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Simultaneous reception of AMCC signals and QPSK signals by a single coherent receiver with DSP

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Abstract

This paper investigates an auxiliary management and control channel (AMCC) signal extraction method using digital signal processing (DSP) blocks with 3-step moving averaging that allows a single coherent receiver to receive main signal and AMCC signal simultaneously. Receiver sensitivity characteristics versus the modulation index (MI) and average number of the proposed DSP blocks are elucidated. Based on the results, we discuss a policy for designing the parameters. Experiments apply the design policy to achieve receiver sensitivity of –41.8 dBm with both 25 Gbit/s QPSK main signal and 128 kbit/s AMCC signal; the main signal sensitivity penalty is just 0.2 dB.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Recently, large-capacity and low-latency networks have been studied to realize various new services such as virtual reality and e-sports. In wireless access, the 5 G mobile service with large-capacity and low-latency has started as a next generation wireless system. In the optical access network, wavelength division multiplexing passive optical network (WDM-PON) or the WDM-overlay which is an option of next-generation passive optical network 2 (NG-PON2), is one of the candidates to realize such large-capacity and low-latency networks because a wavelength channel is exclusively allocated to each user and service [1]. So far, many studies have used the WDM-PON/WDM-overlay for supporting delay-sensitive mobile services [2]. Another candidate is the all-photonics network (APN), which expands the coverage area of photonics-based networks [3], [4] into the access network [5]. In [5], by directly connecting user terminals via optical switches, the bandwidth limitation and latency caused by conventional electrical switches can be eliminated allowing large-capacity and low-latency networks to be built. Since both WDM-PON/WDM-overlay and APN accommodate the user terminals located outside of the network operator’s premises, the use of auxiliary management and control channel (AMCC) has been studied to remotely control user terminal wavelength and/or to monitor the user terminal during operation [611]. The AMCC is a low-latency control channel, realized by superimposing a low speed control signal in a low-frequency band of the main signal with relatively small modulation index (MI) so as to suppress interference on the main signal. While many published research of AMCC are for intensity modulation-direct detection systems [611], recently, its application to digital coherent systems which enables large-capacity transmission has been reported [12], [13]. In [12], [13], different receivers are used to capture an intensity modulated AMCC signal or a phase modulated QPSK signal. This approach demands the use of an optical splitter and two different receivers, which raises user equipment cost and optical loss. To address this issue, we proposed a method that allows a single coherent receiver to receive the main signal and AMCC signal by dividing them by digital signal processing (DSP) [14]. To extract the AMCC signal, our DSP proposal removes the main signal and sub-carrier from the received signal. There are three key blocks for AMCC signal extraction; (i) Remove main signal, (ii) DC estimation, (iii) Sub-carrier removal. These blocks are implemented by simple moving average based filters in order to reduce DSP loads. Our previous work experimentally demonstrated that our DSP algorithm could successfully decode the AMCC signal and examined the bit error rate (BER) (not receiver sensitivity) for the average number of proposed DSP blocks, given a certain MI and received optical power [14]. However, the receiver sensitivity with different values of MI and average number, which directly affect the characteristics, has not been examined. In this work, we study the impact of MI and average number on receiver sensitivity characteristics (not BER), and discuss the design policy to identify the best parameters. With the design policy, receiver sensitivity of –41.8 dBm was achieved with both 25 G bit/s QPSK main signal and 128 K bit/s AMCC signal; the penalty imposed on main signal sensitivity was just 0.2 dB.

This paper is organized as follows. Section 2 describes the proposed configuration and DSP algorithm. In Section 3, the BER characteristics of main signal and AMCC signal are experimentally investigated given a certain MI. Section 4 shows the receiver sensitivity of main signal and AMCC signal with different MI values. Then, design policy of the parameters is discussed. Finally, our proposal’s tolerance to chromatic dispersion is confirmed in a transmission experiment.

2. Proposed system

2.1 Use cases of AMCC

Figure 1(a) shows the configuration of the WDM-PON based mobile fronthaul network. In the mobile system, the antennas placed at outside are connected to the central office through an optical fiber network. In the 5 G mobile system, since the area covered by one antenna becomes more constrained due to the use of the high frequency band, many antennas must be installed. In such a situation, WDM-PON application is effective. This is because the PON system enables the number of fibers to be reduced by sharing the transmission line among multiple antennas, and WDM technology allocates a wavelength channel exclusively to each user so that large-capacity and low-latency networks can be built. The ONU is equipped with a tunable laser for transmitting upstream signals at arbitrary wavelengths. The ONUs transmit upstream signals at the appropriate wavelengths after being notified by the OLT through AMCC.

 figure: Fig. 1.

