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Abstract
We propose to use adaptive bit loading based on time-domain hybrid QAM (TDHQ) to maximize the capacity of subcarrier-multiplexing (SCM) systems in meshed optical networks with cascaded reconfigurable optical add and drop multiplexers (ROADMs). Note that the capacity is defined as the achievable net bit rate at the soft-decision FEC threshold of BER = 2 × 10−2 in this work. The capacity improvement is first numerically and experimentally demonstrated in a 4-subcarrier SCM system with an aggregate symbol rate of 34.94 Gbaud. Compared with the conventional SCM system using uniform standard QAM, the proposed system can achieve an average capacity increase of 31.75% and 26.1% over various link conditions in simulations and experiments, respectively. Furthermore, we demonstrate that the proposed SCM system can better approach the channel capacity in the presence of narrow inline optical filtering. An average capacity improvement of 7.59% is also reported over all 17 ROADMs cases from 1 to 17 by simulations at OSNR = 21 dB, compared with its single carrier counterpart using TDHQ.
© 2017 Optical Society of America
1. Introduction
The ever-increasing capacity demand has been driving the evolution of optical networks from a conventional fixed architecture to an agile and intelligent one. It is well known that fiber nonlinearities impose a limit on fiber link capacity, and thus mitigation and compensation of fiber nonlinearities have received great attentions. In this context, digital subcarrier-multiplexing (SCM) systems were numerically shown to achieve a higher tolerance to fiber nonlinearities compared to single carrier systems in [1,2]. This improvement was experimentally demonstrated in [3], which has stimulated extensive investigations on SCM systems recently [4–7]. In order to further overcome the nonlinear Shannon limit, advanced fiber nonlinearities compensation algorithms based on SCM signals have been proposed recently [8–10].
On the other hand, the use of reconfigurable optical add and drop multiplexers (ROADMs) reduces the available channel bandwidth in meshed optical networks [11]. This narrow filtering effect differs from channel to channel depending on the number of cascaded ROADMs. In this case, in addition to fiber nonlinearities, the channel capacity is also limited by the dynamic inline filtering. Therefore, designing a flexible transceiver that can fully exploit all the available bandwidth of each link is essential to postpone the coming capacity crunch. As for the SCM system, edge subcarriers suffer from severe optical filtering penalties, which limits the system performance. Recently, several methods have been investigated to address this issue including Walsh-Hadamard Transform (WHT), pairwise coding, and adaptive bit loading with standard QAM. WHT increases filtering tolerance by averaging the performance of all subcarriers [12]. Pairwise coding is conducted among outmost subcarriers to eliminate the performance imbalance between subcarriers [13]. For the adaptive bit loading scheme used in [14], it was experimentally demonstrated that the system allocating QPSK on edge subcarriers and 16QAM on central subcarriers could achieve a much higher filtering tolerance than the system allocating 8QAM on all subcarriers. However, all these methods cannot fully utilize link margins in an environment with diverse filtering effects. Time-domain hybrid QAM (TDHQ) has been proposed in single carrier systems to realize a continuous tradeoff between transmission distance and spectral efficiency [15]. In addition, the benefit of using TDHQ instead of standard QAMs for single carrier transmissions in the presence of strong filtering effects has been demonstrated [16–18]. In [17], the use of TDHQ along with a variable symbol rate has been reported as a viable solution to achieve more bit rate in a single carrier system with diverse and dynamic optical filtering. Nonetheless, a variable symbol rate with a finer granularity can be costly to implement.
