## 2 Experimental Setup and Signal Bandwidth Estimation
There are 16,384 points for the ADC raw data, and FFT is then applied to the whole data set. The raw spectra from FFT are shown in Figure 3a. However, the data  
Figure 1: Block diagram of coherent line-card and optical line system. FEC: forward error correction, CPE: carrier phase estimation. Network management layer is not shown for simplicity. Figure 2: Experimental setup to emulate the bandwidth narrowing effect together with other impairments during the transmission. VOA: variable optical attenuator, OSA: optical spectrum analyzer. modulation makes it difficult to estimate the exact bandwidth. Thus, we apply the Savitzky-Golay filter [18] to smooth the raw spectrum. The length of the filter tap is 11, and the polynomial order of the filter is three. The Savitzky-Golay filter can improve the SNR with minimum distortion to the signal. It performs much better than the averaging filter, which filters out a significant portion of high frequency content of the signal. Figure 3b shows the spectrum after the Savitzky-Golay filter being applied. Next, we adjust the bandwidth of the optical tunable filter to emulate the narrowing effect for the coherent signal's bandwidth. We define this parameter as the signal's bandwidth. The spectra of the X-polarization in-phase tributary (XI) under different bandwidth are shown in Figure 3c. Clearly, the bandwidth narrowing effect is presented in the spectrum of the received signal. We defined the difference between the signal's power at the spectrum's edge (Nyquist frequency) and the one at the spectrum's center as \(Attn_{Edge}\). This parameter is closely related to the spectral shape of the signal and can be used to characterize the bandwidth of the signal. This value was further averaged over four tributaries to improve the accuracy. Figure 4 shows a roughly linear relationship between \(Attn_{Edge}\) and the signal's bandwidth. There is small variation for \(Attn_{Edge}\) over different measurements, thus multiple measurements are used to improve the accuracy. It is also noticeable that \(Attn_{Edge}\) is dependent on the SNR level. To estimate the signal's bandwidth (BW) from \(Attn_{Edge}\), one must approximately determine the SNR. In our experiment, the noise is emulated by an external ASE source. In such a condition, the SNR is approximately equivalent to the OSNR. One can thus use the pre-FEC BER to estimate the SNR [19]. In the long-haul optical communications system utilizing dense wavelength division multiplexing (DWDM), the noise is also coming from the nonlinear effect. In a modern DWDM system where coherent transponder is widely deployed, CD is continuously accumulated, and it is not compensated by the inline dispersion compensation module (DCM) anymore. Consequently, uncompensated CD broadens the spectrum of a coherent signal to a Gaussian-like shape. In the nonlinear regime where the per-channel power is larger than the optimal launching power, cross phase modulation (XPM) is the main source of fiber nonlinearity. However, most systems operate in the linear regime or weakly nonlinear regime where the per-channel power is smaller than the optimal launching power. Here, four wave mixing (FWM) is the main source of fiber nonlinearity. The noise generated from FWM approximately acts as the additive white Gaussian noise (AWGN) to the channel under consideration due to its Gaussian-like spectrum [20]. As a result, SNR is further reduced to a value smaller than OSNR. A well-known Gaussian noise (GN) model has been developed as a simple yet reliable tool to predict the performance of uncompensated coherent systems [21]. Thus, the pre-FEC BER can also be used to estimate SNR using the GN model. Based on the discussion above, the measured \(Attn_{Edge}\) can be used to reversely estimate the signal's bandwidth at the coherent receiver. In turn, the FIR filter in the receiver's data path can be adaptive adjusted to compensate the bandwidth-narrowing effect based on the value of \(Attn_{Edge}\). Figure 3: \(Cont.\)