Fig. 1. Use cases of AMCC. (a) WDM-PON. (b) All-Photonics Network.

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Figure 1(b) shows the configuration of the APN. APN provides end-to-end optical paths by directly connecting the user equipment through optical switching nodes, which minimizes the electronic processing needed for packet conversion, multiplexing/switching control, etc. Thus, routing latency can be minimized and bandwidth is not constrained by upper layer switching equipment. In APN, individual wavelengths and paths are dynamically allocated to each user equipment by the controller. To allocate a wavelength and an optical path, the controller has to gather information from user equipment, and then send the control message to them in the C-Plane. To realize this scheme, it is expected that the user equipment and the nearest optical node are connected by using AMCC (Case 1 in Fig. 1(b)) [15]. After the optical path is allocated and established, user equipment will start communication; the optical signal can leak into an unexpected path if the node has a malfunctioning optical switch and/or optical filter. Therefore, it is important that user equipment can identify whether the received signal is transmitted from the correct equipment. This can be realized by reading the AMCC signal from received signal, which is superimposed at the transmitter and includes the transmitter’s identifier. In this case, the AMCC signal traverses the same optical path as the main signal (Case 2 in Fig. 1(b)). As described above, while there are several paths the AMCC signal can traverse in the APN, in this paper, as a common path with WDM-PON, we assume that the AMCC signal uses the same optical path as the main signal.

In previous works, intensity modulation is used to transmit the AMCC signal [611]. Figure 2(a) shows the conventional configuration in a digital coherent system [13]. Here, a semiconductor optical amplifier (SOA) is employed as an external intensity modulator for AMCC signal superimposition. At the transmitter side, the AMCC signal is superimposed by a polarization independent SOA installed after the IQ modulator. At receiver side, AMCC signal must be extracted from the main signal. The conventional configuration divides the main and AMCC signals by an optical splitter, thus, two dedicated receivers are needed for the two signals, which raises user equipment costs and optical loss. To address this problem, we proposed a method to receive the main signal and AMCC signal with single coherent receiver and divide them by digital signal processing (DSP) [14] (see Fig. 2(b)). We detail the proposed DSP algorithm in the next sub-section.

 figure: Fig. 2.

Fig. 2. Optical transmission system using AMCC. (a) Conventional configuration. (b) Proposed configuration of receiver.

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2.2 Proposed DSP for AMCC extraction

Figure 3(a) shows the proposed receiver DSP algorithm. The upper part shows the flow for main signal detection; the blocks perform adaptive finite impulse response (FIR) filtering, carrier frequency offset compensation (CFOC), carrier phase recovery (CPR), and decoding. The lower part shows the flow for AMCC signal detection. Here, we assume the use of sub-carrier based AMCC signals to eliminate the undesirable direct current (DC) component [611]. First, the absolute value is calculated from the complex amplitude of the IQ signal output from the coherent receiver (see Point A). High speed main signal is removed in (i) Remove main signal block which performs 1st moving averaging as a simple low pass filter (see Point B). (ii) DC estimator block estimates the DC component in the output of block (i) by 2nd moving averaging, which is subtracted (see Point C). After the absolute value is calculated, the sub-carrier component is removed in (iii) Remove sub-carrier block which applies 3rd moving averaging (see Point D). Finally, decision is performed. In this study, we propose to use moving averaging as a simple low pass filter to reduce the computational complexity. Averaging consumes far fewer DSP resources than the general DSP for the main signal e.g. the adaptive FIR filter, CFOC and CPR. Thus we consider the impact of this proposal on implementation practicality is negligible.

 figure: Fig. 3.

Fig. 3. Proposed DSP algorithm. (a) Block diagram for decoding QPSK signal and NRZ based AMCC signal. (b) Waveform in the flow for AMCC signal detection.

