Power allocation using the waterfilling algorithm with binary search. This function allocates power across subcarriers in an OFDM system to maximize the channel capacity under a total power constraint using the waterfilling principle, which allocates more power to better channels.
Inputs
* H: The array of channel gains for each subcarrier. Each element represents the gain of a subcarrier. For waterfilling, only the magnitude squared (|H|^2) is relevant.
* P_total : The total power budget available for allocation across all subcarriers.
* N0 : The noise power spectral density. Assumed to be constant across all subcarriers.
* epsilon : Tolerance factor for the binary search algorithm. Defines a small threshold for when binary search stops.
Outputs
* P_alloc : The power allocated to each subcarrier. This array has the same dimensions as H and contains the power for each subcarrier to maximize the overall channel capacity under the given constraints.
* water_level : The final water level (lambda) achieved in the waterfilling algorithm. Subcarriers with a channel gain to noise ratio above this level receive power, while others do not.```