Spectrally constrained unimodular sequence design without spectral level mask

Due to the freedom degree loss resulted from the unimodular constraints, it is not easy to specify proper and feasible stopband and passband levels for frequency grids of interest in spectrally constrained sequence design problems. In an attempt to avoid this difficulty, we devise a cost function that minimizes the ratio of the maximal stopband level to the minimal passband level. Next, we introduce auxiliary variables to simplify the optimization problem via decoupling the numerator and denominator. Then, the feasible solution is obtained by approximating the nondifferentiable objective function with a smooth function. We also apply an acceleration scheme to increase the algorithm convergence speed. The effectiveness of the proposed approach is demonstrated via numerical examples.