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3. Characteristics of averaging number and received optical power

3.1 Experimental setup

An experiment was conducted to investigate the feasibility of our proposal. As mentioned in Section 2.1, we assume that the AMCC signal traverses the same optical path as the main signal. The experimental setup is shown in Fig. 4(a). The transmitter consisted of a distributed feedback laser diode (DFB-LD), an IQ modulator and a SOA. The output wavelength and linewidth of the DFB-LD were 1552 nm and 100 kHz, respectively. Here, we employed 12.5 Gbaud QPSK (25 Gbit/s) as the main signal for optical access networks. The main signal was generated by an arbitrary waveform generator (AWG) and mapped to optical phase by the IQ modulator. In order to superimpose the AMCC signal, the SOA was driven by 128 kbit/s non-return-to-zero (NRZ) signals with 500 kHz sub-carrier generated by another AWG. The bit streams of QPSK main signals and AMCC signals contained pseudo-random bit sequences (PRBSs) of 215–1 and 27–1, respectively. Figure 4(b) shows the waveform output by the SOA without main signal. Here, the MI is given by

$$\textrm{MI}\,[\mathrm{\%} ]= \frac{{{P_{max}}-{P_{min}}}}{{{P_{ave}}}} \times 100$$
where Pmax, Pmin, is maximum and minimum power of the AMCC signal, respectively [13]. Pave is average optical power given by (Pmax + Pmin)/2. As MI is an important parameter, it determines receiver sensitivity of main and AMCC signals, first, we set the MI to 7.4%. The input and output power of the SOA were –2 and 2.9 dBm, respectively. After passing through the SOA, the optical power of the signal (with AMCC signal) was attenuated by the variable optical attenuator (VOA) which emulated the transmission loss.

 figure: Fig. 4.

Fig. 4. Experimental setup. (a) Configuration. (b) Intensity of AMCC signal without main signal.

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The receiver consisted of an erbium doped fiber amplifier (EDFA) as a pre-amplifier, a band-pass filter (BPF), a coherent receiver and a DFB-LD as a local oscillator (LO). The gain and the noise figure of the EDFA were 21.5 dB and 5.7 dB, respectively. The LO had output power of 10.0 dBm with linewidth of 100 kHz. The states of polarization of the received signals were aligned to the principal axis of the coherent receiver. A BPF (loss and bandwidth of 1.2 dB and 0.48 nm) was installed after EDFA to reduce ASE. Received signal was sampled at 25 GSamples/s (2 times oversampling) and processed by offline DSP. The DSP blocks for main signal consisted of an FIR filter realized by a constant modulus algorithm (CMA) [16], CFOC [17] and CPR using the 4-th power method [18], and a decoder. FIR filter tap number was set to 7.

3.2 BER characteristics of main signal

To evaluate the BER characteristics of main signals, we have to consider the fluctuation in received signal intensity caused by superimposing the AMCC signal. Figure 5 shows the time fluctuation of BER characteristics for main signal and received signal intensity. As shown in the figure, the BER of the main signal changes on the period of the sub-carrier. In order to consider the worst case, we evaluated the worst BER of main signal in one sub-carrier period at the AMCC symbol position. BER of main signal with and without AMCC signal is shown in Fig. 6. Assuming that the forward error correction (FEC) limit for the main signal is BER =10–3, receiver sensitivity of –41.8 dBm was achieved with AMCC signal imposed, where the penalty caused by superimposition of the AMCC signal was just 0.2 dB.

 figure: Fig. 5.

Fig. 5. BER of main signal versus time.

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 figure: Fig. 6.

Fig. 6. BER of main signal versus ROP.

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3.3 BER characteristics of AMCC signal

