## 4 Low Complexity Non-Linear Detection
### Two Approaches for Non-Linear Data Detection
#### 4.2.2 Near ML Detection
It was shown that reception in challenging high-mobility environments can be achieved with the proposed scheme, also exhibiting a manageable computational complexity. The proposal consists of an efficient treatment of the data frequency dispersion, a time-varying channel estimation using the two dimensional basic expansion model, and sub-optimal non-linear detectors. The results show a performance close to the one obtained

Figure 11: BER vs. SNR for the iteration [1,2] of the Near-ML detection proposed without convolutional encoder, using QR decomposition with MMSE as criteria. The channel model uses a Jake’s Doppler profile for each channel tap. The power delay profile is exponentially decaying with RMS delay spread of 0.4 μs and frequency Doppler spread of 1 kHz modeling a Rayleigh fading NLOS scenario. by the ML algorithm. Furthermore, with only two iterations, it was shown that with true low complexity, the proposed system performed equally or better, in terms of BER, than other approximations presented as the state of the art, confirming its capacity to exploit the available frequency diversity in doubly selective channels. Conceptualization, J.A.D.P.-F. and R.P.-M.; methodology, J.A.D.P.-F. and F.P.-C.; software, J.A.D.P.-F.; validation, F.P.-C., R.P.-M., and C.D.-V.-S.; formal analysis, J.A.D.P.-F. and F.P.-C.; investigation, J.A.D.P.-F., F.P.-C., R.P.-M., and C.D.-V.-S.; resources, J.A.D.P.-F., F.P.-C., R.P.-M., and C.D.-V.-S.; writing, original draft preparation, J.A.D.P.-F., writing, review and editing, F.P.-C., R.P.-M., and C.D.-V.-S.; supervision, C.D.-V.-S.; project administration, J.A.D.P.-F. and F.P.-C.; funding acquisition, J.A.D.P.-F. and C.D.-V.-S. All authors read and agreed to the published version of the manuscript. The authors would like to thank the founding from Universidad Panamericana. Not applicable. The data presented in this study are available on request from the corresponding author. The authors would like to thank [PERSON] (RIP) for his partitioning in the work. The authors declare no conflicts of interest. ## References

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