In this thesis, we investigate the ergodic capacity under several power adaption schemes, including optimal power and rate algorithm (OPRA), optimal rate algo rithm (ORA), channel inversion (CI), and truncated channel inversion (TCI), over fluctuating two-ray (FTR) fading channels and Fisher-Snedecor F fading channels. After some mathematical manipulations, the exact expressions for the EC under those power adaption schemes are derived. To simplify the expressions and also get some insights from the analysis, the corresponding asymptotic expressions for the EC are also derived in order to show the slope and power offset of the EC in the high signal-to-noise ratio (SNR) region. These two metrics, i.e., slope and power offset, govern the EC behaviour in the high SNR region. Specifically, from the derived asymptotic expressions, we find that the slope of the EC of OPRA and ORA over FTR fading channels is always unity with respect to the average SNR in the log-scale in high SNRs, while the asymptotic EC of the TCI method is not a line function in the log-scale. For the Fisher-Snedecor F fading channel, the slope of asymptotic EC under OPRA, ORA, and CI (m > 1) schemes is unity in the log-scale, where m is the fading parameter. The slope of the TCI method depends on m, i.e., unity for m > 1 and m for m > 1, while the asymptotic EC of TCI is not a line function for m = 1. Finally, Monte-Carlo simulations are used to demonstrate the correctness of the derived expressions.