Window function design via fractional programming

The window functions formed from simple functions (e.g. trigonometric functions) have not utilized the degree of freedom (DOF) sufficiently, and thus they may not be optimal. In this paper, we derive two new window design algorithms via optimizing all window elements rather than the weighting coefficients of such simple functions, which are formulated as fractional programming models that only focus on minimizing the ratio of the maximum sidelobe level to the minimum level of the user-defined main energy region and that do not require masks or particular sidelobe level constraints. Especially, the first method is based on only the spectral mainlobe and sidelobe region information, whereas the second method is developed with only the range sidelobe region information from the view of pulse compression. Moreover, the solutions to the resultant nonlinear and nonconvex optimization problems are derived. Finally, simulation results show that proposed windows have advantages of enhanced spectral characteristics, better filtering performance, and improved range sidelobe suppression over their counterparts.