Direct detection transmission of a PAM signal with power fading mitigation based on Alamouti coding and dual-drive MZM

Yixiao Zhu; Yixiao Zhu; Xiansong Fang; Fan Zhang; Fan Zhang; Weisheng Hu; Weisheng Hu

doi:10.1364/OE.446676

1. Introduction

With the emerging of bandwidth-consuming broadband services including high-definition television (HDTV), cloud computing (CC) and augmented/virtual reality (AR/VR), the capacity of data-center interconnects (DCIs) is expected to grow with the Internet traffic. In general, optical receivers can be categorized into coherent detection and direct detection (DD), depending on whether to use a local oscillator (LO) laser. Although coherent detection can recover the full-field phase- and polarization-diversity signal and compensate for transmission impairments with digital signal processing (DSP) [1], its cost and power consumption needs to be further reduced before widely deployed in such cost-sensitive scenario. On the contrary, 4/8-lane parallel intensity modulation direct detection (IM-DD) solution is still preferred [2–4]. However, for IM signals, the two conjugated sidebands are dispersed during fiber transmission, and then interference with each other after square-law detection, which results in spectral nulls. Therefore, such frequency-selective power fading effect is a predominant obstacle limiting the transmission distance or available modulation bandwidth of IM-DD systems [5].

To tackle with the power fading impairment, lots of efforts have been made in the literature [6–23]. When the spectral notches fall into the signal bandwidth, the performance of conventional linear equalizers is severely degraded since they will greatly enhance the noise around fading frequencies. Decision-feedback equalizer (DFE) [6], maximum likelihood sequence estimation (MLSE) [7], Tomlinson-Harashima precoding (THP) [8] and other algorithms [9–11] can be implemented at the transmitter or receiver to partially mitigate the fading-induced inter-symbol interference (ISI). On the other hand, self-coherent schemes [12–22] capable of optical field reconstruction are promising candidates. In Ref [12]., block-wise phase switch (BPS) scheme is proposed, which rotates the carrier phase in neighboring time slots and obtains the in-phase and quadrature components in a time-interleaved manner. However, it requires 2 IQ modulators and 4 digital-to-analog convertors (DACs) for signal and carrier modulation, respectively. Alternatively, a signal phase switch scheme [13] is reported later, which changes the signal phase carrier by 90° instead of carrier. Consequently, the transmitter can be simplified to one IQ modulator with 2 DACs, and an additional unmodulated optical branch. In Ref [14]., by combining the virtual carrier and signal in the electrical domain, the transmitter becomes more compact with only one IQ modulator, while 4 DACs are used to guarantee the electrical signal-to-noise ratio (SNR) under 1-bit quantization. Besides, the configuration of carrier and signal can be modified from frequency domain to time domain. Based on this, half-symbol delay and switching of carrier [15], and signal-carrier interleaved [16] schemes are proposed. Besides, vestigial- [17] or single-sideband [18–20] (VSB/SSB) signal can suppress power fading by breaking the symmetry and avoiding the interference of two sidebands. However, the former requires optical filter with sharp edge for VSB generation, and the latter uses Kramers-Kronig receiver to mitigated the signal-signal beat interference (SSBI) from photodiode (PD) detection, requiring high sampling rate due to spectral broaden of nonlinear operations. Furthermore, frequency chirp can be introduced to alleviate power fading. In Ref [23]., Mach-Zehnder modulator (MZM) is operating at single-arm driven mode for pre-chirping, and the first fading notch is thus shifted to higher frequency. With a parallel IM/phase modulator (PM) transmitter and bandwidth allocation [24], the response fluctuation is suppressed to less than 3 dB. For dual-drive MZM (DDMZM)-based transmitter, a four-state chirp control scheme [25] is designed for discrete multi-tone (DMT) signal with dedicated subcarrier allocation.

In this paper, by extending our previous work [26], we report a cost-effective direct detection transmission scheme for pulse amplitude modulation (PAM) signal enabled by Alamouti coding and DDMZM. The neighboring symbol blocks are coded and then fed into the upper- and lower-arms of DDMZM, respectively. The power fading can be eliminated after superposition of the photocurrent at odd and even time slots. In the experimental demonstration, up to 160Gb/s PAM-4, 140Gb/s PAM-6 and 108Gb/s PAM-8 signals can be successfully transmitted over 80 km standard single-mode fiber (SSMF) with bit-error rates (BERs) below the 20% soft-decision forward error correction (SD-FEC) threshold of 2.0×10⁻². For wavelength division multiplexing (WDM) demonstration, 8×150Gb/s PAM-4 signals with 100 GHz channel spacing is also transmitted over 80 km fiber. The gross bitrate is 1.2Tb/s, and the net bitrate is 945.3Gb/s (=1.2Tb/s×1/(1 + 20%)×40960/(2048 + 320 + 40960)) with consideration of both FEC and frame redundancy, showing the potential for terabit inter-DCI applications. Moreover, we numerically compare the performance between the Alamouti coding-based scheme and SSB scheme with DDMZM-based transmitter.

The rest of this paper is organized as follows. In Section 2, the principle of Alamouti coding-based transmission scheme is described. In Section 3, the experimental setup and DSP stacks are presented. In Section 4, the experimental results are provided and explained. The OSNR performance comparison with SSB signal and bias tolerance are discussed numerically in Section 5. Finally, we summarized this paper in Section 6.

