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. Index TermsPrototype filters, filter bank multicarrier, FBMC design, quadratic programming, convex optimization.

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SUMMARYThis work analyzes multi-cell MIMO systems equipped with a very large number of antennas in the basestation (BS) side and with low-complexity zero-forcing and matched-filter receivers. Cooperation between BSs in a multi-cell scenarios is analyzed in order to avoid the well-known pilot contamination effect on massive MIMO systems, while the effects of asynchronism between users and BSs in training phase using different pilot sequences, for example, Walsh-Hadamard, Gold, and Kasami sequence sets on the system performance are examined. As low-complexity processing is deployed, the synchronism offset in training phase may introduce errors on the channel estimation process, adding its effect to the pilot contamination, resulting in an aggressive detection scenario. Numerical results using the BER as a performance figure of merit measure in downlink have corroborated our finding. It was also developed an analytical error formula for channel estimation subject to synchronization offset levels in terms of fractional unit of symbol time duration, which was validated through channel mean squared error and BER performance simulation results. Through these both performance figures and under practical scenarios, the use of pseudo-random sequence sets may be preferable instead of orthogonal ones, mainly because of their out-of-phase cross-correlation levels.

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