Coherent Versus Incoherent SNR

9008-031

The graph of (9008-032) dramatically illustrates one of the most important advantages of coherent optical detection over its incoherent counterpart.  The graph also indicates the inherent 3 dB difference in SNR per unit bandwidth between the two approaches.

The ability to make the electrical output bandwidth B_e very small in a coherent system means that the effective noise bandwidth can also be very small.  The noise from the received background radiation P_b that beats with the local oscillator (P_o) and whose products fall within the I.F. bandwidth (B_e = B_I.F.), is generally much less than the quantum noise floor produced by the local oscillator laser.  P_b is the product of the background (mainly Planck) spectral density and the optical input bandwidth B_o, i.e., N_plB_o, where B_o >> B_e.  If N_pl and B_e are large enough, even though P_b may be much larger than the received signal power P_r, i.e., the ratio P_r/P_b >> 1, the noise floor as set by the level of the local oscillator is unaffected.  In contrast, in a very sensitive shot-noise limited incoherent (direct) detection system, the optical input bandwidth is again large, i.e., B_o >> B_e, and if P_b rises to the level of the received signal power P_r, the SNR is degraded by a further 3 dB.  This occurs even though B_e is very small, since every photon arriving at the photodetector, whether it be from signal or background radiation, adds to the mean optical power received, and hence to the shot-noise level.