Optical Communications, 2nd Edition

9.3 EFFECT OF ATMOSPHERE ON DIRECT DETECTION RECEIVERS

When a direct detection optical link is operated over the atmospheric channel, the communication analysis in Chapter 4 must be modified to take into account the channel effects. Since the received signal field can now be random from the scattering, the collected signal power at the receiver aperture will evolve as a random variable. If the received random signal field is denoted f(t, r), with field intensity I(t, r) = |f(t, r|², then the average received signal power over an aperture area A is

where the overbar denotes averaging. This average power can be written in terms of the received-field coherence function, because

For the class of stationary and homogenious coherence functions given in Eq. (9.2.4) for the scatter channel,

and

Thus the average power is the free space average power (A), reduced by the additional loss due to the extinction loss of the channel.

An indication of the variation of this power around its mean value ...