2. Principle

2.1 Case I: IM/PM switching

We start from Case I with IM/PM switching configuration [12,24], which is shown in Fig. 1(a). By biasing at the π/4 quadrature point of DDMZM, the modulated optical signal at odd and even slots can be written as

(1)$${E_{odd}} = \exp \left( {j\frac{s}{{{V_\pi }}}\pi + j\frac{\pi }{4}} \right) + \exp \left( { - j\frac{s}{{{V_\pi }}}\pi - j\frac{\pi }{4}} \right) \approx \sqrt 2 - \sqrt 2 \frac{\pi }{{{V_\pi }}}s$$

(2)$${E_{even}} = \exp \left( {j\frac{s}{{{V_\pi }}}\pi + j\frac{\pi }{4}} \right) + \exp \left( {j\frac{s}{{{V_\pi }}}\pi - j\frac{\pi }{4}} \right) \approx \sqrt 2 + \sqrt 2 j\frac{\pi }{{{V_\pi }}}s$$

Here s denotes the transmitted symbol and V_π is the half-wave voltage of the modulator. 1^st-order approximation of ${e^x} \approx 1 + x,\;({|x |\ll 1} )$ is used. After fiber transmission, the received photocurrents after PD detection are as follows:

(3)$${I_{odd}} = {\left|{\left( {\sqrt 2 - \sqrt 2 \frac{\pi }{{{V_\pi }}}s} \right) \otimes h(t )} \right|^2} = 2 - 2\frac{\pi }{{{V_\pi }}}s \otimes [{h(t )+ {h^ \ast }(t )} ]+ 2{\left|{\frac{\pi }{{{V_\pi }}}s \otimes h(t )} \right|^2}$$

(4)$${I_{even}} = {\left|{\left( {\sqrt 2 + \sqrt 2 j\frac{\pi }{{{V_\pi }}}s} \right) \otimes h(t )} \right|^2} = 2 + 2j\frac{\pi }{{{V_\pi }}}s \otimes [{h(t )- {h^ \ast }(t )} ]+ 2{\left|{\frac{\pi }{{{V_\pi }}}s \otimes h(t )} \right|^2}$$

Here h(t) is the impulse response of fiber dispersion, and the PD responsivity is set as 1 for simplicity. The 1^st-order terms in Eq. (3) and Eq. (4) correspond to two kinds of power fading, which converts channel response from phase delay into amplitude deviation in the frequency domain. The induced spectral zeros make the end-to-end response nonlinear, and the corresponding ISI cannot be effectively compensated by linear equalizers. Fortunately, we can combine the two photocurrents to cancel the fading terms as in Eq. (5).

(5)$${I_{odd}} + j{I_{even}} = 2({1 + j} )- 4\frac{\pi }{{{V_\pi }}}s \otimes h(t )+ 2({1 + j} ){\left|{\frac{\pi }{{{V_\pi }}}s \otimes h(t )} \right|^2}$$

Fig. 1. Illustration of (a) case I: IM/PM switching; (b) case II: upper/lower-arm switching; (c) Almouti coding-based signals generation schemes with dual-drive Mach-Zehnder modulator.

Download Full Size | PDF

By this means, the 1^st-order term becomes linear again, and the transmitted symbol can be recovered by convoluting the inverse channel response of h⁻¹(t). Then the 2^nd-order term, namely signal-signal beat interference, needs to be suppressed with the help of Volterra series equalizer [27] or iterative cancellation [12,13]. However, the drawback of Case I is that two symbol periods are used to transmit the same information, leading to halved data rate.

2.2 Case II: upper/lower-arm switching

The goal of fading-free transmission can be also achieved by Case II as in Fig. 1(b), in which the symbol sequence is alternately loaded to the upper- and lower-arm of MZM [16]. Similarly, the received photocurrents at two consecutive slots can be deduced as

(6)$${I_{odd}} = {\left|{\left( {\sqrt 2 + j\gamma \frac{\pi }{{{V_\pi }}}s} \right) \otimes h(t )} \right|^2} = 2 + \sqrt 2 j\frac{\pi }{{{V_\pi }}}s \otimes [{\gamma h(t )- {\gamma^ \ast }{h^ \ast }(t )} ]+ {\left|{\gamma \frac{\pi }{{{V_\pi }}}s \otimes h(t )} \right|^2}$$

(7)$${I_{even}} = {\left|{\left( {\sqrt 2 - \gamma \frac{\pi }{{{V_\pi }}}s} \right) \otimes h(t )} \right|^2} = 2 - \sqrt 2 \frac{\pi }{{{V_\pi }}}s \otimes [{\gamma h(t )+ {\gamma^ \ast }{h^ \ast }(t )} ]+ {\left|{\gamma \frac{\pi }{{{V_\pi }}}s \otimes h(t )} \right|^2}$$

Here $\gamma = \exp ({j{\pi / 4}} )$ is a constant phase shift. Again, the two photocurrents I_odd and I_even are combined as follows

(8)$${I_{odd}} - j{I_{even}} = 2({1 - j} )+ 2\sqrt 2 j\frac{\pi }{{{V_\pi }}}s \otimes \gamma h(t )+ ({1 - j} ){\left|{\gamma \frac{\pi }{{{V_\pi }}}s \otimes h(t )} \right|^2}$$

The linear term is similar to Eq. (5) in Case I. Consequently, the power fading is avoided at the expense of 50% reduction in data rate.

