Channel dependent adaptive modulation and coding without channel state information at the transmitter

In this paper, we consider the problem of communicating over an Additive White Gaussian Noise (AWGN) channel with an unknown noise power without feedback. For the case where the noise power is drawn from a distribution with K distinct values, we model the channel as a K-user broadcast channel, with a user for each of the K possible noise powers. We propose two metrics for measuring the loss of using a broadcast code compared to an omniscient transmitter. Using these metrics, we solve for the optimal power allocation in a superposition code. For the case of K = 2, we prove several interesting properties of the optimal power allocation and the minimum loss.