Optimum power control over fading channels

We study optimal constant-rate coding schemes for a block-fading channel wi th strict transmission delay constraint, under the assumption that both the transmitter and the receiver have perfect channel-state information. We sh ow that the information outage probability is minimized by concatenating a standard "Gaussian" code with an optimal power controller, which allocates the transmitted power dynamically to the transmitted symbols. We solve the minimum outage probability problem under different constraints on the trans mitted power and we derive the corresponding power-allocation strategies. I n addition, we propose an algorithm that approaches the optimal power alloc ation when the fading statistics are not known. Numerical examples for diff erent fading channels are provided, and some applications discussed. In par ticular, we show that minimum outage probability and delay-limited capacity are closely related quantities, and we find a closed-form expression for t he delay-limited capacity of the Rayleigh block-fading channel with transmi ssion over two independent blocks. We also discuss repetition diversity and its relation with direct-sequence or multicarrier spread-spectrum transmis sion. The optimal power-allocation strategy in this case corresponds to sel ection diversity at the transmitter. From the single-user point of view con sidered in this paper, there exists an optimal repetition diversity order ( or spreading factor) that minimizes the information outage probability for given rate, power, and fading statistics.