## 4 Results and Discussions  
It is known that the CSPR is a critical parameter for self-coherent systems. Under a fixed transmit power, the CSPR affects the power proportion of the carrier in the transmitted signal. Regarding the impact of CSPR on signal transmission quality, Figure 4 presents the bit error rate (BER) versus CSPR for the PDM-OFDM FASCD at back-to-back (BTB) and 320 km of fiber transmission when the transmission rate is 224 Gbit/s. To identify the required CSPR, we fixed the bandwidth and Gaussian order of the OBPF to 3 GHz and 4, respectively. The OSNR are fixed as 23 dB. When the CSPR is small, it cannot amplify the signal term effectively. In order to effectively recover the signal during reception, we amplify the carrier using EDFA, which also amplifies the noise in the system, exacerbating  
Figure 3: (**a**) Transmitter-side DSP. (**b**) Receiver-side DSP.  
the effect of noise on the system. OSNR in a system is defined as the ratio of the sum of the power of the signal and the carrier to the noise. When the CSPR is large, the signal-to-noise ratio in the system is small, which directly leads to the degradation of system performance. As we can see from the results, the optimal value for CSPR is \(-3\) dB at 320 km transmission. Therefore, the CSPR is set to \(-3\) dB in the following simulations.  
In the description of the second section, extracting the optical carrier using an OBPF is a crucial step for achieving field recovery of the optical signal. To better align with practical scenarios, Gaussian filters of different orders are employed to simulate the OBPF. Figure 5 displays the system performance at different OSNR for back-to-back transmission under the optimal CSPR, with the Gaussian filter orders set to 2, 3, 4, and 5, respectively. When the filter order increases from 2 to 3, the system's BER performance improves significantly. As the filter order increases, it effectively separates the signal and the carrier. When the filter order is further increased to 4, at an OSNR of 23 dB, the system's BER is below the HD-FEC threshold of \(3.8\times 10^{-3}\), enabling error-free transmission. Continuing to increase the filter order does not result in noticeable further improvement in the BER. Therefore, the OBPF order is set to 4, which will be used for the next simulations.  
As mentioned in the second section, signals are subject to chromatic dispersion and polarization mode dispersion during transmission. For OFDM systems, a channel estimation method based on LS is commonly employed. However, since the noise in the channel is not taken into account, the estimated channel information is not entirely accurate. This leads to slight discrepancies between the equalized received signal and the actual signal during subsequent processing. Figure 6 illustrates the trend of the BER versus OSNR for  
Figure 4: BER versus CSPR for the PDM-OFDM FASCD at BTB and after 320 km transmission.  
Figure 5: BER versus OSNR for the PDM-OFDM FASCD under different filter orders (**a**) at BTB and (**b**) after 320 fiber transmission.  
both the conventional LS-based channel estimation method and the improved method after 320 km transmission. The improved method demonstrates about a 1 dB enhancement in OSNR performance.  
To validate the proposed PDM-OFDM FASCD scheme in this paper, a comparison was made with traditional coherent detection under identical system parameter configurations. The BER curves as a function of OSNR for both reception schemes are depicted in Figure 7, with both schemes operating at a transmission rate of 224 Gbit/s. While the self-coherent system incurs an OSNR penalty of 3 dB due to the reduction of one laser, this trade-off is entirely acceptable given the high cost of lasers. Combined with the aforementioned analysis of carrier extraction, CSPR impact, and OSNR tolerance, this demonstrates the feasibility of the proposed scheme.