Memory-based pulse amplitude modulation for short-reach fiber communications with intensity modulation and direct detection

Bo Xu; Lei Zhang; Kun Qiu

doi:10.1364/OE.24.011876

1. Introduction

Short-reach fiber communication technologies are the keys to meet the increasing bandwidth demand for data center and optical interconnects. For this purpose, carrierless amplitude and phase modulation (CAP) and discrete multi-tone (DMT) modulation have been studied as two possible choices. CAP systems with different modulation formats and orders have been experimentally demonstrated [1,2]. With the help of high-speed AWG and EML, multi-band CAP can be used to achieve 102 Gb/s signal transmission over 15km [3]. DMT is another form of orthogonal frequency division multiplexing using direct detection (DD-OFDM) for its low-cost implementation. A 52.8 Gb/s DMT signal has been achieved with a distributed feedback laser to transmit over 20km standard single-mode fiber (SSMF) [4]. A 101 Gb/s DMT signal generated with high-speed DAC chips has been verified by experiments to be able to transmit over 10km of SSMF [5]. Though both CAP and DMT can achieve good system performance with high spectrum efficiency and flexible multi-level coding, complicated signal processing is required at both transmitter side and receiver side.

Pulse amplitude modulation (PAM) is another promising choice that may provide good system performance and high data rate with low-cost implementation using intensity modulation and direct detection (IM/DD). In [6], a SiP Mach-Zehnder modulator working at 1310nm was demonstrated for the generation of 112 Gb/s PAM-4 signals [7–9]. demonstrated analytical and experimental results for PAM-4 transmission with different wavelengths using either multi-mode fiber or single-mode fiber. However, if 1550nm is used for its lowest attenuation for SSMF, then equalization at the receiver side is prerequisite to recover PAM-4 signals with 50 Gb/s rate and above due to the serious inter-symbol interference (ISI) caused by fiber dispersion. Though feed-forward equalization (FFE) and decision-feedback equalization (DFE) can be used [10,11], their performance deteriorates as the fiber transmission length increases. Compared with FFE and DFE, maximum likelihood sequence estimation (MLSE) can achieve a better performance for both linear and nonlinear ISI [12,13] at the cost of increased complexity.

Spectrum shaping and memory-based modulation can improve a system’s performance by modifying the spectrum of the transmitted signals. Spectrum shaping has been used in long-distance high-speed fiber optic communication systems [14,15]. For example, Nyquist signal-based spectrum shaping can effectively increase the spectrum efficiency of a WDM system [14]. In short-reach fiber communications with PAM, both root raised-cosine (RRC) and Nyquist pulse have been studied [16]. Meanwhile, memory-based modulation like continuous-phase modulation has found applications in long-distance fiber optic communications for reduction on the fiber nonlinear effects [17,18]. However, a limited modulation index in practice might cause a high power penalty to the system. Instead, this paper proposes a new way to include memory effect in PAM modulation which has the advantage of both low cost and effectively compressed spectrum. Its performance under an IM/DD short-reach fiber optic communication system will be studied in detail in the following.

Strong filtering-based duobinary-4-PAM has been proposed as a solution for achieving 100G transmission with low cost 10G-class devices for 100GE or 400GE LAN applications [19,20]. Though similar, the proposed memory-based PAM provides an efficient and flexible approach to construct a much wider range of signaling with compressed spectrum. Different from strong filtering-based duobinary-4-PAM, the flexibility of the memory-based PAM using simple pre-coding allows system performance optimization to further extend fiber transmission length. A detailed comparison between the conventional memory-less PAM and memory-based PAM is included in this paper.

2. Principles of the memory-based PAM

Figure 1 gives the schematic of an IM/DD-based PAM-4 system. At the transmitter side, the light from the laser diode (LD) is intensity modulated by an electro-absorption modulator (EAM) with the PAM symbol sequence. After transmission with SSMF, the signal is converted into electrical signal by the photo-diode (PD) and is then sampled with analog-to-digital converter (ADC) at one sample per symbol. Finally, MLSE is used to recover the PAM sequence. In Fig. 1, {I_k} is the information symbol sequence and E₀ is the magnitude of the optical field signal. If pre-coding is used for memory-based PAM as shown later in this section, sequence {J_k} is used instead of {I_k} for modulation.

