The thesis analyses and validates Beamforming methods using Convex Optimization.  CVX which is a Matlab supported tool for convex optimization has been used to develop this concept. An algorithm is designed by which an appropriate system has been identified by varying parameters such as number of antennas, passband width, and stopbands widths of a beamformer. We have observed the beamformer by minimizing the error for Least-square and Infinity norms. A graph obtained by the optimum values between least-square and infinity norms shows us a trade-off between these two norms. We have observed convex optimization for double passband of a beamformer which has proven the flexibility of convex optimization. On extension for this, we designed a filter in which stopband is arbitrary. A constraint is used by which the stopband would be varying depending upon the upper boundary (limiting) line which varies w.r.t y-axis (dB). The beamformer has been observed for feasibility by varying parameters such as number of antennas, arbitrary upper boundaries, stopbands and passband. This proves that there is flexibility for designing a beamformer as desired.