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Coherent Versus Incoherent SNR



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 Be very small in a coherent system means that the effective noise bandwidth can also be very small.  The noise from the received background radiation Pb that beats with the local oscillator (Po) and whose products fall within the I.F. bandwidth (Be = BI.F.), is generally much less than the quantum noise floor produced by the local oscillator laser.  Pb is the product of the background (mainly Planck) spectral density and the optical input bandwidth Bo, i.e., NplBo, where Bo >> Be.  If Npl and Be are large enough, even though Pb may be much larger than the received signal power Pr, i.e., the ratio Pr/Pb >> 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., Bo >> Be, and if Pb rises to the level of the received signal power Pr, the SNR is degraded by a further 3 dB.  This occurs even though Be 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.








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