In this work, we propose to use TDHQ based adaptive bit loading in SCM systems to maximize the capacity of a meshed optical network with cascaded ROADMs. Note that in this work the capacity is defined as the achievable net bit rate at the soft-decision forward error correction (FEC) threshold of bit error ratio (BER) = 2 × 10−2. We demonstrate that the proposed SCM system with finer subcarrier granularities enables to further approach the channel capacity in the presence of ROADM-induced narrow optical filtering. In the proposed scheme, an appropriate TDHQ format is selected for each subcarrier according to its specific signal-to-noise ratio (SNR) for the purpose of maximizing the overall bit rate. Note that this work is extended from our previous experimental work presented in [19], and more detailed analysis is conducted here with extensive simulations. This paper is organized as follows: in Section 2, we introduce the simulation setup and the impact of filtering on SCM signals; In Section 3, we describe the principle of the proposed adaptive bit loading based on TDHQ. In Section 4, we carry out extensive simulations and experiments to verify the increased filtering tolerance on SCM signals. We focus on the average capacity, which is the average net bit rate over various link conditions, e.g. links with different OSNRs and/or number of loops, as the metric in meshed optical networks. In a 4-subcarrier SCM system with an aggregate symbol rate of 34.94 Gbaud, the proposed scheme can ensure an average capacity increase of 31.75% and 26.1% in simulations and experiments, respectively, compared with the conventional scheme using uniform standard QAMs. In Section 5, we numerically investigate the impact of the subcarrier granularity and show that the finer subcarrier granularity enables the proposed SCM system a higher capacity compared with the single carrier system using TDHQ. Specifically, the former can achieve an average capacity improvement of 7.59% over all 17 ROADMs cases from 1 to 17 at OSNR = 21 dB than the latter. The conclusion is finally drawn in Section 6.
2. Simulation setup and impact of filtering on SCM signals
To examine the impact of cascaded ROADMs induced filtering on SCM signals with subcarriers, we consider a single channel system as shown in Fig. 1. The aggregate baud rate is 34.94 Gbaud and dual-polarization (DP) signals are under investigation. At the transmitter-side, the number of subcarriers and the applied modulation formats for each subcarrier are determined according to the specific conditions. For the up-sampling and root raised-cosine (RRC) shaping, the symbols of each subcarrier are up-sampled to 2 samples per symbol by first interpolating zeros between them, and then applying a 64-tap RRC time-domain finite impulse response (FIR) filter with a roll-off factorof 0.1. Afterwards, the signals of each subcarrier are first up-sampled byusing frequency domain zero padding, and then shifted to different frequencies in the spectrum for subcarrier multiplexing. The spacing between subcarriers is, which means no excess guard band is inserted between subcarriers. Therefore, the signal bandwidth with different number of subcarriers (including the single carrier) is the same. In order to combat the limited bandwidth of the transmitter, pre-compensation is carried out based on the measured transmitter frequency response. Finally, the pre-compensated signals are re-sampled to match the sampling rate of the digital-to-analog converters’ (DACs) and sent to DACs for digital-to-analog conversion. To emulate an overall implementation noise of 20 dB SNR from the transceiver, additive white Gaussian noise (AWGN) is equally loaded at the transmitter and receiver sides. Laser phase noise, frequency offset (FO) and chromatic dispersion (CD) are also considered in our simulations. Specifically, the combined linewidth is 40 kHz, the FO is set to be 1 GHz and the accumulated CD of each span is 1360 ps/nm at 1554 nm wavelength. In the transmission link, AWGN is loaded after each ROADM to emulate the amplified spontaneous emission (ASE) noise introduced by gain-controlled erbium doped fiber amplifiers (EDFAs). The variance of the noise added after each ROADM is assumed to be identical, and the total noise accumulated over the link is quantified by optical signal-to-noise ratio (OSNR) with a 0.1 nm resolution. The ROADM filter model is based on the following equation with aof 12 GHz [20]:
