4.7 DIRECT DETECTION WITH MULTIMODE SIGNALS
The SNR in Section 4.3 was based on a modulated source field occupying a single-field mode. That is, the source was considered a point source transmitting to the receiver with a single mode. When a source is spread over many modes (as with an extended source space field or multimode fiber), the arriving field now requires a multimode description. Because noise may be present in all modes as well, the resulting computation of the photodetected SNR at the receiver must be modified. In this section, we examine photodetection of these multimode signals.
Consider the space system in Figure 4.13. A direct detection receiver with an area A and field of view Ωfv encompasses Ds spatial modes. An extended source transmits signal energy in Ms signal modes. If Ms < Ds the receiver observes the entire source in its field of view. If Ms > Ds, only a portion of the source is observed. In the ith mode, the signal field intensity is assumed
where m(t) is again the modulating signal imposed at the transmitter, Isi is the signal intensity in the ith mode, and we use β = 1. Equation (4.7.1) implies a signal field with the source intensity modulation m(t) distributed over all modes. The average signal power in the ith mode ...