Effect of optical amplifier bandwidth on receiver sensitivity

For a binary fiber-optic communication system in which an optical preamplifier is used, and for which the amplifier bandwidth (B) is large compared to the bit rate (1/T), it is shown that the minimum number of photons per bit required to achieve an error probability P/sub e/=10/sup -9/ is given by 36+6 square root BT. This generalizes a result of P.S. Henry (1989) who showed that if the amplifier bandwidth is matched to the signal bandwidth, the sensitivity is 38 photons/bit.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>