## 4 Theoretical Analysis of the Influence of AL on Coherent/Non-Coherent OOK Reception
### AL Research on the Coherent OOK Receiver  
The experimental structure of the influence of AL on OOK coherent reception is shown in Figure 12.  
In the coherent OOK reception experiment, channels I and Q have the same SNR; thus, the SNR of channel I is equivalent to the SNR of the entire system. This experiment analyzed the SNR of channel I to evaluate the impact of AL. In the experiment, an ASE light source was used to simulate  
Figure 11: SSPSD of AL–AL beat noise. Figure 12: Experimental structure of the influence of AL on OOK coherent reception. AL. In the following description, we refer to the light output by the ASE light source as the simulated ambient light (SAL). The LO power was 12.8 mW and the corresponding I-channel noise voltage variance is expressed as follows. The voltage variance is equal to the current variance multiplied by the square of the detector impedance. \[\sigma_{Vs}^{2}\approx eRP_{LO}B_{e}r^{2}=1.088\times 10^{-4}\,\left(V^{2} \right), \tag{46}\]  
where \(B_{e}\) is the noise bandwidth of the BDs, \(B_{e}=2.5\) GHz; \(r\) is the detector impedance, \(r=5\) k\(\Omega\). In this experiment, the wavelength range of the ASE light source used was 1526.65 nm to 1570.85 nm. The tunable optical filter was adjusted, such that its central wavelength was equal to the signal optical wavelength (1555.74 nm): the bandwidth was 2 nm, from 1554.74 nm to 1556.74 nm. The frequency interval corresponding to the wavelength interval was \(2.48\times 10^{11}\) Hz. By adjusting the attenuator, the SAL powers entering the \(2\times 1\) coupler were 1.15 uW, 0.86 uW, 0.58 uW, 0.29 uW, 0.14 uW, 57.56 nW, 46.05 nW, 28.78 nW, and 5.76 nW. The PSD of the SAL was considered to be flat in the filter passband. According to the power and frequency intervals, we can obtain the corresponding PSD of the SAL with different powers, as shown in Table 2.  
Equation (47) was used for calculations in the third column of Table 2.  
\[\sigma_{Valn-lo}^{2}=R^{2}P_{LO}S_{altn}r^{2}B_{e}, \tag{47}\]  
In this experiment, before adding the SAL, the voltage variance of the shot noise was the main noise component. Adding SAL with different PSDs can yield new voltage noise variances. The new voltage variance consists of shot noise and AL-LO beat noise; both are white noise. The ratio of the new voltage noise variance to the shot noise variance represents the change in noise, and the deterioration of system sensitivity. The calculated and experimentally measured ratios are presented in Table 3. Equation (35) was used for calculations in the second column of Table 3. Actual measured data were calculated and used for the third column of Table 3.  
The measured ratio was smaller than the theoretical ratio because the measured value of the voltage variance of the shot noise was larger than the theoretical value. This may have been due to oscilloscope quantization error. We tested the sensitivity in four conditions: A, B, C, and D (Table 3), and coherently received OOK signals at a communication rate of 1 Gbit/s. The relationship curves for coherent reception between the BER and the optical signal power in different conditions are shown in Figure 11:0  
Figure 13 shows the theoretical curve, the curve without SAL, and the curves in conditions D, C, B, and A. When the BER is \(10^{-3}\), the deterioration in sensitivity of D, C, B, and A was 14.3 dB, 11.3 dB, 6.1 dB, and 3.09 dB, respectively, consistent with the theoretical calculation in Figure 11:1 The noise bandwidth of the BD in this experiment was 2.5 GHz. The SAL noise outside the band did not increase SAL-LO beat noise voltage variance, but increased part of the shot noise. However, the power of the LO was dominant; the shot noise generated by the SAL can be ignored. When the filter bandwidth was 0.2 nm-5 nm, the noise voltage variance was essentially the same as that at 2 nm, with the PSD of the SAL and the central wavelength of the optical filter unchanged.