In this thesis, the author presents and analyzes two 4-dimensional Constant Envelope Quadrature-Quadrature Phase Shift Keying constellations. Optimal demodulators for the two constellations are presented, and one of them was designed and implemented by the author. In addition, a novel expanded 16-dimensional CEQ2PSK constellation that doubles the number of points without decreasing the distance between points or increasing the peak energy is generated by concatenating the aforementioned constellations with a particular method and restrictions. This original 16-dimensional set of symbols is set-partitioned and used in a multidimensional Trellis-Coded Modulation scheme along with a convolutional encoder of rate 2/3. Effective gain of 2.67 dB over uncoded CEQ2PSK constellation with low complexity is achieved theoretically. A coding gain of 2.4 dB with 8 dB SNR is obtained by using Monte Carlo simulations. The TCM systems and demodulators were tested under an Additive White Gaussian Noise channel by using Matlab's Simulink block diagrams.