Simultaneous Iterative Water-Filling for Gaussian Frequency-Selective Interference Channels

The sequential iterative water-filling algorithm (IWFA) proposed by Yu et al. is by now a popular low-complexity algorithm to compute the Nash equilibrium point of the power allocation game in a Gaussian frequency-selective multiuser interference channel. The algorithm is based on a distributed sequential updating where, at each iteration, the users choose their power allocation, one after the other. However, this sequential updating strategy may slow down its convergence time excessively when the number of users is high. In this paper, we propose an alternative distributed algorithm, called simultaneous iterative water-filling algorithm (SIWFA), where at each iteration, all the users update their power allocations simultaneously, rather than sequentially. This reduces the convergence time considerably, specially when the number of users is large. Our main contribution is to provide a unified set of sufficient conditions for the convergence of both IWFA and SIWFA, that are less stringent than those known in the literature for IWFA. These conditions guarantee the convergence of both algorithms also in the presence of spectral mask constraints imposed on the power allocations of the users