power
We also evaluate the receiver sensitivity for both back-to-back and 20 km transmission cases for both systems, as shown in Fig. 14. In the back-to-back case, the proposed PTBC demonstrates slightly better performance than the A-PTBC system at high ROP. This enhancement aligns with the simulation results in Fig. 7(b). However, at a transmission distance of 20 km, the performance of the both systems is nearly comparable. The similarity in performance at 20 km transmission could be attributed to the greater impact of residual PMD in the fiber optic channel on the proposed PTBC system. Consequently, for 20 km transmission, there is no significant performance difference between the two systems. A power budget of 34 dB is achieved with a transmit power of 7 dBm and a receiver sensitivity of -27 dBm at the BER of $1 \times {10^{ - 2}}$ for distances ranging from 0 to 20 km.
Fig. 14. BER as a function of received power. A-PTBC : Alamouti-PTBC, PTBC : polarization time block code, ROP : received optical power, BtB : back-to-back
4. Conclusions
Polarization-time block code (PTBC) based single-polarization coherent receivers are considered as a promising alternative for reducing the cost and complexity of dual-polarization receiver in future optical access networks. However, the digital signal processing (DSP) required for data recovery in high-speed single-carrier coherent systems using conventional Alamouti-coded PTBC algorithm is not straightforward. In this paper, we proposed a novel algorithm aimed at simplifying the complexity of the Alamouti-PTBC decoder. In contrast to the A-PTBC, the proposed PTBC decoder requires only half of the equalizers employed by the A-PTBC decoder. We verified the performance of the proposed PTBC system through simulations and experimental demonstrations of a 100 Gb/s 16-QAM single-carrier PTBC system employing a single-polarization coherent receiver over 20 km of standard single-mode fiber (SMF). In our simulations, the proposed PTBC demonstrated greater robustness to bandwidth limiting effects compared to A-PTBC, and also exhibited twice the tolerance performance in terms of frequency offset tolerance. However, regarding PMD impairment, the performance of the proposed PTBC degraded compared to the A-PTBC due to the reduction in the number of equalizers by half. Specifically, when DGD was 4 ps, the A-PTBC system exhibited a sensitivity penalty of 0.42 dB, while the proposed PTBC showed a sensitivity penalty of 0.71 dB. Through our experiments, we confirmed that the sensitivity penalty of the proposed PTBC remained within 1 dB when DGD was 4.3 ps. Considering the maximum average PMD parameter for standard SMF at a distance of 20 km, where the mean DGD corresponds to 3.12 ps, the performance degradation of the proposed PTBC at this level could be acceptable at the cost of lowering DSP complexity. In the 20 km transmission experiments, there was no noticeable performance difference between the two systems, and a power budget of 34 dB was achieved at a transmit power of 7 dBm and a receiver sensitivity of -27 dBm for distances ranging from 0 to 20 km. We are confident that the proposed algorithm enables coherent-lite technology for upcoming optical access networks, by reducing complexity, power consumption, and cost.
Funding
Institute for Information and Communications Technology Promotion (IITP) grant funded by the Ministry of Science and ICT, South Korea (MSIT) (Development of Tbps Optical Communication Technology) (2021-0-00809).
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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