Costly Power and Symbol Rate Allocation to Sub-Channels for Optimal Real Performance: Water-Filling for Maximal Throughput

We analytically allocate to sub-channels costly power and symbol rate to maximise a general throughput function. Link parameters (e.g., modulation order and packet length) are explicitly considered. We provide the structure of the general solution, and for certain scenarios give an explicit solution, which includes the optimal link configuration. A channel can be immediately discarded if its normalised gain is less than the normalised power price. Moreover, when power is "low", all of it should go to the best sub-channel. In general, the best "M" channels operate at maximal symbol rate, with the SNR that satisfies a single-variable optimising condition; and at most one additional channel operate at the "low power" optimum. Previously, we had analysed costly power allocation under a channel performance function that generalises the Gaussian capacity formula. However, the power allocation that would be optimal if each sub-channel operated at "capacity" could differ significantly from the maximiser of actual performance. Hence, the power allocation obtained herein is preferable.