# Pilot Sequence Allocation Schemes in Massive MIMO Systems Using Heuristic Approaches
## 4 Proposed Solutions
### Variable Neighbourhood Search
The cell size impact analysis offered clear conclusions that the system is not interference bounded and that the performance of SPV-PSO and all its derivations have far better performance in terms of system spectral efficiency, as well as average maximum and minimum spectral efficiency when compared to the RA, BPSO and GA solutions. We further investigated the impact of system loading and found that RA, BPSO and GA solutions are directly affected by user density, while the other algorithms presented a more robust performance. We found that average minimum spectral efficiency may be increased in up to 1.7 million % when compared from RA, BPSO and GA solutions to a SPV-PSO-based one during the described investigations. Finally, it is important to point out that SPV-PSO with \(\omega=0.1\), \(v_{\text{max}}=3\), \(c_{1}=5\) and \(c=1\) achieved the best results for the \(R=1000\) m and \(K=20\) users scenario. ## 7 Future Works

Future works include testing and comparing more different approaches to solve this problem such as: micro GAs, Differential Evolution, such as in [25], other versions of the PSO, as in [26; 27], greed search algorithms, supervised learning with the Convolutional Neural network (CNN) and Multilayer Perceptron (MLP) as well as further investigating at which cell size or path-loss configurations the system becomes interference bounded. Conceptualization, L.D.H.S. ; Investigation, E.A.M. ; Methodology, D.S.S. ; Project administration, L.D.H.S. ; Software, E.A.M. ; Supervision, D.S.S. and R.S.P. ; Validation, R.P.B. and L.D.H.S. ; Writing--original draft, E.A.M. ; Writing--review & editing, R.P.B., R.S.P. and L.D.H.S. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Publicly available datasets were analyzed in this study. This data can be found here: github.com/evertonalex/utfpr-ppgi-pilotontamination (accessed on 16 May 2022). The authors declare no conflict of interest. ## References

* (1) Cisco. Cisco Visual Networking Index: Forecast and Trends, 2018 2023 White Paper. Avaliable online: [[https://www.cisco.com/c/en/us/solutions/collateral/service-provider/visual-networking-index-vni/white-paper-c11-741490.html](https://www.cisco.com/c/en/us/solutions/collateral/service-provider/visual-networking-index-vni/white-paper-c11-741490.html)]([https://www.cisco.com/c/en/us/solutions/collateral/service-provider/visual-networking-index-vni/white-paper-c11-741490.html](https://www.cisco.com/c/en/us/solutions/collateral/service-provider/visual-networking-index-vni/white-paper-c11-741490.html)) (accessed on 11 November 2021). * (2) United Nations, Department of Economic and Social Affairs. World Population Prospects 2019. Available online: [[https://population.un.org/wpp/](https://population.un.org/wpp/)]([https://population.un.org/wpp/](https://population.un.org/wpp/)) (accessed on 11 November 2021). * (3) Ericsson. Ericsson Mobility Report, Ericsson Mobility Report. Available online: [[https://www.ericsson.com/assets/local/reports-papers/mobility-report/documents/2019/emr-november-2019.pdf](https://www.ericsson.com/assets/local/reports-papers/mobility-report/documents/2019/emr-november-2019.pdf)]([https://www.ericsson.com/assets/local/reports-papers/mobility-report/documents/2019/emr-november-2019.pdf](https://www.ericsson.com/assets/local/reports-papers/mobility-report/documents/2019/emr-november-2019.pdf)) (accessed on 11 November 2021)
* (4) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON] Joint Design of Communication and Control for Connected Cars in 5G Communication Systems. In Proceedings of the 2016 IEEE Globecom Workshops (GC Wkshps), Washington, DC, USA, 2016; pp. 1-7. [CrossRef]
* (5) [PERSON] Noncooperative cellular wireless with unlimited numbers of base station antennas. _IEEE Trans. Wirel. Commun._**2010**, 9, 3590-3600.