Performance of optical direct receivers using noise corrupted decision threshold

The decision threshold of digital binary detectors has to be selected in the optimum position between 0 and 1 symbol amplitudes in order to minimize the bit error rate, This optimum has to be determined by acquiring the bit amplitudes from the signal itself. In packet, or burst-mode, transmission systems the decision threshold must be rapidly acquired from a short strip of bits, and the intrinsic reception noise may have not been completely averaged. This introduces a sensitivity penalty which is shown to be given by a simple expression for the situation when additive Gaussian noise is dominant. An extension to the nonadditive Gaussian noise is given in an appendix. Special attention is devoted to the case when adaptive threshold acquisition is done by means of a peak detector and it is found that the penalty is always higher than that of the ideal integrator. The optimum decision threshold must be estimated numerically in each case and varies along the burst with the number of acquired peaks