Performance evaluations of hybrid modulation with different optical labels over PDQ in high bit-rate OLS network systems

M. Xu; Y. Li; T.Z. Kang; T.S. Zhang; J.H. Ji; S.W. Yang

doi:10.1364/OE.24.026228

1. Introduction

Optical label switch using orthogonal modulation formats has been emerged in the early 1990’s, worked by Leonid Kazovsky’s group at Standford University on the STARNET network [1,2], and was revived and followed by a number of groups worldwide in the early to mid-2000’s, just like European project STOLAS (Switching Technologies for Optically Labeled Signals) [3]. With the development of big data and cloud computing,100Gb/s backbone network is applied to commercial network now [4]. Data centers are seriously facing the rapid increase of network traffic and require an alternative solution to replace current electrical packet switching networks. Therefore, ultra-fast all-optical switching and routing are important technique in ultrahigh speed optical communication systems [5,6]. Optical label switching (OLS) over 100Gb/s network can offer high-capacity and energy-efficient switching networks [7].

Over the past few years, many labels have been proposed, such as amplitude shift keying (ASK or OOK), frequency shift keying (FSK), binary phase shift keying (BPSK), and polarization shift keying (PolSK) [8–11]. Compared with these conventional modulation formats, duobinray (DB) modulation is known as its high spectral efficiency and easy to detect with direct detection [12,13]. The pulse position modulation (PPM) is sensitive to pulse position and its intensity is constant, so that it can solve the extinction ratio (ER) conflict of intensity modulation and phase modulation and offer high tolerance to dispersion [14,15]. These two types of coding are well suited to transceiver with low power consumption. In addition, POLMUX-DQPSK (or PDQ) used as the optical payload may be a sensible choice in high capacity communications and low structural complexity system. For system capacity of DQPSK is the double of different phase shift keying (DPSK) with same symbol rate and 3dB better than that of ASK, PDQ can offer four times the capacity of the system than DPSK system upon a given symbol rate in two polarization directions multiplexing system [16]. In this paper, the OLS systems based on payload of PDQ and the optical labels of DB and PPM are studied.

The theoretical BER performance of DB with direct detection in optical fiber communication was studied in paper [13]. The optical signal-to-noise ratio (OSNR) of DB is about 0.91dB better than ASK at BER = 10⁻⁹. The BER performance of PPM in atmospheric optical communication and optical fiber communication were given in papers [16–18]. The combination BER of PPM and POLMUX-QPSK (or PQ) was researched in paper [19]. The receiver sensitivity of PQ-PPM was 2.8dB better than PQ. The theoretical BER performance of DQPSK can be founded in papers [20,21] but not in hybrid modulation forms. In fact, the optical label modulated on the optical payload and transmitted together is an application of hybrid modulation, which has been researched in wireless communications [22,23]. Hybrid modulation schemes but in unbalancing baud rate between the label and payload signals in OLS system are different from that combined modulation, which have same relatively low symbol rates, for example of, PQ modulated with M-ary PPM or other researches [19,22]. There is very little theoretical research on the BER of hybrid modulation of label and payload, and seldom studied about the effect of optical label on optical payload in the OLS system. In this paper, the hybrid modulation BER of PDQ payload and PPM or DB label in their different ratio coefficients of bit rates are analyzed in OLS systems and are demonstrated by the simulation.

2. Theoretical BER expressions of hybrid modulation PDQ-PPM and PDQ-DB

2.1 Theoretical BER expression of PDQ

Based on Gaussian approximation, BER of signal can be approximated by error function erfc(x) or Q factor as follows:

B E R \approx \frac{1}{2} e r f c (\frac{Q}{\sqrt{2}}) \approx \frac{\exp (- \frac{Q^{2}}{2})}{Q \sqrt{2 π}}

