  This paper thoroughly investigates the performance of variable-rate hybrid
automatic repeat request with incremental redundancy (HARQ-IR) over Beckmann
fading channels, where Beckmann channel model is used to characterize the
impacts of line-of-sight (LOS) path, time correlation between fading channels
and unequal means & variances between the in-phase and the quadrature
components. The intricate channel model and variable-rate transmission strategy
significantly complicate the performance analysis. The complex form of the
joint distribution of channel coefficients makes the exact analysis rather
difficult. Hence, the asymptotic analysis of HARQ-IR is conducted to obtain
tractable results. The outage probability and the long term average throughput
(LTAT) are then derived in closed-form with clear insights. Furthermore, the
simplicity of the obtained expressions enables the maximization of the LTAT
given an outage constraint through choosing appropriate transmission rates.
Particularly, the increasing monotonicity and the convexity of outage
probability with respect to transmission rates allow us to solve the problem
suboptimally by combining together alternately iterating optimization and
concave fractional programming, and the proposed suboptimal algorithm has a
lower computational complexity than the exhaustive search algorithm.