In this sub-section, receiver sensitivity of AMCC signal versus the averaging number of the proposed DSP is described. In block (i) at Fig. 3, although increasing the averaging number strengthens the removal of the high frequency component (main signal) and thus enhances the signal to noise ratio (SNR), moving averaging with excessively large averaging numbers leads to the removal of the AMCC signal. Thus, there is some optimal averaging number. Block (iii) also has an optimal averaging number for the same reason. BER of AMCC signal versus averaging number of blocks (i) and (iii) with received optical power (ROP) = –50 dBm is shown in Fig. 7(a). While the estimation accuracy of the DC component increases as the averaging number of block (ii) increases, the improvement saturates. Here, the averaging number of block (ii) was set to 75000 to estimate the DC component accurately. It is found that BER distribution does not shape the local minimum for moving average number of blocks (i) and (iii); there is an area that yields better BER. We investigated BER characteristics with different ROP values. BER of AMCC signal for averaging number of block (i) and (iii) with ROP values of –51, –52, –53, –54 dBm is shown in Fig. 7(b)–(e). The receiver sensitivity of AMCC signal calculated for 1st and 3rd averaging number based on Fig. 7(a)–(e) is shown in Fig. 8. Here, FEC limit for AMCC signal was assumed to be BER = 10–6 [19]. In the offline experiment, BER 10–3 or less cannot be evaluated because the amount of data sampled for such a region is excessive (128 kbps AMCC signal is sampled with 25 G Sample/s). Thus, we calculated the receiver sensitivity of AMCC signals from the obtained BER given the target of BER = 10–6. Better receiver sensitivity was achieved when blocks (i) and (iii) had averaging numbers of 21 × 103, and 15 × 104, respectively (Case X). BER versus ROP in Case X is shown in Fig. 9. As can be seen, AMCC signal receiver sensitivity of –45.5 dBm was achieved in Case X. Since the frequency band to be removed differs in blocks (i) and (iii), the optimal averaging number for minimizing the receiver sensitivity also differs. Optimal averaging number of block (i), 21 × 103, is 42% of the sub-carrier period. Since the frequency component of the sub-carrier to be extracted in block (i) will be removed when the averaging number exceeds one half the subcarrier period, the optimal average number, 42%, is a reasonable value. In block (iii), the moving average function works as a low pass filter for baseband signals. Focusing on the case of the continuous symbol pattern that alternates between 0 and 1 (e.g. 0, 1, 0, 1…) which forms the higher frequency component in the AMCC signals, the waveform repetition period is double the symbol period of the NRZ signal (TNRZ). Similar to block (i), the frequency component of the symbol pattern will be removed when the averaging number exceeds one half the repetition period (2×TNRZ). Therefore, optimal averaging number of block (iii), 15 × 104, is 38.4% of 2×TNRZ, which is also a reasonable value. Better receiver sensitivity can be achieved by setting the average number of proposed DSP blocks as high as possible without removing the signal.

 figure: Fig. 7.

Fig. 7. BER of AMCC signal for 1st and 3rd moving averaging. (a) ROP = -50 dBm. (b) ROP = -51 dBm. (c) ROP = -52 dBm. (d) ROP = -53 dBm. (e) ROP = -54 dBm.

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 figure: Fig. 8.

Fig. 8. Receiver sensitivity of AMCC signal for 1st and 3rd moving averaging.

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 figure: Fig. 9.

Fig. 9. BER of AMCC signal versus ROP.

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4. Characteristics yielded by modulation index and transmission

Receiver sensitivity of the main signal and the AMCC signal are in a trade-off relationship with MI, making it important to clarify this relationship and find the proper value. In this section, we describe the receiver sensitivity of the main signal and AMCC signal with different MI values and the average number. Based on the results, we discuss the parameter design of the MI and the average number. Furthermore, the results of a 100 km transmission experiment are also shown.

4.1 Characteristics of main and AMCC signals for MI

BER characteristics of the main signal with different MI values are shown in Fig. 10. Assuming the FEC limit is 10–3 for the main signal, the receiver sensitivity with MI of 4.6%, 7.4%, 12.2%, 16.4% was –42.0 dBm, –41.8 dBm, –41.6 dBm, –41.4 dBm, respectively, thus the respective penalties due to superimposition of AMCC signal were 0.0 dB, 0.2 dB, 0.4 dB, 0.6 dB. As MI increases, the intensity fluctuation also increases, which worsens the main signal’s receiver sensitivity penalty.

 figure: Fig. 10.

Fig. 10. BER of main signal versus ROP.

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Receiver sensitivity of AMCC signal for averaging number of block (i) and (iii) with MI values of 4.6%, 7.4%, 12.2%, 16.4% are shown in Fig. 11(a)–(d). It can be seen that the area with better receiver sensitivity does not depend on MI. When the MI is 7.4% or 12.2%, BER of AMCC signal is minimized in Case X (1st averaging number is 21 × 103, 3rd averaging number is 15 × 104). When the MI is 4.6% or 16.4%, although BER is not minimized in Case X, the discrepancy from the minimum point is just 0.2 dB and 0.3 dB, respectively, which is negligible.

 figure: Fig. 11.

