We investigate energy-efficiency issues and resource allocation policies fortime division multi-access (TDMA) over fading channels in the power-limitedregime. Supposing that the channels are frequency-flat block-fading andtransmitters have full or quantized channel state information (CSI), we firstminimize power under a weighted sum-rate constraint and show that the optimalrate and time allocation policies can be obtained by water-filling overrealizations of convex envelopes of the minima for cost-reward functions. Wethen address a related minimization under individual rate constraints andderive the optimal allocation policies via greedy water-filling. Usingwater-filling across frequencies and fading states, we also extend our resultsto frequency-selective channels. Our approaches not only provide fundamentalpower limits when each user can support an infinite number ofcapacity-achieving codebooks, but also yield guidelines for practical designswhere users can only support a finite number of adaptive modulation and coding(AMC) modes with prescribed symbol error probabilities, and also for systemswhere only discrete-time allocations are allowed.
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