To improve the robustness and reliability of wireless transmissions, two complementary link adaptation techniques are employed: adaptive modulation and coding (AMC) at the physical layer and hybrid automatic retransmission request (HARQ) at the medium access control layer. Because of their effectiveness in combating errors induced by the wireless channel, AMC and HARQ are now integral components of most emerging broadband wireless system standards, for example, LTE and WiMAX. Spectral efficiency (SE) as measured in bit per second per Hertz is one important parameter used to characterize a wireless system for comparison between different systems or between different configurations of the same system. This work provides a holistic approach of cross-layer optimizations with the intent of maximizing SE by combining AMC and HARQ. It formulates closed-form equations for calculating the average SE for wireless systems with the Rayleigh fading channel model. A new online algorithm is developed to optimize SE for both Rayleigh and non-Rayleigh fading channel. Simulations using proven LTE model are performed to compare SE obtained from closed-form equations and the developed algorithm for different system configurations. With the developed algorithm to determine how many retransmissions required in addition to the initial transmission in advance depending on the current wireless channel condition, the latency can be reduced up to 24 ms when sending the initial transmission and all of its retransmissions sooner than waiting for retransmission requests as is done previously.