Optical Communications, 2nd Edition

5.2 HETERODYNE SIGNAL-TO-NOISE RATIOS

The modulated heterodyne carrier generated from photodetection can now be filtered out to recover the modulations. The overall system following the photodetector is shown in Figure 5.4a. A bandpass filter F(ω) is used to recover the modulated carrier, which is then RF demodulated to produce the information signal. The filtered output spectrum then appears as

where S_i(ω) is the photodetected output current spectrum, and N_0c is the spectral level of the output thermal noise current. The filter is generally tuned to the bandpass characteristic of the desired signal spectrum. If we assume a wideband optical detector [H(ω) = e] and a flat filter function [F(ω) = 1] over the bandwidth of the heterodyned signal, the filtered signal power after heterodyning is

Figure 5.4. (a) Postdetection filtering. (b) Output filtered spectrum (strong local field).

where is the time-average signal intensity of the heterodyned carrier in Eq. (5.1.10). Since I_mA is the heterodyned carrier power, we can use Eq. (5.1.13) to write this in terms of the received laser power ...