# An Overview of FIR Filter Design in Future Multicarrier Communication Systems
## 3 FIR Prototype Filter Design
### Optimization Based Methods
#### 3.3.5 Karaboga's Method
By analyzing the simulation of the filters with the same order, it is noted that different evolutionary algorithms achieve similar PSD and BER performances. Compared with frequency sampling techniques and windowing based techniques, the corresponding filter parameters of optimization based methods, that is more concerned with the local optimization and algorithm convergence problem, can be optimized depending on different evaluation criteria, and the selected design parameters determine the effectiveness of the solution to the optimization problem. The complexity of this type of design techniques seems to be much higher than other two techniques, for instance, the complexity of PSO based method is about the order of \(L\mathcal{PO}(N^{2})\), where \(L\) is the iteration size and \(P\) is the population size. This complexity is much less than QCQP based methods or non-convex optimization methods, of which the complexity is up to \(\mathcal{O}(N^{3})\) or higher [164]. Nevertheless, optimization based methods are much more flexible as they focus on local optimization to support the constraints imposed by various scenarios such as cognitive radio [157], massive MIMO [156] and so on. For example, when FBMC is applied for opportunistic spectrum sharing, in order to avoid interfering with other bands, well localized filters in time and frequency are prone to be designed to minimize Out of Band [140]. Similarly, there are also some optimization based methods for different waveform candidates, for example, OFDM [154], FBMC [155; 156; 140], GFDM [158; 159; 160; 161], UFMC [162; 163]. In general, the establishment and constraints imposed on objective functions are often highly non-linear, which increases the computational complexity and also sensitive to the selection of initial values. In addition, it is possible to fall into local optimal range and fail to identify global optimal solution, which is one of the major issues to be solved in optimization based design methods. As discussed earlier, since multicarrier modulation can enlarge the system capacity and have the relative immunity to defend the multipath fading effect, it dominates the main stream in future communication technology. The critical part of multicarrier modulation lies in the FIR filter design. A good filter design scheme can improve some important performances not only including PSD andBER but also some other crucial aspects, consequently increasing the competitiveness of waveform candidates and improving the communication quality to suit various application scenarios of 5G or future networks. FIR filters have been widely used in many engineering applications involved with digital signal processing, such as the communication signal [165; 166], the speech signal [167; 168] and the medical signal [169]. We can conclude without exaggeration that where digital signal processing is needed, where there is a shadow of FIR. ## 5 Conclusions

The prototype filter plays an important role in multicarrier modulation systems and the FIR filter is considered to be the suitable choice in wireless communication systems. This paper has reviewed existing FIR filter design methods which are categorized into frequency sampling methods, windowing based methods and optimization based methods. The concept and principle of each method are described in detail, and the merits and drawbacks of corresponding prototype filters are summarized. Finally, the performances of FIR design methods in different multicarrier modulation systems are evaluated and discussed in terms of PSD and BER. It is expected that this survey work can provide a basis for the selection of prototype filters in future wireless communication systems. Conceptualization, P.L. and H.Z. ; methodology, H.L. and P.L. ; investigation, L.J. and S.C.; writing--original draft preparation, S.C., H.L. and P.L. ; writing--review and editing, L.J. and H.Z. ; funding acquisition, H.Z. All authors have read and agreed to the published version of the manuscript.