Global Convergence of An Iterative Gradient Algorithm for The Nash Equilibrium in An Extended OSNR Game

This paper considers the problem of optical signal-to-noise ratio (OSNR) optimization with link capacity constraints within a Nash game framework. In optical wavelength-division multiplexed (WDM) networks, all wavelength-multiplexed channels share the optical fiber. Even when individually channel parameters are adjusted, the total launched power has to be limited below the nonlinearity threshold. This can be regarded as the optical link capacity constraint. In the previous work of Pan & Pavel (2005), the authors have proposed an extended OSNR Nash game. Channel utility has been related to OSNR and the status of the optical link has been considered directly in channel cost function. The difficulty is that the unique Nash equilibrium (NE) solution of this OSNR Nash game is highly nonlinear and thus analytically intractable. The main contribution of this paper is to develop an iterative, distributed gradient algorithm towards finding the NE solution. The algorithm uses only local measurements and the current load of the network (or link). The authors proved that the iterative gradient algorithm converges globally to this NE solution under sufficient conditions.