# Two-Channel OTDM System for Data-Center Interconnects: A Review
## 2 Two-Channel OTDM System with Constant-Phase Pulse
### OTDM System Using the Symbol-Spaced MIMO Equalizer
#### 2.2.2 Roles of the MIMO Equalizer  
A numerical simulation was performed to evaluate the role of the MIMO equalizer [21]. The following assumptions were made to ensure consistency with the experiment: (1) the bit rate of the OTDM signal was \(150\) Gb/s; (2) the sinusoidal pulse was generated using a laser diode (LD) and an MZM; (3) the two divided optical pulses were converted into the RZ-PAM-\(N\) (\(N=2,4,8\)) signals by the two MZMs (biased at quadrature points); (4) the peak-to-peak amplitude (\(\Delta V\)) of the electrical PAM signals were \(0.6V_{\pi}\) (\(V_{\pi}\): half-wave voltage); (5) all the MZMs had sufficient bandwidth (i.e., \(3\) dB bandwidth = \(75/N\) GHz); (6) the OTDM signal was detected using a receiver comprising a PIN PD (\(3\) dB bandwidth = \(150/N\) GHz, responsivity = \(1\) A/W), \(50\)\(\Omega\) load resistor at \(20\,^{\circ}\)C, and an electrical amplifier (noise figure = \(6\) dB); and (7) the FEC limit was set to a BER of \(3.8\times 10^{-3}\).  
The MIMO equalizer can successfully eliminate crosstalk between RZ signals caused by the finite ER of the optical pulse. In this simulation, the MIMO equalizer consisted of symbol-spaced \(11\)-tap FFEs. When the MIMO equalizer was not used, a \(2\) dB power penalty was observed when the pulse ER was \(6\) dB, \(9\) dB, and \(14\) dB, respectively, compared to the case when the pulse ER was \(25\) dB (as shown in Figure 4). Since the penalty was primarily caused by crosstalk, the higher-order modulated signal was more sensitive. However, when the MIMO equalizer was used, a \(2\) dB penalty was observed when the pulse ER was \(5\) dB, \(5\) dB, and \(6\) dB, respectively. The receiver sensitivity was less sensitive to the modulation format because the crosstalk was effectively compensated. The residual penalty was primarily caused by the reduced ER of the OTDM signal and can be expressed as follows:  
\[\text{Penalty}(\text{dB})=10\text{log}\left(\frac{\epsilon_{\text{pulse}}+1}{ \epsilon_{\text{pulse}}}\right), \tag{1}\]  
where \(\epsilon_{\text{pulse}}\) denotes the pulse's ER. The results indicated that the two-channel OTDM system was operable as long as the ER of the pulse was \(>\)\(5\) dB [21].  
Figure 3: (**a**) BER curves of a \(75\) Gb/s PAM-8 signal generated by a single MZM and a \(150\) Gb/s OTDM-PAM-8 signal. (**b**) BERs of OTDM-PAM-8 signals as a function of bit rate.  
The MIMO equalizer effectively operated even when there was imperfect multiplexing. During the simulation, the pulse ER was set to 10 dB. A power mismatch can be caused by either the mismatched loss of waveguides propagating two RZ signals in the transmitter or the polarization-dependent loss (when two RZ signals in different polarization domains are combined). Figure 5 displays the co-plots (dashed lines) of receiver sensitivities as a function of the power difference between two multiplexed signals. The residual penalty can be interpreted as a crosstalk penalty due to the imperfections of the MIMO equalizer. Although the RZ1 signal with a lower power was more sensitive to power mismatch, the residual penalty was as low as \(<\)0.2 dB (which is negligible) when the power mismatch was \(<\)1.5 dB. Moreover, a timing mismatch could be caused by either the imperfect delay line in the transmitter or the polarization-mode dispersion (when the two RZ signals in different polarization domains were combined). The timing mismatch can be expressed as follows:  
\[\text{Timing mismatch}\ =\ \frac{|\tau-T_{s}|}{T_{s}}, \tag{2}\]  
where \(\tau\) denotes the delay time caused by the optical delay line, and \(T_{s}\) denotes the symbol period of the OTDM signal. When the timing mismatch was \(>\)16%, a 1 dB penalty was observed, as shown in Figure 5b. The MIMO equalizer can be implemented with half-symbol-spaced FEs to eliminate the penalty.