Fig. 1 Schematic of an IM/DD-based PAM-4 system with MLSE. The red part refers to the proposed pre-coding for the memory-based PAM.

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For a back-to-back system, the received signal after the square-law detection of the PD can be written as

r (t) = η P_{0} {| \sum_{k} \sqrt{I_{k}} g (t - k T) |}^{2} + n (t)

where

P_{0} = E_{0}^{2}

, η is the PD’s conversion coefficient and T is the symbol period. {I_k} is the conventional memory-less PAM-4 information sequence and

I_{k} \in {0, 1, 2, 3}

for intensity modulation. n(t) is the thermal noise from PD and g(t) is the pulse waveform which determines the power spectrum of the modulated signal. If the pulses g(t-kT) are not time-overlapping, for example, an ideal rectangular pulse with

g (t) = 1, 0 < t < T,

then

r (t) = η P_{0} \sum_{k} I_{k} g^{2} (t - k T) + n (t) = η P_{0} \sum_{k} I_{k} f (t - k T) + n (t) .

After matched filtering, the sampled signal after normalization can be written as

r_{k} = I_{k} + n_{k}

with a ISI-free operation. Suppose that the thermal noise signal sample n_k has a variance of

σ_{n}^{2}

, the symbol error probability of the conventional PAM-4 under this ideal ISI-free IM/DD channel is found to be

P_{s} = \frac{6}{4} Q {\frac{Δ / 2}{σ_{n}}} = 1.5 \times Q {\frac{Δ}{2 σ_{n}}} .

where

Q (x)

is the Q-function for Gaussian distribution and

Δ

is the minimum distance of the constellation diagram of the received signal. For the intensity modulated conventional PAM-4,

I_{k} \in {0, 1, 2, 3}

and

Δ = 1

.

For an IM/DD optical fiber communication system, the average power of the optical signal is

P_{AVE} = \lim_{K \to \infty} \frac{P_{0}}{K T} \int_{0}^{K T} | \sum_{k = 1}^{K} \sqrt{I_{k}} g (t - k T) |^{2} d t \propto E [I_{k}]

where

E [I_{k}]

refers to the mean value of I_k. For conventional memory-less PAM-4 with intensity modulation,

E [I_{k}] = 1.5

, and thus

P_{s} = 1.5 \times Q {\frac{E [I_{k}]}{3 σ_{n}}} .

The proposed memory-based PAM scheme achieves memory in the modulation by extending g(t) into the following symbols as

g (t) = 1, 0 < t < N T

where N is a parameter defining the memory length of the memory-based PAM. Or equivalently, the memory effect can be achieved with a simple pre-coding at the transmitter side as

J_{k} = I_{k} + I_{k - 1} + \dots + I_{k - (N - 1)}

where I_k is the conventional PAM-4 symbol before pre-coding and J_k is the symbol after pre-coding. For the case of N = 2,

J_{k} \in {0, 1, 2, 3, 4, 5, 6}

. Exemplary information system sequences before and after pre-coding are included in Fig. 1. The corresponding electrical modulating signals to the EAM are also shown with a rectangular pulse waveform. With pre-coding for memory-based PAM, the sampled signal after matched filtering is

r_{k} = J_{k} + n_{k}

with a controlled ISI in J_k. The average power of the optical signal becomes

P_{AVE} \propto E [J_{k}] = 3.

That is, in order to achieve the same minimum distance in the received signal’s constellation, the memory-based PAM-4 with N = 2 requires 3dB higher average optical receiving power.

