Power Allocation in Wireless Systems Subject to Long-Term and Short-Term Power Constraints

We consider several fading channel models for which we aim to maximize ergodic capacity assuming that channel state information (CSI) is available at both the receiver and the transmitter. We characterize the optimal power allocation structure in the single-input-single-output (SISO), multiple input-single-output (MISO), and multiple-input-multiple-output (MIMO) models subject to both long- and short-term power constraints. The optimal power policy in each of the channel models depends upon the ratio of the two power constraints and the average signal-to-noise-ratio (SNR) of the system. We characterize the conditions, for which the short-term power constraint can be eliminated without being violated in the optimal power policy. Numerical results suggest that for the Rayleigh fading case, a short-term power constraint that is larger than a long-term power constraint does not significantly impact the ergodic capacity of the channel.