Achieving optimal design of phase-locked loop (PLL) is a major challenge in WiMax technology in order to improve system behavior against noise and to enhance Quality of Service (QOS). A new loop filter design method for phase locked loop (PLLs) is introduced taking into consideration various design objectives: small settling time, small overshoot and meeting Mobile WiMax requirements. Optimizing conflicting objectives is accomplished via linear programming and semidefinite programming (especially Linear Matrix Inequality (LMI)) in conjunction with appropriate adjustment of certain design...