2.3 Case III: Alamouti coding

In Case III, we adopt Alamouti coding for power fading elimination without sacrificing data rate as in Fig. 1(c). Assume the input symbol pair at the (2k+1)^th and (2k+2)^th time slot to be ${s_{2k + 1}}$ and ${s_{2k + 2}}$, the coded symbol pairs are $[{{s_{2k + 1}}, - {s_{2k + 2}}} ]$ and $[{{s_{2k + 2}},{s_{2k + 1}}} ]$ for upper- and lower-arms, respectively. The Alamouti coding can be applied on not only pair of symbols but also symbol blocks, leaving the flexibility in block length and processing latency. In this case, the output optical signal at odd and even slots can be expressed as

(9)$${E_{odd}} = \exp \left( {j\frac{{{s_{2k + 1}}}}{{{V_\pi }}}\pi + j\frac{\pi }{4}} \right) + \exp \left( {j\frac{{{s_{2k + 2}}}}{{{V_\pi }}}\pi - j\frac{\pi }{4}} \right) \approx \sqrt 2 + \gamma \frac{\pi }{{{V_\pi }}}({j{s_{2k + 1}} + {s_{2k + 2}}} )$$

(10)$${E_{even}} = \exp \left( { - j\frac{{{s_{2k + 2}}}}{{{V_\pi }}}\pi + j\frac{\pi }{4}} \right) + \exp \left( {j\frac{{{s_{2k + 1}}}}{{{V_\pi }}}\pi - j\frac{\pi }{4}} \right) \approx \sqrt 2 + \gamma \frac{\pi }{{{V_\pi }}}({ - j{s_{2k + 2}} + {s_{2k + 1}}} )$$

After fiber transmission, the photocurrents at odd and even time slots are

(11)$${I_{odd}} = 2 + \sqrt 2 j\frac{\pi }{{{V_\pi }}}{s_{2k + 1}} \otimes [{\gamma h(t )- {\gamma^ \ast }{h^ \ast }(t )} ]+ \sqrt 2 \frac{\pi }{{{V_\pi }}}{s_{2k + 2}} \otimes [{\gamma h(t )+ {\gamma^ \ast }{h^ \ast }(t )} ]+ \cdots$$

(12)$${I_{even}} = 2 + \sqrt 2 \frac{\pi }{{{V_\pi }}}{s_{2k + 1}} \otimes [{\gamma h(t )+ {\gamma^ \ast }{h^ \ast }(t )} ]- \sqrt 2 j\frac{\pi }{{{V_\pi }}}{s_{2k + 2}} \otimes [{\gamma h(t )- {\gamma^ \ast }{h^ \ast }(t )} ]+ \cdots$$

Here the 2^nd-order nonlinear distortion is not fully provided. The end-to-end system response of 1^st-order terms is the same as Eq. (6) and Eq. (7) of Case II. Finally, the 1^st-order terms can be simplified as in Eq. (13).

(13)$${I_{odd}} + j{I_{even}} = 2({1 + j} )+ 2\sqrt 2 \frac{\pi }{{{V_\pi }}}({j{s_{2k + 1}} + {s_{2k + 2}}} )\otimes \gamma h(t )+ ({1 + j} ){\left|{\gamma \frac{\pi }{{{V_\pi }}}({j{s_{2k + 1}} + {s_{2k + 2}}} )\otimes h(t )} \right|^2}$$

Note that the fiber dispersion h(t) itself has no zero points in the frequency domain, making it possible to eliminate the ISI with receiver-side feed forward equalizer (FFE) only. Such property is also valid for another combination as in Eq. (14). To be specific, if we use ${s_{2k + 1}} + j{s_{2k + 2}}$ as training sequence instead of $j{s_{2k + 1}} + {s_{2k + 2}}$, the conjugated channel response ${h^ \ast }(t )$ can be estimated and compensated with the help of least mean square (LMS) or recursive least square (RLS) algorithms and so on. In summary, the key point of the Alamouti coding-based scheme is to cancel the spectral nulls caused by the interference between fiber dispersion h(t) and its conjugation, and flexibility is left in the receiver-side DSP.

(14)$${I_{odd}} - j{I_{even}} = 2({1 - j} )- 2\sqrt 2 j\frac{\pi }{{{V_\pi }}}[{{s_{2k + 1}} + j{s_{2k + 2}}} ]\otimes {\gamma ^ \ast }{h^ \ast }(t )+ \cdots$$

2.4 Numerical visualization

To get an intuitive understanding, Fig. 2(a) and 2(b) illustrate the calculated end-to-end system responses of linear terms in Case I and Case II/III, respectively. The fiber length is set as 80 km with 17ps/km/nm dispersion for C-band transmission. In Fig. 2(a), the blue and green curves actually correspond to the scenarios of IM-DD and PM-DD links, respectively. There are multiple notches can be observed, which severely restrict the available modulation bandwidth. The first fading frequency of standard is approximately 6.8 GHz, which is inverse proportional to the transmission distance. As frequency gets higher, the spectral nulls become denser because the dispersion-induced phase delay is proportional to the square of frequency. Fortunately, all fading frequencies of either blue or green curve are exactly consistent with the peak frequencies of the other curve. After linear combination, the system response can be turned back to H(f) (red curve), which exhibits flat magnitude response. On the other hand, although the fading frequencies are changed for Case II/III as in Fig. 2(b), the complementary nature still holds for the blue and green curves. As a consequence, fading-free transmission can be also achieved by digital combining the photocurrents at odd and even time slots.

Fig. 2. Calculated end-to-end system response in the frequency domain of (a) Case I; (b) Case II/III.

