In this thesis, we develop a cross-layer design scheme which combines adaptive modulation and coding (AMC) with several retransmission schemes known as hybrid automatic repeat request (HARQ) at the physical layer, automatic repeat request (ARQ) at the medium access control (MAC) layer and HARQ combined with ARQ in order to analyze the performance in terms of spectral efficiency and transmission delay. To evaluate the performance of spectral efficiency and transmission delay, we derive equations of the average packet error rate (PER) used in HARQ and ARQ, respectively. Numerical results reveal that maximizing the average spectral efficiency depends on the number of transmissions, not on the type of retransmission implemented. However, a noticeable gain in the average transmission delay has been offered by AMC with HARQ over AMC with ARQ. When retransmission schemes are exploited both at the PHY and MAC layer, HARQ and ARQ scheme respectively, the performance of ARQ relies on the performance of HARQ, which indicates that only HARQ would be desirable as long as it works perfect.