On the bit error rate of lightwave systems with optical amplifiers

Abstract

We revisit the problem of evaluating the performances of communication systems with optical amplifiers and a wideband optical filter. We compute the exact probability of error and the optimal threshold and compare them with those predicted by Gaussian approximations for ASK, FSK or DPSK modulations, both for ideal photodetectors and for the case where shot noise is significant.

Statistical evaluation of transmission performance degradation originating with cross‐phase modulation

“…Consider square-law detection dominated by amplified spontaneous emission (ASE). Let the probability density function of the "1" side (with the optical signal amplitude being x) be f 1 (y|x), and let the probability density function of the "0" side be f 0 (y) [10]. Letting the probability density function for the waveform degraded by XPM be f xpm (x), the error rate is calculated as follows [11]:…”

Statistical Errors in Biasing Monte Carlo Simulations With Applications to Polarization-Mode Dispersion Compensators

“…2. This basic model has been the subject of careful studies by us and by others [37], dating back to early work by Marcuse [38] and Humblet and Azizoglu [39], which followed the invention of the erbium-doped amplifier. Prior to that, most work on optical receivers focused on reducing electrical noise, which was the major source of impairments in optical communications systems based on repeaters [40].…”

On the optimality of equal gain combining for energy detection of unknown signals

“…From [4], we can show that y i has a central or non-central chisquare distribution, respectively, for the noise-only and signalplus-noise hypotheses:…”

“…where M is the approximate dimensionality of the signal space, which is obtained from the time-bandwidth product 2 [4], θ i is the energy of the signal for the ith observation, We start with the assumption that the signal has the same energy in different observations; that is, θ i = θ ∀i. Then, we extend the results to the more general case in Section IV.…”

“…For an additive white Gaussian noise (AWGN) channel model, the energy of the signal can be modeled by central and non-central chi-square distributed random variables, respectively, for noise-only and signal-plus-noise hypotheses [4]. Under this model, it is well-known that comparing the energy level to a threshold corresponding to the maximum allowable false-alarm (FA) rate is the uniformly most powerful (UMP) test for signal detection [5].…”