  In this work, we propose a prototype filter design for Filter Bank
MultiCarrier (FBMC) systems based on convex optimization, aiming superior
spectrum features while maintaining a high symbol reconstruction quality.
Initially, the proposed design is written as a non-convex Quadratically
Constrained Quadratic Programming (QCQP), which is relaxed into a convex QCQP
guided by a line search. Through the resulting problem, we design three
prototype filters: Type-I, II and III. In particular, the Type-II filter shows
a slightly better performance than the classical Mirabasi-Martin design, while
Type-I and III filters offer a much more contained spectrum than most of the
prototype filters suitable for FBMC applications. Furthermore, numerical
results corroborate the effectiveness of the designed filters as the proposed
filters offer fast decay and contained spectrum while not jeopardizing symbol
reconstruction in practice.
