  In hybrid digital-analog (HDA) systems, resource allocation has been utilized
to achieve desired distortion performance. However, existing studies on this
issue assume error-free digital transmission, which is not valid for fading
channels. With time-varying channel fading, the exact channel state information
is not available at the transmitter. Thus, random outage and resulting digital
distortion cannot be ignored. Moreover, rate allocation should be considered in
resource allocation, since it not only determines the amount of information for
digital transmission and that for analog transmission, but also affects the
outage probability. Based on above observations, in this paper, we attempt to
perform joint rate and resource allocation strategies to optimize system
distortion in HDA systems over fading channels. Consider a bandwidth expansion
scenario where a memoryless Gaussian source is transmitted in an HDA system
with the entropy-constrained scalar quantizer (ECSQ). Firstly, we formulate the
joint allocation problem as an expected system distortion minimization problem
where both analog and digital distortion are considered. Then, in the limit of
low outage probability, we decompose the problem into two coupled sub-problems
based on the block coordinate descent method, and propose an iterative gradient
algorithm to approach the optimal solution. Furthermore, we extend our work to
the multivariate Gaussian source scenario where a two-stage fast algorithm
integrating rounding and greedy strategies is proposed to optimize the joint
rate and resource allocation problem. Finally, simulation results demonstrate
that the proposed algorithms can achieve up to 2.3dB gains in terms of
signal-to-distortion ratio over existing schemes under the single Gaussian
source scenario, and up to 3.5dB gains under the multivariate Gaussian source
scenario.
