Optical Communications, 2nd Edition

4.3 SIGNAL-TO-NOISE RATIO IN DIRECT DETECTION RECEIVERS

In this section, we compute the electronic signal-to-noise ratio (SNR) following photodetection in a direct detection receiver. We assume an ideal filter F(ω) is used as in Figure 4.8a to extract the source modulation m(t), the filter having a unit level transfer function over the bandwidth B_m of the signal spectrum S_m(ω), as shown in Figure 4.8b. The filtered output SNR can now be determined by calculating the output signal and noise powers from the filtered spectrum of y(t) in Eq. (4.2.3). (We neglect the de contribution to SNR by contending that this de current can be easily removed and does not contribute to either the signal or noise powers.) The output signal power will be

where P_m is the total power in the spectrum S_m(ω). We assume β²P_m ≤ 1, because β|m(t)| ≤ 1 due to the restricted intensity modulation. The output filtered noise can be determined from the contributions from the shot noise and thermal noise. Neglecting the dc terms, this noise power is

Hence the photodetected SNR in the modulation bandwidth is

The result holds for any modulation signal m(t) as long as the filter F(ω) is ideally tuned to it (passes it without ...