whereis the 6-dB bandwidth of the ROADM, and it is set to 45.34 GHz in a legacy 50-GHz grid. The corresponding 3-dB bandwidth is about 40 GHz. The ROADM response from Eq. (1) is also shown in Fig. 1. We can see that since the transfer function of a ROADM is not ideally rectangular, cascading multiple ROADMs induces narrow pass-band filtering and thus reduces the available channel bandwidth. After coherent detection, the receiver-side digital signal processing (DSP) flow is firstly started with the overlapped frequency-domain CD compensation followed by the coarse FO compensation [21]. After subcarrier de-multiplexing, the signals are down-sampled to 2 samples per symbol for each subcarrier. Matched filtering is then carried out by a 64-tap RRC time-domain FIR filter with a roll-off factor of 0.1. Afterwards, the adaptive equalization is implemented with a 25-tap T/2 spaced butterfly FIR filter with the decision-directed least-mean-square (DD-LMS) algorithm. Within the DD-LMS loop, a phase lock loop (PLL) is applied for carrier phase recovery [22]. Training symbols are sent at the beginning of the transmission for the pre-convergence of the butterfly filter and PLL. Note that for SCM signals, the DSP blocks before down-sampling are applied to the multiplexed signal (with black color in Fig. 1) and the rest of the processing is done independently for each subcarrier (with red color in Fig. 1). The BER is finally calculated as an average value over all the subcarriers.To investigate the impact of filtering on SCM signals, we evaluate the relationship between the number of ROADMs and required OSNR @ BER = 2 × 10−2 for the 16QAM SCM signals in Fig. 2(a). The 3-dB bandwidth of cascaded ROADMs according to Eq. (1) is also presented in Fig. 2(a) [20]. It can be seen that the SCM system is less tolerant to the filtering induced by the cascaded ROADMs compared with the single carrier system. Moreover, the performance of the SCM system further degrades as the number of subcarrier increases. This degradation results from the uneven SNRs across the SCM signal spectrum after filtering, and the outer subcarriers limit the overall performance. Next, we send known QPSK symbols to measure the received SNR, which is the ratio between the signal power and noise variance on the received symbols after carrier phase recovery, for each subcarrier in an 8-subarrier system as shown in Fig. 2(b). Obviously, the received SNRs of the innermost 4 subcarriers remain almost the same as the filtering bandwidth varies, whereas the received SNRs of the outermost 2 subcarriers decrease rapidly as the filtering bandwidth reduces because their power is significantly reduced. The received SNRs of the rest 2 subcarriers decrease at a slower pace. Consequently, optical filtering leads to a colored-SNR distribution for the SCM signals, namely a variety of SNRs across the subcarriers. Since the outermost 2 subcarriers are severely filtered, the performance of these 2 subcarriers are greatly degraded, which limits the overall performance of the SCM system.
Fig. 2 (a) Required OSNR versus number of cascaded ROADMs. (b) Received SNR versus number of cascaded ROADMs for each subcarrier in an 8-subcarrier system.
3. Principle of adaptive bit loading based on TDHQ
In a conventional SCM system, uniform standard QAM is adopted for all subcarriers. However, as described in Section 2 the SNRs over subcarriers may vary in the presence of inline optical filtering and/or transceiver bandwidth limitation, and overall system performance will be limited by edge subcarriers which have the lowest SNRs. Generally, a widely-adopted sub-optimal approximation to the theoretically-optimal water-filling capacity-approaching scheme is the bit loading scheme in the context of a colored SNR distribution, which is widely used in OFDM systems [23,24]. However, when it is applied to the SCM systems, the coarse subcarrier granularities along with the big gaps between the spectral efficiency of standard QAMs limit the achievable capacity of the SCM system. Here, we propose to use TDHQ based adaptive bit loading in order to maximize the capacity of SCM systems. In particular, the modulation format selected from TDHQ options on each subcarrier is optimized with the target of maximizing the overall bit rate according to the specific colored-SNR distribution, as shown in Fig. 3(a). The TDHQ signals are constructed by time interleaving standard M1-QAM symbols with standard M2-QAM symbols on a symbol by symbol basis for each subcarrier. Alternatively, we can also use probabilistic constellation shaping modulation formats as suggested in [25]. In principle, this bit loading optimization on each subcarrier can be achieved by a brute-force search method. However, it will inevitably cause a slow connection start-up process and is thus undesired especially in dynamic optical networks.
Fig. 3 (a) Adaptive bit loading based on TDHQ in SCM systems. (b) TDHQ frame structure under investigation. (c) Required SNRs for various TDHQ modulation formats.
