Optimum configuration for cascaded fiber amplifiers in attenuation limited transmission systems

Fiber amplifiers play an important part in optical transmission systems to overcome the impact of attenuation. Together with the transmitter and receiver the positions of amplifiers on the optical path as well as the design of the amplifiers itself determine the bit error probability of the digital communication link. We present a simple method how to derive the optimum configuration for an optical transmission link with cascaded fiber amplifiers for an attenuation limited system. The bit error probability is calculated in dependence of the positions of the line amplifiers and the lengths of the doped fibers for systems with and without booster and optical preamplifier. In a first step we search the optimum configuration by numerical minimization of the bit error probability for a given transmission length, transmitter power and optical receiver. We have found a very simple rule how to determine the lengths of the transmission fibers and the doped fibers of the amplifiers for the minimum bit error probability when the length of the first transmission fiber is given. Therefore, the search for the optimum configuration reduces to the search of the appropriate length of the first transmission fiber which results in an enormous reduction of computing effort. We have investigated the effect on the bit error probability when one deviates from the optimum configuration. For the case, when the transmission length is reduced me have found that the bit error probability decreases always, when the lengths of the single transmission fibers are cut.