Download Full Size | PDF

3. Experimental setup and DSP stack

Figure 3 shows the experimental setup and DSP diagrams of Alamouti coding-based DD transmission system. At the transmitter, the binary bit stream is mapped into PAM-4/6/8 formats, respectively. PAM-6 mapping is realized by transmitting the in-phase and quadrature components of standard 32-QAM constellation at two consecutive symbols. Then a 2048-symbol sequence is added as preamble, which is employed both for synchronization and channel estimation. To cut off the interference between coded blocks, 320 zero symbols are employed as guard interval, which is divided into 20 segments and inserted uniformly. The following payload consists of 40960 data symbols. The payload percentage is therefore 94.5% (=40960/(2048 + 320 + 40960)). The framed sequence is Alamouti coded at 1 sample per symbol (SPS). Afterwards, the two output sequences are 2-times up-sampled and shaped by digital root-raised cosine (RRC) filter with 0.01 roll-off. To match the 120GSa/s sampling rate of arbitrary waveform generator (AWG, Keysight M8194), the generated signals are re-sampled from 2 SPSs to 120/B SPSs. Here B is the target baud rate. A pair of electrical amplifier (EA) with 50 GHz bandwidth and 23 dB gain is placed between AWG and DDMZM to boost the electrical waveforms. An external cavity laser (ECL) centered at 1549.96 nm is employed to generate the continuous light at 15dBm. The signal is modulated onto the optical carrier though DDMZM (Fujitsu, FTM7937) biased at the quadrature point. An erbium-doped fiber amplifier (EDFA) is placed after DDMZM to control the launch power. To emulate the inter-DCI scenario, 80 km SSMF is used as transmission link.

Fig. 3. Experimental setup and DSP stacks. AWG: arbitrary waveform generator; EA: electrical amplifier; ECL: external cavity laser; DDMZM: dual-drive Mach-Zehnder modulator; EDFA: erbium-doped fiber amplifier; SSMF: standard single-mode fiber; VOA: variable optical attenuator; PD: photodiode; DSO: digital storage oscilloscope; RRC: root-raised cosine; FFE: feed forward equalizer; VNE: Volterra nonlinear equalizer.

Download Full Size | PDF

At the receiver, another EDFA is adopted to compensate for the fiber loss. Afterwards, a variable optical attenuator (VOA) is employed to adjust the received optical power. The optical signal is detected by 50 GHz PD and amplified by 50 GHz EA. Finally, digital storage oscilloscope (DSO, Keysight DSX96204Q) operating at 160GSa/s samples and digitizes the electrical waveforms. For offline DSP, the received waveform is firstly re-sampled to 2 samples per symbol (SPSs). After convoluted by match RRC filter, the first 128 symbol of the preamble is extracted for synchronization by calculating the cross-correlation function. Then the odd and even time slots are separated and combined according to Eq. (13). For transceiver and fiber-induced ISI elimination, we use training sequence-based time-domain FFE or diagonal terms-only Volterra nonlinear equalizer. The linear taps are 161 for both FFE and VNE, and the 2^nd-order taps are 25 for VNE only. The equalized sequence is down-sampled to 1 SPS. Finally, the real and imaginary parts of combined symbol are separated and interleaved before PAM de-mapping and BER calculation. The BER is obtained by counting >4×10⁵ bits.

4. Experimental results

4.1 Single channel transmission

We first evaluate the single channel transmission performance. Figure 4(a) depicts the transmitted and received optical spectra of 75Gbaud PAM-4 signal. The resolution is set as 0.01 nm to show the details. After 80 km SSMF transmission, the amplified spontaneous emission (ASE) noise floor is lifted, leading to reduced optical signal-to-noise ratio (OSNR). Here the OSNR is defined as the ratio between signal power (including the carrier power) and noise power within 0.1 nm effective optical bandwidth. Following this definition, the OSNR values are measured as 53.8 dB and 43.9 dB for back-to-back (BTB) and 80 km transmission scenarios, respectively. Note that the effective OSNR is in the range of 20dB∼30 dB, if the carrier power is excluded from the high OSNR values. Figure 4(b) displays the optical spectra with different baud rates varying from 32Gbaud to 75Gbaud. Thanks to the digital RRC filter, the occupied optical bandwidth is almost the same as symbol rate with spectrally-efficient rectangular shape. Figure 4(c) plots the electrical spectra of BTB and 80 km transmission cases. The DSO bandwidth brings a brick-wall low-pass filtering, and removes all the frequency components outside 63 GHz. The red curve coincides with the blue curve in the interval of [−37.5 GHz, 37.5 GHz], confirming that power fading can be mostly avoided by the Alamouti coding scheme. For 80 km SSMF transmission case, the noise floor around the signal spectrum is higher than the BTB case, which can be attributed to the increased optical noise from EDFA.

Fig. 4. (a) Transmitted and received optical spectrum of 75Gbaud PAM-4 signal. (b) Transmitted optical spectra with different baud rates. (c) Received electrical spectra of 75Gbaud PAM-4 signal at BTB and after 80 km SSMF transmission. (d) Measured BER versus guard interval for 75Gbaud PAM-4 signal after 80 km SSMF transmission. (e) Measured BER versus launch power with FFE/VNE, respectively. (f) Measured optical spectra after 80 km SSMF transmission with different launch power, respectively.

Download Full Size | PDF

In the Alamouti coding-based scheme, the channel responses of odd and even data blocks are different according to Eq. (11) and Eq. (12). Therefore, the ISI inside each block can be compensated by equalizer, while the ISI from the previous block would lead to wrong channel estimation. To address this issue, we insert guard interval consisted of zero symbols in the time domain between neighboring data blocks. In general, larger guard interval is required for higher baud rate or longer transmission distance to cut off the influence of pulse broadening. Figure 4(d) shows the measured BER as a function of guard interval for 75Gbaud PAM-4 signal after 80 km SSMF transmission. The BER decreases as the guard interval increases. Considering both BER performance and bandwidth efficiency, 16-symbol guard interval is chosen with respect to 2048-symbol data block, corresponding to 0.8% frame redundancy.