To realize a fast optimization of bit loading, we propose a SNR-based optimization process. Given the colored-SNR distribution and the bits-per-subcarrier distribution, we can calculate the average BER of all the subcarriers as
whereis a function of SNR and with an output being BER.is the number of subcarriers. Here, we consider the TDHQ format, whose BER can be calculated aswhereandare the bits-per-symbol of the two adjacent standard QAMs in the TDHQ frame. denotes the format ratio, which is defined as the proportion of the lower order standard QAM in the frame. Therefore, we can get. is the power ratio between the two standard QAMs. andare the functions to obtain BER for the two standard QAMs, respectively, based on the input SNR [26]. The TDHQ frame structure under investigation is shown in Fig. 3(b). Each TDHQ frame contains 8 symbols, where the first consecutive symbols are lower order standard QAM and the restsymbols are higher order standard QAM. Note that the TDHQ frames of all the subcarriers are time aligned. The required SNRs at the BER of 2 × 10−2 for different TDHQ formats are shown in Fig. 3(c). Specifically, the required SNRs for QPSK, 8QAM, 16QAM, 32QAM, and 64QAM are 6.25 dB, 10.37 dB, 12.71 dB, 15.74 dB, and 18.43 dB, respectively. For the generation of TDHQ, the between two adjacent QAM formats are 0.5, 0.65, 0.6, 0.7, respectively. For the optimization, a maximum is expected at a target BER, which is assumed to be the soft-decision FEC (20% overhead) threshold of BER = 2 × 10−2 in this work. Particularly, the optimization procedure can be described as the following three steps:Step 1: Known QPSK symbols on all subcarriers are sent to calculate the SNR distribution.
Step 2: Based on the obtained SNR distribution, all the bit loading configurations that satisfy BER≤2 × 10−2 are selected according to Eqs. (2) and (3).
Step 3: These configurations are tested in the order of decreasing. The first configuration that achieves BER≤2 × 10−2, which gives the maximum, is provisioned for the link.
4. Capacity improvement in a 4-subcarrier system
4.1 Simulations
In this section, we first demonstrate the capacity improvement with the proposed adaptive TDHQ loading based on simulations of a 34.94 Gbaud dual-polarization 4-subcarrier system. Figure. 4(a) shows the achievable capacity of the proposed SCM system with respect to different OSNRs after transmitting through 12 cascaded ROADMs, in which the overall 3-dB bandwidth of the cascaded ROADMs is 25.9 GHz. The SCM systems using uniform standard QAM and TDHQ are also evaluated for comparison. In the case of uniform standard QAM, QPSK is employed for all the OSNRs because in such a severe filtering circumstance even at OSNR = 21 dB the use of uniform 8QAM is prohibited. As for the scheme using uniform TDHQ, when OSNR is above 17 dB, the use of TDHQ can convert extra SNR margins into capacity improvement. Finally, the proposed adaptive TDHQ loading significantly improves the system tolerance to narrow optical filtering, and meanwhile maximizes the achievable capacity for each link condition.
Fig. 4 (a) Achievable capacity versus OSNRs with 12 ROADMs. (b) Achievable capacity versus number of cascaded ROADMs at OSNR = 21 dB.
In Fig. 4(b), we show the dependence of achievable capacity on the number of cascaded ROADMs by varying the ROADM number at OSNR = 21 dB. The number of cascaded ROADMs under investigation is swept from 1 to, where is defined as the maximum number of ROADMs that the SCM system using uniform QPSK on each subcarrier can tolerate. For the scheme using uniform standard QAM, the modulation formats are switched from 16QAM to 8QAM and then to QPSK as the number of ROADMs increases. Maximum 17 ROADMs can be tolerated with uniform QPSK on all subcarriers at OSNR = 21 dB. For the scheme using uniform TDHQ, the SNR margin can be converted into additional capacity, leading to an average capacity improvement of 10.5% over all 17 ROADMs cases from 1 to 17, compared with the scheme using uniform standard QAM. Note that when the number of ROADMs is 6, 10, 16 and 17, no capacity difference is observed compared with the scheme using uniform standard QAM, since using uniform 16QAM, 8QAM, QPSK and QPSK are the best choice for each case, respectively. However, the achievable capacity still decreases rapidly with an increased number of ROADMs. On the other hand, the proposed scheme can reach the largest capacity under all the cases of ROADM filtering in Fig. 4(b), since it can make the best use of the SNR margin on each subcarrier. This improvement becomes very prominent when the number of ROADMs is larger than 10. Overall, an average capacity improvement of 35.7% over all 17 ROADMs cases from 1 to 17 is obtained compared with the scheme using uniform standard QAM.