Different modulation formats have different Q factor expressions. Q factor expression of DQPSK with differential direct detection can be found in Nicola and Peng’s research [20,21], which have not only included a optimal value in a matched optical filter but also considered the dispersion and nonlinearlities. The other theoretical $B E R_{D Q P S K}$ equation can be seen in X.Liu [16] but no considered the transmission impairments. In OLS systems, the bit rate of payload is commonly very large than that of label and cannot be ignored the transmission impairments. Therefore, Nicola and Peng’s BER expression of DQPSK are more practical than that of X.Liu’s. The theoretical expression of BER for PDQ is same as DQPSK, but the numbers of bit per symbol are different. For DQPSK, the SNR per bit ( $S N R_{b}$ ) is related to the SNR per symbol ( $S N R_{s y m}$ ) by $S N R_{s y m} = 2 S N R_{b}$ . For PDQ, one symbol contains four bits, the $S N R_{b}$ is related to the $S N R_{s y m}$ by $S N R_{s y m} = 4 S N R_{b}$ . BER of PDQ can be expressed as follows:

B E R_{P D Q} = \frac{1}{2} e r f c ((\frac{π}{4} {(\frac{1}{2 ρ} {(\frac{ξ}{\sin (ξ)})}^{2} + σ_{N L}^{2})}^{- 1 / 2}) / \sqrt{2})

where

ξ = \frac{π}{4} / (1 + 8 σ_{N L}^{2} S N R_{b})

, the variance of nonlinear phase noise

σ_{N L}^{2} = σ_{S P M}^{2} + σ_{X P M}^{2}

, including the variance of Self phase modulation (SPM) noise

σ_{S P M}^{2}

and Cross phase modulation (XPM) noise

σ_{X P M}^{2}

. The XPM noise is absent here, for only one optical carrier wave is used. For SPM,

σ_{S P M}^{2} = 4 ϕ_{N L}^{2} / 3 S N R_{s y m}

ϕ_{N L}^{} = γ P_{0} L_{e f f} N

where the

ϕ_{N L}^{}

is the max nonlinear phase shift of pulse center,

γ

,

P_{0}

and

L_{e f f}

is the nonlinear parameter, input power and effective length, respectively. N is the number of loop of fiber spans.

The theoretical BER performance of DQPSK and PDQ as a function of $S N R_{b}$ with different $ϕ_{N L}^{2}$ are shown in Fig. 1. The BER performance of PDQ is always better than that of DQPSK in the same value of $ϕ_{N L}^{2}$ _. The smaller $ϕ_{N L}^{2}$ , the better receiver performance. There is about 3dB receiver sensitivity advantage in PDQ compared to DPQSK, when $ϕ_{N L}^{2} = 0$ and $B E R = 10^{- 9}$ .

Fig. 1 BER vs. $S N R_{b}$ of DQPSK and PDQ with different $ϕ_{N L}^{2}$ .

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2.2 Theoretical BER expression of PDQ-PPM

In OLS system, the hybrid modulation of the label and the payload is different with normal combination modulation. The bit-rate of payload is commonly much higher than that of label, for example 100Gb/s PDQ payload labeled with 2.5Gb/s PPM. To the best of our knowledge, no research has been made on the exact definition of this. Here we define that combination modulation is mixed with various encodings which have the same baud rate. But hybrid modulation is mixed with various encodings which can have the diverse baud rates. The combination modulation is a special form of hybrid modulation. At present, the theoretical BER formula of hybrid modulation coding is very little. Here we also define that $δ$ is the bit-rate ratio of payload and label which is reversed of label modulating depth(LMD), if the label was modulated on payload. Higher $δ$ means smaller LMD.

The BER of PDQ-PPM comes from two aspects: the contribution of incorrectly threshold decision of the PPM and the PDQ. Incorrectly threshold decision of the PPM pulse accounts for the bit errors $\frac{1}{2} δ + 1$ , which leads to $\frac{1}{2} \frac{R_{P D Q}}{R_{P P M}}$ bit errors in PDQ decoding and 1 bit error in PPM decoding. $R_{P D Q}$ and $R_{P P M}$ are the bit rate of PPM and PDQ here, respectively. Then the Error contribution of PPM must be $B E R_{P P M} (\frac{1}{2} δ + 1)$ . A symbol of PDQ contains 4 bits information, but a symbol of PDQ-PPM contains 5 bits. When the PDQ is wrongfully decoded and the PPM correctly identified, the error contribution of PDQ must be $(1 - B E R_{P P M}) \cdot 4 \cdot B E R_{P D Q}$ . $B E R_{P P M}$ and $B E R_{P D Q}$ are the BER of PPM and PDQ at a given SNR per PDQ-PPM symbol here, respectively. Obtained from this analysis method of hybrid modulation encoding, the BER of a PDQ-PPM signal can be expressed as follows:

