Analysis of iterative waterfilling algorithm for multiuser power control in digital subscriber lines

We present an equivalent linear complementarity problem (LCP)formulation of the noncooperative Nash game resulting from the DSLpower control problem. Based on this LCP reformulation, weestablish the linear convergence of the popular distributediterative waterfilling algorithm (IWFA) for arbitrary symmetricinterference environment and for certain asymmetric channelconditions with any number of users. In the case of symmetricinterference crosstalk coefficients, we show that the users ofIWFA in fact, unknowingly but willingly, cooperate to minimize acommon quadratic cost function whose gradient measures thereceived signal power from all users. This is surprising since theDSL users in the IWFA have no intention to cooperate as eachmaximizes its own rate to reach a Nash equilibrium. In the case ofasymmetric coefficients, the convergence of the IWFA is due to acontraction property of the iterates. In addition, the LCPreformulation enables us to solve the DSL power control problemunder no restrictions on the interference coefficients usingexisting LCP algorithms, for example, Lemke's method. Indeed, weuse the latter method to benchmark the empirical performance ofIWFA in the presence of strong crosstalk interference.