Figure 4(e) measures the BER versus optical launch power for 80 km transmission with FFE or VNE, respectively. As the launch power increases from 5dBm to 8dBm, the BER reduces due to the increase in received SNR. With the help of VNE, the BER can be improved from 1.47×10⁻² to 1.28×10⁻² at optimal launch power of 8dBm. After that, the BER rises again when launch power increases to 11dBm. Such degradation is caused by the fiber nonlinearity especially the stimulated Brillouin scattering (SBS). The explanation can be supported by Fig. 4(f), which compares the received optical spectra at various launch powers. We can observe that there is a small peak inside the purple circle. The peak frequency is approximately 11 GHz (or 0.09 nm equivalently) lower than the center carrier, which coincides with the characterization of 1^st-order Stokes wave [28]. The 1^st-order Stokes wave becomes stronger as the launch power increases, resulting in worse BER.

Figure 5(a)–5(c) show the measured BER as a function of bitrate for PAM-4/6/8 formats at BTB and after 80 km SSMF transmission, respectively. The launch power is fixed at 8dBm and the received optical power is 1dBm. Diagonal-term only 2^nd-order Volterra nonlinear equalizer is applied on both cases. At BTB, the BERs of 160Gb/s (80Gbaud) PAM-4, 140Gb/s (56Gbaud) PAM-6, and 108Gb/s (36Gbaud) PAM-8 are 1.4×10⁻³, 1.8×10⁻³, and 4.9×10⁻³, respectively. With the help of Alamouti coding-based scheme, the maximum bitrates for PAM-4/6/8 formats are 160Gb/s, 140Gb/s and 120Gb/s at the 20% SD-FEC threshold of 2.0×10⁻² after 80 km SSMF transmission. Higher modulation format is more sensitive to both linear noise and nonlinear SSBI distortion, and the achievable baud rate is thus reduced at the same BER threshold. The BER gap between BTB and 80 km is mainly caused by the ∼9.9 dB OSNR reduction after transmission. The typical eye-diagrams of PAM-4/6/8 are displayed in Fig. 5(i)–5(vi). The eyes after 80 km transmission are smaller than at BTB due to the accumulation of ASE noise.

Fig. 5. Measured BER versus bitrate for (a) PAM-4 (b) PAM-6, and (c) PAM-8 at BTB and after 80 km SSMF transmission scenarios, respectively. (i)∼(vi) Typical eye-diagrams of PAM-4/6/8 signal after 80 km SSMF transmission and at BTB, respectively.

Download Full Size | PDF

4.2 WDM transmission

Then we test the WDM transmission performance of the Alamouti coding-based scheme to show the potential for terabit DCI applications. For WDM channel aggregation, 8 ECLs spacing at 100 GHz are directly combined by 8×1 polarization maintaining optical coupler (PM-OC) and then fed into the same DDMZM to carry 75Gbaud Nyquist PAM-4 signal, emulating gross capacity of 1.2Tb/s (=75Gbaud×2bit/symbol×8λ). At the receiver-side, an optical band-pass filter (OBPF) with 800 dB/nm roll-off is placed between EDFA2 and VOA to extract the target channel and suppress the inter-channel interference (ICI). In our experiment, the odd and even channel interleaving is not implemented due to the lack of available DDMZM. Nevertheless, since the channel spacing of 100 GHz is large enough compared with signal bandwidth of 75 GHz, the linear ICI can be neglected. For cross-phase modulation (XPM) caused by fiber Kerr effect, Ref. [29] and [30] have validated both in simulation and experiment that the correlated WDM transmission would suffer from more severe nonlinear phase noise than uncorrelated WDM schemes. Therefore, the experimental results in this subsection can be regarded as the lower bound of WDM transmission performance based on the above analysis.

Figure 6(a) shows the transmitted and received optical spectra of WDM PAM-4 signal at 0.01 nm resolution. The OSNR values are measured as 42.9 dB and 39.7 dB at BTB and after 80 km SSMF transmission, respectively. The OSNR for WDM signal is 10.9 dB lower than single channel at BTB, which can be attributed to the 12.0 dB measured insertion loss of the used 8×1 PM-OC, which is much higher than the theoretical value of 9 dB. The OSNR reduction after transmission is smaller for WDM signal compared with single channel. It is because that for the attenuation and amplification process, noisy signal is more likely to get saturated. The curve after OBPF (red) confirms that the out-of-band noise and ICI can be removed simultaneously. Figure 6(b) shows the measured BER of the 5^th-wavelength channel versus total launch power after 80 km transmission. The channel index is numbered according to the wavelength from the smallest to the largest. The lowest BER is achieved at 16dBm launch power, corresponding to 7dBm optical power per channel. Compared with the results in Fig. 4(b), the optimal launch power is decreased by 1 dB per channel, which is mainly resulted from the influence of XPM. Figure 6(c) displays the measured BERs of 8 wavelength channels with FFE and VNE, respectively. With the help of VNE, the average BER can be reduced from 1.95×10⁻² to 1.76×10⁻², and all 8 channels can achieve the 20% SD-FEC threshold.

Fig. 6. (a) Transmitted and received optical spectra of WDM PAM-4 signal at 0.01 nm resolution. (b) Measured BER versus total launch power of WDM PAM-4 signal with FFE and VNE after 80 km SSMF transmission, respectively. (c) Measured BERs of 8 WDM channels with FFE and VNE after 80 km SSMF transmission.