B E R_{P D Q - P P M} = {B E R_{P P M} (\frac{1}{2} δ + 1) + (1 - B E R_{P P M}) \cdot 4 \cdot B E R_{P D Q}} / 5

The theoretical $B E R_{P P M}$ can be found in Liu's research, such as papers [16,19], in which was expressed as the probability density function and need to give a decision threshold $V_{t h}$ . There is a concise expression of $B E R_{P P M}$ under the optimal decision criterion in direct detection of receiver [24,25]:

B E R_{P P M} = 1 / 2 \exp (- \frac{S N R_{b}}{2})

In the case of combination modulation, PDQ have same symbol rate with PPM, $δ = 4$ (2.5Gb/s payload and label). Figure 2 shows the theoretical BER performance of PDQ-PPM obtained from the formula (5)(6) as a function of $S N R_{b}$ in the case. ASE noise is polarization filtered and $ϕ_{N L}^{2} = 0.01$ here. The combination of two kinds of coding is higher receiver sensitivity advantage than the individual coding. When $B E R = 10^{- 9}$ , the gain of the receiver sensitivity of PDQ-PPM is about 4.2dB and 5dB better than that of PDQ and PPM, respectively. These amazing results may be explained as that the hybrid modulation seems to be introduced into a new type of error control coding. These results are also very identical with [19].

Fig. 2 BER vs. $S N R_{b}$ of PDQ-PPM, PDQ and PPM.

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The BER of PDQ-PPM with different $δ$ in OLS system are shown in Fig. 3. The bit-rate of PDQ payload is 100Gb/s, and the bit-rate of PPM label is set as 10Gb/s ( $δ = 10$ ), 2.5Gb/s( $δ = 40$ )and 1Gb/s( $δ = 100$ ) respectively. BER as a function of $S N R_{b}$ of 10Gb/s PPM is the best, and the worst in situation of 1Gb/s PPM. The larger the value of $δ$ , the larger SNR penalty of the receiver sensitivity at same BER. The reason for this is that the BER of PDQ-PPM is mainly be depended on $B E R_{P P M}$ when $δ$ is very large and parts of $B E R_{P D Q}$ contributing can be ignored (derived from Eq. (5)). There is an exception. The normal combination modulation $δ = 4$ is very close to result of 2.5Gb/s PPM ( $δ = 40$ ) Comparing the Fig. 2 with the Fig. 3, we can see that the gain of the receiver sensitivity for hybrid 100Gb/s payload and 2.5Gb/s label is about 4.5dB better than that of PDQ.

Fig. 3 BER vs. $S N R_{b}$ of PDQ-PPM with different $δ$ .

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2.3 Theoretical BER expression of PDQ-DB

The BER analysis method of hybrid modulated encoding, which can be applied to other n-ary hybrid modulation or combination modulation systems, can offer the BER expression of PDQ-DB as follows:

B E R_{P D Q - D B} = {B E R_{D B} (δ + 1) + (1 - B E R_{D B}) \cdot 4 \cdot B E R_{P D Q}} / 5

where

B E R_{D B}

is the BER of DB,

δ = \frac{R_{P D Q}}{R_{D B}}

, and

R_{D B}

is the bit-rate of DB. The coefficient 1/2 of

δ

in the Eq. (5) is caused by the pulse of PPM occupied only half of symbol period, and not existed in the DB case. There is Bosco and Lyubomirsky 's research for

B E R_{D B}

[13,26]:

B E R_{D B} = 0.5 {(1 + V_{t h}) \exp (- V_{t h}) + 1 - Q_{2} (π \sqrt{O S N R}, \sqrt{2 V_{t h}})}

where

V_{t h}

is the normalized decision threshold that must be optimized for OSNR,

Q_{2} (a, b)

is the second-order Marcum function which is suited to detect the waveform of the DB pulse. The DB pulse shape is selected with the smallest possible bandwidth occupation:

s (t) = \frac{\cos (π [\frac{t}{T} - \frac{1}{2}])}{π \frac{t}{T} (1 - \frac{t}{T})}

where T is the bit period of DB.

