Ionospheric irregularities are small-scale structures in plasma density aligned with the magnetic field that are formed by plasma instability processes and occur frequently in the auroral region of the ionosphere. Coherent scatter radar echoes from these irregularities convey information about the fine-scale structure of the auroral ionosphere during periods of geomagnetic activity. This subject has been studied extensively, however, the relationship between the coherent scatter spectral measurements and the ionospheric state parameters is not fully understood. Models of plasma waves, instability mechanisms, irregularities, and coherent echoes are required to further develop this understanding. This thesis presents three studies of the auroral E region ionosphere that use radar measurements and computational models to understand the significance of radar backscatter from field aligned irregularities observed by a 30 MHz coherent scatter radar in Homer, Alaska. The first study models the Farley Buneman instability by combining the global, 2-D ionospheric model, SAMI2, with a local, heuristic model developed by Milikh and Dimant [2002]. The model estimates profiles of wave phase speed, magnetic aspect width, wave heating rates, and ionospheric state variables. This model shows promising agreement with incoherent scatter radar measurements from the Poker Flat Incoherent Scatter Radar (PFISR) and coherent scatter radar measurements from the Homer radar. The second study uses an empirical model to invert measured coherent scatter spectra into estimates of convection velocity and then fits for the overall convection pattern. This model is informed by the simulations of Oppenheim et al. [2008]; Oppenheim and Dimant [2013] and formulas calculated by Nielsen and Schlegel [1985]. Comprehensive agreement between the convection velocity estimates and the convection pattern indicates an incompressible flow and validates the inversion. The third study examines E region ionospheric modification experiments that cause plasma instabilities and artificial irregularities. The study analyzes the threshold power needed to generate artificial irregularities due to the thermal parametric instability. SAMI2 was modified to simulate the propagation of the HF pump waves and their heating effects. The model revealed that active suppression of the artificial irregularities occurs entirely due to D region absorption. This thesis concludes with a summary of these studies and suggestions for future research.