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The achievable rate of an individual transmission (n=1,..N) , can be given as log2(1+SNRn(p)) The signal-to-noise ratio is given as SNRn(pn)=gnpn/N0 where gn denotes the nth channel gain for the channel, pn is the corresponding power allocation and N0 is a fixed noise-level. For the sake of notational simplicity, we consider the noise level to be the same for all transmissions. The sum-rate (throughput) for all N orthogonal channels is given by the sum of their individual rates. That is, £(1àN) log2(1+SNRn(pn)) To get to the capacity of the said system, we need to set some constraints on the SNR. We will use the sum power budget (P ), which limits the available power across the channels as £ pn =P Now, we can write the capacity as C=£log2(1+SNRn(pn*)) where pn* is the sum-rate maximizing power allocation for channel n . Now, we have the basic premise set up to come up with an algorithm that finds the optimal power allocation, namely, the water-filling algorithm. Made with nCreator - tiplanet.org