On power adaptation in adaptive signaling systems

The Shannon capacity of a fading channel under an average-power constraint with channel side information at the transmitter and receiver is only negligibly larger than the capacity of the same channel when constant-power transmission is employed. However, power adaptation has been shown to be quite useful in practical systems, where it has been conjectured that it allows for compensation of the effect of rate quantization. Here, an average bit-error probability constraint is employed instead of the conventional instantaneous bit-error probability constraint. When the set of rates available to the transmitter is unrestricted in practical systems, necessary conditions for jointly optimal power and rate allocation are derived and used to demonstrate that power adaptation is of limited utility. However, when the rates available to the transmitter are restricted to the nonnegative integers for the example of uncoded quadrature amplitude modulation over frequency-nonselective Rayleigh fading channels, a 0.5-0.75 dB loss in power efficiency is incurred when employing only a single power level for each constellation, and a 0.5-bits/symbol loss in rate is incurred when constant power transmission is employed.