Figure 2 compares the symbol error probability performance of the conventional PAM-4 and the memory-based PAM-4 for an ideal IM/DD channel. For conventional PAM, Eq. (4) for the ideal ISI-free channel model is used with $I_{k} \in {0, 1, 2, 3}$ for intensity modulation in the simulations. For a reliable estimation on the symbol error probability, it is required that over 100 errors should be counted before the simulation terminates. From the above analytical discussion, it is known that the system’s error probability is determined by $E [I_{k}] / σ_{n}$ as shown in Eq. (7) for the ideal IM/DD channel with conventional PAM-4. The theoretical result of Eq. (7) is also included in Fig. 2 where it is confirmed to be the same as the simulation result. For the case of memory-based PAM, the memory length is set to be 2 in the simulations. MLSE with 4 states is used for symbol detection to account for the controlled ISI. The symbol error probability is estimated after MLSE for this case. For relatively high P_s like 0.1, the receiver power penalty for the memory-based PAM-4 is about 3.5dB. However, as the error probability decreases, the receiver power penalty is also decreasing. For example, as P_s decreases from 10⁻¹ to 10⁻⁵, the receiver power penalty can be reduced from 3.5dB to about 2dB.

Fig. 2 Symbol error probability comparison between conventional PAM-4 and memory-based PAM-4 with N = 2 for an ideal IM/DD channel.

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Though the memory-based PAM requires a higher optical receiving power than the conventional memory-less PAM to achieve the same error probability for an ideal IM/DD channel, a more concise spectrum is obtained with the memory-based PAM as shown in Fig. 3. Figure 3 is obtained assuming a transmitting bit rate of 50 Gb/s with an ideal rectangular pulse waveform. For the conventional PAM-4, it is easy to see that its power spectrum has a main lobe of 25GHz bandwidth. Instead, the main lobe of power spectrum is halved to 12.5GHz for the PAM-4 with a memory length of 2. For fiber transmission over 1550nm, a reduction in the dispersion-induced ISI is expected due to a smaller signal bandwidth for the memory-based PAM-4. The overall system performance is determined by a compromise between the reduced ISI and the increased power level for the memory-based PAM-4.

Fig. 3 Signal spectrum comparison between conventional PAM-4 and memory-based PAM-4.

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At the receiver side, the memory-based PAM-4 should be detected with MLSE and the number of MLSE states should be set according to the memory length of the modulation, that is, the number of MLSE states M = 4^N⁻¹. Figure 1 also includes the trellis diagram of the Viterbi algorithm for the case of N = 2 where 4 MLSE states are included. In practical fiber transmission over 1550nm for 50 Gb/s rate and above, the memory length at the receiver side becomes much longer due to the fiber dispersive channel-induced ISI. A much larger number of MLSE states should be used instead to take into account the memory effect from the dispersive channel. No extra complexity on the MLSE-based receiver design is thus necessary for memory-based PAM.

3. Performance of the memory-based PAM

The performance of the memory-based PAM-4 is studied in detail and compared with the conventional PAM-4 based on simulation results in this section. VPI Transmission Maker is used to simulate the optical link with received signal processed in MATLAB for MLSE detection. Throughout the simulations, SSMF is assumed with a working wavelength of 1550nm which has the lowest attenuation. The transmission rate of the PAM-4 signal is set at 50 Gb/s. A 100GbE signal can be transmitted by multiplexing two sub-carriers with 50Gb/s on each with for instance polarization division multiplexing [9]. The schematic of the simulations follows Fig. 1 except for some minor changes. 5th-order Bessel low pass filters with electrical bandwidth of 20GHz are assumed throughout the following simulations to approximate the bandwidth of practical devices like EAM and PD for both conventional PAM and memory-based PAM. Different from the works in [19,20] where strong filtering is the dominant source of ISI, we focus on the fiber dispersion-induced ISI in this work for a much longer fiber transmission length. The output power of the LD is set at 3dBm and an optical attenuator is added before PD to vary the tested optical receiving power. The modulation index for EAM is set to be the default value of 0.9 in VPI and the chirp factor of EAM is also set to be its default value of 0.0 in the simulations. After PD, the signal is sampled by the ADC with one sample per symbol. MLSE with 4³, 4⁴ or 4⁵ states is used for symbol detection. The bit error rate is estimated after MLSE based on error counting in the simulations. For applications in short-reach fiber transmission with a fiber transmission length less than 100km, fiber nonlinear effects can be neglected. Optical amplifier noise is also neglected for such a single-span fiber transmission.

