Abstract-Non-uniform leaky-wave antennas (LWAs) are analyzed and synthesized using a lossy transmission line model. The analysis is based on a general waveguide circuit theory. Compared to the classical approach, the model yields a higher accuracy in the computation of both aperture field distribution and radiation patterns. The proposed analysis is also able to provide scattering parameters of the whole structure in a fraction of a second, which is valuable for antenna optimization. Based on the analysis, a general method for far-field pattern synthesis utilizing global optimization is presented. As an application demonstration, the Half-Mode Substrate-Integrated Waveguide, or half-width microstrip line, has been selected as basis structure for the LWA designs. Two antennas have been optimized targeting different specifications, i.e. a low sidelobe level and a wide null in the radiation pattern. Experimental results are provided for these selected examples of non-uniform LWAs, which ultimately validate the proposed technique as an improvement over the classical approach.Index Terms-Leaky-wave antenna (LWA), pattern synthesis, transmission line model, non-uniform structure, HalfMode Substrate-Integrated Waveguide (HMSIW), half-width microstrip line.