Download Full Size | PDF

Finally, we measure the received optical power (ROP) sensitivity of single channel and WDM signals both at BTB and after 80 km SSMF transmission cases as in Fig. 7(a) and 7(b). For 1dBm ROP at BTB case, OSNR difference lead to the BER gap between single channel and WDM signal. As ROP gets smaller, PD-induced electrical noise including thermal noise, shot noise and dark current gradually becomes larger than optical noise. Therefore, the blue and red curves are very close to each other in the electrical noise-dominant region, and there is only 0.3 dB penalty in ROP sensitivity at the 20% SD-FEC threshold. For the 80 km transmission scenario, the BER of WDM signal is 1.88×10⁻², which is slightly smaller than 2.0×10⁻². In this case, the WDM signal is still in the optical noise-dominant region at the FEC threshold while single channel signal is more influenced by electrical noise. Hence, the penalty is enlarged to approximately 2.5 dB. In addition, the ROP sensitivity of single channel is degraded from −5.6dBm at BTB to −2.7dBm at 80 km. The reason for such penalty is that the OSNR is decreased by 9.9 dB after transmission. The BER as a function of OSNR is further measured for single channel and WDM signals at BTB as in Fig. 7(c). BER floor can be observed for single channel with OSNR larger than 45 dB. At the 20% SD-FEC threshold, WDM signals has a penalty of ∼0.3 dB compared with single channel.

Fig. 7. Measured received optical power sensitivity of signal channel and WDM signals for (a) BTB and (b) 80 km transmission scenarios, respectively. (c) Measured BER versus OSNR of single channel and WDM signals at BTB case.

Download Full Size | PDF

5. Discussion

5.1 Comparison with SSB scheme

In this subsection, a transmission performance comparison between the proposed scheme and SSB transmission is provided. The numerical co-simulation system is implemented by combining MATLAB and VPItransmissionMaker. The transmitter- and receiver-side DSP are conducted in MATLAB, while the transceiver components and fiber link are modelled in VPI. Both Alamouti coding-based scheme and SSB scheme adopt 75Gbaud Nyquist PAM-4 signal with the same modulation index for fair comparison. The dispersion parameter and nonlinear coefficient of fiber is set as 17ps/nm/km and 0 to investigate the impact of dispersion. The thermal noise, shot noise and dark current of PD are all neglected. The DSP stack and parameter of Alamouti coding-based scheme are the same as Fig. 3 in the experiment. At the transmitter-side DSP, SSB scheme uses Hilbert transform to remove one of the sidebands, which has higher computational complexity than Alamouti coding. Meanwhile, for SSB reception, we use Kramer-Kronig relation (KK) or up-sampling-free Kramers-Kronig receiver (USF-KK) [31] followed by real part operation for field recovery, which is performed between re-sampling and matched RRC filter. 2 SPSs is adopted in the receiver-side DSP of both SSB and Alamouti coding system for comparison.

Figure 8(a)–8(c) show the simulated OSNR performance of SSB and Alamouti coding schemes with transmission distance varying from 0 to 80 km, respectively. As shown in Fig. 8(a), since there is no dispersion-induced ISI at BTB case, no extra gain is obtained with larger guard interval. And the OSNR performance are almost the same in the noise-dominated regime for both schemes, which is mainly determined by the modulation index or the effective OSNR equivalently. For standard KK detection, the BER is slightly higher than the Alamouti coding scheme in the high OSNR regime. The reason is that the nonlinear operation such as square root and logarithm in KK algorithm leads to spectral broaden, resulting in penalties under 2 SPSs processing. It can be also confirmed that by using up-sampling-free KK detection, the BER can be further reduced. As the transmission distance increases to 40 km, Alamouti coding-based scheme with guard interval of 16 begins to exhibit a higher BER floor in the high OSNR region. Similar phenomenon can be observed in the 80 km case with guard interval up to 32, which indicating that the channel-induced ISI length is extended by distance. Nevertheless, with enough guard interval, the interference between neighboring symbol blocks can be cut off, and the OSNR performance of Alamouti coding scheme is still comparable with SSB scheme, confirming the ability of fading-free transmission. In addition, note that the symbol block length can be increased appropriately to reduce the redundancy of frame for longer transmission distance, at the expense of larger storage depth of transmitter.

Fig. 8. Simulated BER versus OSNR of SSB and Alamouti coding-based scheme at BTB, after 40 km and 80 km SSMF transmission, respectively. KK: Kramers-Kronig; USF: up-sampling-free; GI: guard interval.

Download Full Size | PDF

Fig. 9. Simulated BER versus bias phase of Alamouti coding-based scheme with OSNR varying from 43 dB to 47 dB at BTB, after 40 km and 80 km SSMF transmission, respectively.

Download Full Size | PDF

5.2 Bias deviation tolerance

We also simulate the tolerance of bias deviation of the Alamouti coding-based scheme with 43/45/47 dB OSNR at the BTB, 40 km and 80 km SSMF transmission scenarios, respectively. Here the DDMZM bias point is described in phase, which can be calculated from radian by φ/π×180°. As shown in Fig. 9, for all the distances, the curves are symmetric about 90° with two error valleys around 45° and 135°, which confirms that both quadrature points can be chosen for Alamouti coding-based scheme to ensure the orthogonality of Eq. (9) and Eq. (10). It is also observed that the optimal bias phase is more deviated toward the null point of 90° with a lower OSNR value. The reason is that for a fixed OSNR, the suppression of carrier would lead to increased effective OSNR of signal, and the gain from OSNR improvement exceeds the penalty caused by the orthogonality violation and partially modulation nonlinearity. At the BTB case, since there is no fading impairment, thus the bias requirement can be relaxed, leading to even bottom of the curves. As the transmission distance increases, the curves become steeper with narrowed bias interval for optimal performance. It is because that additional phase shift would result in residual fading terms in the cancellation process from Eq. (11) and Eq. (12) to Eq. (13), and thus stricter bias condition is needed for more severely faded scenarios.

