Different power allocation schemes at the transmitter with arbitrary input distributions
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, an high-power approximation (based on the high-power expansion of the MMSE function), and the optimal power allocation (OPA) derived through the Monte Carlo method.
A new algorithm was developed for the derivation of the MWF OPA, based on the bisection method. It worked for the more general cases (n parallel sub-channels) as well.