Analysis of avalanche diode receivers by saddlepoint integration

Calculating the performance of optical communication systems with modal noise by saddlepoint method

“…For practical optical systems, the shapes of h(t) and W ( t ) may dispersion may reduce the capacity of optical fiber systems. At these situations we refer [9].…”

“…The probability density functions f j ( v ) , j = 0, 1 can be computed by using the Laplace inversion integral [9] n -u where the contour is located at the left-hand side of the singularities of p j ( s ) in the complex s-plane. To compute (8) and (9) we integrate the right hand side of (29) and change the order of integration to obtain the error probabilities By integrating the right-hand side of (46) over (0, 00 ) with respect to y, we obtain the so called saddlepoint approximation…”

“…To compute (8) and (9) we integrate the right hand side of (29) and change the order of integration to obtain the error probabilities By integrating the right-hand side of (46) over (0, 00 ) with respect to y, we obtain the so called saddlepoint approximation…”

“…When we integrate along the contour, we need to solve s in (26) for M efficiently. For the detailed method we refer [9].…”

Modeling Errors in Long-Haul Optical Fiber Transmission Systems by Using Instantons and Edgeworth Expansion

“…This method allows one to reformulate the stochastic problem of pulse deterioration due to short correlated amplifier noise in terms of the deterministic problem of "the most damaging" noise configuration. This approach is very similar to numerical saddle point approaches used in [10] and [11], but in contrast to those papers we calculate the saddle point, i.e., "the most damaging" noise configuration, analytically. The details are given in Section II.…”