This thesis investigates the performance of cross-layer design in data communication over wireless channels. This involves a joint use of two well known techniques; namely, the link adaptation technique of adaptive modulation and coding (AMC) at the physical layer (PHY) and the automatic repeat request (ARQ) scheme at the data link layer (DLL). The motivation behind the design arises from the time-varying characteristic of the wireless channel, where fading may lead to signicant impairment in the content of the received information, thereby aecting the quality of service (QoS) (e.g. at application layer level). Rayleigh distribution is used for modelling the channel statistics. The overall objective is to design an AMC scheme that maximises the ASE, which is a measure of performance at the physical layer, while a condition on the rate (probability) of receiving erroneous packets is satised at the data link layer of the received node; hence the term cross-layer design. This is translated into an optimization problem where the objective function is the ASE, and the constraint function involves the average or instantaneous packet error rate (PER) bounded by a given target, which in turn is set by QoS requirements from higher layers of communication protocol stack. The problem can then be solved by methods such as nonlinear programming. The result is an optimised AMC scheme, where the data rate is adapted according to the estimate of the channel signal-to-noise ratio (SNR). At rst, a continuous variable rate scheme is derived for a point-to-point link between two nodes. As a side contribution, a tight closed-form approximation for PER is obtained as a function of data rate and imperfect estimate of channel SNR. This serves as a generalised case of a practical discrete-rate adaptation. Secondly, the joint DLL and PHY design is applied to communication between two nodes under cognitive radio (CR) resource restraint, where a cooperative node assists the ARQ operation. The performance is compared to that of a single non-cooperative transmission under the same CR constraint.