Delay-limited capacity of parallel fading channels

The delay-limited capacity is defined as the transmission rate that can be guaranteed in all fading states under finite long-term power constraints. For the single-input single-output Rayleigh fading channel it is zero. In contrast it is greater than zero in channels with a certain kind of diversity, e.g., multiple antennas at one side of the link. The optimal transmission strategy in single-channel systems is channel inversion. If multiple parallel channels are available for transmission, the power allocation across channels influences the temporal power allocation. In this work, we study the delay-limited capacity of parallel fading channels. We implicitly characterize it using the temporal waterfilling-level and derive two lower bounds that are tight either for small or high SNR. Then, the results are applied to parallel weighted Gaussian fading channels and the impact of the weights is derived. Finally, we apply the result to the broadcast channel with common downlink information.