Power allocation for block-fading channels with arbitrary input constellations

Abstract

We consider power allocation strategies for arbitrary input channels with peak, average and peak-to-average power ratio (PAPR) constraints. We are focusing on systems with a fixed and finite input constellation, as encountered in most practical systems. Generalizing previous results, we derive the optimal power allocation scheme that minimizes the outage probability of block-fading channels with arbitrary input constellations, subject to PAPR constraints. We further show that the signal-to-noise ratio exponent for any finite peak-to-average power ratio is the same as that of the peak-power limited problem, resulting in an error floor. We also derive the optimal power allocation strategies that maximize the ergodic capacity for arbitrary input channels, subject to average and PAPR constraints.We show that capacities with peak-to-average power ratio constraints, even for small ratios, are close to capacities without peak-power restrictions. For both delay-limited and ergodic block-fading channels, the optimal power allocation strategies rely on the first derivative of the input-output mutual information, which may be computationally prohibitive for efficient practical implementation. To overcome this limitation, we develop suboptimal power allocation schemes that resemble the traditional water-filling technique. The suboptimal power allocation schemes significantly reduce computational and storage requirements, while enjoying minimal performance losses as compared to optimal schemes.