Furthermore, we present the simulated BER as a function of carrier-to-signal power ratio (CSPR) for Alamouti coding scheme, which is a critical parameter for DD links. Note that for DDMZM-based optical transmitter, once the peak-to-peak voltage is optimized in the linear modulation region, the bias phase completely determines the CSPR of the generated optical signal. Such one-to-one mapping relation is reflected through the right-Y-axis of Fig. 10. As the OSNR grows from 43 dB to 45 dB, the optimal CSPR value increases accordingly, leading to higher bias phase.

Fig. 10. Simulated BER versus CSPR of Alamouti coding-based scheme with OSNR varying from 43 dB to 47 dB at BTB, after 40 km and 80 km SSMF transmission, respectively.

Download Full Size | PDF

6. Conclusions

In summary, we propose a fading-free direct detection transmission scheme for PAM signals based on Alamouti coding and DDMZM. The transmitted symbol blocks are interleaved in the time domain and drive the upper- and lower-arm of DDMZM, respectively. After linearly combining the photocurrents at odd and even time slots, the end-to-end frequency response is flat without spectral nulls. For single channel demonstration, we experimentally transmit 160Gb/s PAM-4, 140Gb/s PAM-6 and 108Gb/s PAM-8 over 80 km SSMF with BERs below the 20% SD-FEC threshold of 2.0×10⁻². For wavelength division multiplexing (WDM) transmission, 1.2Tb/s (8λ×150Gb/s) PAM-4 signals spacing at 100 GHz can also achieve 80 km reach. Moreover, through numerical simulation, the OSNR performance of the Alamouti coding-scheme is similar to SSB scheme with KK detection. The proposed Alamouti coding-based scheme offers a hardware-efficient and dispersion-tolerant candidate for high-speed inter-DCI applications.

Funding

National Natural Science Foundation of China (62001287); China Postdoctoral Science Foundation (2021M692098); National Key Research and Development Program of China (2018YFB1800904).

Disclosures

The authors declare no conflict 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.

References

1. S. J. Savory, “Digital Coherent Optical Receivers: Algorithms and Subsystems,” IEEE J. Select. Topics Quantum Electron. 16(5), 1164–1179 (2010). [CrossRef]

2. K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital Signal Processing for Short-Reach Optical Communications: A Review of Current Technologies and Future Trends,” J. Lightwave Technol. 36(2), 377–400 (2018). [CrossRef]

3. G. N. Liu, L. Zhang, T. Zuo, and Q. Zhang, “IM/DD Transmission Techniques for Emerging 5G Fronthaul, DCI, and Metro Applications,” J. Lightwave Technol. 36(2), 560–567 (2018). [CrossRef]

4. X. Pang, A. Udalcovs, R. Schatz, V. Bobrovs, G. Jacobsen, S. Popov, and O. Ozolins, “Short Reach Communication Technologies for Client-Side Optics Beyond 400Gbps,” IEEE Photonics Technol. Lett. 33(18), 1046–1049 (2021). [CrossRef]

5. K. Zhang, Q. Zhuge, H. Xin, W. Hu, and D. V. Plant, “Performance comparison of DML, EML and MZM in dispersion-unmanaged short reach transmissions with digital signal processing,” Opt. Express 26(26), 34288–34304 (2018). [CrossRef]

6. X. Tang, S. Liu, Z. Sun, H. Cui, X. Xu, J. Qi, M. Guo, Y. Lu, and Y. Qiao, “C-band 56-Gb/s PAM4 transmission over 80-km SSMF with electrical equalization at receiver,” Opt. Express 27(18), 25708–25717 (2019). [CrossRef]

7. H. Wang, J. Zhou, D. Guo, Y. Feng, W. Liu, C. Yum, and Z. Li, “Adaptive Channel-Matched Detection for C-Band 64-Gbit/s Optical OOK System Over 100-km Dispersion-Uncompensated Link,” J. Lightwave Technol. 38(18), 5048–5055 (2020). [CrossRef]

8. R. Rath, D. Clausen, S. Ohlendorf, S. Pachnicke, and W. Rosenkranz, “Tomlinson–Harashima Precoding For Dispersion Uncompensated PAM-4 Transmission With Direct-Detection,” J. Lightwave Technol. 35(18), 3909–3917 (2017). [CrossRef]

9. X. Wu, A. S. Karar, K. Zhong, A. P. T. Lau, and C. Lu, “Experimental demonstration of pre-electronic dispersion compensation in IM/DD systems using an iterative algorithm,” Opt. Express 29(16), 24735–24749 (2021). [CrossRef]

10. Z. Xu, C. Sun, T. Ji, J. H. Manton, and W. Shieh, “Cascade recurrent neural network-assisted nonlinear equalization for a 100 Gb/s PAM4 short-reach direct detection system,” Opt. Lett. 45(15), 4216–4219 (2020). [CrossRef]

11. S. Hu, J. Zhang, J. Tang, W. Jin, R. Giddings, and K. Qiu, “Data-Aided Iterative Algorithms for Linearizing IM/DD Optical Transmission Systems,” J. Lightwave Technol. 39(9), 2864–2872 (2021). [CrossRef]

12. X. Chen, A. Li, D. Che, Q. Hu, Y. Wang, J. He, and W. Shieh, “Block-wise phase switching for double-sideband direct detected optical OFDM signals,” Opt. Express 21(11), 13436–13441 (2013). [CrossRef]

13. A. Li, D. Che, X. Chen, Q. Hu, Y. Wang, and W. Shieh, “61 Gbits/s direct-detection optical OFDM based on blockwise signal phase switching with signal-to-signal beat noise cancellation,” Opt. Lett. 38(14), 2614–2617 (2013). [CrossRef]

14. Z. Chen, Z. Wu, J. Huang, S. Zhang, X. Ao, Z. Wang, J. Ke, L. Yi, and Q. Yang, “4 × 32-Gbps Block-Wise QPSK 1200-km SSMF Direct Detection Transmission Based on Delta-Sigma Virtual Carrier Generation,” IEEE Photonics J. 11(6), 1–7 (2019). [CrossRef]

15. J. Peng, B. Liu, J. Wu, Q. Zhu, C. Qiu, Y. Zhang, R. Liu, C. Tremblay, and Y. Su, “Spectrally-Efficient Direct Detection of QAM Signal by Orthogonal Carrier Interleaving,” Proc. Conference on Lasers and Electro-Optics, paper SM4F.5 (2016).

