Optical Communications, 2nd Edition

5.3 DEMODULATED SIGNAL-TO-NOISE RATIO FOLLOWING OPTICAL HETERODYNING

The SNR derived in Eqs. (5.2.4), (5.2.6), and (5.2.8), for optical heterodyning refers to signals at the output of the photodetector filter F(ω) (see Fig. 5.4). Of ultimate interest, however, is the SNR of the recovered information waveform. To determine this, we must take into account the postdetection demodulation and its effect on the previously derived heterodyned SNR, as shown in Figure 5.5. This processing depends on the manner in which the information waveform d(t) is demodulated from the heterodyned carrier.

Figure 5.5. Heterodyne postdetection filtering and demodulation.

5.3.1 Amplitude Modulation with Heterodyne Detection

If amplitude modulation (AM) is used to modulate an information waveform d(t) onto the optical carrier, we can write a_s(t) in Eq. (5.1.7) as

where we constrain |d(t)| < 1 to prevent overmodulation, and let I_s be the average intensity of the optical signal field. Note that the carrier amplitude is nonnegative and its intensity spectrum is

where S_d(ω) is the spectrum of d(t). [This is valid whether d(t) is deterministic or random, so long as s_d(ω) is properly defined.] The total power in ...