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In the case of antennas applications for radio communication system, special antenna radiation patterns such as low side lobes and unsymmetrical side lobes are requested. In mobile communication systems, unsymmetrical side lobes are achieved at base station array antennas. There, based on a radiation pattern synthesis method, excitation coefficients of array elements are designed. In this lecture, first of all, fundamental radiation pattern synthesis methods are overviewed. Then, a MATLAB program based on a least mean squared (LMS) concept is explained. Through operations of MATLAB program, practical design process is explained. In other communication systems such as terrestrial and satellite communications, aperture antennas such as reflector or lens antennas are employed. There, low side lobe radiation patters are achieved through shaping reflector or lens surface shapes. These design methods are based on ray tracing method. In this lecture, fundamental characteristics of radiation patterns in a aperture antenna are explained. Next, antenna surface design equations and MATLAB programs are explained. Through operations of MATLAB program, practical design process is explained. Additionally, at the same time of radiation rays, received ray characteristics are interesting in reflector antenna designing. Fundamental equations, MATLAB program and operation examples are shown.