## 2 Principle and Device of Coherent/Non-Coherent OOK Reception without AL
 \tag{1}\]  
\[\vspace{-0.2 cm}\vspace{-0.2 cm}l_{b0}(t)&=R\Big{[}\frac{1}{2}(s(t ))^{2}k_{S}P_{S}+\frac{1}{2}k_{LO}P_{\Omega}+\sqrt{k_{S}}\sqrt{k_{LO}}\sqrt{ P_{\Omega}P_{S}}(t)\sin(\omega st-\omega_{LO}t+\varphi_{S}(t)-\varphi_{LO}(t)) +n_{\Omega}(t),\end{split} \tag{2}\]  
\[\vspace{-0.2 cm}l_{b0}(t)&=R\Big{[}\frac{1}{2}(s(t))^{2}(1-k_{S})P _{S}+\frac{1}{2}(1-k_{LO})P_{\Omega}-\sqrt{1-k_{S}}\sqrt{1-k_{LO}}\sqrt{P_{ \Omega}P_{S}}(t)\cos(\omega st-\omega_{LO}t+\varphi_{S}(t)-\varphi_{LO}(t)) \Big{]}+n_{\Omega}(t),\end{split} \tag{3}\]  
\[\vspace{-0.2 cm}l_{b20}(t)&=R\Big{[}\frac{1}{2}(s(t))^{2}k_{S}P_{S }+\frac{1}{2}k_{LO}P_{\Omega}-\sqrt{k_{S}}\sqrt{k_{LO}}\sqrt{P_{\Omega}P_{S}}( t)\sin(\omega st-\omega_{LO}t+\varphi_{S}(t)-\varphi_{LO}(t))\Big{]}+n_{\Omega}(t),\end{split} \tag{4}\]  
where \(R\) is the detector responsivity; \(r\) is the detector transimpedance; \(s(t)\) is the modulation term of the communication signal; \(s(t)=0\) or \(1\); \(k_{S}\) and \(k_{LO}\) are the signal light splitting ratio and the LO light splitting ratio of the optical 90\({}^{\circ}\) hybrid, respectively, both of which are 0.5 in this study; \(P_{S}\) and \(P_{LO}\) are the signal optical power and LO optical power, respectively; \(\omega_{S}\) and \(\omega_{LO}\) are the signal optical angular frequency and LO optical angular frequency,  
Figure 3: Experimental structure of coherent OOK receiver. Figure 2: Curve between BER and received signal power of OOK DD with a communication rate of 1 Gbit/s. respectively; \(\varphi_{S}(t)\) and \(\varphi_{LO}(t)\) are the random phase of the signal optical carrier and the random phase of the LO optical carrier, respectively; \(n_{0}(t)\), \(n_{180}(t)\), \(n_{00}(t)\), and \(n_{270}(t)\) are additive noise of the four voltage signals, respectively. With no preamplifier and LO power of 12.8 mW, the four additive noise signals are mainly LO shot noise. After the two BDs are completely subtracted to eliminate the communication square term and direct current (DC) term, I and Q voltage signals are obtained as follows with \(k_{S}=k_{LO}=0.5\)[37]  
\[U_{I}(t)=U_{0}(t)-U_{180}(t)=As(t)\cos(\Delta\varphi(t))+n_{I}(t), \tag{5}\]  
\[U_{Q}(t)=U_{90}(t)-U_{270}(t)=As(t)\sin(\Delta\varphi(t))+n_{Q}(t), \tag{6}\]  
where \(A=Rr\sqrt{P_{S}P_{LO}}\); \(\Delta\varphi(t)=\omega_{S}-\omega_{LO}t+\varphi_{s}(t)-\varphi_{LO}(t)\); \(n_{I}(t)=n_{0}(t)-n_{180}(t)\) and \(n_{Q}(t)=n_{90}(t)-n_{270}(t)\); \(n_{I}(t)\) and \(n_{Q}(t)\) are I and Q noise, respectively. After synchronous sampling, the I and Q signals were complexly transformed, expressed as  
\[U_{COOOK}[k]=U_{I}[k]+j\times U_{Q}[k]=As[k]\exp(j\times\Delta\varphi[k])+n_{ I}[k]+j\times n_{Q}[k], \tag{7}\]  
where \(k\) is the index of the sampled signal and \(j=\sqrt{-1}\). The modulus of the sampled complex signal is expressed as  
\[U_{ABSOOK}[k]=(real(U_{COOOK}[k]))^{2}+(imag(U_{COOOK}[k]))^{2}\approx(As[k]) ^{2}, \tag{8}\]  
where \(real(\cdot)\) represents the real part of the complex signal; and \(imag(\cdot)\) represents the imaginary part of the complex signal. Equation (9) can be obtained by taking the square root of the signal. \[U_{EXTOOK}[k]=\sqrt{U_{ABSOOK}[k]}=As[k], \tag{9}\]  
As \(s[k]=0\)_or_ 1, the coherent demodulation of the OOK signal can be determined only by selecting an appropriate threshold. The communication rate was also 1 Gbit/s in the coherent OOK reception experiment to ensure consistency with non-coherent reception. The two analog-to-digital converters (ADC) in Figure 3 were replaced by a high-speed oscilloscope (Figure 1); the oscilloscope settings were consistent with those during non-coherent reception. The two oscilloscope channels synchronously sampled the output signals of the two BDs. Before receiving the signal, the LO frequency was adjusted such that the frequency difference between the LO light and the signal light was far less than the communication rate; thus, intradyne detection was implemented. One advantage of this method is that it reduces the electrical bandwidth requirement of the detector.