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Recently, filter bank multicarrier (FBMC) modulations have attracted increasing attention. The filter banks of FBMC are derived from a prototype filter that determines the system performance, such as stopband attenuation, intersymbol interference (ISI) and interchannel interference (ICI). In this paper, we formulate a problem of direct optimization of the filter impulse-response coefficients for the FBMC systems to minimize the stopband energy and constrain the ISI/ICI. Unfortunately, this filter optimization problem is nonconvex and highly nonlinear. Nevertheless, observing that all the functions in the optimization problem are twice-differentiable, we propose using the -based Branch and Bound ( BB) algorithm to obtain the optimal solution. However, the convergence time of the algorithm is unacceptable because the number of unknowns (i.e., the filter coefficients) in the optimization problem is too large. The main …