An algorithm for highly efficient waterfilling with guaranteed convergence

This paper derives a novel and highly efficient algorithm for calculating the waterfilling parameter λ (i.e., the water level) for maximization of transmitted information, given a set of channel-power coefficients, and a sum-energy constraint. The resultant fixed-point algorithm calculates λ in at most 9 iterations for 1000 given Rayleigh-distributed channel-power coefficients, each with scale-parameter σ = 0.2. The proposed fixed-point algorithm guarantees convergence of λ to a unique optimum value, without restricting validity to practically relevant channel-power coefficient distributions.