Capacity comparison between different power allocation schemes with arbitrary input distributions and different channel gains
The setting of two parallel sub-channels were used first, with different channel gains and QPSK, 16-QAM, 64-QAM, 256-QAM inputs.
Then the setting of three parallel sub-channels were considered as an extension, with different channel gains and QPSK, 16-QAM, 64-QAM inputs.
The power allocation schemes include the Mercury/Waterfilling (MWF), the constellation constrained waterfilling (an approximation of the MWF based on sphere packing), the classic waterfilling, uniform power allocation, putting all the the power to the stronger sub-channel, and the optimal power allocation (OPA) derived through the Monte Carlo method.
The results showed that the MWF performed almost identically to the optimal power allocation (OPA) derived through the Monte Carlo method, proving the optimality of the MWF. The constellation constrained waterfilling, on the other hand, had close performance to the MWF, demonstrating that it was a decent approximation of the MWF.