Figure 4 shows the theoretical BER performance of PDQ-DB, PDQ and DBas a function of $S N R_{b}$ with $δ = 4$ and $σ_{N L}^{2} = 0.01$ . The theoretical BER performance is decreased with the increase of $S N R_{b}$ . The theoretical $S N R_{b}$ limit of PDQ-DB, PDQ and DB at $B E R = 10^{- 9}$ are 12dB (15.8 photons/bit), 15.5dB (35.5 photons/bit) and 19dB (79.4 photons/bit), respectively. Theoretical limit of 19dB DB $S N R_{b}$ is large than 15dB ( $O S N R \approx 11 d B$ , 31.6 photons/bit) from the results of [26] in condition of 10Gb/s bit rate. The BER performance of PDQ-DB is better than PDQ and DB, just same as results of Fig. 2. The gain of receiver sensitivity of PDQ-DB is about 3.5dB better than PDQ and 7dB better than DB when $B E R = 10^{- 9}$ . The $S N R_{b}$ theoretical limit in three cases at $B E R = 10^{- 12}$ are also calculated about 13.5dB, 18.3dB and 20.3dB from theoretical Eqs. (7), (2) and (8), respectively. There have similar conclusions at different bit error conditions.

Fig. 4 BER vs. $S N R_{b}$ of PDQ-DB, PDQ and DB.

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The BER of PDQ-DB with different $δ$ in OLS system are shown in Fig. 5. The receiver sensitivity of hybrid 100Gb/s payload and 2.5Gb/s label is about 0.5dB worse than that of normal combination modulation when $B E R = 10^{- 9}$ , but still has about 3dB advantage than that of PDQ. Under different $δ$ conditions, the BER rules of PDQ-DB in Fig. 5 and PDQ-PPM in Fig. 3 are similar. To illustrate the sensitivity advantage of PDQ-PPM and PDQ-DB, the theoretical BER expression of PDQ-ASK can be given as follows by analysis method of ASK and PDQ encoding:

Fig. 5 BER vs. $S N R_{b}$ of PDQ-DB with different $δ$ .

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B E R_{P D Q - A S K} = {B E R_{A S K} (δ + 1) + (1 - B E R_{A S K}) \cdot 4 \cdot B E R_{P D Q}} / 5

The BER of PDQ-ASK with different $δ$ in OLS system are given in Fig. 6. Compared Figs. 3 and 5 with Fig. 6, the gain of the receiver sensitivity for PDQ-PPM has been gotten about 1dB and 2dB than that of PDQ-DB and PDQ-ASK in condition of $δ = 4$ , respectively. This means that label PPM based OLS system has better performance than that of DB and ASK.

Fig. 6 BER vs. $S N R_{b}$ of PDQ-ASK with different $δ$ .

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3. Simulation of two proposed OLS schemes

The above theoretical results would be verified by commercial software package of OptiWaves System 8.0. The system architectures of the proposed POLMUX-DQPSK/DB and POLMUX -DQPSK/PPM schemes are presented in Fig. 7. u and v are signals of 25Gb/s pseudo-random bit sequence (PRBS) with length of 2¹¹ −1, which are modulated into a 50Gb/s DQPSK signal, and formed a 100Gb/s PDQ signal after POLMUX. The 15 $μ s$ time delay is used to remove the correlation of two polar1zations in POLMUX. DB and PPM label are modulated in the PDQ payload by Mach-Zehnder modulation (MZM). The 0.2ns time delay is used to ensure the PPM pulse moved from first half bit to last half bit, which is just half bit period of 2.5Gb/s label bit-rate. The label and payload are directly detected separately in the receiver. The electro-absorption modulation (EAM) is used to erase label from the payload. Parameters of two systems are listed in Table 1.

Fig. 7 Schematic OLS system of PDQ-DB and PDQ-PPM.

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Table 1. Parameters of two systems of PDQ-PPM and PDQ-DB.

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4. Results and discussions

The 2.5Gb/s DB, PPM label signal and 100Gb/s hybrid modulation waveforms of PDQ-DB and PDQ-PPM are shown in Fig. 8. Data information is carried by the phase of payload and routing information is expressed by DB or PPM label, which is changed with varying the magnitude of the payload. The theoretical BER performance of PDQ-PPM, PDQ-DB and PDQ-ASK with 100Gb/s payload and 2.5Gb/s label ( $δ = 40$ ) are given in Fig. 9 at 1560km transmission distance. The receiver sensitivity of PDQ-PPM is the best, which is about 1.5dB and 2.3dB gain better than PDQ-DB and PDQ-ASK at $B E R = 10^{- 9}$ , respectively.