Figure 4 compares the system’s error probability performance for the conventional PAM-4 with N = 1 and the memory-based PAM-4 with N = 2 under different fiber transmission lengths. In the simulations, the number of MLSE states at the receiver side is fixed to be 256. For the back-to-back case, the memory-based PAM-4 is found to have an optical receiving power loss of about 3dB at an error probability of 10⁻² which confirms with the theoretical result from Fig. 2. However, as the fiber transmission length increases with increased fiber dispersive effects, the performance gap between the PAM-4 without and with memory is decreasing. When the fiber transmission length is increased to 65km for conventional PAM-4, the fiber dispersion-induced ISI is so serious that the system’s error probability shows an error floor above 10⁻³ no matter how optical receiving power is increased. As a result, the maximum fiber transmission length is limited to 60km for conventional PAM-4. For comparison, over 70km SSMF transmission can be supported if the memory-based PAM-4 is used.

Fig. 4 Bit error probability performance comparison for conventional PAM-4 and memory-based PAM-4 with N = 2.

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Figure 5 compares the receiver sensitivity penalty as the fiber transmission length increases for the conventional PAM-4 and the memory-based PAM-4 with N = 2. The receiver sensitivity is defined as the required optical receiving power for a required error probability limit of 2 × 10⁻³. Different MLSE states are also included in the figure. For short fiber transmission length where the system’s impairment is dominated by PD noise, the error performance of the system is independent of the MLSE states. As fiber transmission length increases, the increased ISI from fiber dispersion becomes the dominant impairment. Longer fiber transmission length can be supported with more MLSE states used. Compared with the conventional PAM-4, the memory-based PAM-4 with N = 2 is able to effectively extend the fiber transmission length where about 10km more fiber transmission can be supported.

Fig. 5 Receiver sensitivity penalty comparison for conventional PAM-4 and memory-based PAM-4.

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To further optimize the performance of the memory-based PAM-4, a modified modulating pulse waveform could be used as shown in the following

g (t) = {\begin{matrix} 1, 0 < t < T_{s} \\ α, T_{s} < t < 2 T_{s} \\ 0, for other t \end{matrix}

where α is an amplitude parameter defined within (0,1). For the case of α = 0 and α = 1, g(t) becomes the conventional PAM-4 and the memory-based PAM-4 defined in Eq. (8) with N = 2.

Figure 6 compares the receiver sensitivity penalty of the memory-based PAM-4 under different values of α as the fiber transmission length increases. 256 MLSE states are used for MLSE in the simulations. It is seen that the maximum achievable fiber transmission length can be further extended to 75km for memory-based PAM-4 with an optimized amplitude parameter of 0.5 or 0.75 if 5dB receiver sensitivity penalty is allowed.

Fig. 6 Receiver sensitivity penalty comparison for memory-based PAM-4 with different pulse shapes.

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5. Conclusion

PAM-4 is an attractive choice for low-cost short-reach optical fiber transmissions. The combination with MLSE made it possible for an IM/DD system to support longer fiber transmission length. In this paper, memory-based PAM-4 is proposed for the first time to obtain an effective compression on the signal’s spectrum. Based on theoretical and simulation studies, it is confirmed that the mainlobe bandwidth can be halved by introducing a memory length of two. The memory-based PAM-4 is also very simple in implementation where only a simple pre-coding is required at the transmitter side. No increasing to the MLSE states or receiver complexity is necessary.

Due to its compressed signal spectrum, the memory-based PAM-4 has a higher tolerance to fiber dispersion than the conventional PAM-4. Based on simulation results with IM/DD fiber dispersive channels, the memory-based PAM-4 is confirmed to be able to effectively extend the maximum achievable fiber transmission length. When 256 MLSE states are used at the receiver, the maximum achievable fiber transmission length can be extended from 60km for the conventional PAM-4 to over 70km for memory-based PAM-4. Moreover, a further optimization on the memory-based PAM-4 is proposed in this paper for a further extension on the maximum achievable fiber transmission length.

Acknowledgment

This work was supported by Natural Science Foundation of China (#61471088).

References and links

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Memory-based pulse amplitude modulation for short-reach fiber communications with intensity modulation and direct detection

Abstract

1. Introduction

2. Principles of the memory-based PAM

3. Performance of the memory-based PAM

5. Conclusion

Acknowledgment

References and links

Cited By

Figures (6)

Equations (12)

Optics Express