**6. Conclusions**

This work presented six different heuristics to solve the pilot sequence allocation problem in Massive MIMO systems. We optimized the heuristics parameters to achieve the best performance in the discussed problem while still considering the computational time constraints inherent to the problem's nature.

We analyzed the impact of different scenario configurations on the performances of the algorithms. 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 *ω* = 0.1, *v*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.

**Author Contributions:** 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.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Publicly available datasets were analyzed in this study. This data can be found here: github.com/evertonalex/utfpr-ppgi-pilotcontamination (accessed on 16 May 2022).

**Conflicts of Interest:** The authors declare no conflict of interest.