Fig. 8 The 2.5Gb/s label signal waveforms of DB (a), PPM (c) and 100G/s payload waveforms of PDQ-DB (b) and PDQ-PPM (d) in OLS hybrid modulation systems.

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Fig. 9 BER vs. $S N R_{b}$ of three hybrid modulation code .

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The impacts of different labels on BER of PDQ payload after erased label over 1560km transmission are shown in Fig. 10. The payload of PDQ combined with PPM may contributes about 1.8dB and 1.2dB gain of receiver sensitivity than ASK and DB at BER = 10⁻⁹, respectively. The receiver sensitivity of payload with PPM label is the best, which is about 1.2dB and 1.8dB gain better than that of DB and ASK label, respectively. This is in agreement with the results of previous theoretical analysis in part 2 or Fig. 9. The receiver sensitivity of payload which carries label is better than payload without label, and effects of different labels are different. This conclusion is very significant. We believe that the sizes of receiver sensitivity gain of payload obtained from hybrid modulation are related to the different types of label. The multi position modulation may superior to the multi level modulation and multilevel modulation may better than low level modulation in advantage of receiver sensitivity.

Fig. 10 BER of PDQ with different labels after erased.

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The BER performances of PDQ-DB, PDQ-PPM and PDQ-ASK systems are also compared in different transmission distance shown in Fig. 11. It can be seen that the transmission performance of PPM label system is about 240km and 50km better than that of DB and ASK at BER = 10⁻⁹, respectively. The higher receiver sensitivity of PPM label is helpful to improve transmission distance of the OLS system.

Fig. 11 BER of PDQ/PPM, PDQ/DB and PDQ/ASK at different transmission distance system.

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In the intensity modulation systems, such as ASK and DB, the large ER value are more conducive to the signal detection. But in the phase modulation systems, such as DQPSK and DPSK, it is accessible to detect the “0” signal in condition of the lower ER value. In hybrid modulation or orthogonal modulation, such as PDQ-DB and PDQ-ASK, there will be ER contradiction [27]. But the PPM carries the information by position of the pulse, rather than the intensity or phase. so the PDQ-PPM which can solve the ER confliction must be tolerated slightly larger value for favorable receiving signals.

The Q performance of PDQ-DB system over 1560km transmission at different extinction ratio (ER) is simulated in Fig. 12. The Q factor of PDQ payload is decreased with increasing of ER, but the Q factor of DB label is gradually increased with increasing of ER. To ensure good transmission performance of payload and label, the intersection of 2 dB ER value of payload and label can be preferred in Fig. 12. This optimized ER value may be tend to smaller at longer transmission distance.

Fig. 12 Q factors of DB label system at different ERs.

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The different transmission lengths may have different optimal ER values for PDQ-PPM, PDQ-DB and PDQ-ASK. The Q performance of payload and label from three cases after 3000km transmission at different ERs are compared in Fig. 13. With the increase of ER between 0.1 and 0.6dB, the Q values of PDQ payload in solid line with PPM label are slowly increased but ASK label and DB label decreased instead. This rarely happens in hybrid modulation codes of the intensity and phase hybrid class. The Q values of label in dotted line from three cases are increased with ERs, which are consistent with those of other investigators [27]. The optimal intersection ER value of ASK label is about 0.37dB, far less than that of 40G/s short distance ASK label’s system [27]. The intersection ER value of PPM label system is about 0.12dB and 0.06dB better than that system of ASK label and DB label, respectively. This means that the PPM label is able to have a larger ER margin to achieve a better system performance in OLS system.

Fig. 13 Q factor of PDQ-PPM, PDQ-DB and PDQ-ASK with ERs.