16. D. Che, X. Chen, J. He, A. Li, and W. Shieh, “102.4-Gb/s Single-Polarization Direct-Detection Reception using Signal Carrier Interleaved Optical OFDM,” Proc. Optical Fiber Communication Conf., paper Tu3G.7 (2014).

17. J. Zhang, J. Yu, X. Li, Y. Wei, K. Wang, L. Zhao, W. Zhou, M. Kong, X. Pan, B. Liu, and X. Xin, “100 Gbit/s VSB-PAM-n IM/DD transmission system based on 10 GHz DML with optical filtering and joint nonlinear equalization,” Opt. Express 27(5), 6098–6105 (2019). [CrossRef]

18. A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers–Kronig coherent receiver,” Optica 3(11), 1220–1227 (2016). [CrossRef]

19. Z. Li, M. Erkılınç, K. Shi, E. Sillekens, L. Galdino, B. Thomsen, P. Bayvel, and R. Killey, “SSBI mitigation and the Kramers-Kronig scheme in single-sideband direct-detection transmission with receiver-based electronic dispersion compensation,” J. Lightwave Technol. 35(10), 1887–1893 (2017). [CrossRef]

20. S. T. Le, K. Schuh, M. Chagnon, F. Buchali, R. Dischler, V. Aref, H. Buelow, and K. M. Engenhardt, “1.72-Tb/s Virtual-Carrier-Assisted Direct-Detection Transmission Over 200 km,” J. Lightwave Technol. 36(6), 1347–1353 (2018). [CrossRef]

21. W. Shieh, C. Sun, and H. Ji, “Carrier-assisted differential detection,” Light: Sci. Appl. 9(1), 18 (2020). [CrossRef]

22. C. Sun, T. Ji, H. Ji, Z. Xu, and W. Shieh, “Experimental Demonstration of Complex-Valued DSB Signal Field Recovery via Direct Detection,” IEEE Photonics Technol. Lett. 32(10), 585–588 (2020). [CrossRef]

23. D. Zou, F. Li, Z. Li, W. Wang, Q. Sui, Z. Cao, and Z. Li, “100G PAM-6 and PAM-8 Signal Transmission Enabled by Pre-Chirping for 10-km Intra-DCI Utilizing MZM in C-band,” J. Lightwave Technol. 38(13), 3445–3453 (2020). [CrossRef]

24. S. Ishimura, A. Bekkali, K. Tanaka, K. Nishimura, and M. Suzuki, “1.032-Tb/s CPRI-Equivalent Rate IF-Over-Fiber Transmission Using a Parallel IM/PM Transmitter for High-Capacity Mobile Fronthaul Links,” J. Lightwave Technol. 36(8), 1478–1484 (2018). [CrossRef]

25. S. Ishimura and K. Nishimura, “Direct-Detection OFDM Transmission Using Four-State Chirp Control With a Dual-Electrode MZM for Dispersion Compensation,” IEEE Photonics J. 10(5), 1–8 (2018). [CrossRef]

26. Y. Zhu, L. Li, X. Miao, L. Yin, X. Chen, and W. Hu, “Fading-free Block-wise PAM Signal Transmission with Direct Detection Based on Alamouti Coding and DDMZM,” Proc. Asia Communications and Photonics Conf., paper S4H.3 (2020).

27. K. V. Peddanarappagari and M. Brandt-Pearce, “Volterra series approach for optimizing fiber-optic communications system designs,” J. Lightwave Technol. 16(11), 2046–2055 (1998). [CrossRef]

28. A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photonics 2(1), 1–59 (2010). [CrossRef]

29. W. R. Peng, I. Morita, H. Takahashi, and T. Tsuritani, “Transmission of high-speed (> 100 Gb/s) direct-detection optical OFDM superchannel,” J. Lightwave Technol. 30(12), 2025–2034 (2012). [CrossRef]

30. Z. Li, X. Xiao, T. Gui, Q. Yang, R. Hu, Z. He, M. Luo, C. Li, X. Zhang, D. Xue, S. You, and S. Yu, “432-Gb/s Direct-Detection Optical OFDM Superchannel Transmission Over 3040-km SSMF,” IEEE Photonics Technol. Lett. 25(15), 1524–1526 (2013). [CrossRef]

31. T. Bo and H. Kim, “Kramers-Kronig receiver operable without digital upsampling,” Opt. Express 26(11), 13810–13818 (2018). [CrossRef]

Direct detection transmission of a PAM signal with power fading mitigation based on Alamouti coding and dual-drive MZM

Abstract

1. Introduction

2. Principle

2.1 Case I: IM/PM switching

2.2 Case II: upper/lower-arm switching

2.3 Case III: Alamouti coding

2.4 Numerical visualization

3. Experimental setup and DSP stack

4. Experimental results

4.1 Single channel transmission

4.2 WDM transmission

5. Discussion

5.1 Comparison with SSB scheme

5.2 Bias deviation tolerance

6. Conclusions

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (10)

Equations (14)

Optics Express