Fig. 11. Receiver sensitivity versus 1st average number. (a) MI = 4.6%. (b) MI = 7.4%. (c) MI = 12.2%. (d) MI = 16.4%.

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4.2 Parameter design for modulation index and average number

As mentioned in previous sub-section, MI and average number of proposed DSP blocks affect receiver sensitivity of the main and AMCC signals. Here, we discuss the parameter design of the MI and the average number based on the main signal and AMCC signal receiver sensitivity examined in the previous sub-section.

Figure 12(a) plots the penalty of main signal sensitivity versus MI. It can be seen that the penalty increases with MI. As mentioned in Section 2, we assume that the AMCC signal uses the same optical path as the main signal. In this case, it is preferable for AMCC to have receiver sensitivity greater than that of the main signal so that the C-plane can remain active even if the main signal cannot reach due to insufficient received optical power. This margin has to be properly set according to each network’s requirements. In this study, we set the required receiver sensitivity of AMCC signal to –43 dBm for considering the receiver sensitivity of main signal without AMCC superimposition (–42 dBm) with 1 dB margin. From the result of Section 3.3, while the minimum receiver sensitivity of –45.5 dBm can be obtained at Case X (1st average: 21 × 103, 2nd average: 15 × 104, the total average number (1st + 2nd stages) is 171000), relaxing the required AMCC signal receiver sensitivity to –43 dBm yields room to reduce total average number to lessen the computation resource requirements. Here, we defined the smallest total average number while attaining the required AMCC signal receiver sensitivity as the ‘Minimum average number’. In the case of MI = 7.4%, if the required receiver sensitivity for AMCC signal is reduced to –43 dBm, the average number can be reduced to 45000, as can be seen from Case Y in Fig. 11(b) (1st average: 15000, 2nd average: 30000). The ‘Minimum average number’ versus MI is shown in Fig. 12(b). It should be noted that MI values less than 7.4% cannot be employed because AMCC receiver sensitivity does not reach the required AMCC receiver sensitivity (–43 dBm) as also can be seen in Fig. 11(a). As shown in Fig. 12(b), the minimum average number decreases as MI increases since AMCC signal amplitude increases. A comparison of Fig. 12(a) and (b) finds that the ‘Minimum average number’ and the receiver sensitivity penalty of the main signal are in a trade-off relationship. From the above, to select the proper parameter value, it is important to examine the Minimum average number based on the required receiver sensitivity of the AMCC signal, and then determine the MI value considering the allowable average number (DSP circuit scale) and sensitivity penalty of the main signal.

 figure: Fig. 12.

Fig. 12. (a) Penalty of main signal sensitivity versus MI. (b) Minimum average number versus MI.

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4.3 Transmission

From the standpoint of the main signal, the superimposition of AMCC signal can be regarded as creating very slow amplitude fluctuations, so waveform distortion due to chromatic dispersion happens in the same manner as in conventional transmission systems and thus can be compensated by receiver side equalization in digital coherent transmission systems. The nonlinear waveform degradation will have little effect on the main signal because the output power from the SOA was only +2.9 dBm (see Section 3.1) and the maximum intensity increase by superimposing the AMCC signal with MI = 7.4% is only +0.16 dB. Since the data rate of AMCC is much lower than that of the main signal, it is expected that AMCC will be basically unaffected by chromatic dispersion and nonlinearity. To confirm the assumptions that the BER characteristics of the main and AMCC signals do not degrade with transmission, we conducted a 100 km transmission experiment. Figure 13(a) plots BER of main signal in back-to-back and 100 km transmission. From Section 4.2, MI was set to 7.4% so as to minimize the penalty of main signal receiver sensitivity while maintaining AMCC sensitivity of –43 dBm. As shown in Fig. 13(a), there is no penalty due to transmission of the main signal. Receiver sensitivity of 100 km transmission at FEC limit of main signal (BER = 10–3) was almost same as the back to back (B2B) case (–41.8 dBm). Figure 13(b) plots BER of AMCC signal in the case of back-to-back and 100 km transmission, respectively. Based on the discussion in Section 4.2, average numbers of blocks (i) and (iii) were set to Case Y. As shown in Fig. 13(b), there is no penalty due to transmission of the AMCC signal. This is attributed to the small AMCC frequency band. Receiver sensitivity of 100 km transmission at FEC limit of AMCC signal (BER = 10–6) was –43 dBm. From the above, adequate receiver sensitivity including the main signal and AMCC signal of –41.8 dBm was achieved with 100 km transmission.

 figure: Fig. 13.

