A Nash game approach for OSNR optimization with capacity constraint in optical links

This paper develops a Nash game towards optimizing optical signal-to-noise ratio (OSNR) in the presence of link capacity constraint. In optical wavelength-division multiplexing (WDM) networks, all wavelength-multiplexed channels in a link share the optical fiber. In order to limit nonlinear effects, the total power launched into a fiber has to be below a nonlinearity threshold. This can be regarded as the optical link capacity constraint. We formulate an extended OSNR Nash game that incorporates this underlying system constraint. The status of an optical link is considered directly in the cost function. Sufficient conditions for existence and uniqueness of the Nash equilibrium (NE) solution are given. Two iterative algorithms for channel power control are proposed to compute the NE solution: a parallel update algorithm (PUA) and a relaxed PUA (r-PUA). Their convergence is studied under different conditions, both theoretically and numerically.