Power Allocation in MIMO Wireless Systems Subject to Long-Term, Short-Term, and Per-Antenna Power Constraints

We consider several fading channel models for which we aim to maximize ergodic capacity subject to different power constraints assuming that channel state information (CSI) is available at both the transmitter and the receiver. We characterize the optimal power allocation structure in the single-inputsingle-output (SISO), multiple-input-single-output (MISO), and multiple-input-multiple-output (MIMO) models subject to longand 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. Additionally, we find suboptimal power allocation policies when the input power is subject to long-term and per-antenna power constraints and when the input power is subject to long-term, short-term, and per-antenna power constraints. 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. Index Terms Adaptive transmission, channel state information (CSI), fading channels, multiple-input multipleoutput (MIMO) systems, optimization methods, power control, resource allocation. This work was supported in part by NSF grant CCF05-46618. Mostafa Khoshnevisan and J. Nicholas Laneman are with the Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, 46556 USA, (e-mails: {mkhoshne, jnl}@nd.edu). 2