Fig. 13. BER characteristics with back to back and 100 km transmission. (a) Main signal. (b) AMCC signal.

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5. Conclusion

As conventional approaches to AMCC signaling pass the received signal through an optical power splitter and employ a dedicated AMCC signal receiver, they increase device number and degrade receiver sensitivity due to splitting loss. To avoid these problems, we proposed a method that uses a single coherent receiver to receive main signal and AMCC signal simultaneously and then divides them by DSP. Our proposed DSP algorithm has three key blocks, (i) Main signal removal, (ii) Sub-carrier removal, and (iii) DC estimation. These blocks are implemented by simple moving averaging which reduces DSP resource requirements. We experimentally demonstrated that our DSP algorithm successfully decoded both the AMCC signal and main signal. We investigated the receiver sensitivity of the main signal and AMCC signal with different MI values and average number. Consequently, it was revealed that receiver sensitivity of AMCC signal can be minimized with a certain average number (Case X). If the AMCC signal receiver sensitivity required in the network has some margin compared to the minimum one in Case X, there is room to reduce total average number. We discussed the design policy of MI and the average number for this situation. Based on the characteristics of the minimum average number and the receiver sensitivity penalty of the main signal with different MI values, the network operator can determine the optimal MI value and average number to reduce DSP circuit scale and sensitivity penalty of the main signal. With the MI value of 7.4%, AMCC receiver sensitivity of –41.8 dBm, which is better than that of the main signal, was achieved with main signal penalty of just 0.2 dB. Finally, we conducted a transmission experiment to clarify the effect of the chromatic dispersion. It was confirmed that there is no penalty in terms of AMCC receiver sensitivity with 100 km transmission. While reducing the device number and optical loss, our proposed configuration allows the main signal and AMCC signal to be decoded with just 0.2 dB penalty. Our proposed DSP based on moving averaging consumes far fewer DSP resources than general DSP for the main signal e.g. the adaptive FIR filter, CFOC and CPR. Thus we consider the impact of this proposal on implementation is negligible.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (13)

Fig. 1.
Fig. 1. Use cases of AMCC. (a) WDM-PON. (b) All-Photonics Network.
Fig. 2.
Fig. 2. Optical transmission system using AMCC. (a) Conventional configuration. (b) Proposed configuration of receiver.
Fig. 3.
Fig. 3. Proposed DSP algorithm. (a) Block diagram for decoding QPSK signal and NRZ based AMCC signal. (b) Waveform in the flow for AMCC signal detection.
Fig. 4.
Fig. 4. Experimental setup. (a) Configuration. (b) Intensity of AMCC signal without main signal.
Fig. 5.
Fig. 5. BER of main signal versus time.
Fig. 6.
Fig. 6. BER of main signal versus ROP.
Fig. 7.
Fig. 7. BER of AMCC signal for 1st and 3rd moving averaging. (a) ROP = -50 dBm. (b) ROP = -51 dBm. (c) ROP = -52 dBm. (d) ROP = -53 dBm. (e) ROP = -54 dBm.
Fig. 8.
Fig. 8. Receiver sensitivity of AMCC signal for 1st and 3rd moving averaging.
Fig. 9.
Fig. 9. BER of AMCC signal versus ROP.
Fig. 10.
Fig. 10. BER of main signal versus ROP.
Fig. 11.
Fig. 11. Receiver sensitivity versus 1st average number. (a) MI = 4.6%. (b) MI = 7.4%. (c) MI = 12.2%. (d) MI = 16.4%.
Fig. 12.
Fig. 12. (a) Penalty of main signal sensitivity versus MI. (b) Minimum average number versus MI.
Fig. 13.
Fig. 13. BER characteristics with back to back and 100 km transmission. (a) Main signal. (b) AMCC signal.

Equations (1)

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MI [ % ] = P m a x P m i n P a v e × 100
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