exp hv,B

where Pm is the average power. This ideal situation when only shot noise is present is referred as the quantum limit and is used as a reference in optical communications. Relation (14) shows that an error probability of 10"9 requires p? to be equal to 10, which in other terms means that 10 photons must be transmitted per transmitted bit.

4.3 Computation of the bit error probability for a direct detection receiver

Assuming the case of binary equally distributed data, the average value of the signal at the photodetector output at sampling time can take on two values Iq and /[ according to the transmitted data. Noise contributions are respectively the signal dependent and non gaussian shot noise and signal independent and gaussian noise. Considering the total noise as gaussian with a signal dependent variance cr^ or o2), and assuming an optimal decision threshold, the error probability can be expressed by the following relationship:

P = J- erfc |
f V/° |
= — erfc |

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