A Distributed Optimization Approach to Constrained OSNR Problem

This paper studies constrained optical signal-to-noise ratio (OSNR) problem via a distributed optimization approach. In multi-channel optical systems, the signal over an optical link can be regarded as an interfering noise for others, which leads to OSNR degradation. Regulating the input optical power at the Source (transmitter) aims to achieve satisfactory OSNR level at the Destination (receiver) for each channel. Moreover, because all wavelengthmultiplexed channels in a link share the same optical fiber, the total input power in a link has to be below the nonlinearity threshold, which corresponds to a link capacity constraint. We formulate the OSNR optimization problem as one of utility maximization with the objectives of achieving an OSNR target level for each channel while minimizing the interference and also satisfying the link capacity constraint. We derive conditions for the existence of a unique optimal solution, leading to a basis for an admission control scheme. By using a Lagrangian relaxation approach we propose two distributed update algorithms: a primal algorithm and a dual algorithm, and study their convergence properties both theoretically and numerically.