A QAM receiver based on the minimum mean square error criterion has been studied. It has both an adaptive equalization and a data-aided phase tracking loop in addition to the main function of data detection. In this thesis, the jointly adaptive estimation for the above two functions has been analyzed using different methods. For the basic structure of the adaptation scheme, two estimation algorithm have been considered, the stochastic gradient following algorithm and the best least square estimation algorithm. The latter algorithm has been derived from the control theory and its properties are described qualitatively. In the phase tracking loop, the phase error variance and the sinusoidal phase jitter response have been investigated. Assuming linear equalization, both linear and nonlinear PLL theories have been used. A new method for phase error variance is derived, where the mean square phase error is computed directly form the loop equation. It is shown by computer simulation that the new method gives a better result than the others. The phase jotter response analysis and the convergence of the joint estimation algorithm have been verified by computer simulation. And the performances of adaptive linear equalizer and adaptive decision feedback equalizer are compared when operating with the phase tracking loop.