Adaptive transmission with finite code rates

This work examines a transmission system which adapts a finite set of code rates and a continuously varying transmit power. We propose a technique for finding the average reliable throughput (ART)-maximizing policy satisfying an average power constraint for a slow fading additive white Gaussian noise (AWGN) channel. ART is a measure motivated by the information outage and can, for example, be argued to characterize the long-term average throughput of a data packet transmission system with a transmit queue and a feedback protocol which requests retransmission of erroneously received packets. Given the size of the code rate set L, the ART-maximizing policy has the following properties. 1. For a given set of code rates, the optimum allocation policy suggests quantizing the fading state space into a set of L+1 corresponding intervals. For each quantization interval the optimal policy specifies a minimum transmitted power assignment which guarantees zero information outage. The optimum average power assignments across quantization intervals have a waterfilling relationship with respect to the interval channel quality measure. 2. The joint optimization of quantization intervals and the corresponding rate assignments are shown to have multiple local maxima. Nevertheless, this optimization problem can be reduced to a simple one-dimensional search over a parameter which determines the outage interval. Numerical results show that, in a Rayleigh-fading channel, there is only a 1-dB gap between the ergodic capacity and the throughput of a two-rate adaptive transmission system when the throughput is less than 6 bits/s/Hz. A special case of our optimal policy assignment is the optimal power and rate policy for an adaptive M-QAM system.