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Results indicate that PPM as a label is better than FSK [9] and DPSK [10] in the BER performance and transmission capacity for the optical label switching. The multidimensional coded modulation [28,29], which is similar to the hybrid modulation, have function of Forward Error Correction (FEC) and can achieve the same high speed and longer distance transmission. But the complex software and hardware processing methods are used at receiver, and there is no report for optical label switching network as known. In Fig. 7, the EAM and Gaussian filter are used to erase the optical label from the payload, which lead to the loss of signal power. Therefore, the BER before the label erasure is better than that after erasure in the same $S N R_{b}$ . Figures 9 and 10 are results of before and after erasure at 1560km for three cases. Comparison of the two figures can draw some conclusions (although Fig. 9 is theoretical results, but does not affect the result of the comparison). Seen from Fig. 9 and Fig. 10, the $S N R_{b}$ of PDQ-PPM, PDQ-DB and PDQ-ASK are 11dB, 12.5dB and 13.4dB before erasure at BER = 10⁻⁹, respectively. After the erasure, $S N R_{b}$ for three cases are 14dB, 15.2dB and 15.7dB, respectively. The penalties of erasure of PDQ-PPM, PDQ-DB and PDQ-ASK are 3dB, 2.7dB and 2.3dB, indicating that the simpler the signal structure is, the less the cost is. Actual erasure costs may be smaller than these values seen from the Fig. 14. The BER performance of payload before (PDQ-PPM) and after PPM label erased over 3000km transmission are shown in Fig. 14. The receiver sensitivity of payload is 18.4dB and 18.8dB before and after label erased when BER = 10⁻⁹, respectively. The penalty of label erased is 0.4dB. The OLS system performance observed from the eye diagram is still acceptable at 3000km transmission.

Fig. 14 BER of payload before (PDQ-PPM) and after (PDQ) PPM label erased.

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5. Conclusion

Two OLS schemes based on PDQ-PPM and PDQ-DB are proposed and analyzed in this paper. The theoretical BER performance of PDQ (Eq. (2)), PDQ-PPM (Eq. (5)) and PDQ-DB (Eq. (7)) are be derived from analysis method of hybrid modulated encoding. The combination modulation which has the same baud rate between the payload and the label is a special form of hybrid modulation. The result of simulation is in agreement with theoretical analysis. The larger the bit-rate ratio of payload and label $δ$ , the larger SNR penalty of the receiver sensitivity at same BER. The receiver sensitivity of payload can be improved about 2dB and 3.2dB when hybrid modulated with DB label and PPM label at $δ = 40$ and $B E R = 10^{- 9}$ _, respectively. The receiver sensitivity of payload with PPM label is about 1.2dB and 1.8dB gain better than that of DB and ASK label at $B E R = 10^{- 9}$ , respectively. The multi position modulation may superior to the multi level modulation and multilevel modulation may better than low level modulation in advantage of receiver sensitivity. The advantage of PDQ-PPM is that it can solve the ER conflict between type coding of phase and intensity to a certain extent in OLS system. The proposed two systems can be potential candidates for the future high bit rate OLS network. Further work will focus on the bit error analysis of ultra - binary hybrid modulation coding.

Funding

National Natural Science Foundation of China (NSFC) (No.61671306); Shenzhen Science Technology Project (No.JCYJ20160328145357990); Shenzhen Key Lab of ACIP.

Acknowledgments

The authors would like to thank Reviewers for their insightful and constructive comments that help to improve the quality of this paper.

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Parameter	Value
Power of CW laser Frequency of CW laser Dispersion management cycle Length of PRBS ER of MZM	0.22mw 193.1THz 120km 2¹¹ −1 2dB for DB label 0.6dB for PPM label
Length of DCF	10km
Dispersion coefficient of DCF	−85ps/ns/km
Attenuation coefficient of DCF	0.5dB/km
Length of SMF	50km
Dispersion coefficient of SMF	17ps/ns/km
Attenuation coefficient of SMF Gain of EDFA1 Noise figure of EDFA1 Gain of EDFA2 Noise figure of EDFA2	0.2dB/km 5dB 4dB 10dB 4dB
Duty ratio of PPM Duty ratio of clock	0.2 0.4

Performance evaluations of hybrid modulation with different optical labels over PDQ in high bit-rate OLS network systems

Abstract

1. Introduction

2. Theoretical BER expressions of hybrid modulation PDQ-PPM and PDQ-DB

2.1 Theoretical BER expression of PDQ

2.2 Theoretical BER expression of PDQ-PPM

2.3 Theoretical BER expression of PDQ-DB

3. Simulation of two proposed OLS schemes

4. Results and discussions

5. Conclusion

Funding

Acknowledgments

References and links

Cited By

Figures (14)

Tables (1)

Equations (10)

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