To thoroughly investigate the capacity improvement, we sweep the OSNR from 23 dB to 15 dB with a step size of 1 dB and then for each OSNR calculate the average capacity improvement over various ROADM cases, which is from 1 to. Obviously, increases with a higher OSNR value. The obtained results are summarized in Table 1. As for the system using uniform standard QAM, the average capacity over various ROADM cases is reduced as the OSNR decreases, and an overall average capacity of 146.7 Gb/s is obtained by further averaging the capacity over 9 OSNR cases from 15 to 23 dB. Compared to it, the uniform TDHQ and bit loading TDHQ schemes can increase the overall average capacity by 15.15% and 31.75%, respectively. And these improvements correspond to 22.22 Gb/s and 46.58 Gb/s more capacities for the two systems, respectively. Note that in this study the average capacity improvement is obtained based on a uniform distribution of link conditions in terms of the link length and number of ROADMs, which provides a general reference. In practical applications, the network topology varies dramatically, leading to a wide range in the capacity benefit for different cases.
Table 1. Simulated average capacity improvement over various ROADM cases compared with the SCM scheme using uniform standard QAM.
In above discussions, we assume the carrier frequency of the transmitter-side laser and the central frequency of the ROADMs are ideally aligned. However, in practice both of them may randomly drift, leading to a frequency mismatch. In this situation, the SCM signal’s spectrum is asymmetrically filtered, and it’s essential to investigate the impact of the frequency mismatch. In Fig. 5(a), we first evaluate the achievable capacity versus the frequency mismatch in a 4-subcarrier system given OSNR = 21 dB and 6 cascaded ROADMs. For all of the systems, the achievable capacity decreases with the increasing of the frequency mismatch, since one edge subcarrier of the SCM signal is more severely filtered which degrades the overall performance. The proposed system using adaptive TDHQ loading is much more robust to the frequency mismatch. Considering a 2.5 GHz frequency mismatch [27], the capacity of the proposed system compared to the case without frequency mismatch is reduced by only 12.2 Gb/s, whereas the capacity is reduced by 48.9 Gb/s and 55.9 Gb/s for the systems using uniform TDHQ and uniform standard QAM, respectively. Then we fix the frequency mismatch at 2.5 GHz and calculate the relationship between the achievable capacity and number of cascaded ROADMs given OSNR = 21 dB, as shown in Fig. 5(b). Note the system using uniform QPSK can only tolerate 10 cascaded ROADMs in the presence of a 2.5 GHz frequency mismatch. Again, the proposed system using adaptive TDHQ loading can achieve more capacity under all ROADM cases. The average capacity over all ROADMs cases from 1 to 10 is 156.53 Gb/s and 176.1 Gb/s for the systems using uniform standard QAM and uniform TDHQ, respectively. And it increases to 221.87 Gb/s for the proposed system using adaptive TDHQ loading, indicating 41.7% improvement compared to the scheme using uniform standard QAM. Further, we find the average capacities over all ROADM cases from 1 to 10 for the schemes using standard QAM, uniform TDHQ and proposed adaptive TDHQ loading are reduced by 44.7 Gb/s, 39.8 Gb/s and 6.64 Gb/s in the presence of a 2.5 GHz central frequency offset, respectively, compared to the cases without frequency mismatch.
Fig. 5 (a) Achievable capacity versus the frequency mismatch given OSNR = 21 dB and 6 cascaded ROADMs. (b) Achievable capacity versus number of cascaded ROADMs given OSNR = 21 dB and the frequency mismatch = 2.5 GHz.
4.2 Experiments
In this part, the capacity improvement using TDHQ based bit loading in SCM systems is experimentally investigated. The experimental setup is shown in Fig. 6. Dual-polarization 4-subcarrier signals are first generated offline in MATLAB, and then the real and imaginary components are loaded to the transmitter module of a Ciena WaveLogic3 transceiver, which incorporates an external cavity laser (ECL), four 39.4 GS/s DACs and a DP Inphase/Quadrature modulator [28]. The total symbol rate, i.e. 34.94 Gbaud, is the same as that in the simulations. The ECL wavelength is set to be 1554.94 nm and the linewidth is measured to be < 20 kHz. The transmission loop contains 320 km of standard single mode fiber (SSMF), and the EDFAs are employed after every 80 km fiber to compensate the loss. To emulate cascaded ROADMs induced filtering, a Finisar WaveShaper (WS) with a variable 3-dB bandwidth is inserted after the second EDFA. The central frequency of the WS is aligned to the carrier frequency of the transmitter-side laser. At the receiver-side, a four-channel real-time oscilloscope with a sampling rate of 80 GSa/s per channel is used to digitize the waveform after coherent detection. The frequency offset between the transmitter-side laser and local oscillator (LO) is measured to be < 2 GHz. The transmitter-side and receiver-side DSP are the same as that in simulations except that a timing recovery module is added before the adaptive equalization [29].
