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Dynamic power and rate allocation through adaptive modulation is known as a powerful means to gain high spectral efficiencies over time-varying channels. A common objective in optimizing the transmit power and rate in fading environments is to maximize the average number of bits per symbol that can be reliably sent through the channel. It is shown that the ergodic capacity of fading channels can be achieved by variable rate and power transmission. According to, the Shannon capacity of a fading channel is also achieved by just varying the transmit power.
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