On Optimal Power Allocation for Gaussian Broadcast Channel

We derive the optimal power allocation for Gaussian two users broadcast channel. To find the optimal power allocation between the two users, two optimization schemes are considered. In each optimization scheme, an analytical expression for the optimal power allocation between the two users is derived. The first optimization criterion finds the optimal power allocation between the two users such that they have equal rates. Then, the optimal power allocation that maximizes the sum rate capacity is studied. In addition, numerical examples are provided to verify the optimality of the derived schemes. Keywords: Gaussian Broadcast Channel, Capacity Region, Optimization

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