Achieving "full diversity gain over a Rayleigh fading channel" refers to maximizing the benefits of multiple independent fading paths in wireless communications. A Rayleigh channel is characterized by random amplitude and phase fluctuations, commonly experienced in urban environments with moving transmitters. Diversity techniques, such as antenna switching and advanced signal coding, help mitigate the effects of multipath propagation. In MIMO systems, independent paths allow for multiple data streams, enhancing capacity and throughput. Full diversity gain occurs when multiple receive antennas exploit these independent paths, resulting in improved signal reliability and performance.