## 7 Conclusions  
In this paper, we have studied an adaptive combination of MISO filters, based on the adaptation by the multichannel APA, which allows the filters to be differentiated according to the step size or to the projection order. We have analyzed the steady-state performance of such a combined scheme, thus deriving a theoretical value for the EMSE based on the energy conservation properties. Simulation results have proven the validity of such a theoretical study. We have also assessed the performance improvement involved by an adaptive combined MISO filter using different projection orders in a changing scenario. Future research lines include the analysis of tracking and the transient performance of a combined MISO filter, as well as the extension to multi-stage combined filtering architectures. Moreover, the scheme can be evaluated in practical system identification problems, like acoustics or communications applications, where its performance can be compared with that of alternative single-MISO adaptive filters, such as multichannel variable step-size APA filters. **Author Contributions:** Conceptualization, D.C.; formal analysis, D.C.; investigation, D.C., M.S., and L.A.A.-R.; methodology, D.C.; software, D.C.; supervision, A.U. ; validation, D.C.; writing, original draft, D.C.; writing, review and editing, D.C., M.S., and L.A.A.-R.  
**Funding:** The work of [PERSON], [PERSON] and [PERSON] has been supported by the project: \"Vehicular Fog energy-efficient QoS mining and dissemination of multimedia Big Data streams (V-FoG and V-Fog2)\", funded by Sapienza University of Rome Bando 2016 and 2017. The work of [PERSON] and [PERSON] has been also supported by the project: \"GAUChO - A Green Adaptive Fog Computing and networking Architectures\" funded by the MIUR Progetti di Ricerca di Rilevante Interesse Nazionale (PRIN) Bando 2015, grant 2015 YPXH4W_004. The work of [PERSON] is partially supported by the Spanish Ministry of Economy and Competitiveness (under grant DAMA (TIN2015-70308-REDT) and grants TEC2014-52289-R and TEC2017-83838-R), and by the European Union. **Conflicts of Interest:** The authors declare no conflict of interest. Appendix A Steady-State Approximation for the EMSE of Individual MISO Filters with Multiple Projections  
We evaluate the term \(\mathrm{E}\left\{\mathbf{e}_{an}^{(j)}\mathbf{e}_{an}^{(j),T}\right\}\). We remind the reader that the vectors \(\mathbf{e}_{an}^{(j)}\in\mathbb{R}^{K_{j}\times 1}\) and \(\mathbf{e}_{p}^{(j)}\in\mathbb{R}^{K_{j}\times 1}\), with \(j=1,2\), contain the projections of the a priori and a posteriori estimation errors, respectively, at the \(n^{\mathrm{th}}\) time instant, and they can be written as:  
\[\mathbf{e}_{an}^{(j)}=\left[ \begin{array}{ccc}e_{a_{0}}^{(j)}\left[n\right] &\ldots&e_{a_{K_{\mathrm{max}-1}}}^{(j)}\left[n\right]\end{array} \right]^{T} \tag{1}\]  
Figure 5: Convergence performance of a combined MISO filter using different projection orders with the related evolution of the mixing parameter \(\lambda_{0}\left[n\right]\). \[\mathbf{e}_{\mathrm{p}_{n}}^{(j)}=\left[ \begin{array}{cccc}e_{\mathrm{p}_{0}}^{(j) }\left[n\right]&\ldots&e_{\mathrm{p}_{K_{\mathrm{max}}^{-1}}}^{(j)}\left[n \right]\end{array} \right]^{T}.