First, the received average SNRs for edge and central subcarriers as a function of the WS 3-dB bandwidth after transmitting 7 loops are shown in Fig. 7(a). The launch power is 1 dBm. The received SNR of the central subcarriers remains almost the same as the 3-dB bandwidth varies, whereas the received SNR of the edge subcarriers decreases as the 3-dB bandwidth reduces because the edge subcarriers are severely filtered. Then in Fig. 7(b), we investigate the achievable capacity as a function of the WS 3-dB bandwidth after transmitting 7 loops. For a large WS 3-dB bandwidth, e.g. 46 GHz, the SNR difference between edge and central subcarriers is small. Therefore, the optimal solution is to use the same format, which is 16QAM in the experiment. In this case, the achievable capacity is the same for all the SCM schemes. However, as the bandwidth decreases, the edge subcarriers are severely filtered and the SNR difference becomes large. When the 3-dB bandwidth is small, e.g. 36 GHz, the received SNR of the edge and central subcarriers is 6.6 dB and 13.3 dB, respectively. In this scenario, compared with the scheme using uniform standard QAMs on all subcarriers, the system using uniform TDHQ on all subcarriers achieves a capacity improvement of 37.5%. The proposed system with the adaptive TDHQ loading further increases the achievable capacity and a capacity improvement of 62.5% is obtained. Furthermore, by averaging the capacity improvement over all the 5 WS 3-dB bandwidth cases from 36 GHz to 46 GHz, the average capacity improvement is 14.2% and 28.8% for the system using uniform TDHQ and the adaptive TDHQ loading, respectively.
Fig. 7 (a) Received SNR of subcarriers after transmitting 7 loops. (b) Achievable capacity versus WS 3-dB bandwidth after transmitting 7 loops.
In Fig. 8, we fix the WS 3-dB bandwidth at 40 GHz and investigate the achievable capacity as a function of transmission distance. Note that only 11 loops with 11 cascaded WSs can be tolerated for the scheme using uniform QPSK on each subcarrier, due to the noise induced by the 4 EDFAs and fiber nonlinearities. As expected, using TDHQ can achieve a continuous tradeoff between capacity and distance, which enables to convert the SNR margin into capacity for each specific link. However, using uniform TDHQ over subcarriers is still vulnerable to the narrow optical filtering. The proposed scheme with TDHQ based bit loading can significantly increase the capacity especially at longer distances where more cascaded filtering happens as shown in Fig. 8. The average capacity over all 9 transmission distance cases from 3 loops to 11 loops for the scheme using uniform standard QAM is 161.52 Gb/s, and the average capacity improvement obtained by using uniform TDHQ and adaptive TDHQ loading is 10.2% (16.47 Gb/s) and 26.1% (42.16 Gb/s), respectively.
5. Capacity: SCM versus single carrier
In the previous section, we have demonstrated that the adaptive TDHQ loading can significantly increase the filtering tolerance and ensure higher achievable capacity for SCM systems. As mentioned earlier, in a capacity-approaching scenario, mitigating fiber nonlinearities and increasing tolerance to diverse inline optical filtering are both key to squeeze more capacity. The SCM system was first employed for its improved tolerance to fiber nonlinearities compared with a single carrier system [1–3]. In this section, we will show by simulations that equipped with the adaptive TDHQ loading the SCM system can also outperform its single carrier counterpart in terms of the optical filtering induced by cascaded ROADMs.
