Abstract
A variable-length cross-packet hybrid automatic repeat request (VL-XP-HARQ)
is proposed to boost the spectral efficiency (SE) and the energy efficiency
(EE) of communications. The SE is firstly derived in terms of the outage
probabilities, with which the SE is proved to be upper bounded by the ergodic
capacity (EC). Moreover, to facilitate the maximization of the SE, the
asymptotic outage probability is obtained at high signal-to-noise ratio (SNR),
with which the SE is maximized by properly choosing the number of new
information bits while guaranteeing outage requirement. By applying
Dinkelbach's transform, the fractional objective function is transformed into a
subtraction form, which can be decomposed into multiple sub-problems through
alternating optimization. By noticing that the asymptotic outage probability is
a convex function, each sub-problem can be easily relaxed to a convex problem
by adopting successive convex approximation (SCA). Besides, the EE of
VL-XP-HARQ is also investigated. An upper bound of the EE is found and proved
to be attainable. Furthermore, by aiming at maximizing the EE via power
allocation while confining outage within a certain constraint, the methods to
the maximization of SE are invoked to solve the similar fractional problem.
Finally, numerical results are presented for verification.