Rate Allocation for Transmission of Two Gaussian Sources over Multiple Access Fading Channels

We perform optimal rate allocation of two independent Gaussian sources on a two-user multiple access Rayleigh fading channel by minimizing the sum distortion at the common receiver. We first consider the case of fast fading, where we use the ergodic capacity region, and analytically solve for the optimal pair of rates. We then address the case of slow fading, where we determine the optimal pair of rates that minimizes the sum distortion, using outage probabilities. Results show that the sum distortion for slow fading is larger than for fast fading and that the use of individual outage probabilities outperforms the use of common outage probability. The higher variance source requires higher rates in both fast and slow fading.