First, we numerically evaluate the capacity as a function of OSNRs as shown in Fig. 9(a). Systems with 1 (single carrier), 4, 8 and 12 subcarriers are investigated and compared. In this section, the simulation setup and corresponding parameters can be found in Section 2 and we assume the carrier frequency of the transmitter-side laser and the central frequency of the ROADMs are ideally aligned. The adaptive TDHQ loading is applied to all the systems. The number of cascaded ROADMs is set to 12, which leads to a relatively strong filtering effect. As per Fig. 9(a), the achievable capacity becomes higher as the number of subcarriers increases, and start to saturate with 12 subcarriers. We owe this result to the fact that more subcarriers are needed to better approximate the theoretically-optimal water-filling approach with a colored SNR distribution. Also, the capacity improvement becomes larger for higher OSNR because the ratio of the noise induced by the optical filtering increases in this case. Specifically, considering the capacity of 200 Gb/s, about 2 dB OSNR sensitivity improvement can be obtained by the SCM system with 12 subcarriers with respect to the single carrier system. Moreover, by averaging the capacity improvement over all 8 OSNR cases from 16 dB to 23 dB in Fig. 9(a), the proposed system can achieve an average capacity improvement of 11.8% compared with the single carrier system.
Fig. 9 (a) Achievable capacity versus OSNRs. (b) Achievable capacity versus the number of cascaded ROADMs.
Next, we numerically fix the OSNR at 21 dB and evaluate the capacity as a function of the number of cascaded ROADMs. As shown in Fig. 9(b), the performance of all the systems degrade with an increasing number of cascaded ROADMs. When there are less than 6 ROADMs, all the schemes show similar performance. However, as the number of ROADMs goes beyond 7, the benefit of the proposed TDHQ based adaptive bit loading begins to appear. Moreover, the improvement over the single carrier system becomes larger with more ROADMs. For instance, when the number of ROADMs increases from 10 to 16, the capacity improvement increases from 11.7 Gb/s to 37.3 Gb/s. The bits-per-symbol on each subcarrier given 10 and 16 cascaded ROADMs are shown in Fig. 10(a) and 10(b), respectively. The achievable bits-per-symbol on each subcarrier depends on the corresponding received SNR. We take the 8-subcarrier scheme as an example. When the number of ROADMs is increased from 10 to 16, the received SNRs of the innermost 4 subcarriers remain almost the same, whereas the received SNRs of the outermost 2 subcarriers decrease rapidly. The received SNRs of the rest 2 subcarriers decrease at a slower pace. As a result, the bits-per-symbol on the innermost 4 subcarriers keeps the same (4.5 bits). The bits-per-symbol on the outermost 2 subcarriers is reduced rapidly from 2 bits to 1 bits. The bits-per-symbol of the rest 2 subcarriers is reduced slightly from 4.375 bits to 4.125 bits. We can see that the adaptive TDHQ loading can exploit the SNR margin on each subcarrier to approach the channel capacity with narrow optical filtering. Finally, the average capacity improvement over all 17 ROADM cases from 1 to 17 with respect to the single carrier system are summarized in Table 2. With 12 subcarriers, it can get 7.59% improvement, corresponding to 15.73 Gb/s more capacity. Note that the adaptive TDHQ loading method can also improve the performance of future high-baud-rate optical systems where transceiver bandwidth is limited.
Fig. 10 Bits-per-symbol on each subcarrier given (a) 10 ROADMs; (b) 16 ROADMs. OSNR = 21 dB,: symbol rate.
Table 2. Simulated average capacity improvement over various ROADM cases, compared with the single carrier system. OSNR = 21 dB.
6. Conclusions
In this paper, we investigate the capacity improvement using TDHQ based adaptive bit loading in digital SCM systems in the presence of cascaded ROADMs induced optical filtering. In a 4-subcarrier SCM system with an aggregate symbol rate of 34.94 Gbaud, the average capacity improvements of 31.75% and 26.1% are achieved compared with that using uniform standard QAM in simulations and experiments over various link conditions, respectively. Moreover, using TDHQ based adaptive bit loading enables the SCM system to further approach the channel capacity in optical links with narrow filtering because of the finer subcarrier granularity. Compared with its single carrier counterpart using TDHQ, an average capacity improvement of 7.59% is obtained in our simulations over all 17 ROADMs cases from 1 to 17 at OSNR = 21 dB.
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